YES(O(1), O(n^1)) 330.51/101.40 YES(O(1), O(n^1)) 330.51/101.45 330.51/101.45 330.51/101.45 330.51/101.45 330.51/101.45 330.51/101.45 Runtime Complexity (innermost) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml.xml 330.51/101.45 330.51/101.45 330.51/101.45
330.51/101.45
330.51/101.45
330.51/101.45
The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(O(1), O(n^1)).

0 CpxTRS
330.51/101.45 
↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳2 CdtProblem
330.51/101.45 
↳3 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳4 CdtProblem
330.51/101.45 
↳5 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳6 CdtProblem
330.51/101.45 
↳7 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳8 CdtProblem
330.51/101.45 
↳9 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳10 CdtProblem
330.51/101.45 
↳11 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳12 CdtProblem
330.51/101.45 
↳13 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳14 CdtProblem
330.51/101.45 
↳15 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳16 CdtProblem
330.51/101.45 
↳17 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳18 CdtProblem
330.51/101.45 
↳19 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳20 CdtProblem
330.51/101.45 
↳21 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳22 CdtProblem
330.51/101.45 
↳23 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳24 CdtProblem
330.51/101.45 
↳25 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳26 CdtProblem
330.51/101.45 
↳27 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳28 CdtProblem
330.51/101.45 
↳29 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳30 CdtProblem
330.51/101.45 
↳31 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳32 CdtProblem
330.51/101.45 
↳33 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳34 CdtProblem
330.51/101.45 
↳35 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳36 CdtProblem
330.51/101.45 
↳37 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳38 CdtProblem
330.51/101.45 
↳39 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳40 CdtProblem
330.51/101.45 
↳41 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳42 CdtProblem
330.51/101.45 
↳43 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳44 CdtProblem
330.51/101.45 
↳45 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳46 CdtProblem
330.51/101.45 
↳47 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳48 CdtProblem
330.51/101.45 
↳49 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳50 CdtProblem
330.51/101.45 
↳51 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳52 CdtProblem
330.51/101.45 
↳53 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳54 CdtProblem
330.51/101.45 
↳55 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳56 CdtProblem
330.51/101.45 
↳57 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳58 CdtProblem
330.51/101.45 
↳59 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳60 CdtProblem
330.51/101.45 
↳61 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳62 CdtProblem
330.51/101.45 
↳63 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳64 CdtProblem
330.51/101.45 
↳65 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳66 CdtProblem
330.51/101.45 
↳67 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳68 CdtProblem
330.51/101.45 
↳69 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳70 CdtProblem
330.51/101.45 
↳71 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳72 CdtProblem
330.51/101.45 
↳73 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳74 CdtProblem
330.51/101.45 
↳75 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳76 CdtProblem
330.51/101.45 
↳77 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳78 CdtProblem
330.51/101.45 
↳79 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳80 CdtProblem
330.51/101.45 
↳81 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳82 CdtProblem
330.51/101.45 
↳83 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳84 CdtProblem
330.51/101.45 
↳85 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳86 CdtProblem
330.51/101.45 
↳87 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳88 CdtProblem
330.51/101.45 
↳89 CdtUnreachableProof (⇔)
330.51/101.45 
↳90 CdtProblem
330.51/101.45 
↳91 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳92 CdtProblem
330.51/101.45 
↳93 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳94 CdtProblem
330.51/101.45 
↳95 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
330.51/101.45 
↳96 CdtProblem
330.51/101.45 
↳97 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
330.51/101.45 
↳98 CdtProblem
330.51/101.45 
↳99 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
330.51/101.45 
↳100 CdtProblem
330.51/101.45 
↳101 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
330.51/101.45 
↳102 CdtProblem
330.51/101.45 
↳103 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
330.51/101.45 
↳104 CdtProblem
330.51/101.45 
↳105 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
330.51/101.45 
↳106 CdtProblem
330.51/101.45 
↳107 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
330.51/101.45 
↳108 CdtProblem
330.51/101.45 
↳109 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
330.51/101.45 
↳110 CdtProblem
330.51/101.45 
↳111 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
330.51/101.45 
↳112 CdtProblem
330.51/101.45 
↳113 SIsEmptyProof (BOTH BOUNDS(ID, ID))
330.51/101.45 
↳114 BOUNDS(O(1), O(1))
330.51/101.45
330.51/101.45 330.51/101.45
330.51/101.45
330.51/101.45

(0) Obligation:

Runtime Complexity TRS:
The TRS R consists of the following rules:

active(U11(tt, M, N)) → mark(U12(tt, M, N)) 330.51/101.45
active(U12(tt, M, N)) → mark(s(plus(N, M))) 330.51/101.45
active(U21(tt, M, N)) → mark(U22(tt, M, N)) 330.51/101.45
active(U22(tt, M, N)) → mark(plus(x(N, M), N)) 330.51/101.45
active(plus(N, 0)) → mark(N) 330.51/101.45
active(plus(N, s(M))) → mark(U11(tt, M, N)) 330.51/101.45
active(x(N, 0)) → mark(0) 330.51/101.45
active(x(N, s(M))) → mark(U21(tt, M, N)) 330.51/101.45
active(U11(X1, X2, X3)) → U11(active(X1), X2, X3) 330.51/101.45
active(U12(X1, X2, X3)) → U12(active(X1), X2, X3) 330.51/101.45
active(s(X)) → s(active(X)) 330.51/101.45
active(plus(X1, X2)) → plus(active(X1), X2) 330.51/101.45
active(plus(X1, X2)) → plus(X1, active(X2)) 330.51/101.45
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3) 330.86/101.50
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3) 330.86/101.50
active(x(X1, X2)) → x(active(X1), X2) 330.86/101.50
active(x(X1, X2)) → x(X1, active(X2)) 330.86/101.50
U11(mark(X1), X2, X3) → mark(U11(X1, X2, X3)) 330.86/101.50
U12(mark(X1), X2, X3) → mark(U12(X1, X2, X3)) 330.86/101.50
s(mark(X)) → mark(s(X)) 330.86/101.50
plus(mark(X1), X2) → mark(plus(X1, X2)) 330.86/101.50
plus(X1, mark(X2)) → mark(plus(X1, X2)) 330.86/101.50
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3)) 330.86/101.50
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3)) 330.86/101.50
x(mark(X1), X2) → mark(x(X1, X2)) 330.86/101.50
x(X1, mark(X2)) → mark(x(X1, X2)) 330.86/101.50
proper(U11(X1, X2, X3)) → U11(proper(X1), proper(X2), proper(X3)) 330.86/101.50
proper(tt) → ok(tt) 330.86/101.50
proper(U12(X1, X2, X3)) → U12(proper(X1), proper(X2), proper(X3)) 330.86/101.50
proper(s(X)) → s(proper(X)) 330.86/101.50
proper(plus(X1, X2)) → plus(proper(X1), proper(X2)) 330.86/101.50
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3)) 330.86/101.50
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3)) 330.86/101.50
proper(x(X1, X2)) → x(proper(X1), proper(X2)) 330.86/101.50
proper(0) → ok(0) 330.86/101.50
U11(ok(X1), ok(X2), ok(X3)) → ok(U11(X1, X2, X3)) 330.86/101.50
U12(ok(X1), ok(X2), ok(X3)) → ok(U12(X1, X2, X3)) 330.86/101.50
s(ok(X)) → ok(s(X)) 330.86/101.50
plus(ok(X1), ok(X2)) → ok(plus(X1, X2)) 330.86/101.50
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3)) 330.86/101.50
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3)) 330.86/101.50
x(ok(X1), ok(X2)) → ok(x(X1, X2)) 330.86/101.50
top(mark(X)) → top(proper(X)) 330.86/101.50
top(ok(X)) → top(active(X))

Rewrite Strategy: INNERMOST
330.86/101.50
330.86/101.50

(1) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID) transformation)

Converted CpxTRS to CDT
330.86/101.50
330.86/101.50

(2) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 330.86/101.50
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 330.86/101.50
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 330.86/101.50
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 330.86/101.50
active(plus(z0, 0)) → mark(z0) 330.86/101.50
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 330.86/101.50
active(x(z0, 0)) → mark(0) 330.86/101.50
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 330.86/101.50
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 330.86/101.50
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 330.86/101.50
active(s(z0)) → s(active(z0)) 330.86/101.50
active(plus(z0, z1)) → plus(active(z0), z1) 330.86/101.50
active(plus(z0, z1)) → plus(z0, active(z1)) 330.86/101.50
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 330.86/101.50
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 330.86/101.50
active(x(z0, z1)) → x(active(z0), z1) 330.86/101.50
active(x(z0, z1)) → x(z0, active(z1)) 330.86/101.50
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 330.86/101.50
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 330.86/101.50
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 330.86/101.50
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 330.86/101.50
s(mark(z0)) → mark(s(z0)) 330.86/101.50
s(ok(z0)) → ok(s(z0)) 330.86/101.50
plus(mark(z0), z1) → mark(plus(z0, z1)) 330.86/101.50
plus(z0, mark(z1)) → mark(plus(z0, z1)) 330.86/101.50
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 330.86/101.50
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 330.86/101.50
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 330.86/101.50
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 330.86/101.50
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 330.86/101.50
x(mark(z0), z1) → mark(x(z0, z1)) 330.86/101.50
x(z0, mark(z1)) → mark(x(z0, z1)) 330.86/101.50
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 330.86/101.50
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 330.86/101.50
proper(tt) → ok(tt) 330.86/101.50
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 330.86/101.50
proper(s(z0)) → s(proper(z0)) 330.86/101.50
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 330.86/101.50
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 330.86/101.50
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 330.86/101.50
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 330.86/101.50
proper(0) → ok(0) 330.86/101.50
top(mark(z0)) → top(proper(z0)) 330.86/101.50
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(U11(tt, z0, z1)) → c(U12'(tt, z0, z1)) 330.86/101.50
ACTIVE(U12(tt, z0, z1)) → c1(S(plus(z1, z0)), PLUS(z1, z0)) 330.86/101.50
ACTIVE(U21(tt, z0, z1)) → c2(U22'(tt, z0, z1)) 330.86/101.50
ACTIVE(U22(tt, z0, z1)) → c3(PLUS(x(z1, z0), z1), X(z1, z0)) 330.86/101.50
ACTIVE(plus(z0, s(z1))) → c5(U11'(tt, z1, z0)) 330.86/101.50
ACTIVE(x(z0, s(z1))) → c7(U21'(tt, z1, z0)) 330.86/101.50
ACTIVE(U11(z0, z1, z2)) → c8(U11'(active(z0), z1, z2), ACTIVE(z0)) 330.86/101.50
ACTIVE(U12(z0, z1, z2)) → c9(U12'(active(z0), z1, z2), ACTIVE(z0)) 330.86/101.50
ACTIVE(s(z0)) → c10(S(active(z0)), ACTIVE(z0)) 330.86/101.50
ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 330.86/101.50
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 330.86/101.50
ACTIVE(U21(z0, z1, z2)) → c13(U21'(active(z0), z1, z2), ACTIVE(z0)) 330.86/101.50
ACTIVE(U22(z0, z1, z2)) → c14(U22'(active(z0), z1, z2), ACTIVE(z0)) 330.86/101.50
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 330.86/101.50
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 330.86/101.50
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 330.86/101.50
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 330.86/101.50
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 330.86/101.50
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 330.86/101.50
S(mark(z0)) → c21(S(z0)) 330.86/101.50
S(ok(z0)) → c22(S(z0)) 330.86/101.50
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 330.86/101.50
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 330.86/101.50
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 330.86/101.50
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 330.86/101.50
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 330.86/101.50
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 330.86/101.50
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 330.86/101.50
X(mark(z0), z1) → c30(X(z0, z1)) 330.86/101.50
X(z0, mark(z1)) → c31(X(z0, z1)) 330.86/101.50
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 330.86/101.50
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 330.86/101.50
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 330.86/101.50
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 330.86/101.50
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 330.86/101.50
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 330.86/101.50
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 330.86/101.50
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 330.86/101.50
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 330.86/101.50
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0))
S tuples:

ACTIVE(U11(tt, z0, z1)) → c(U12'(tt, z0, z1)) 330.86/101.50
ACTIVE(U12(tt, z0, z1)) → c1(S(plus(z1, z0)), PLUS(z1, z0)) 330.86/101.50
ACTIVE(U21(tt, z0, z1)) → c2(U22'(tt, z0, z1)) 330.86/101.50
ACTIVE(U22(tt, z0, z1)) → c3(PLUS(x(z1, z0), z1), X(z1, z0)) 330.86/101.50
ACTIVE(plus(z0, s(z1))) → c5(U11'(tt, z1, z0)) 330.86/101.50
ACTIVE(x(z0, s(z1))) → c7(U21'(tt, z1, z0)) 330.86/101.50
ACTIVE(U11(z0, z1, z2)) → c8(U11'(active(z0), z1, z2), ACTIVE(z0)) 330.86/101.50
ACTIVE(U12(z0, z1, z2)) → c9(U12'(active(z0), z1, z2), ACTIVE(z0)) 330.86/101.50
ACTIVE(s(z0)) → c10(S(active(z0)), ACTIVE(z0)) 330.86/101.50
ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 330.86/101.50
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 330.86/101.50
ACTIVE(U21(z0, z1, z2)) → c13(U21'(active(z0), z1, z2), ACTIVE(z0)) 330.86/101.50
ACTIVE(U22(z0, z1, z2)) → c14(U22'(active(z0), z1, z2), ACTIVE(z0)) 330.86/101.50
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 330.86/101.50
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 330.86/101.50
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 330.86/101.50
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 330.86/101.50
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 330.86/101.50
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 330.86/101.50
S(mark(z0)) → c21(S(z0)) 330.86/101.50
S(ok(z0)) → c22(S(z0)) 330.86/101.50
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 330.86/101.50
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 330.86/101.50
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 330.86/101.50
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 330.86/101.50
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 330.86/101.50
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 331.31/101.64
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 331.31/101.64
X(mark(z0), z1) → c30(X(z0, z1)) 331.31/101.64
X(z0, mark(z1)) → c31(X(z0, z1)) 331.31/101.64
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 331.31/101.64
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 331.31/101.64
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.31/101.64
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.31/101.64
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 331.31/101.64
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c, c1, c2, c3, c5, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c35, c36, c37, c38, c39, c40, c42, c43

331.31/101.64
331.31/101.64

(3) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 4 trailing tuple parts
331.31/101.64
331.31/101.64

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 331.31/101.64
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 331.31/101.64
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 331.31/101.64
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 331.31/101.64
active(plus(z0, 0)) → mark(z0) 331.31/101.64
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 331.31/101.64
active(x(z0, 0)) → mark(0) 331.31/101.64
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 331.31/101.64
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 331.31/101.64
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 331.31/101.64
active(s(z0)) → s(active(z0)) 331.31/101.64
active(plus(z0, z1)) → plus(active(z0), z1) 331.31/101.64
active(plus(z0, z1)) → plus(z0, active(z1)) 331.31/101.64
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 331.31/101.64
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 331.31/101.64
active(x(z0, z1)) → x(active(z0), z1) 331.31/101.64
active(x(z0, z1)) → x(z0, active(z1)) 331.31/101.64
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 331.31/101.64
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 331.31/101.64
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 331.31/101.64
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 331.31/101.64
s(mark(z0)) → mark(s(z0)) 331.31/101.64
s(ok(z0)) → ok(s(z0)) 331.31/101.64
plus(mark(z0), z1) → mark(plus(z0, z1)) 331.31/101.64
plus(z0, mark(z1)) → mark(plus(z0, z1)) 331.31/101.64
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 331.31/101.64
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 331.31/101.64
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 331.31/101.64
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 331.31/101.64
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 331.31/101.64
x(mark(z0), z1) → mark(x(z0, z1)) 331.31/101.64
x(z0, mark(z1)) → mark(x(z0, z1)) 331.31/101.64
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 331.31/101.64
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 331.31/101.64
proper(tt) → ok(tt) 331.31/101.64
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 331.31/101.64
proper(s(z0)) → s(proper(z0)) 331.31/101.64
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 331.31/101.64
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 331.31/101.64
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 331.31/101.64
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 331.31/101.64
proper(0) → ok(0) 331.31/101.64
top(mark(z0)) → top(proper(z0)) 331.31/101.64
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(U12(tt, z0, z1)) → c1(S(plus(z1, z0)), PLUS(z1, z0)) 331.31/101.64
ACTIVE(U22(tt, z0, z1)) → c3(PLUS(x(z1, z0), z1), X(z1, z0)) 331.31/101.64
ACTIVE(U11(z0, z1, z2)) → c8(U11'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(U12(z0, z1, z2)) → c9(U12'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(s(z0)) → c10(S(active(z0)), ACTIVE(z0)) 331.31/101.64
ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 331.31/101.64
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 331.31/101.64
ACTIVE(U21(z0, z1, z2)) → c13(U21'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(U22(z0, z1, z2)) → c14(U22'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 331.31/101.64
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 331.31/101.64
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 331.31/101.64
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 331.31/101.64
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 331.31/101.64
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 331.31/101.64
S(mark(z0)) → c21(S(z0)) 331.31/101.64
S(ok(z0)) → c22(S(z0)) 331.31/101.64
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 331.31/101.64
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 331.31/101.64
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 331.31/101.64
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 331.31/101.64
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 331.31/101.64
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 331.31/101.64
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 331.31/101.64
X(mark(z0), z1) → c30(X(z0, z1)) 331.31/101.64
X(z0, mark(z1)) → c31(X(z0, z1)) 331.31/101.64
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 331.31/101.64
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 331.31/101.64
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.31/101.64
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.31/101.64
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 331.31/101.64
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 331.31/101.64
ACTIVE(U11(tt, z0, z1)) → c 331.31/101.64
ACTIVE(U21(tt, z0, z1)) → c2 331.31/101.64
ACTIVE(plus(z0, s(z1))) → c5 331.31/101.64
ACTIVE(x(z0, s(z1))) → c7
S tuples:

ACTIVE(U12(tt, z0, z1)) → c1(S(plus(z1, z0)), PLUS(z1, z0)) 331.31/101.64
ACTIVE(U22(tt, z0, z1)) → c3(PLUS(x(z1, z0), z1), X(z1, z0)) 331.31/101.64
ACTIVE(U11(z0, z1, z2)) → c8(U11'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(U12(z0, z1, z2)) → c9(U12'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(s(z0)) → c10(S(active(z0)), ACTIVE(z0)) 331.31/101.64
ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 331.31/101.64
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 331.31/101.64
ACTIVE(U21(z0, z1, z2)) → c13(U21'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(U22(z0, z1, z2)) → c14(U22'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 331.31/101.64
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 331.31/101.64
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 331.31/101.64
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 331.31/101.64
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 331.31/101.64
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 331.31/101.64
S(mark(z0)) → c21(S(z0)) 331.31/101.64
S(ok(z0)) → c22(S(z0)) 331.31/101.64
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 331.31/101.64
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 331.31/101.64
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 331.31/101.64
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 331.31/101.64
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 331.31/101.64
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 331.31/101.64
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 331.31/101.64
X(mark(z0), z1) → c30(X(z0, z1)) 331.31/101.64
X(z0, mark(z1)) → c31(X(z0, z1)) 331.31/101.64
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 331.31/101.64
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 331.31/101.64
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.31/101.64
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.31/101.64
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 331.31/101.64
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 331.31/101.64
ACTIVE(U11(tt, z0, z1)) → c 331.31/101.64
ACTIVE(U21(tt, z0, z1)) → c2 331.31/101.64
ACTIVE(plus(z0, s(z1))) → c5 331.31/101.64
ACTIVE(x(z0, s(z1))) → c7
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c1, c3, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c35, c36, c37, c38, c39, c40, c42, c43, c, c2, c5, c7

331.31/101.64
331.31/101.64

(5) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)

Split RHS of tuples not part of any SCC
331.31/101.64
331.31/101.64

(6) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 331.31/101.64
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 331.31/101.64
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 331.31/101.64
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 331.31/101.64
active(plus(z0, 0)) → mark(z0) 331.31/101.64
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 331.31/101.64
active(x(z0, 0)) → mark(0) 331.31/101.64
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 331.31/101.64
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 331.31/101.64
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 331.31/101.64
active(s(z0)) → s(active(z0)) 331.31/101.64
active(plus(z0, z1)) → plus(active(z0), z1) 331.31/101.64
active(plus(z0, z1)) → plus(z0, active(z1)) 331.31/101.64
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 331.31/101.64
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 331.31/101.64
active(x(z0, z1)) → x(active(z0), z1) 331.31/101.64
active(x(z0, z1)) → x(z0, active(z1)) 331.31/101.64
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 331.31/101.64
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 331.31/101.64
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 331.31/101.64
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 331.31/101.64
s(mark(z0)) → mark(s(z0)) 331.31/101.64
s(ok(z0)) → ok(s(z0)) 331.31/101.64
plus(mark(z0), z1) → mark(plus(z0, z1)) 331.31/101.64
plus(z0, mark(z1)) → mark(plus(z0, z1)) 331.31/101.64
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 331.31/101.64
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 331.31/101.64
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 331.31/101.64
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 331.31/101.64
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 331.31/101.64
x(mark(z0), z1) → mark(x(z0, z1)) 331.31/101.64
x(z0, mark(z1)) → mark(x(z0, z1)) 331.31/101.64
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 331.31/101.64
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 331.31/101.64
proper(tt) → ok(tt) 331.31/101.64
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 331.31/101.64
proper(s(z0)) → s(proper(z0)) 331.31/101.64
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 331.31/101.64
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 331.31/101.64
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 331.31/101.64
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 331.31/101.64
proper(0) → ok(0) 331.31/101.64
top(mark(z0)) → top(proper(z0)) 331.31/101.64
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(U11(z0, z1, z2)) → c8(U11'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(U12(z0, z1, z2)) → c9(U12'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(s(z0)) → c10(S(active(z0)), ACTIVE(z0)) 331.31/101.64
ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 331.31/101.64
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 331.31/101.64
ACTIVE(U21(z0, z1, z2)) → c13(U21'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(U22(z0, z1, z2)) → c14(U22'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 331.31/101.64
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 331.31/101.64
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 331.31/101.64
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 331.31/101.64
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 331.31/101.64
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 331.31/101.64
S(mark(z0)) → c21(S(z0)) 331.31/101.64
S(ok(z0)) → c22(S(z0)) 331.31/101.64
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 331.31/101.64
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 331.31/101.64
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 331.31/101.64
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 331.31/101.64
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 331.31/101.64
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 331.31/101.64
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 331.31/101.64
X(mark(z0), z1) → c30(X(z0, z1)) 331.31/101.64
X(z0, mark(z1)) → c31(X(z0, z1)) 331.31/101.64
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 331.31/101.64
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 331.31/101.64
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.31/101.64
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.31/101.64
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 331.31/101.64
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 331.31/101.64
ACTIVE(U11(tt, z0, z1)) → c 331.31/101.64
ACTIVE(U21(tt, z0, z1)) → c2 331.31/101.64
ACTIVE(plus(z0, s(z1))) → c5 331.31/101.64
ACTIVE(x(z0, s(z1))) → c7 331.31/101.64
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 331.31/101.64
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 331.31/101.64
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 331.31/101.64
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0))
S tuples:

ACTIVE(U11(z0, z1, z2)) → c8(U11'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(U12(z0, z1, z2)) → c9(U12'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(s(z0)) → c10(S(active(z0)), ACTIVE(z0)) 331.31/101.64
ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 331.31/101.64
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 331.31/101.64
ACTIVE(U21(z0, z1, z2)) → c13(U21'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(U22(z0, z1, z2)) → c14(U22'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 331.31/101.64
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 331.31/101.64
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 331.31/101.64
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 331.31/101.64
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 331.31/101.64
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 331.31/101.64
S(mark(z0)) → c21(S(z0)) 331.31/101.64
S(ok(z0)) → c22(S(z0)) 331.31/101.64
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 331.31/101.64
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 331.31/101.64
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 331.31/101.64
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 331.31/101.64
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 331.31/101.64
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 331.31/101.64
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 331.31/101.64
X(mark(z0), z1) → c30(X(z0, z1)) 331.31/101.64
X(z0, mark(z1)) → c31(X(z0, z1)) 331.31/101.64
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 331.31/101.64
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 331.31/101.64
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.31/101.64
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.31/101.64
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 331.31/101.64
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 331.31/101.64
ACTIVE(U11(tt, z0, z1)) → c 331.31/101.64
ACTIVE(U21(tt, z0, z1)) → c2 331.31/101.64
ACTIVE(plus(z0, s(z1))) → c5 331.31/101.64
ACTIVE(x(z0, s(z1))) → c7 331.31/101.64
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 331.31/101.64
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 331.31/101.64
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 331.31/101.64
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c35, c36, c37, c38, c39, c40, c42, c43, c, c2, c5, c7, c4

331.31/101.64
331.31/101.64

(7) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

Removed 4 trailing nodes:

ACTIVE(U21(tt, z0, z1)) → c2 331.31/101.64
ACTIVE(x(z0, s(z1))) → c7 331.31/101.64
ACTIVE(U11(tt, z0, z1)) → c 331.31/101.64
ACTIVE(plus(z0, s(z1))) → c5
331.31/101.64
331.31/101.64

(8) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 331.31/101.64
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 331.31/101.64
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 331.31/101.64
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 331.31/101.64
active(plus(z0, 0)) → mark(z0) 331.31/101.64
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 331.31/101.64
active(x(z0, 0)) → mark(0) 331.31/101.64
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 331.31/101.64
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 331.31/101.64
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 331.31/101.64
active(s(z0)) → s(active(z0)) 331.31/101.64
active(plus(z0, z1)) → plus(active(z0), z1) 331.31/101.64
active(plus(z0, z1)) → plus(z0, active(z1)) 331.31/101.64
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 331.31/101.64
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 331.31/101.64
active(x(z0, z1)) → x(active(z0), z1) 331.31/101.64
active(x(z0, z1)) → x(z0, active(z1)) 331.31/101.64
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 331.31/101.64
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 331.31/101.64
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 331.31/101.64
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 331.31/101.64
s(mark(z0)) → mark(s(z0)) 331.31/101.64
s(ok(z0)) → ok(s(z0)) 331.31/101.64
plus(mark(z0), z1) → mark(plus(z0, z1)) 331.31/101.64
plus(z0, mark(z1)) → mark(plus(z0, z1)) 331.31/101.64
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 331.31/101.64
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 331.31/101.64
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 331.31/101.64
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 331.31/101.64
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 331.31/101.64
x(mark(z0), z1) → mark(x(z0, z1)) 331.31/101.64
x(z0, mark(z1)) → mark(x(z0, z1)) 331.31/101.64
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 331.31/101.64
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 331.31/101.64
proper(tt) → ok(tt) 331.31/101.64
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 331.31/101.64
proper(s(z0)) → s(proper(z0)) 331.31/101.64
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 331.31/101.64
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 331.31/101.64
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 331.31/101.64
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 331.31/101.64
proper(0) → ok(0) 331.31/101.64
top(mark(z0)) → top(proper(z0)) 331.31/101.64
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(U11(z0, z1, z2)) → c8(U11'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(U12(z0, z1, z2)) → c9(U12'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(s(z0)) → c10(S(active(z0)), ACTIVE(z0)) 331.31/101.64
ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 331.31/101.64
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 331.31/101.64
ACTIVE(U21(z0, z1, z2)) → c13(U21'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(U22(z0, z1, z2)) → c14(U22'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 331.31/101.64
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 331.31/101.64
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 331.31/101.64
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 331.31/101.64
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 331.31/101.64
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 331.31/101.64
S(mark(z0)) → c21(S(z0)) 331.31/101.64
S(ok(z0)) → c22(S(z0)) 331.31/101.64
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 331.31/101.64
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 331.31/101.64
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 331.31/101.64
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 331.31/101.64
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 331.31/101.64
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 331.31/101.64
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 331.31/101.64
X(mark(z0), z1) → c30(X(z0, z1)) 331.31/101.64
X(z0, mark(z1)) → c31(X(z0, z1)) 331.31/101.64
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 331.31/101.64
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 331.31/101.64
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.31/101.64
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.31/101.64
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 331.31/101.64
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 331.31/101.64
ACTIVE(U11(tt, z0, z1)) → c 331.31/101.64
ACTIVE(U21(tt, z0, z1)) → c2 331.31/101.64
ACTIVE(plus(z0, s(z1))) → c5 331.31/101.64
ACTIVE(x(z0, s(z1))) → c7 331.31/101.64
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 331.31/101.64
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 331.31/101.64
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 331.31/101.64
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0))
S tuples:

ACTIVE(U11(z0, z1, z2)) → c8(U11'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(U12(z0, z1, z2)) → c9(U12'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(s(z0)) → c10(S(active(z0)), ACTIVE(z0)) 331.31/101.64
ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 331.31/101.64
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 331.31/101.64
ACTIVE(U21(z0, z1, z2)) → c13(U21'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(U22(z0, z1, z2)) → c14(U22'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 331.31/101.64
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 331.31/101.64
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 331.31/101.64
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 331.31/101.64
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 331.31/101.64
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 331.31/101.64
S(mark(z0)) → c21(S(z0)) 331.31/101.64
S(ok(z0)) → c22(S(z0)) 331.31/101.64
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 331.31/101.64
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 331.31/101.64
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 331.31/101.64
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 331.31/101.64
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 331.31/101.64
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 331.31/101.64
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 331.31/101.64
X(mark(z0), z1) → c30(X(z0, z1)) 331.31/101.64
X(z0, mark(z1)) → c31(X(z0, z1)) 331.31/101.64
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 331.31/101.64
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 331.31/101.64
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.31/101.64
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.31/101.64
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 331.31/101.64
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 331.31/101.64
ACTIVE(U11(tt, z0, z1)) → c 331.31/101.64
ACTIVE(U21(tt, z0, z1)) → c2 331.31/101.64
ACTIVE(plus(z0, s(z1))) → c5 331.31/101.64
ACTIVE(x(z0, s(z1))) → c7 331.31/101.64
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 331.31/101.64
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 331.31/101.64
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 331.31/101.64
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c35, c36, c37, c38, c39, c40, c42, c43, c, c2, c5, c7, c4

331.31/101.64
331.31/101.64

(9) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace ACTIVE(U11(z0, z1, z2)) → c8(U11'(active(z0), z1, z2), ACTIVE(z0)) by

ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c8(U11'(mark(U12(tt, z0, z1)), x1, x2), ACTIVE(U11(tt, z0, z1))) 331.31/101.64
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c8(U11'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U12(tt, z0, z1))) 331.31/101.64
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c8(U11'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.31/101.64
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c8(U11'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.31/101.64
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 331.31/101.64
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 331.31/101.64
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 331.31/101.64
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 331.31/101.64
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 331.31/101.64
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 331.31/101.64
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 331.31/101.64
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 331.31/101.64
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 331.31/101.64
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 331.31/101.64
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 331.31/101.64
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 331.31/101.64
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
331.31/101.64
331.31/101.64

(10) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 331.31/101.64
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 331.31/101.64
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 331.31/101.64
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 331.31/101.64
active(plus(z0, 0)) → mark(z0) 331.31/101.64
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 331.31/101.64
active(x(z0, 0)) → mark(0) 331.31/101.64
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 331.31/101.64
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 331.31/101.64
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 331.31/101.64
active(s(z0)) → s(active(z0)) 331.31/101.64
active(plus(z0, z1)) → plus(active(z0), z1) 331.31/101.64
active(plus(z0, z1)) → plus(z0, active(z1)) 331.31/101.64
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 331.31/101.64
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 331.31/101.64
active(x(z0, z1)) → x(active(z0), z1) 331.31/101.64
active(x(z0, z1)) → x(z0, active(z1)) 331.31/101.64
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 331.31/101.64
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 331.31/101.64
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 331.31/101.64
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 331.31/101.64
s(mark(z0)) → mark(s(z0)) 331.31/101.64
s(ok(z0)) → ok(s(z0)) 331.31/101.64
plus(mark(z0), z1) → mark(plus(z0, z1)) 331.31/101.64
plus(z0, mark(z1)) → mark(plus(z0, z1)) 331.31/101.64
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 331.31/101.64
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 331.31/101.64
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 331.31/101.64
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 331.31/101.64
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 331.31/101.64
x(mark(z0), z1) → mark(x(z0, z1)) 331.31/101.64
x(z0, mark(z1)) → mark(x(z0, z1)) 331.31/101.64
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 331.31/101.64
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 331.31/101.64
proper(tt) → ok(tt) 331.31/101.64
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 331.31/101.64
proper(s(z0)) → s(proper(z0)) 331.31/101.64
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 331.31/101.64
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 331.31/101.64
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 331.31/101.64
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 331.31/101.64
proper(0) → ok(0) 331.31/101.64
top(mark(z0)) → top(proper(z0)) 331.31/101.64
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(U12(z0, z1, z2)) → c9(U12'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(s(z0)) → c10(S(active(z0)), ACTIVE(z0)) 331.31/101.64
ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 331.31/101.64
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 331.31/101.64
ACTIVE(U21(z0, z1, z2)) → c13(U21'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(U22(z0, z1, z2)) → c14(U22'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 331.31/101.64
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 331.31/101.64
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 331.31/101.64
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 331.31/101.64
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 331.31/101.64
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 331.31/101.64
S(mark(z0)) → c21(S(z0)) 331.31/101.64
S(ok(z0)) → c22(S(z0)) 331.31/101.64
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 331.31/101.64
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 331.31/101.64
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 331.31/101.64
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 331.31/101.64
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 331.31/101.64
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 331.31/101.64
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 331.31/101.64
X(mark(z0), z1) → c30(X(z0, z1)) 331.31/101.64
X(z0, mark(z1)) → c31(X(z0, z1)) 331.31/101.64
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 331.31/101.64
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 331.31/101.64
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.31/101.64
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.31/101.64
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 331.31/101.64
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 331.31/101.64
ACTIVE(U11(tt, z0, z1)) → c 331.31/101.64
ACTIVE(U21(tt, z0, z1)) → c2 331.31/101.64
ACTIVE(plus(z0, s(z1))) → c5 331.31/101.64
ACTIVE(x(z0, s(z1))) → c7 331.31/101.64
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 331.31/101.64
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 331.31/101.64
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 331.31/101.64
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 331.31/101.64
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c8(U11'(mark(U12(tt, z0, z1)), x1, x2), ACTIVE(U11(tt, z0, z1))) 331.31/101.64
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c8(U11'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U12(tt, z0, z1))) 331.31/101.64
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c8(U11'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.31/101.64
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c8(U11'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.31/101.64
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 331.31/101.64
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 331.31/101.64
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 331.31/101.64
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 331.31/101.64
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 331.31/101.64
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 331.31/101.64
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 331.31/101.64
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 331.31/101.64
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 331.31/101.64
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 331.31/101.64
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 331.31/101.64
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 331.31/101.64
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
S tuples:

ACTIVE(U12(z0, z1, z2)) → c9(U12'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(s(z0)) → c10(S(active(z0)), ACTIVE(z0)) 331.31/101.64
ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 331.31/101.64
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 331.31/101.64
ACTIVE(U21(z0, z1, z2)) → c13(U21'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(U22(z0, z1, z2)) → c14(U22'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 331.31/101.64
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 331.31/101.64
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 331.31/101.64
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 331.31/101.64
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 331.31/101.64
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 331.31/101.64
S(mark(z0)) → c21(S(z0)) 331.31/101.64
S(ok(z0)) → c22(S(z0)) 331.31/101.64
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 331.31/101.64
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 331.31/101.64
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 331.31/101.64
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 331.31/101.64
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 331.31/101.64
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 331.31/101.64
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 331.31/101.64
X(mark(z0), z1) → c30(X(z0, z1)) 331.31/101.64
X(z0, mark(z1)) → c31(X(z0, z1)) 331.31/101.64
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 331.31/101.64
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 331.31/101.64
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.31/101.64
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.31/101.64
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 331.31/101.64
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 331.31/101.64
ACTIVE(U11(tt, z0, z1)) → c 331.31/101.64
ACTIVE(U21(tt, z0, z1)) → c2 331.31/101.64
ACTIVE(plus(z0, s(z1))) → c5 331.31/101.64
ACTIVE(x(z0, s(z1))) → c7 331.31/101.64
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 331.31/101.64
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 331.31/101.64
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 331.31/101.64
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 331.31/101.64
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c8(U11'(mark(U12(tt, z0, z1)), x1, x2), ACTIVE(U11(tt, z0, z1))) 331.31/101.64
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c8(U11'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U12(tt, z0, z1))) 331.31/101.64
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c8(U11'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.31/101.64
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c8(U11'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.31/101.64
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 331.31/101.64
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 331.31/101.64
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 331.31/101.64
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 331.31/101.64
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 331.31/101.64
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 331.31/101.64
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 331.31/101.64
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 331.31/101.64
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 331.31/101.64
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 331.31/101.64
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 331.31/101.64
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 331.31/101.64
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c35, c36, c37, c38, c39, c40, c42, c43, c, c2, c5, c7, c4, c8

331.31/101.64
331.31/101.64

(11) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)

Split RHS of tuples not part of any SCC
331.31/101.64
331.31/101.64

(12) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 331.31/101.64
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 331.31/101.64
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 331.31/101.64
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 331.31/101.64
active(plus(z0, 0)) → mark(z0) 331.31/101.64
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 331.31/101.64
active(x(z0, 0)) → mark(0) 331.31/101.64
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 331.31/101.64
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 331.31/101.64
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 331.31/101.64
active(s(z0)) → s(active(z0)) 331.31/101.64
active(plus(z0, z1)) → plus(active(z0), z1) 331.31/101.64
active(plus(z0, z1)) → plus(z0, active(z1)) 331.31/101.64
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 331.31/101.64
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 331.31/101.64
active(x(z0, z1)) → x(active(z0), z1) 331.31/101.64
active(x(z0, z1)) → x(z0, active(z1)) 331.31/101.64
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 331.31/101.64
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 331.31/101.64
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 331.31/101.64
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 331.31/101.64
s(mark(z0)) → mark(s(z0)) 331.31/101.64
s(ok(z0)) → ok(s(z0)) 331.31/101.64
plus(mark(z0), z1) → mark(plus(z0, z1)) 331.31/101.64
plus(z0, mark(z1)) → mark(plus(z0, z1)) 331.31/101.64
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 331.31/101.64
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 331.31/101.64
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 331.31/101.64
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 331.31/101.64
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 331.31/101.64
x(mark(z0), z1) → mark(x(z0, z1)) 331.31/101.64
x(z0, mark(z1)) → mark(x(z0, z1)) 331.31/101.64
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 331.31/101.64
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 331.31/101.64
proper(tt) → ok(tt) 331.31/101.64
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 331.31/101.64
proper(s(z0)) → s(proper(z0)) 331.31/101.64
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 331.31/101.64
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 331.31/101.64
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 331.31/101.64
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 331.31/101.64
proper(0) → ok(0) 331.31/101.64
top(mark(z0)) → top(proper(z0)) 331.31/101.64
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(U12(z0, z1, z2)) → c9(U12'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(s(z0)) → c10(S(active(z0)), ACTIVE(z0)) 331.31/101.64
ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 331.31/101.64
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 331.31/101.64
ACTIVE(U21(z0, z1, z2)) → c13(U21'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(U22(z0, z1, z2)) → c14(U22'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 331.31/101.64
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 331.31/101.64
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 331.31/101.64
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 331.31/101.64
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 331.31/101.64
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 331.31/101.64
S(mark(z0)) → c21(S(z0)) 331.31/101.64
S(ok(z0)) → c22(S(z0)) 331.31/101.64
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 331.31/101.64
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 331.31/101.64
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 331.31/101.64
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 331.31/101.64
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 331.31/101.64
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 331.31/101.64
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 331.31/101.64
X(mark(z0), z1) → c30(X(z0, z1)) 331.31/101.64
X(z0, mark(z1)) → c31(X(z0, z1)) 331.31/101.64
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 331.31/101.64
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 331.31/101.64
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.31/101.64
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.31/101.64
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 331.31/101.64
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 331.31/101.64
ACTIVE(U11(tt, z0, z1)) → c 331.31/101.64
ACTIVE(U21(tt, z0, z1)) → c2 331.31/101.64
ACTIVE(plus(z0, s(z1))) → c5 331.31/101.64
ACTIVE(x(z0, s(z1))) → c7 331.31/101.64
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 331.31/101.64
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 331.31/101.64
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 331.31/101.64
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 331.31/101.64
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c8(U11'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U12(tt, z0, z1))) 331.31/101.64
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c8(U11'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.31/101.64
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c8(U11'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.31/101.64
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 331.31/101.64
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 331.31/101.64
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 331.31/101.64
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 331.31/101.64
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 331.31/101.64
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 331.31/101.64
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 331.31/101.64
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 331.31/101.64
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 331.31/101.64
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 331.31/101.64
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 331.31/101.64
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 331.31/101.64
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 331.31/101.64
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 331.31/101.64
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1)))
S tuples:

ACTIVE(U12(z0, z1, z2)) → c9(U12'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(s(z0)) → c10(S(active(z0)), ACTIVE(z0)) 331.31/101.64
ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 331.31/101.64
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 331.31/101.64
ACTIVE(U21(z0, z1, z2)) → c13(U21'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(U22(z0, z1, z2)) → c14(U22'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 331.31/101.64
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 331.31/101.64
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 331.31/101.64
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 331.31/101.64
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 331.31/101.64
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 331.31/101.64
S(mark(z0)) → c21(S(z0)) 331.31/101.64
S(ok(z0)) → c22(S(z0)) 331.31/101.64
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 331.31/101.64
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 331.31/101.64
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 331.31/101.64
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 331.31/101.64
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 331.31/101.64
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 331.31/101.64
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 331.31/101.64
X(mark(z0), z1) → c30(X(z0, z1)) 331.31/101.64
X(z0, mark(z1)) → c31(X(z0, z1)) 331.31/101.64
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 331.31/101.64
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 331.31/101.64
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.31/101.64
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.31/101.64
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 331.31/101.64
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 331.31/101.64
ACTIVE(U11(tt, z0, z1)) → c 331.31/101.64
ACTIVE(U21(tt, z0, z1)) → c2 331.31/101.64
ACTIVE(plus(z0, s(z1))) → c5 331.31/101.64
ACTIVE(x(z0, s(z1))) → c7 331.31/101.64
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 331.31/101.64
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 331.31/101.64
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 331.31/101.64
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 331.31/101.64
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c8(U11'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U12(tt, z0, z1))) 331.31/101.64
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c8(U11'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.31/101.64
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c8(U11'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.31/101.64
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 331.31/101.64
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 331.31/101.64
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 331.31/101.64
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 331.31/101.64
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 331.31/101.64
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 331.31/101.64
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 331.31/101.64
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 331.31/101.64
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 331.31/101.64
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 331.31/101.64
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 331.31/101.64
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 331.31/101.64
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 331.31/101.64
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 331.31/101.64
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c35, c36, c37, c38, c39, c40, c42, c43, c, c2, c5, c7, c4, c8, c1

331.31/101.64
331.31/101.64

(13) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

Removed 5 trailing nodes:

ACTIVE(U21(tt, z0, z1)) → c2 331.31/101.64
ACTIVE(x(z0, s(z1))) → c7 331.31/101.64
ACTIVE(U11(tt, z0, z1)) → c 331.31/101.64
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 331.31/101.64
ACTIVE(plus(z0, s(z1))) → c5
331.31/101.64
331.31/101.64

(14) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 331.31/101.64
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 331.31/101.64
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 331.31/101.64
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 331.31/101.64
active(plus(z0, 0)) → mark(z0) 331.31/101.64
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 331.31/101.64
active(x(z0, 0)) → mark(0) 331.31/101.64
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 331.31/101.64
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 331.31/101.64
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 331.31/101.64
active(s(z0)) → s(active(z0)) 331.31/101.64
active(plus(z0, z1)) → plus(active(z0), z1) 331.31/101.64
active(plus(z0, z1)) → plus(z0, active(z1)) 331.31/101.64
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 331.31/101.64
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 331.31/101.64
active(x(z0, z1)) → x(active(z0), z1) 331.31/101.64
active(x(z0, z1)) → x(z0, active(z1)) 331.31/101.64
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 331.31/101.64
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 331.31/101.64
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 331.31/101.64
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 331.31/101.64
s(mark(z0)) → mark(s(z0)) 331.31/101.64
s(ok(z0)) → ok(s(z0)) 331.31/101.64
plus(mark(z0), z1) → mark(plus(z0, z1)) 331.31/101.64
plus(z0, mark(z1)) → mark(plus(z0, z1)) 331.31/101.64
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 331.31/101.64
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 331.31/101.64
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 331.31/101.64
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 331.31/101.64
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 331.31/101.64
x(mark(z0), z1) → mark(x(z0, z1)) 331.31/101.64
x(z0, mark(z1)) → mark(x(z0, z1)) 331.31/101.64
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 331.31/101.64
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 331.31/101.64
proper(tt) → ok(tt) 331.31/101.64
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 331.31/101.64
proper(s(z0)) → s(proper(z0)) 331.31/101.64
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 331.31/101.64
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 331.31/101.64
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 331.31/101.64
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 331.31/101.64
proper(0) → ok(0) 331.31/101.64
top(mark(z0)) → top(proper(z0)) 331.31/101.64
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(U12(z0, z1, z2)) → c9(U12'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(s(z0)) → c10(S(active(z0)), ACTIVE(z0)) 331.31/101.64
ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 331.31/101.64
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 331.31/101.64
ACTIVE(U21(z0, z1, z2)) → c13(U21'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(U22(z0, z1, z2)) → c14(U22'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 331.31/101.64
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 331.31/101.64
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 331.31/101.64
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 331.31/101.64
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 331.31/101.64
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 331.31/101.64
S(mark(z0)) → c21(S(z0)) 331.31/101.64
S(ok(z0)) → c22(S(z0)) 331.31/101.64
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 331.31/101.64
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 331.31/101.64
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 331.31/101.64
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 331.31/101.64
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 331.31/101.64
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 331.31/101.64
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 331.31/101.64
X(mark(z0), z1) → c30(X(z0, z1)) 331.31/101.64
X(z0, mark(z1)) → c31(X(z0, z1)) 331.31/101.64
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 331.31/101.64
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 331.31/101.64
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.31/101.64
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.31/101.64
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 331.31/101.64
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 331.31/101.64
ACTIVE(U11(tt, z0, z1)) → c 331.31/101.64
ACTIVE(U21(tt, z0, z1)) → c2 331.31/101.64
ACTIVE(plus(z0, s(z1))) → c5 331.31/101.64
ACTIVE(x(z0, s(z1))) → c7 331.31/101.64
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 331.31/101.64
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 331.31/101.64
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 331.31/101.64
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 331.31/101.64
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c8(U11'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U12(tt, z0, z1))) 331.31/101.64
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c8(U11'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.31/101.64
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c8(U11'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.31/101.64
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 331.31/101.64
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 331.31/101.64
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 331.31/101.64
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 331.31/101.64
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 331.31/101.64
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 331.31/101.64
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 331.31/101.64
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 331.31/101.64
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 331.31/101.64
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 331.31/101.64
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 331.31/101.64
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 331.31/101.64
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 331.31/101.64
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 331.31/101.64
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1)))
S tuples:

ACTIVE(U12(z0, z1, z2)) → c9(U12'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(s(z0)) → c10(S(active(z0)), ACTIVE(z0)) 331.31/101.64
ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 331.31/101.64
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 331.31/101.64
ACTIVE(U21(z0, z1, z2)) → c13(U21'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(U22(z0, z1, z2)) → c14(U22'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 331.31/101.64
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 331.31/101.64
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 331.31/101.64
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 331.31/101.64
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 331.31/101.64
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 331.31/101.64
S(mark(z0)) → c21(S(z0)) 331.31/101.64
S(ok(z0)) → c22(S(z0)) 331.31/101.64
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 331.31/101.64
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 331.31/101.64
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 331.31/101.64
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 331.31/101.64
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 331.31/101.64
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 331.31/101.64
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 331.31/101.64
X(mark(z0), z1) → c30(X(z0, z1)) 331.31/101.64
X(z0, mark(z1)) → c31(X(z0, z1)) 331.31/101.64
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 331.31/101.64
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 331.31/101.64
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.31/101.64
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.31/101.64
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 331.31/101.64
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 331.31/101.64
ACTIVE(U11(tt, z0, z1)) → c 331.31/101.64
ACTIVE(U21(tt, z0, z1)) → c2 331.31/101.64
ACTIVE(plus(z0, s(z1))) → c5 331.31/101.64
ACTIVE(x(z0, s(z1))) → c7 331.31/101.64
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 331.31/101.64
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 331.31/101.64
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 331.31/101.64
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 331.31/101.64
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c8(U11'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U12(tt, z0, z1))) 331.31/101.64
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c8(U11'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.31/101.64
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c8(U11'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.31/101.64
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 331.31/101.64
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 331.31/101.64
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 331.31/101.64
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 331.31/101.64
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 331.31/101.64
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 331.31/101.64
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 331.31/101.64
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 331.31/101.64
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 331.31/101.64
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 331.31/101.64
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 331.31/101.64
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 331.31/101.64
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 331.31/101.64
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 331.31/101.64
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c35, c36, c37, c38, c39, c40, c42, c43, c, c2, c5, c7, c4, c8, c1

331.31/101.64
331.31/101.64

(15) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace ACTIVE(U12(z0, z1, z2)) → c9(U12'(active(z0), z1, z2), ACTIVE(z0)) by

ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c9(U12'(mark(U12(tt, z0, z1)), x1, x2), ACTIVE(U11(tt, z0, z1))) 331.31/101.64
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c9(U12'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U12(tt, z0, z1))) 331.31/101.64
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c9(U12'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.31/101.64
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c9(U12'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.31/101.64
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 331.31/101.64
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 331.31/101.64
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 331.31/101.64
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 331.31/101.64
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 331.31/101.64
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 331.31/101.64
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 331.31/101.64
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 331.31/101.64
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 331.31/101.64
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 331.31/101.64
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 331.31/101.64
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 331.31/101.64
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
331.31/101.64
331.31/101.64

(16) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 331.31/101.64
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 331.31/101.64
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 331.31/101.64
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 331.31/101.64
active(plus(z0, 0)) → mark(z0) 331.31/101.64
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 331.31/101.64
active(x(z0, 0)) → mark(0) 331.31/101.64
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 331.31/101.64
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 331.31/101.64
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 331.31/101.64
active(s(z0)) → s(active(z0)) 331.31/101.64
active(plus(z0, z1)) → plus(active(z0), z1) 331.31/101.64
active(plus(z0, z1)) → plus(z0, active(z1)) 331.31/101.64
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 331.31/101.64
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 331.31/101.64
active(x(z0, z1)) → x(active(z0), z1) 331.31/101.64
active(x(z0, z1)) → x(z0, active(z1)) 331.31/101.64
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 331.31/101.64
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 331.31/101.64
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 331.31/101.64
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 331.31/101.64
s(mark(z0)) → mark(s(z0)) 331.31/101.64
s(ok(z0)) → ok(s(z0)) 331.31/101.64
plus(mark(z0), z1) → mark(plus(z0, z1)) 331.31/101.64
plus(z0, mark(z1)) → mark(plus(z0, z1)) 331.31/101.64
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 331.31/101.64
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 331.31/101.64
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 331.31/101.64
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 331.31/101.64
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 331.31/101.64
x(mark(z0), z1) → mark(x(z0, z1)) 331.31/101.64
x(z0, mark(z1)) → mark(x(z0, z1)) 331.31/101.64
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 331.31/101.64
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 331.31/101.64
proper(tt) → ok(tt) 331.31/101.64
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 331.31/101.64
proper(s(z0)) → s(proper(z0)) 331.31/101.64
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 331.31/101.64
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 331.31/101.64
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 331.31/101.64
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 331.31/101.64
proper(0) → ok(0) 331.31/101.64
top(mark(z0)) → top(proper(z0)) 331.31/101.64
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(s(z0)) → c10(S(active(z0)), ACTIVE(z0)) 331.31/101.64
ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 331.31/101.64
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 331.31/101.64
ACTIVE(U21(z0, z1, z2)) → c13(U21'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(U22(z0, z1, z2)) → c14(U22'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 331.31/101.64
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 331.31/101.64
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 331.31/101.64
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 331.31/101.64
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 331.31/101.64
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 331.31/101.64
S(mark(z0)) → c21(S(z0)) 331.31/101.64
S(ok(z0)) → c22(S(z0)) 331.31/101.64
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 331.31/101.64
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 331.31/101.64
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 331.31/101.64
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 331.31/101.64
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 331.31/101.64
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 331.31/101.64
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 331.31/101.64
X(mark(z0), z1) → c30(X(z0, z1)) 331.31/101.64
X(z0, mark(z1)) → c31(X(z0, z1)) 331.31/101.64
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 331.31/101.64
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 331.31/101.64
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.31/101.64
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.31/101.64
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 331.31/101.64
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 331.31/101.64
ACTIVE(U11(tt, z0, z1)) → c 331.31/101.64
ACTIVE(U21(tt, z0, z1)) → c2 331.31/101.64
ACTIVE(plus(z0, s(z1))) → c5 331.31/101.64
ACTIVE(x(z0, s(z1))) → c7 331.31/101.64
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 331.31/101.64
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 331.31/101.64
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 331.31/101.64
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 331.31/101.64
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c8(U11'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U12(tt, z0, z1))) 331.31/101.64
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c8(U11'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.31/101.64
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c8(U11'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.31/101.64
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 331.31/101.64
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 331.31/101.64
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 331.31/101.64
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 331.31/101.64
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 331.31/101.64
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 331.31/101.64
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 331.31/101.64
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 331.31/101.64
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 331.31/101.64
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 331.31/101.64
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 331.31/101.64
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 331.31/101.64
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 331.31/101.64
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 331.31/101.64
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 331.31/101.64
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c9(U12'(mark(U12(tt, z0, z1)), x1, x2), ACTIVE(U11(tt, z0, z1))) 331.31/101.64
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c9(U12'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U12(tt, z0, z1))) 331.31/101.64
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c9(U12'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.31/101.64
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c9(U12'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.31/101.64
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 331.31/101.64
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 331.31/101.64
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 331.31/101.64
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 331.31/101.64
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 331.31/101.64
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 331.31/101.64
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 331.31/101.64
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 331.31/101.64
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 331.31/101.64
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 331.31/101.64
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 331.31/101.64
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 331.31/101.64
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
S tuples:

ACTIVE(s(z0)) → c10(S(active(z0)), ACTIVE(z0)) 331.31/101.64
ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 331.31/101.64
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 331.31/101.64
ACTIVE(U21(z0, z1, z2)) → c13(U21'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(U22(z0, z1, z2)) → c14(U22'(active(z0), z1, z2), ACTIVE(z0)) 331.31/101.64
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 331.31/101.64
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 331.31/101.64
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 331.31/101.64
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 331.31/101.64
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 331.31/101.64
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 331.31/101.64
S(mark(z0)) → c21(S(z0)) 331.31/101.64
S(ok(z0)) → c22(S(z0)) 331.31/101.64
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 331.31/101.64
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 331.31/101.64
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 331.31/101.64
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 331.31/101.64
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 331.31/101.64
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 331.31/101.64
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 331.31/101.64
X(mark(z0), z1) → c30(X(z0, z1)) 331.31/101.64
X(z0, mark(z1)) → c31(X(z0, z1)) 331.31/101.64
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 331.31/101.64
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 331.31/101.64
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.31/101.64
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.31/101.64
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.31/101.64
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 331.31/101.64
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 331.31/101.64
ACTIVE(U11(tt, z0, z1)) → c 331.31/101.64
ACTIVE(U21(tt, z0, z1)) → c2 331.31/101.64
ACTIVE(plus(z0, s(z1))) → c5 331.31/101.64
ACTIVE(x(z0, s(z1))) → c7 331.31/101.64
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 331.31/101.64
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 331.31/101.64
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 331.31/101.64
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 331.31/101.64
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c8(U11'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U12(tt, z0, z1))) 331.31/101.64
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c8(U11'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.31/101.64
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c8(U11'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.31/101.64
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 331.31/101.64
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 331.31/101.64
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 331.31/101.64
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 331.31/101.64
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 331.31/101.64
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 331.31/101.64
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 331.31/101.64
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 331.31/101.64
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 331.31/101.64
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 331.31/101.64
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 331.31/101.64
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 331.31/101.64
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 331.31/101.64
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 331.31/101.64
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 331.31/101.64
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c9(U12'(mark(U12(tt, z0, z1)), x1, x2), ACTIVE(U11(tt, z0, z1))) 331.31/101.64
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c9(U12'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U12(tt, z0, z1))) 331.31/101.64
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c9(U12'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.31/101.64
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c9(U12'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.31/101.64
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 331.31/101.64
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 331.31/101.64
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 331.63/101.74
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 331.63/101.74
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 331.63/101.74
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 331.63/101.74
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 331.63/101.74
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.74
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.74
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 331.63/101.74
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 331.63/101.74
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.74
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c35, c36, c37, c38, c39, c40, c42, c43, c, c2, c5, c7, c4, c8, c1, c9

331.63/101.74
331.63/101.74

(17) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)

Split RHS of tuples not part of any SCC
331.63/101.74
331.63/101.74

(18) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 331.63/101.74
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 331.63/101.74
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 331.63/101.74
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 331.63/101.74
active(plus(z0, 0)) → mark(z0) 331.63/101.74
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 331.63/101.74
active(x(z0, 0)) → mark(0) 331.63/101.74
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 331.63/101.74
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 331.63/101.74
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 331.63/101.74
active(s(z0)) → s(active(z0)) 331.63/101.74
active(plus(z0, z1)) → plus(active(z0), z1) 331.63/101.74
active(plus(z0, z1)) → plus(z0, active(z1)) 331.63/101.74
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 331.63/101.74
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 331.63/101.74
active(x(z0, z1)) → x(active(z0), z1) 331.63/101.74
active(x(z0, z1)) → x(z0, active(z1)) 331.63/101.74
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 331.63/101.74
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 331.63/101.74
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 331.63/101.74
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 331.63/101.74
s(mark(z0)) → mark(s(z0)) 331.63/101.74
s(ok(z0)) → ok(s(z0)) 331.63/101.74
plus(mark(z0), z1) → mark(plus(z0, z1)) 331.63/101.74
plus(z0, mark(z1)) → mark(plus(z0, z1)) 331.63/101.74
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 331.63/101.74
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 331.63/101.74
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 331.63/101.74
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 331.63/101.74
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 331.63/101.74
x(mark(z0), z1) → mark(x(z0, z1)) 331.63/101.74
x(z0, mark(z1)) → mark(x(z0, z1)) 331.63/101.74
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 331.63/101.74
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 331.63/101.74
proper(tt) → ok(tt) 331.63/101.74
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 331.63/101.74
proper(s(z0)) → s(proper(z0)) 331.63/101.74
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 331.63/101.74
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 331.63/101.74
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 331.63/101.74
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 331.63/101.74
proper(0) → ok(0) 331.63/101.74
top(mark(z0)) → top(proper(z0)) 331.63/101.74
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(s(z0)) → c10(S(active(z0)), ACTIVE(z0)) 331.63/101.74
ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 331.63/101.74
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 331.63/101.74
ACTIVE(U21(z0, z1, z2)) → c13(U21'(active(z0), z1, z2), ACTIVE(z0)) 331.63/101.74
ACTIVE(U22(z0, z1, z2)) → c14(U22'(active(z0), z1, z2), ACTIVE(z0)) 331.63/101.74
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 331.63/101.74
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 331.63/101.74
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 331.63/101.74
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 331.63/101.74
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 331.63/101.74
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 331.63/101.74
S(mark(z0)) → c21(S(z0)) 331.63/101.74
S(ok(z0)) → c22(S(z0)) 331.63/101.74
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 331.63/101.74
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 331.63/101.74
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 331.63/101.74
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 331.63/101.74
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 331.63/101.74
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 331.63/101.74
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 331.63/101.74
X(mark(z0), z1) → c30(X(z0, z1)) 331.63/101.74
X(z0, mark(z1)) → c31(X(z0, z1)) 331.63/101.74
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 331.63/101.74
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.74
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.74
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 331.63/101.74
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.63/101.74
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.74
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.74
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.63/101.74
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 331.63/101.74
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 331.63/101.74
ACTIVE(U11(tt, z0, z1)) → c 331.63/101.74
ACTIVE(U21(tt, z0, z1)) → c2 331.63/101.74
ACTIVE(plus(z0, s(z1))) → c5 331.63/101.74
ACTIVE(x(z0, s(z1))) → c7 331.63/101.74
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 331.63/101.74
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 331.63/101.74
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 331.63/101.74
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 331.63/101.74
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c8(U11'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.63/101.74
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c8(U11'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.63/101.74
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 331.63/101.74
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 331.63/101.74
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 331.63/101.74
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 331.63/101.74
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 331.63/101.74
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 331.63/101.74
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 331.63/101.74
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.74
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.74
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 331.63/101.74
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 331.63/101.74
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.74
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.74
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 331.63/101.74
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 331.63/101.74
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c9(U12'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.63/101.74
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c9(U12'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.63/101.74
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 331.63/101.74
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 331.63/101.74
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 331.63/101.74
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 331.63/101.74
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 331.63/101.74
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 331.63/101.74
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 331.63/101.74
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.74
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.74
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 331.63/101.74
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 331.63/101.74
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.74
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.74
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 331.63/101.74
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 331.63/101.74
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 331.63/101.74
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 331.63/101.74
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 331.63/101.74
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1)))
S tuples:

ACTIVE(s(z0)) → c10(S(active(z0)), ACTIVE(z0)) 331.63/101.74
ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 331.63/101.74
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 331.63/101.74
ACTIVE(U21(z0, z1, z2)) → c13(U21'(active(z0), z1, z2), ACTIVE(z0)) 331.63/101.74
ACTIVE(U22(z0, z1, z2)) → c14(U22'(active(z0), z1, z2), ACTIVE(z0)) 331.63/101.74
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 331.63/101.74
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 331.63/101.75
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 331.63/101.75
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 331.63/101.75
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 331.63/101.75
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 331.63/101.75
S(mark(z0)) → c21(S(z0)) 331.63/101.75
S(ok(z0)) → c22(S(z0)) 331.63/101.75
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 331.63/101.75
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 331.63/101.75
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 331.63/101.75
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 331.63/101.75
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 331.63/101.75
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 331.63/101.75
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 331.63/101.75
X(mark(z0), z1) → c30(X(z0, z1)) 331.63/101.75
X(z0, mark(z1)) → c31(X(z0, z1)) 331.63/101.75
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 331.63/101.75
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 331.63/101.75
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.63/101.75
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.63/101.75
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 331.63/101.75
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 331.63/101.75
ACTIVE(U11(tt, z0, z1)) → c 331.63/101.75
ACTIVE(U21(tt, z0, z1)) → c2 331.63/101.75
ACTIVE(plus(z0, s(z1))) → c5 331.63/101.75
ACTIVE(x(z0, s(z1))) → c7 331.63/101.75
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 331.63/101.75
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 331.63/101.75
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 331.63/101.75
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 331.63/101.75
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c8(U11'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.63/101.75
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c8(U11'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.63/101.75
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 331.63/101.75
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 331.63/101.75
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 331.63/101.75
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 331.63/101.75
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 331.63/101.75
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 331.63/101.75
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c9(U12'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c9(U12'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 331.63/101.75
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 331.63/101.75
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 331.63/101.75
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 331.63/101.75
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 331.63/101.75
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 331.63/101.75
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 331.63/101.75
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 331.63/101.75
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c35, c36, c37, c38, c39, c40, c42, c43, c, c2, c5, c7, c4, c8, c1, c9, c3

331.63/101.75
331.63/101.75

(19) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

Removed 6 trailing nodes:

ACTIVE(U21(tt, z0, z1)) → c2 331.63/101.75
ACTIVE(x(z0, s(z1))) → c7 331.63/101.75
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 331.63/101.75
ACTIVE(U11(tt, z0, z1)) → c 331.63/101.75
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 331.63/101.75
ACTIVE(plus(z0, s(z1))) → c5
331.63/101.75
331.63/101.75

(20) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 331.63/101.75
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 331.63/101.75
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 331.63/101.75
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 331.63/101.75
active(plus(z0, 0)) → mark(z0) 331.63/101.75
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 331.63/101.75
active(x(z0, 0)) → mark(0) 331.63/101.75
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 331.63/101.75
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 331.63/101.75
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 331.63/101.75
active(s(z0)) → s(active(z0)) 331.63/101.75
active(plus(z0, z1)) → plus(active(z0), z1) 331.63/101.75
active(plus(z0, z1)) → plus(z0, active(z1)) 331.63/101.75
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 331.63/101.75
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 331.63/101.75
active(x(z0, z1)) → x(active(z0), z1) 331.63/101.75
active(x(z0, z1)) → x(z0, active(z1)) 331.63/101.75
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 331.63/101.75
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 331.63/101.75
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 331.63/101.75
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 331.63/101.75
s(mark(z0)) → mark(s(z0)) 331.63/101.75
s(ok(z0)) → ok(s(z0)) 331.63/101.75
plus(mark(z0), z1) → mark(plus(z0, z1)) 331.63/101.75
plus(z0, mark(z1)) → mark(plus(z0, z1)) 331.63/101.75
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 331.63/101.75
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 331.63/101.75
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 331.63/101.75
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 331.63/101.75
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 331.63/101.75
x(mark(z0), z1) → mark(x(z0, z1)) 331.63/101.75
x(z0, mark(z1)) → mark(x(z0, z1)) 331.63/101.75
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 331.63/101.75
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 331.63/101.75
proper(tt) → ok(tt) 331.63/101.75
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 331.63/101.75
proper(s(z0)) → s(proper(z0)) 331.63/101.75
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 331.63/101.75
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 331.63/101.75
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 331.63/101.75
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 331.63/101.75
proper(0) → ok(0) 331.63/101.75
top(mark(z0)) → top(proper(z0)) 331.63/101.75
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(s(z0)) → c10(S(active(z0)), ACTIVE(z0)) 331.63/101.75
ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 331.63/101.75
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 331.63/101.75
ACTIVE(U21(z0, z1, z2)) → c13(U21'(active(z0), z1, z2), ACTIVE(z0)) 331.63/101.75
ACTIVE(U22(z0, z1, z2)) → c14(U22'(active(z0), z1, z2), ACTIVE(z0)) 331.63/101.75
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 331.63/101.75
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 331.63/101.75
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 331.63/101.75
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 331.63/101.75
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 331.63/101.75
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 331.63/101.75
S(mark(z0)) → c21(S(z0)) 331.63/101.75
S(ok(z0)) → c22(S(z0)) 331.63/101.75
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 331.63/101.75
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 331.63/101.75
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 331.63/101.75
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 331.63/101.75
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 331.63/101.75
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 331.63/101.75
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 331.63/101.75
X(mark(z0), z1) → c30(X(z0, z1)) 331.63/101.75
X(z0, mark(z1)) → c31(X(z0, z1)) 331.63/101.75
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 331.63/101.75
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 331.63/101.75
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.63/101.75
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.63/101.75
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 331.63/101.75
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 331.63/101.75
ACTIVE(U11(tt, z0, z1)) → c 331.63/101.75
ACTIVE(U21(tt, z0, z1)) → c2 331.63/101.75
ACTIVE(plus(z0, s(z1))) → c5 331.63/101.75
ACTIVE(x(z0, s(z1))) → c7 331.63/101.75
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 331.63/101.75
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 331.63/101.75
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 331.63/101.75
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 331.63/101.75
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c8(U11'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.63/101.75
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c8(U11'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.63/101.75
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 331.63/101.75
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 331.63/101.75
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 331.63/101.75
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 331.63/101.75
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 331.63/101.75
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 331.63/101.75
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c9(U12'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c9(U12'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 331.63/101.75
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 331.63/101.75
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 331.63/101.75
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 331.63/101.75
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 331.63/101.75
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 331.63/101.75
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 331.63/101.75
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 331.63/101.75
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1)))
S tuples:

ACTIVE(s(z0)) → c10(S(active(z0)), ACTIVE(z0)) 331.63/101.75
ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 331.63/101.75
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 331.63/101.75
ACTIVE(U21(z0, z1, z2)) → c13(U21'(active(z0), z1, z2), ACTIVE(z0)) 331.63/101.75
ACTIVE(U22(z0, z1, z2)) → c14(U22'(active(z0), z1, z2), ACTIVE(z0)) 331.63/101.75
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 331.63/101.75
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 331.63/101.75
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 331.63/101.75
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 331.63/101.75
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 331.63/101.75
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 331.63/101.75
S(mark(z0)) → c21(S(z0)) 331.63/101.75
S(ok(z0)) → c22(S(z0)) 331.63/101.75
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 331.63/101.75
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 331.63/101.75
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 331.63/101.75
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 331.63/101.75
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 331.63/101.75
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 331.63/101.75
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 331.63/101.75
X(mark(z0), z1) → c30(X(z0, z1)) 331.63/101.75
X(z0, mark(z1)) → c31(X(z0, z1)) 331.63/101.75
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 331.63/101.75
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 331.63/101.75
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.63/101.75
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.63/101.75
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 331.63/101.75
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 331.63/101.75
ACTIVE(U11(tt, z0, z1)) → c 331.63/101.75
ACTIVE(U21(tt, z0, z1)) → c2 331.63/101.75
ACTIVE(plus(z0, s(z1))) → c5 331.63/101.75
ACTIVE(x(z0, s(z1))) → c7 331.63/101.75
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 331.63/101.75
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 331.63/101.75
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 331.63/101.75
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 331.63/101.75
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c8(U11'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.63/101.75
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c8(U11'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.63/101.75
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 331.63/101.75
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 331.63/101.75
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 331.63/101.75
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 331.63/101.75
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 331.63/101.75
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 331.63/101.75
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c9(U12'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c9(U12'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 331.63/101.75
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 331.63/101.75
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 331.63/101.75
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 331.63/101.75
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 331.63/101.75
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 331.63/101.75
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 331.63/101.75
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 331.63/101.75
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c35, c36, c37, c38, c39, c40, c42, c43, c, c2, c5, c7, c4, c8, c1, c9, c3

331.63/101.75
331.63/101.75

(21) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace ACTIVE(s(z0)) → c10(S(active(z0)), ACTIVE(z0)) by

ACTIVE(s(U11(tt, z0, z1))) → c10(S(mark(U12(tt, z0, z1))), ACTIVE(U11(tt, z0, z1))) 331.63/101.75
ACTIVE(s(U12(tt, z0, z1))) → c10(S(mark(s(plus(z1, z0)))), ACTIVE(U12(tt, z0, z1))) 331.63/101.75
ACTIVE(s(U21(tt, z0, z1))) → c10(S(mark(U22(tt, z0, z1))), ACTIVE(U21(tt, z0, z1))) 331.63/101.75
ACTIVE(s(U22(tt, z0, z1))) → c10(S(mark(plus(x(z1, z0), z1))), ACTIVE(U22(tt, z0, z1))) 331.63/101.75
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 331.63/101.75
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 331.63/101.75
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 331.63/101.75
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 331.63/101.75
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 331.63/101.75
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 331.63/101.75
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 331.63/101.75
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 331.63/101.75
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 331.63/101.75
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
331.63/101.75
331.63/101.75

(22) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 331.63/101.75
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 331.63/101.75
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 331.63/101.75
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 331.63/101.75
active(plus(z0, 0)) → mark(z0) 331.63/101.75
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 331.63/101.75
active(x(z0, 0)) → mark(0) 331.63/101.75
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 331.63/101.75
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 331.63/101.75
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 331.63/101.75
active(s(z0)) → s(active(z0)) 331.63/101.75
active(plus(z0, z1)) → plus(active(z0), z1) 331.63/101.75
active(plus(z0, z1)) → plus(z0, active(z1)) 331.63/101.75
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 331.63/101.75
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 331.63/101.75
active(x(z0, z1)) → x(active(z0), z1) 331.63/101.75
active(x(z0, z1)) → x(z0, active(z1)) 331.63/101.75
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 331.63/101.75
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 331.63/101.75
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 331.63/101.75
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 331.63/101.75
s(mark(z0)) → mark(s(z0)) 331.63/101.75
s(ok(z0)) → ok(s(z0)) 331.63/101.75
plus(mark(z0), z1) → mark(plus(z0, z1)) 331.63/101.75
plus(z0, mark(z1)) → mark(plus(z0, z1)) 331.63/101.75
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 331.63/101.75
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 331.63/101.75
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 331.63/101.75
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 331.63/101.75
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 331.63/101.75
x(mark(z0), z1) → mark(x(z0, z1)) 331.63/101.75
x(z0, mark(z1)) → mark(x(z0, z1)) 331.63/101.75
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 331.63/101.75
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 331.63/101.75
proper(tt) → ok(tt) 331.63/101.75
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 331.63/101.75
proper(s(z0)) → s(proper(z0)) 331.63/101.75
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 331.63/101.75
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 331.63/101.75
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 331.63/101.75
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 331.63/101.75
proper(0) → ok(0) 331.63/101.75
top(mark(z0)) → top(proper(z0)) 331.63/101.75
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 331.63/101.75
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 331.63/101.75
ACTIVE(U21(z0, z1, z2)) → c13(U21'(active(z0), z1, z2), ACTIVE(z0)) 331.63/101.75
ACTIVE(U22(z0, z1, z2)) → c14(U22'(active(z0), z1, z2), ACTIVE(z0)) 331.63/101.75
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 331.63/101.75
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 331.63/101.75
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 331.63/101.75
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 331.63/101.75
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 331.63/101.75
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 331.63/101.75
S(mark(z0)) → c21(S(z0)) 331.63/101.75
S(ok(z0)) → c22(S(z0)) 331.63/101.75
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 331.63/101.75
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 331.63/101.75
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 331.63/101.75
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 331.63/101.75
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 331.63/101.75
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 331.63/101.75
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 331.63/101.75
X(mark(z0), z1) → c30(X(z0, z1)) 331.63/101.75
X(z0, mark(z1)) → c31(X(z0, z1)) 331.63/101.75
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 331.63/101.75
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 331.63/101.75
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.63/101.75
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.63/101.75
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 331.63/101.75
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 331.63/101.75
ACTIVE(U11(tt, z0, z1)) → c 331.63/101.75
ACTIVE(U21(tt, z0, z1)) → c2 331.63/101.75
ACTIVE(plus(z0, s(z1))) → c5 331.63/101.75
ACTIVE(x(z0, s(z1))) → c7 331.63/101.75
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 331.63/101.75
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 331.63/101.75
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 331.63/101.75
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 331.63/101.75
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c8(U11'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.63/101.75
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c8(U11'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.63/101.75
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 331.63/101.75
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 331.63/101.75
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 331.63/101.75
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 331.63/101.75
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 331.63/101.75
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 331.63/101.75
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c9(U12'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c9(U12'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 331.63/101.75
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 331.63/101.75
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 331.63/101.75
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 331.63/101.75
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 331.63/101.75
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 331.63/101.75
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 331.63/101.75
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 331.63/101.75
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 331.63/101.75
ACTIVE(s(U11(tt, z0, z1))) → c10(S(mark(U12(tt, z0, z1))), ACTIVE(U11(tt, z0, z1))) 331.63/101.75
ACTIVE(s(U12(tt, z0, z1))) → c10(S(mark(s(plus(z1, z0)))), ACTIVE(U12(tt, z0, z1))) 331.63/101.75
ACTIVE(s(U21(tt, z0, z1))) → c10(S(mark(U22(tt, z0, z1))), ACTIVE(U21(tt, z0, z1))) 331.63/101.75
ACTIVE(s(U22(tt, z0, z1))) → c10(S(mark(plus(x(z1, z0), z1))), ACTIVE(U22(tt, z0, z1))) 331.63/101.75
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 331.63/101.75
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 331.63/101.75
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 331.63/101.75
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 331.63/101.75
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 331.63/101.75
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 331.63/101.75
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 331.63/101.75
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 331.63/101.75
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 331.63/101.75
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
S tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 331.63/101.75
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 331.63/101.75
ACTIVE(U21(z0, z1, z2)) → c13(U21'(active(z0), z1, z2), ACTIVE(z0)) 331.63/101.75
ACTIVE(U22(z0, z1, z2)) → c14(U22'(active(z0), z1, z2), ACTIVE(z0)) 331.63/101.75
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 331.63/101.75
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 331.63/101.75
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 331.63/101.75
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 331.63/101.75
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 331.63/101.75
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 331.63/101.75
S(mark(z0)) → c21(S(z0)) 331.63/101.75
S(ok(z0)) → c22(S(z0)) 331.63/101.75
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 331.63/101.75
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 331.63/101.75
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 331.63/101.75
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 331.63/101.75
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 331.63/101.75
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 331.63/101.75
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 331.63/101.75
X(mark(z0), z1) → c30(X(z0, z1)) 331.63/101.75
X(z0, mark(z1)) → c31(X(z0, z1)) 331.63/101.75
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 331.63/101.75
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 331.63/101.75
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.63/101.75
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.63/101.75
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 331.63/101.75
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 331.63/101.75
ACTIVE(U11(tt, z0, z1)) → c 331.63/101.75
ACTIVE(U21(tt, z0, z1)) → c2 331.63/101.75
ACTIVE(plus(z0, s(z1))) → c5 331.63/101.75
ACTIVE(x(z0, s(z1))) → c7 331.63/101.75
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 331.63/101.75
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 331.63/101.75
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 331.63/101.75
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 331.63/101.75
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c8(U11'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.63/101.75
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c8(U11'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.63/101.75
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 331.63/101.75
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 331.63/101.75
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 331.63/101.75
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 331.63/101.75
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 331.63/101.75
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 331.63/101.75
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c9(U12'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c9(U12'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 331.63/101.75
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 331.63/101.75
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 331.63/101.75
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 331.63/101.75
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 331.63/101.75
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 331.63/101.75
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 331.63/101.75
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 331.63/101.75
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 331.63/101.75
ACTIVE(s(U11(tt, z0, z1))) → c10(S(mark(U12(tt, z0, z1))), ACTIVE(U11(tt, z0, z1))) 331.63/101.75
ACTIVE(s(U12(tt, z0, z1))) → c10(S(mark(s(plus(z1, z0)))), ACTIVE(U12(tt, z0, z1))) 331.63/101.75
ACTIVE(s(U21(tt, z0, z1))) → c10(S(mark(U22(tt, z0, z1))), ACTIVE(U21(tt, z0, z1))) 331.63/101.75
ACTIVE(s(U22(tt, z0, z1))) → c10(S(mark(plus(x(z1, z0), z1))), ACTIVE(U22(tt, z0, z1))) 331.63/101.75
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 331.63/101.75
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 331.63/101.75
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 331.63/101.75
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 331.63/101.75
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 331.63/101.75
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 331.63/101.75
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 331.63/101.75
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 331.63/101.75
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 331.63/101.75
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c35, c36, c37, c38, c39, c40, c42, c43, c, c2, c5, c7, c4, c8, c1, c9, c3, c10

331.63/101.75
331.63/101.75

(23) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)

Split RHS of tuples not part of any SCC
331.63/101.75
331.63/101.75

(24) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 331.63/101.75
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 331.63/101.75
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 331.63/101.75
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 331.63/101.75
active(plus(z0, 0)) → mark(z0) 331.63/101.75
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 331.63/101.75
active(x(z0, 0)) → mark(0) 331.63/101.75
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 331.63/101.75
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 331.63/101.75
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 331.63/101.75
active(s(z0)) → s(active(z0)) 331.63/101.75
active(plus(z0, z1)) → plus(active(z0), z1) 331.63/101.75
active(plus(z0, z1)) → plus(z0, active(z1)) 331.63/101.75
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 331.63/101.75
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 331.63/101.75
active(x(z0, z1)) → x(active(z0), z1) 331.63/101.75
active(x(z0, z1)) → x(z0, active(z1)) 331.63/101.75
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 331.63/101.75
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 331.63/101.75
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 331.63/101.75
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 331.63/101.75
s(mark(z0)) → mark(s(z0)) 331.63/101.75
s(ok(z0)) → ok(s(z0)) 331.63/101.75
plus(mark(z0), z1) → mark(plus(z0, z1)) 331.63/101.75
plus(z0, mark(z1)) → mark(plus(z0, z1)) 331.63/101.75
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 331.63/101.75
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 331.63/101.75
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 331.63/101.75
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 331.63/101.75
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 331.63/101.75
x(mark(z0), z1) → mark(x(z0, z1)) 331.63/101.75
x(z0, mark(z1)) → mark(x(z0, z1)) 331.63/101.75
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 331.63/101.75
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 331.63/101.75
proper(tt) → ok(tt) 331.63/101.75
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 331.63/101.75
proper(s(z0)) → s(proper(z0)) 331.63/101.75
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 331.63/101.75
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 331.63/101.75
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 331.63/101.75
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 331.63/101.75
proper(0) → ok(0) 331.63/101.75
top(mark(z0)) → top(proper(z0)) 331.63/101.75
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 331.63/101.75
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 331.63/101.75
ACTIVE(U21(z0, z1, z2)) → c13(U21'(active(z0), z1, z2), ACTIVE(z0)) 331.63/101.75
ACTIVE(U22(z0, z1, z2)) → c14(U22'(active(z0), z1, z2), ACTIVE(z0)) 331.63/101.75
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 331.63/101.75
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 331.63/101.75
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 331.63/101.75
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 331.63/101.75
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 331.63/101.75
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 331.63/101.75
S(mark(z0)) → c21(S(z0)) 331.63/101.75
S(ok(z0)) → c22(S(z0)) 331.63/101.75
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 331.63/101.75
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 331.63/101.75
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 331.63/101.75
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 331.63/101.75
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 331.63/101.75
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 331.63/101.75
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 331.63/101.75
X(mark(z0), z1) → c30(X(z0, z1)) 331.63/101.75
X(z0, mark(z1)) → c31(X(z0, z1)) 331.63/101.75
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 331.63/101.75
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 331.63/101.75
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.63/101.75
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.63/101.75
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 331.63/101.75
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 331.63/101.75
ACTIVE(U11(tt, z0, z1)) → c 331.63/101.75
ACTIVE(U21(tt, z0, z1)) → c2 331.63/101.75
ACTIVE(plus(z0, s(z1))) → c5 331.63/101.75
ACTIVE(x(z0, s(z1))) → c7 331.63/101.75
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 331.63/101.75
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 331.63/101.75
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 331.63/101.75
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 331.63/101.75
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c8(U11'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.63/101.75
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c8(U11'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.63/101.75
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 331.63/101.75
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 331.63/101.75
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 331.63/101.75
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 331.63/101.75
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 331.63/101.75
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 331.63/101.75
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c9(U12'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c9(U12'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 331.63/101.75
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 331.63/101.75
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 331.63/101.75
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 331.63/101.75
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 331.63/101.75
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 331.63/101.75
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 331.63/101.75
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 331.63/101.75
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 331.63/101.75
ACTIVE(s(U21(tt, z0, z1))) → c10(S(mark(U22(tt, z0, z1))), ACTIVE(U21(tt, z0, z1))) 331.63/101.75
ACTIVE(s(U22(tt, z0, z1))) → c10(S(mark(plus(x(z1, z0), z1))), ACTIVE(U22(tt, z0, z1))) 331.63/101.75
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 331.63/101.75
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 331.63/101.75
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 331.63/101.75
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 331.63/101.75
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 331.63/101.75
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 331.63/101.75
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 331.63/101.75
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 331.63/101.75
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 331.63/101.75
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 331.63/101.75
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 331.63/101.75
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 331.63/101.75
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1)))
S tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 331.63/101.75
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 331.63/101.75
ACTIVE(U21(z0, z1, z2)) → c13(U21'(active(z0), z1, z2), ACTIVE(z0)) 331.63/101.75
ACTIVE(U22(z0, z1, z2)) → c14(U22'(active(z0), z1, z2), ACTIVE(z0)) 331.63/101.75
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 331.63/101.75
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 331.63/101.75
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 331.63/101.75
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 331.63/101.75
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 331.63/101.75
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 331.63/101.75
S(mark(z0)) → c21(S(z0)) 331.63/101.75
S(ok(z0)) → c22(S(z0)) 331.63/101.75
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 331.63/101.75
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 331.63/101.75
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 331.63/101.75
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 331.63/101.75
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 331.63/101.75
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 331.63/101.75
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 331.63/101.75
X(mark(z0), z1) → c30(X(z0, z1)) 331.63/101.75
X(z0, mark(z1)) → c31(X(z0, z1)) 331.63/101.75
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 331.63/101.75
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 331.63/101.75
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.63/101.75
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.63/101.75
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 331.63/101.75
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 331.63/101.75
ACTIVE(U11(tt, z0, z1)) → c 331.63/101.75
ACTIVE(U21(tt, z0, z1)) → c2 331.63/101.75
ACTIVE(plus(z0, s(z1))) → c5 331.63/101.75
ACTIVE(x(z0, s(z1))) → c7 331.63/101.75
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 331.63/101.75
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 331.63/101.75
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 331.63/101.75
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 331.63/101.75
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c8(U11'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.63/101.75
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c8(U11'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.63/101.75
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 331.63/101.75
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 331.63/101.75
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 331.63/101.75
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 331.63/101.75
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 331.63/101.75
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 331.63/101.75
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c9(U12'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c9(U12'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 331.63/101.75
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 331.63/101.75
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 331.63/101.75
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 331.63/101.75
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 331.63/101.75
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 331.63/101.75
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 331.63/101.75
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 331.63/101.75
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 331.63/101.75
ACTIVE(s(U21(tt, z0, z1))) → c10(S(mark(U22(tt, z0, z1))), ACTIVE(U21(tt, z0, z1))) 331.63/101.75
ACTIVE(s(U22(tt, z0, z1))) → c10(S(mark(plus(x(z1, z0), z1))), ACTIVE(U22(tt, z0, z1))) 331.63/101.75
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 331.63/101.75
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 331.63/101.75
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 331.63/101.75
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 331.63/101.75
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 331.63/101.75
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 331.63/101.75
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 331.63/101.75
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 331.63/101.75
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 331.63/101.75
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 331.63/101.75
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 331.63/101.75
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 331.63/101.75
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c35, c36, c37, c38, c39, c40, c42, c43, c, c2, c5, c7, c4, c8, c1, c9, c3, c10, c6

331.63/101.75
331.63/101.75

(25) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

Removed 7 trailing nodes:

ACTIVE(U21(tt, z0, z1)) → c2 331.63/101.75
ACTIVE(x(z0, s(z1))) → c7 331.63/101.75
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 331.63/101.75
ACTIVE(U11(tt, z0, z1)) → c 331.63/101.75
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 331.63/101.75
ACTIVE(plus(z0, s(z1))) → c5 331.63/101.75
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1)))
331.63/101.75
331.63/101.75

(26) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 331.63/101.75
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 331.63/101.75
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 331.63/101.75
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 331.63/101.75
active(plus(z0, 0)) → mark(z0) 331.63/101.75
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 331.63/101.75
active(x(z0, 0)) → mark(0) 331.63/101.75
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 331.63/101.75
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 331.63/101.75
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 331.63/101.75
active(s(z0)) → s(active(z0)) 331.63/101.75
active(plus(z0, z1)) → plus(active(z0), z1) 331.63/101.75
active(plus(z0, z1)) → plus(z0, active(z1)) 331.63/101.75
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 331.63/101.75
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 331.63/101.75
active(x(z0, z1)) → x(active(z0), z1) 331.63/101.75
active(x(z0, z1)) → x(z0, active(z1)) 331.63/101.75
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 331.63/101.75
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 331.63/101.75
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 331.63/101.75
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 331.63/101.75
s(mark(z0)) → mark(s(z0)) 331.63/101.75
s(ok(z0)) → ok(s(z0)) 331.63/101.75
plus(mark(z0), z1) → mark(plus(z0, z1)) 331.63/101.75
plus(z0, mark(z1)) → mark(plus(z0, z1)) 331.63/101.75
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 331.63/101.75
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 331.63/101.75
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 331.63/101.75
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 331.63/101.75
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 331.63/101.75
x(mark(z0), z1) → mark(x(z0, z1)) 331.63/101.75
x(z0, mark(z1)) → mark(x(z0, z1)) 331.63/101.75
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 331.63/101.75
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 331.63/101.75
proper(tt) → ok(tt) 331.63/101.75
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 331.63/101.75
proper(s(z0)) → s(proper(z0)) 331.63/101.75
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 331.63/101.75
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 331.63/101.75
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 331.63/101.75
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 331.63/101.75
proper(0) → ok(0) 331.63/101.75
top(mark(z0)) → top(proper(z0)) 331.63/101.75
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 331.63/101.75
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 331.63/101.75
ACTIVE(U21(z0, z1, z2)) → c13(U21'(active(z0), z1, z2), ACTIVE(z0)) 331.63/101.75
ACTIVE(U22(z0, z1, z2)) → c14(U22'(active(z0), z1, z2), ACTIVE(z0)) 331.63/101.75
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 331.63/101.75
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 331.63/101.75
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 331.63/101.75
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 331.63/101.75
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 331.63/101.75
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 331.63/101.75
S(mark(z0)) → c21(S(z0)) 331.63/101.75
S(ok(z0)) → c22(S(z0)) 331.63/101.75
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 331.63/101.75
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 331.63/101.75
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 331.63/101.75
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 331.63/101.75
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 331.63/101.75
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 331.63/101.75
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 331.63/101.75
X(mark(z0), z1) → c30(X(z0, z1)) 331.63/101.75
X(z0, mark(z1)) → c31(X(z0, z1)) 331.63/101.75
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 331.63/101.75
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 331.63/101.75
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.63/101.75
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.63/101.75
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 331.63/101.75
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 331.63/101.75
ACTIVE(U11(tt, z0, z1)) → c 331.63/101.75
ACTIVE(U21(tt, z0, z1)) → c2 331.63/101.75
ACTIVE(plus(z0, s(z1))) → c5 331.63/101.75
ACTIVE(x(z0, s(z1))) → c7 331.63/101.75
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 331.63/101.75
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 331.63/101.75
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 331.63/101.75
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 331.63/101.75
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c8(U11'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.63/101.75
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c8(U11'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.63/101.75
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 331.63/101.75
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 331.63/101.75
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 331.63/101.75
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 331.63/101.75
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 331.63/101.75
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 331.63/101.75
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c9(U12'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c9(U12'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 331.63/101.75
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 331.63/101.75
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 331.63/101.75
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 331.63/101.75
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 331.63/101.75
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 331.63/101.75
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 331.63/101.75
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 331.63/101.75
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 331.63/101.75
ACTIVE(s(U21(tt, z0, z1))) → c10(S(mark(U22(tt, z0, z1))), ACTIVE(U21(tt, z0, z1))) 331.63/101.75
ACTIVE(s(U22(tt, z0, z1))) → c10(S(mark(plus(x(z1, z0), z1))), ACTIVE(U22(tt, z0, z1))) 331.63/101.75
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 331.63/101.75
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 331.63/101.75
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 331.63/101.75
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 331.63/101.75
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 331.63/101.75
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 331.63/101.75
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 331.63/101.75
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 331.63/101.75
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 331.63/101.75
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 331.63/101.75
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 331.63/101.75
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 331.63/101.75
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1)))
S tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 331.63/101.75
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 331.63/101.75
ACTIVE(U21(z0, z1, z2)) → c13(U21'(active(z0), z1, z2), ACTIVE(z0)) 331.63/101.75
ACTIVE(U22(z0, z1, z2)) → c14(U22'(active(z0), z1, z2), ACTIVE(z0)) 331.63/101.75
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 331.63/101.75
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 331.63/101.75
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 331.63/101.75
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 331.63/101.75
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 331.63/101.75
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 331.63/101.75
S(mark(z0)) → c21(S(z0)) 331.63/101.75
S(ok(z0)) → c22(S(z0)) 331.63/101.75
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 331.63/101.75
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 331.63/101.75
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 331.63/101.75
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 331.63/101.75
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 331.63/101.75
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 331.63/101.75
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 331.63/101.75
X(mark(z0), z1) → c30(X(z0, z1)) 331.63/101.75
X(z0, mark(z1)) → c31(X(z0, z1)) 331.63/101.75
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 331.63/101.75
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 331.63/101.75
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.63/101.75
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.63/101.75
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 331.63/101.75
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 331.63/101.75
ACTIVE(U11(tt, z0, z1)) → c 331.63/101.75
ACTIVE(U21(tt, z0, z1)) → c2 331.63/101.75
ACTIVE(plus(z0, s(z1))) → c5 331.63/101.75
ACTIVE(x(z0, s(z1))) → c7 331.63/101.75
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 331.63/101.75
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 331.63/101.75
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 331.63/101.75
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 331.63/101.75
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c8(U11'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.63/101.75
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c8(U11'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.63/101.75
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 331.63/101.75
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 331.63/101.75
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 331.63/101.75
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 331.63/101.75
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 331.63/101.75
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 331.63/101.75
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c9(U12'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c9(U12'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 331.63/101.75
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 331.63/101.75
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 331.63/101.75
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 331.63/101.75
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 331.63/101.75
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 331.63/101.75
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 331.63/101.75
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 331.63/101.75
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 331.63/101.75
ACTIVE(s(U21(tt, z0, z1))) → c10(S(mark(U22(tt, z0, z1))), ACTIVE(U21(tt, z0, z1))) 331.63/101.75
ACTIVE(s(U22(tt, z0, z1))) → c10(S(mark(plus(x(z1, z0), z1))), ACTIVE(U22(tt, z0, z1))) 331.63/101.75
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 331.63/101.75
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 331.63/101.75
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 331.63/101.75
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 331.63/101.75
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 331.63/101.75
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 331.63/101.75
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 331.63/101.75
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 331.63/101.75
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 331.63/101.75
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 331.63/101.75
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 331.63/101.75
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 331.63/101.75
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c35, c36, c37, c38, c39, c40, c42, c43, c, c2, c5, c7, c4, c8, c1, c9, c3, c10, c6

331.63/101.75
331.63/101.75

(27) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace ACTIVE(U21(z0, z1, z2)) → c13(U21'(active(z0), z1, z2), ACTIVE(z0)) by

ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c13(U21'(mark(U12(tt, z0, z1)), x1, x2), ACTIVE(U11(tt, z0, z1))) 331.63/101.75
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c13(U21'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U12(tt, z0, z1))) 331.63/101.75
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c13(U21'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.63/101.75
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c13(U21'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.63/101.75
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 331.63/101.75
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 331.63/101.75
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 331.63/101.75
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 331.63/101.75
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 331.63/101.75
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 331.63/101.75
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 331.63/101.75
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 331.63/101.75
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 331.63/101.75
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
331.63/101.75
331.63/101.75

(28) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 331.63/101.75
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 331.63/101.75
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 331.63/101.75
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 331.63/101.75
active(plus(z0, 0)) → mark(z0) 331.63/101.75
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 331.63/101.75
active(x(z0, 0)) → mark(0) 331.63/101.75
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 331.63/101.75
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 331.63/101.75
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 331.63/101.75
active(s(z0)) → s(active(z0)) 331.63/101.75
active(plus(z0, z1)) → plus(active(z0), z1) 331.63/101.75
active(plus(z0, z1)) → plus(z0, active(z1)) 331.63/101.75
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 331.63/101.75
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 331.63/101.75
active(x(z0, z1)) → x(active(z0), z1) 331.63/101.75
active(x(z0, z1)) → x(z0, active(z1)) 331.63/101.75
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 331.63/101.75
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 331.63/101.75
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 331.63/101.75
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 331.63/101.75
s(mark(z0)) → mark(s(z0)) 331.63/101.75
s(ok(z0)) → ok(s(z0)) 331.63/101.75
plus(mark(z0), z1) → mark(plus(z0, z1)) 331.63/101.75
plus(z0, mark(z1)) → mark(plus(z0, z1)) 331.63/101.75
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 331.63/101.75
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 331.63/101.75
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 331.63/101.75
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 331.63/101.75
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 331.63/101.75
x(mark(z0), z1) → mark(x(z0, z1)) 331.63/101.75
x(z0, mark(z1)) → mark(x(z0, z1)) 331.63/101.75
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 331.63/101.75
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 331.63/101.75
proper(tt) → ok(tt) 331.63/101.75
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 331.63/101.75
proper(s(z0)) → s(proper(z0)) 331.63/101.75
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 331.63/101.75
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 331.63/101.75
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 331.63/101.75
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 331.63/101.75
proper(0) → ok(0) 331.63/101.75
top(mark(z0)) → top(proper(z0)) 331.63/101.75
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 331.63/101.75
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 331.63/101.75
ACTIVE(U22(z0, z1, z2)) → c14(U22'(active(z0), z1, z2), ACTIVE(z0)) 331.63/101.75
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 331.63/101.75
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 331.63/101.75
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 331.63/101.75
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 331.63/101.75
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 331.63/101.75
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 331.63/101.75
S(mark(z0)) → c21(S(z0)) 331.63/101.75
S(ok(z0)) → c22(S(z0)) 331.63/101.75
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 331.63/101.75
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 331.63/101.75
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 331.63/101.75
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 331.63/101.75
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 331.63/101.75
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 331.63/101.75
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 331.63/101.75
X(mark(z0), z1) → c30(X(z0, z1)) 331.63/101.75
X(z0, mark(z1)) → c31(X(z0, z1)) 331.63/101.75
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 331.63/101.75
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 331.63/101.75
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.63/101.75
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.63/101.75
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 331.63/101.75
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 331.63/101.75
ACTIVE(U11(tt, z0, z1)) → c 331.63/101.75
ACTIVE(U21(tt, z0, z1)) → c2 331.63/101.75
ACTIVE(plus(z0, s(z1))) → c5 331.63/101.75
ACTIVE(x(z0, s(z1))) → c7 331.63/101.75
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 331.63/101.75
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 331.63/101.75
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 331.63/101.75
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 331.63/101.75
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c8(U11'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.63/101.75
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c8(U11'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.63/101.75
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 331.63/101.75
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 331.63/101.75
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 331.63/101.75
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 331.63/101.75
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 331.63/101.75
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 331.63/101.75
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 331.63/101.75
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c9(U12'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c9(U12'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 331.63/101.75
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 331.63/101.75
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 331.63/101.75
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 331.63/101.75
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 331.63/101.75
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 331.63/101.75
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 331.63/101.75
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 331.63/101.75
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 331.63/101.75
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 331.63/101.75
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 331.63/101.75
ACTIVE(s(U21(tt, z0, z1))) → c10(S(mark(U22(tt, z0, z1))), ACTIVE(U21(tt, z0, z1))) 331.63/101.75
ACTIVE(s(U22(tt, z0, z1))) → c10(S(mark(plus(x(z1, z0), z1))), ACTIVE(U22(tt, z0, z1))) 331.63/101.75
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 331.63/101.75
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 331.63/101.75
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 331.63/101.75
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 331.63/101.75
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 331.63/101.75
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 331.63/101.75
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 331.63/101.75
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 331.63/101.75
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 331.63/101.75
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 331.63/101.75
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 331.63/101.75
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 331.63/101.75
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 331.63/101.75
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c13(U21'(mark(U12(tt, z0, z1)), x1, x2), ACTIVE(U11(tt, z0, z1))) 331.63/101.75
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c13(U21'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U12(tt, z0, z1))) 331.63/101.75
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c13(U21'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.63/101.75
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c13(U21'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.63/101.75
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 331.63/101.75
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 331.63/101.75
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 331.63/101.75
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 331.63/101.75
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 331.63/101.75
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 331.63/101.75
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 331.63/101.75
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 331.63/101.75
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 331.63/101.75
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 331.63/101.75
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 331.63/101.75
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
S tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 331.63/101.75
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 331.63/101.75
ACTIVE(U22(z0, z1, z2)) → c14(U22'(active(z0), z1, z2), ACTIVE(z0)) 331.63/101.75
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 331.63/101.75
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 331.63/101.75
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 331.63/101.75
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 331.63/101.75
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 331.63/101.75
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 331.63/101.75
S(mark(z0)) → c21(S(z0)) 331.63/101.75
S(ok(z0)) → c22(S(z0)) 331.63/101.75
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 331.63/101.75
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 331.63/101.75
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 331.63/101.75
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 331.63/101.75
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 331.63/101.75
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 331.63/101.75
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 331.63/101.75
X(mark(z0), z1) → c30(X(z0, z1)) 331.63/101.75
X(z0, mark(z1)) → c31(X(z0, z1)) 331.63/101.75
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 331.63/101.75
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 331.63/101.75
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.63/101.75
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 331.63/101.75
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.63/101.75
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 331.63/101.75
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 331.63/101.75
ACTIVE(U11(tt, z0, z1)) → c 331.63/101.75
ACTIVE(U21(tt, z0, z1)) → c2 331.63/101.75
ACTIVE(plus(z0, s(z1))) → c5 331.63/101.75
ACTIVE(x(z0, s(z1))) → c7 331.63/101.75
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 331.63/101.75
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 331.63/101.75
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 331.63/101.75
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 331.63/101.75
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c8(U11'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 331.63/101.75
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c8(U11'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 331.63/101.75
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.37
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.37
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.37
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.37
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.37
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.37
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.37
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.37
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.37
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.37
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.37
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.37
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.37
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.37
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.03/102.37
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c9(U12'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 334.03/102.37
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c9(U12'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 334.03/102.37
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.37
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.37
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.37
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.37
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.37
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.37
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.37
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.37
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.37
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.37
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.37
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.37
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.37
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.37
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.37
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.37
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.03/102.37
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.37
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.37
ACTIVE(s(U21(tt, z0, z1))) → c10(S(mark(U22(tt, z0, z1))), ACTIVE(U21(tt, z0, z1))) 334.03/102.37
ACTIVE(s(U22(tt, z0, z1))) → c10(S(mark(plus(x(z1, z0), z1))), ACTIVE(U22(tt, z0, z1))) 334.03/102.37
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.03/102.37
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.03/102.37
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.03/102.37
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.03/102.37
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.03/102.37
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.03/102.37
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.03/102.37
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.03/102.37
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.03/102.37
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.03/102.37
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.03/102.37
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.03/102.37
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.03/102.37
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.03/102.37
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.03/102.37
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.03/102.37
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.03/102.37
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c13(U21'(mark(U12(tt, z0, z1)), x1, x2), ACTIVE(U11(tt, z0, z1))) 334.03/102.37
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c13(U21'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U12(tt, z0, z1))) 334.03/102.37
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c13(U21'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 334.03/102.37
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c13(U21'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 334.03/102.37
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.37
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.37
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.37
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.37
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.37
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.37
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.37
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.37
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.37
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.37
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.37
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.37
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c35, c36, c37, c38, c39, c40, c42, c43, c, c2, c5, c7, c4, c8, c1, c9, c3, c10, c6, c13

334.03/102.37
334.03/102.37

(29) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)

Split RHS of tuples not part of any SCC
334.03/102.37
334.03/102.37

(30) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.03/102.37
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.03/102.37
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.03/102.37
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.03/102.37
active(plus(z0, 0)) → mark(z0) 334.03/102.37
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.03/102.37
active(x(z0, 0)) → mark(0) 334.03/102.37
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.03/102.37
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.03/102.37
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.03/102.37
active(s(z0)) → s(active(z0)) 334.03/102.37
active(plus(z0, z1)) → plus(active(z0), z1) 334.03/102.37
active(plus(z0, z1)) → plus(z0, active(z1)) 334.03/102.37
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.03/102.37
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.03/102.37
active(x(z0, z1)) → x(active(z0), z1) 334.03/102.37
active(x(z0, z1)) → x(z0, active(z1)) 334.03/102.37
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.03/102.37
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.03/102.37
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.03/102.37
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.03/102.37
s(mark(z0)) → mark(s(z0)) 334.03/102.37
s(ok(z0)) → ok(s(z0)) 334.03/102.37
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.03/102.37
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.03/102.37
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.03/102.37
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.03/102.37
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.03/102.37
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.03/102.37
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.03/102.37
x(mark(z0), z1) → mark(x(z0, z1)) 334.03/102.37
x(z0, mark(z1)) → mark(x(z0, z1)) 334.03/102.37
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.03/102.37
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.03/102.37
proper(tt) → ok(tt) 334.03/102.37
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.03/102.37
proper(s(z0)) → s(proper(z0)) 334.03/102.37
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.03/102.37
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.03/102.37
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.03/102.37
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.03/102.37
proper(0) → ok(0) 334.03/102.37
top(mark(z0)) → top(proper(z0)) 334.03/102.37
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.03/102.37
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.03/102.37
ACTIVE(U22(z0, z1, z2)) → c14(U22'(active(z0), z1, z2), ACTIVE(z0)) 334.03/102.37
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.03/102.37
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.03/102.37
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.03/102.37
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.03/102.37
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.03/102.37
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.03/102.37
S(mark(z0)) → c21(S(z0)) 334.03/102.37
S(ok(z0)) → c22(S(z0)) 334.03/102.37
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.03/102.37
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.03/102.37
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.03/102.37
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.03/102.37
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.03/102.37
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.03/102.37
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.03/102.37
X(mark(z0), z1) → c30(X(z0, z1)) 334.03/102.37
X(z0, mark(z1)) → c31(X(z0, z1)) 334.03/102.37
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.03/102.37
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.37
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.37
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 334.03/102.37
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.37
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.37
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.37
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.37
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.03/102.37
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.03/102.37
ACTIVE(U11(tt, z0, z1)) → c 334.03/102.37
ACTIVE(U21(tt, z0, z1)) → c2 334.03/102.38
ACTIVE(plus(z0, s(z1))) → c5 334.03/102.38
ACTIVE(x(z0, s(z1))) → c7 334.03/102.38
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.03/102.38
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.03/102.38
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.03/102.38
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.03/102.38
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c8(U11'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 334.03/102.38
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c9(U12'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.38
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.38
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(s(U22(tt, z0, z1))) → c10(S(mark(plus(x(z1, z0), z1))), ACTIVE(U22(tt, z0, z1))) 334.03/102.38
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.03/102.38
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.03/102.38
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c13(U21'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.03/102.38
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.38
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1)))
S tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.03/102.38
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.03/102.38
ACTIVE(U22(z0, z1, z2)) → c14(U22'(active(z0), z1, z2), ACTIVE(z0)) 334.03/102.38
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.03/102.38
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.03/102.38
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.03/102.38
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.03/102.38
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.03/102.38
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.03/102.38
S(mark(z0)) → c21(S(z0)) 334.03/102.38
S(ok(z0)) → c22(S(z0)) 334.03/102.38
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.03/102.38
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.03/102.38
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.03/102.38
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.03/102.38
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.03/102.38
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.03/102.38
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.03/102.38
X(mark(z0), z1) → c30(X(z0, z1)) 334.03/102.38
X(z0, mark(z1)) → c31(X(z0, z1)) 334.03/102.38
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.03/102.38
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.38
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.38
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 334.03/102.38
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.38
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.38
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.38
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.38
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.03/102.38
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.03/102.38
ACTIVE(U11(tt, z0, z1)) → c 334.03/102.38
ACTIVE(U21(tt, z0, z1)) → c2 334.03/102.38
ACTIVE(plus(z0, s(z1))) → c5 334.03/102.38
ACTIVE(x(z0, s(z1))) → c7 334.03/102.38
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.03/102.38
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.03/102.38
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.03/102.38
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.03/102.38
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c8(U11'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 334.03/102.38
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c9(U12'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.38
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.38
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(s(U22(tt, z0, z1))) → c10(S(mark(plus(x(z1, z0), z1))), ACTIVE(U22(tt, z0, z1))) 334.03/102.38
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.03/102.38
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.03/102.38
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c13(U21'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.03/102.38
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.38
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c35, c36, c37, c38, c39, c40, c42, c43, c, c2, c5, c7, c4, c8, c1, c9, c3, c10, c6, c13, c34

334.03/102.38
334.03/102.38

(31) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

Removed 12 trailing nodes:

ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(tt, z0, z1)) → c2 334.03/102.38
ACTIVE(x(z0, s(z1))) → c7 334.03/102.38
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U11(tt, z0, z1)) → c 334.03/102.38
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(plus(z0, s(z1))) → c5 334.03/102.38
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1)))
334.03/102.38
334.03/102.38

(32) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.03/102.38
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.03/102.38
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.03/102.38
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.03/102.38
active(plus(z0, 0)) → mark(z0) 334.03/102.38
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.03/102.38
active(x(z0, 0)) → mark(0) 334.03/102.38
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.03/102.38
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.03/102.38
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.03/102.38
active(s(z0)) → s(active(z0)) 334.03/102.38
active(plus(z0, z1)) → plus(active(z0), z1) 334.03/102.38
active(plus(z0, z1)) → plus(z0, active(z1)) 334.03/102.38
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.03/102.38
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.03/102.38
active(x(z0, z1)) → x(active(z0), z1) 334.03/102.38
active(x(z0, z1)) → x(z0, active(z1)) 334.03/102.38
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.03/102.38
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.03/102.38
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.03/102.38
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.03/102.38
s(mark(z0)) → mark(s(z0)) 334.03/102.38
s(ok(z0)) → ok(s(z0)) 334.03/102.38
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.03/102.38
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.03/102.38
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.03/102.38
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.03/102.38
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.03/102.38
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.03/102.38
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.03/102.38
x(mark(z0), z1) → mark(x(z0, z1)) 334.03/102.38
x(z0, mark(z1)) → mark(x(z0, z1)) 334.03/102.38
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.03/102.38
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.03/102.38
proper(tt) → ok(tt) 334.03/102.38
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.03/102.38
proper(s(z0)) → s(proper(z0)) 334.03/102.38
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.03/102.38
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.03/102.38
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.03/102.38
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.03/102.38
proper(0) → ok(0) 334.03/102.38
top(mark(z0)) → top(proper(z0)) 334.03/102.38
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.03/102.38
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.03/102.38
ACTIVE(U22(z0, z1, z2)) → c14(U22'(active(z0), z1, z2), ACTIVE(z0)) 334.03/102.38
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.03/102.38
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.03/102.38
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.03/102.38
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.03/102.38
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.03/102.38
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.03/102.38
S(mark(z0)) → c21(S(z0)) 334.03/102.38
S(ok(z0)) → c22(S(z0)) 334.03/102.38
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.03/102.38
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.03/102.38
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.03/102.38
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.03/102.38
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.03/102.38
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.03/102.38
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.03/102.38
X(mark(z0), z1) → c30(X(z0, z1)) 334.03/102.38
X(z0, mark(z1)) → c31(X(z0, z1)) 334.03/102.38
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.03/102.38
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.38
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.38
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 334.03/102.38
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.38
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.38
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.38
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.38
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.03/102.38
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.03/102.38
ACTIVE(U11(tt, z0, z1)) → c 334.03/102.38
ACTIVE(U21(tt, z0, z1)) → c2 334.03/102.38
ACTIVE(plus(z0, s(z1))) → c5 334.03/102.38
ACTIVE(x(z0, s(z1))) → c7 334.03/102.38
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.03/102.38
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.03/102.38
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.03/102.38
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.03/102.38
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c8(U11'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 334.03/102.38
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c9(U12'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.38
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.38
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(s(U22(tt, z0, z1))) → c10(S(mark(plus(x(z1, z0), z1))), ACTIVE(U22(tt, z0, z1))) 334.03/102.38
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.03/102.38
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.03/102.38
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c13(U21'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.03/102.38
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.38
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1)))
S tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.03/102.38
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.03/102.38
ACTIVE(U22(z0, z1, z2)) → c14(U22'(active(z0), z1, z2), ACTIVE(z0)) 334.03/102.38
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.03/102.38
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.03/102.38
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.03/102.38
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.03/102.38
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.03/102.38
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.03/102.38
S(mark(z0)) → c21(S(z0)) 334.03/102.38
S(ok(z0)) → c22(S(z0)) 334.03/102.38
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.03/102.38
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.03/102.38
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.03/102.38
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.03/102.38
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.03/102.38
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.03/102.38
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.03/102.38
X(mark(z0), z1) → c30(X(z0, z1)) 334.03/102.38
X(z0, mark(z1)) → c31(X(z0, z1)) 334.03/102.38
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.03/102.38
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.38
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.38
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 334.03/102.38
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.38
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.38
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.38
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.38
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.03/102.38
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.03/102.38
ACTIVE(U11(tt, z0, z1)) → c 334.03/102.38
ACTIVE(U21(tt, z0, z1)) → c2 334.03/102.38
ACTIVE(plus(z0, s(z1))) → c5 334.03/102.38
ACTIVE(x(z0, s(z1))) → c7 334.03/102.38
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.03/102.38
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.03/102.38
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.03/102.38
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.03/102.38
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c8(U11'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 334.03/102.38
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c9(U12'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.38
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.38
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(s(U22(tt, z0, z1))) → c10(S(mark(plus(x(z1, z0), z1))), ACTIVE(U22(tt, z0, z1))) 334.03/102.38
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.03/102.38
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.03/102.38
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c13(U21'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.03/102.38
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.38
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c11, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c35, c36, c37, c38, c39, c40, c42, c43, c, c2, c5, c7, c4, c8, c1, c9, c3, c10, c6, c13, c34

334.03/102.38
334.03/102.38

(33) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace ACTIVE(U22(z0, z1, z2)) → c14(U22'(active(z0), z1, z2), ACTIVE(z0)) by

ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c14(U22'(mark(U12(tt, z0, z1)), x1, x2), ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c14(U22'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c14(U22'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c14(U22'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 334.03/102.38
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
334.03/102.38
334.03/102.38

(34) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.03/102.38
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.03/102.38
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.03/102.38
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.03/102.38
active(plus(z0, 0)) → mark(z0) 334.03/102.38
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.03/102.38
active(x(z0, 0)) → mark(0) 334.03/102.38
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.03/102.38
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.03/102.38
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.03/102.38
active(s(z0)) → s(active(z0)) 334.03/102.38
active(plus(z0, z1)) → plus(active(z0), z1) 334.03/102.38
active(plus(z0, z1)) → plus(z0, active(z1)) 334.03/102.38
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.03/102.38
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.03/102.38
active(x(z0, z1)) → x(active(z0), z1) 334.03/102.38
active(x(z0, z1)) → x(z0, active(z1)) 334.03/102.38
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.03/102.38
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.03/102.38
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.03/102.38
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.03/102.38
s(mark(z0)) → mark(s(z0)) 334.03/102.38
s(ok(z0)) → ok(s(z0)) 334.03/102.38
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.03/102.38
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.03/102.38
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.03/102.38
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.03/102.38
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.03/102.38
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.03/102.38
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.03/102.38
x(mark(z0), z1) → mark(x(z0, z1)) 334.03/102.38
x(z0, mark(z1)) → mark(x(z0, z1)) 334.03/102.38
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.03/102.38
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.03/102.38
proper(tt) → ok(tt) 334.03/102.38
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.03/102.38
proper(s(z0)) → s(proper(z0)) 334.03/102.38
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.03/102.38
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.03/102.38
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.03/102.38
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.03/102.38
proper(0) → ok(0) 334.03/102.38
top(mark(z0)) → top(proper(z0)) 334.03/102.38
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.03/102.38
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.03/102.38
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.03/102.38
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.03/102.38
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.03/102.38
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.03/102.38
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.03/102.38
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.03/102.38
S(mark(z0)) → c21(S(z0)) 334.03/102.38
S(ok(z0)) → c22(S(z0)) 334.03/102.38
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.03/102.38
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.03/102.38
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.03/102.38
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.03/102.38
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.03/102.38
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.03/102.38
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.03/102.38
X(mark(z0), z1) → c30(X(z0, z1)) 334.03/102.38
X(z0, mark(z1)) → c31(X(z0, z1)) 334.03/102.38
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.03/102.38
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.38
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.38
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 334.03/102.38
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.38
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.38
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.38
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.38
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.03/102.38
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.03/102.38
ACTIVE(U11(tt, z0, z1)) → c 334.03/102.38
ACTIVE(U21(tt, z0, z1)) → c2 334.03/102.38
ACTIVE(plus(z0, s(z1))) → c5 334.03/102.38
ACTIVE(x(z0, s(z1))) → c7 334.03/102.38
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.03/102.38
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.03/102.38
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.03/102.38
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.03/102.38
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c8(U11'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 334.03/102.38
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c9(U12'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.38
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.38
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(s(U22(tt, z0, z1))) → c10(S(mark(plus(x(z1, z0), z1))), ACTIVE(U22(tt, z0, z1))) 334.03/102.38
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.03/102.38
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.03/102.38
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c13(U21'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.03/102.38
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.38
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c14(U22'(mark(U12(tt, z0, z1)), x1, x2), ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c14(U22'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c14(U22'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c14(U22'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 334.03/102.38
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
S tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.03/102.38
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.03/102.38
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.03/102.38
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.03/102.38
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.03/102.38
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.03/102.38
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.03/102.38
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.03/102.38
S(mark(z0)) → c21(S(z0)) 334.03/102.38
S(ok(z0)) → c22(S(z0)) 334.03/102.38
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.03/102.38
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.03/102.38
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.03/102.38
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.03/102.38
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.03/102.38
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.03/102.38
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.03/102.38
X(mark(z0), z1) → c30(X(z0, z1)) 334.03/102.38
X(z0, mark(z1)) → c31(X(z0, z1)) 334.03/102.38
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.03/102.38
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.38
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.38
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 334.03/102.38
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.38
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.38
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.38
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.38
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.03/102.38
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.03/102.38
ACTIVE(U11(tt, z0, z1)) → c 334.03/102.38
ACTIVE(U21(tt, z0, z1)) → c2 334.03/102.38
ACTIVE(plus(z0, s(z1))) → c5 334.03/102.38
ACTIVE(x(z0, s(z1))) → c7 334.03/102.38
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.03/102.38
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.03/102.38
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.03/102.38
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.03/102.38
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c8(U11'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 334.03/102.38
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c9(U12'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.38
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.38
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(s(U22(tt, z0, z1))) → c10(S(mark(plus(x(z1, z0), z1))), ACTIVE(U22(tt, z0, z1))) 334.03/102.38
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.03/102.38
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.03/102.38
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c13(U21'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.03/102.38
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.38
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c14(U22'(mark(U12(tt, z0, z1)), x1, x2), ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c14(U22'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c14(U22'(mark(U22(tt, z0, z1)), x1, x2), ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c14(U22'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U22(tt, z0, z1))) 334.03/102.38
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c11, c12, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c35, c36, c37, c38, c39, c40, c42, c43, c, c2, c5, c7, c4, c8, c1, c9, c3, c10, c6, c13, c34, c14

334.03/102.38
334.03/102.38

(35) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)

Split RHS of tuples not part of any SCC
334.03/102.38
334.03/102.38

(36) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.03/102.38
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.03/102.38
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.03/102.38
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.03/102.38
active(plus(z0, 0)) → mark(z0) 334.03/102.38
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.03/102.38
active(x(z0, 0)) → mark(0) 334.03/102.38
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.03/102.38
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.03/102.38
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.03/102.38
active(s(z0)) → s(active(z0)) 334.03/102.38
active(plus(z0, z1)) → plus(active(z0), z1) 334.03/102.38
active(plus(z0, z1)) → plus(z0, active(z1)) 334.03/102.38
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.03/102.38
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.03/102.38
active(x(z0, z1)) → x(active(z0), z1) 334.03/102.38
active(x(z0, z1)) → x(z0, active(z1)) 334.03/102.38
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.03/102.38
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.03/102.38
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.03/102.38
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.03/102.38
s(mark(z0)) → mark(s(z0)) 334.03/102.38
s(ok(z0)) → ok(s(z0)) 334.03/102.38
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.03/102.38
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.03/102.38
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.03/102.38
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.03/102.38
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.03/102.38
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.03/102.38
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.03/102.38
x(mark(z0), z1) → mark(x(z0, z1)) 334.03/102.38
x(z0, mark(z1)) → mark(x(z0, z1)) 334.03/102.38
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.03/102.38
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.03/102.38
proper(tt) → ok(tt) 334.03/102.38
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.03/102.38
proper(s(z0)) → s(proper(z0)) 334.03/102.38
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.03/102.38
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.03/102.38
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.03/102.38
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.03/102.38
proper(0) → ok(0) 334.03/102.38
top(mark(z0)) → top(proper(z0)) 334.03/102.38
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.03/102.38
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.03/102.38
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.03/102.38
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.03/102.38
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.03/102.38
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.03/102.38
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.03/102.38
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.03/102.38
S(mark(z0)) → c21(S(z0)) 334.03/102.38
S(ok(z0)) → c22(S(z0)) 334.03/102.38
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.03/102.38
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.03/102.38
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.03/102.38
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.03/102.38
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.03/102.38
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.03/102.38
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.03/102.38
X(mark(z0), z1) → c30(X(z0, z1)) 334.03/102.38
X(z0, mark(z1)) → c31(X(z0, z1)) 334.03/102.38
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.03/102.38
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.38
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.38
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 334.03/102.38
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.38
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.38
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.38
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.38
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.03/102.38
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.03/102.38
ACTIVE(U11(tt, z0, z1)) → c 334.03/102.38
ACTIVE(U21(tt, z0, z1)) → c2 334.03/102.38
ACTIVE(plus(z0, s(z1))) → c5 334.03/102.38
ACTIVE(x(z0, s(z1))) → c7 334.03/102.38
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.03/102.38
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.03/102.38
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.03/102.38
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.03/102.38
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.38
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.38
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.03/102.38
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.03/102.38
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.03/102.38
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.38
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.38
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.38
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.38
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.03/102.38
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.38
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.38
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.38
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.38
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1)))
S tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.03/102.38
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.03/102.38
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.03/102.38
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.03/102.38
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.03/102.38
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.03/102.38
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.03/102.38
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.03/102.38
S(mark(z0)) → c21(S(z0)) 334.03/102.38
S(ok(z0)) → c22(S(z0)) 334.03/102.38
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.03/102.38
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.03/102.38
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.03/102.38
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.03/102.38
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.03/102.38
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.03/102.38
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.03/102.38
X(mark(z0), z1) → c30(X(z0, z1)) 334.03/102.38
X(z0, mark(z1)) → c31(X(z0, z1)) 334.03/102.38
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.03/102.38
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.38
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.38
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 334.03/102.38
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.38
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.38
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.38
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.38
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.03/102.38
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.03/102.38
ACTIVE(U11(tt, z0, z1)) → c 334.03/102.38
ACTIVE(U21(tt, z0, z1)) → c2 334.03/102.38
ACTIVE(plus(z0, s(z1))) → c5 334.03/102.38
ACTIVE(x(z0, s(z1))) → c7 334.03/102.38
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.03/102.38
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.03/102.38
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.03/102.38
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.03/102.38
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.38
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.38
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.03/102.38
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.03/102.38
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.03/102.38
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.38
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.38
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.38
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.38
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.03/102.38
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.38
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.38
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.38
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.38
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c11, c12, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c35, c36, c37, c38, c39, c40, c42, c43, c, c2, c5, c7, c4, c8, c1, c9, c3, c10, c6, c13, c34, c14, c41

334.03/102.38
334.03/102.38

(37) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

Removed 14 trailing nodes:

ACTIVE(x(z0, s(z1))) → c7 334.03/102.38
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U11(tt, z0, z1)) → c 334.03/102.38
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(tt, z0, z1)) → c2 334.03/102.38
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(plus(z0, s(z1))) → c5 334.03/102.38
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1)))
334.03/102.38
334.03/102.38

(38) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.03/102.38
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.03/102.38
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.03/102.38
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.03/102.38
active(plus(z0, 0)) → mark(z0) 334.03/102.38
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.03/102.38
active(x(z0, 0)) → mark(0) 334.03/102.38
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.03/102.38
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.03/102.38
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.03/102.38
active(s(z0)) → s(active(z0)) 334.03/102.38
active(plus(z0, z1)) → plus(active(z0), z1) 334.03/102.38
active(plus(z0, z1)) → plus(z0, active(z1)) 334.03/102.38
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.03/102.38
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.03/102.38
active(x(z0, z1)) → x(active(z0), z1) 334.03/102.38
active(x(z0, z1)) → x(z0, active(z1)) 334.03/102.38
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.03/102.38
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.03/102.38
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.03/102.38
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.03/102.38
s(mark(z0)) → mark(s(z0)) 334.03/102.38
s(ok(z0)) → ok(s(z0)) 334.03/102.38
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.03/102.38
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.03/102.38
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.03/102.38
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.03/102.38
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.03/102.38
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.03/102.38
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.03/102.38
x(mark(z0), z1) → mark(x(z0, z1)) 334.03/102.38
x(z0, mark(z1)) → mark(x(z0, z1)) 334.03/102.38
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.03/102.38
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.03/102.38
proper(tt) → ok(tt) 334.03/102.38
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.03/102.38
proper(s(z0)) → s(proper(z0)) 334.03/102.38
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.03/102.38
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.03/102.38
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.03/102.38
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.03/102.38
proper(0) → ok(0) 334.03/102.38
top(mark(z0)) → top(proper(z0)) 334.03/102.38
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.03/102.38
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.03/102.38
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.03/102.38
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.03/102.38
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.03/102.38
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.03/102.38
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.03/102.38
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.03/102.38
S(mark(z0)) → c21(S(z0)) 334.03/102.38
S(ok(z0)) → c22(S(z0)) 334.03/102.38
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.03/102.38
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.03/102.38
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.03/102.38
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.03/102.38
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.03/102.38
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.03/102.38
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.03/102.38
X(mark(z0), z1) → c30(X(z0, z1)) 334.03/102.38
X(z0, mark(z1)) → c31(X(z0, z1)) 334.03/102.38
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.03/102.38
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.38
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.38
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 334.03/102.38
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.38
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.38
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.38
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.38
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.03/102.38
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.03/102.38
ACTIVE(U11(tt, z0, z1)) → c 334.03/102.38
ACTIVE(U21(tt, z0, z1)) → c2 334.03/102.38
ACTIVE(plus(z0, s(z1))) → c5 334.03/102.38
ACTIVE(x(z0, s(z1))) → c7 334.03/102.38
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.03/102.38
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.03/102.38
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.03/102.38
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.03/102.38
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.38
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.38
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.03/102.38
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.03/102.38
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.03/102.38
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.38
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.03/102.38
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.38
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.38
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.38
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.38
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.38
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.38
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.38
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.38
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.38
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.38
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.38
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.38
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.38
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.38
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.39
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.39
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.39
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.03/102.39
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.39
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.39
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.39
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.03/102.39
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.39
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.03/102.39
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.03/102.39
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.39
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1)))
S tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.03/102.39
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.03/102.39
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.03/102.39
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.03/102.39
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.03/102.39
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.03/102.39
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.03/102.39
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.03/102.39
S(mark(z0)) → c21(S(z0)) 334.03/102.39
S(ok(z0)) → c22(S(z0)) 334.03/102.39
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.03/102.39
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.03/102.39
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.03/102.39
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.03/102.39
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.03/102.39
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.03/102.39
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.03/102.39
X(mark(z0), z1) → c30(X(z0, z1)) 334.03/102.39
X(z0, mark(z1)) → c31(X(z0, z1)) 334.03/102.39
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.03/102.39
PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.39
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.39
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 334.03/102.39
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.39
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.39
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.39
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.39
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.03/102.39
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.03/102.39
ACTIVE(U11(tt, z0, z1)) → c 334.03/102.39
ACTIVE(U21(tt, z0, z1)) → c2 334.03/102.39
ACTIVE(plus(z0, s(z1))) → c5 334.03/102.39
ACTIVE(x(z0, s(z1))) → c7 334.03/102.39
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.03/102.39
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.03/102.39
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.03/102.39
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.03/102.39
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.39
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.39
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.39
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.39
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.39
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.39
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.39
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.39
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.39
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.03/102.39
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.39
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.39
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.39
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.39
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.39
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.39
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.39
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.39
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.39
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.39
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.39
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.03/102.39
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.39
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.39
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.03/102.39
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.03/102.39
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.03/102.39
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.03/102.39
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.03/102.39
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.03/102.39
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.03/102.39
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.03/102.39
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.03/102.39
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.03/102.39
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.03/102.39
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.03/102.39
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.03/102.39
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.39
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.39
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.39
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.39
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.39
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.39
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.39
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.39
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.39
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.39
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.39
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.03/102.39
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.39
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.03/102.39
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.39
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.03/102.39
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.39
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.39
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.39
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.39
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.39
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.39
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.39
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.39
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.39
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.39
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.39
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.39
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.39
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.39
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.03/102.39
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.39
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.39
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.39
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.03/102.39
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.39
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.03/102.39
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.03/102.39
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.39
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c11, c12, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c35, c36, c37, c38, c39, c40, c42, c43, c, c2, c5, c7, c4, c8, c1, c9, c3, c10, c6, c13, c34, c14, c41

334.03/102.39
334.03/102.39

(39) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace PROPER(U11(z0, z1, z2)) → c33(U11'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) by

PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.03/102.39
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1), PROPER(tt)) 334.03/102.39
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.03/102.39
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.03/102.39
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.03/102.39
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.03/102.39
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.03/102.39
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.03/102.39
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1), PROPER(0)) 334.03/102.39
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(tt), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(0), PROPER(x2)) 334.03/102.39
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(tt), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(0), PROPER(x1), PROPER(x2))
334.03/102.39
334.03/102.39

(40) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.03/102.39
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.03/102.39
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.03/102.39
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.03/102.39
active(plus(z0, 0)) → mark(z0) 334.03/102.39
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.03/102.39
active(x(z0, 0)) → mark(0) 334.03/102.39
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.03/102.39
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.03/102.39
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.03/102.39
active(s(z0)) → s(active(z0)) 334.03/102.39
active(plus(z0, z1)) → plus(active(z0), z1) 334.03/102.39
active(plus(z0, z1)) → plus(z0, active(z1)) 334.03/102.39
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.03/102.39
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.03/102.39
active(x(z0, z1)) → x(active(z0), z1) 334.03/102.39
active(x(z0, z1)) → x(z0, active(z1)) 334.03/102.39
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.03/102.39
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.03/102.39
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.03/102.39
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.03/102.39
s(mark(z0)) → mark(s(z0)) 334.03/102.39
s(ok(z0)) → ok(s(z0)) 334.03/102.39
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.03/102.39
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.03/102.39
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.03/102.39
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.03/102.39
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.03/102.39
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.03/102.39
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.03/102.39
x(mark(z0), z1) → mark(x(z0, z1)) 334.03/102.39
x(z0, mark(z1)) → mark(x(z0, z1)) 334.03/102.39
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.03/102.39
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.03/102.39
proper(tt) → ok(tt) 334.03/102.39
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.03/102.39
proper(s(z0)) → s(proper(z0)) 334.03/102.39
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.03/102.39
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.03/102.39
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.03/102.39
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.03/102.39
proper(0) → ok(0) 334.03/102.39
top(mark(z0)) → top(proper(z0)) 334.03/102.39
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.03/102.39
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.03/102.39
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.03/102.39
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.03/102.39
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.03/102.39
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.03/102.39
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.03/102.39
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.03/102.39
S(mark(z0)) → c21(S(z0)) 334.03/102.39
S(ok(z0)) → c22(S(z0)) 334.03/102.39
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.03/102.39
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.03/102.39
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.03/102.39
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.03/102.39
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.03/102.39
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.03/102.39
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.03/102.39
X(mark(z0), z1) → c30(X(z0, z1)) 334.03/102.39
X(z0, mark(z1)) → c31(X(z0, z1)) 334.03/102.39
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.03/102.39
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.39
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 334.03/102.39
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.39
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.39
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.39
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.39
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.03/102.39
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.03/102.39
ACTIVE(U11(tt, z0, z1)) → c 334.03/102.39
ACTIVE(U21(tt, z0, z1)) → c2 334.03/102.39
ACTIVE(plus(z0, s(z1))) → c5 334.03/102.39
ACTIVE(x(z0, s(z1))) → c7 334.03/102.39
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.03/102.39
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.03/102.39
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.03/102.39
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.03/102.39
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.39
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.39
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.39
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.39
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.39
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.39
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.39
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.39
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.39
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.03/102.39
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.39
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.39
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.39
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.39
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.39
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.39
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.39
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.39
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.39
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.39
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.39
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.03/102.39
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.39
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.39
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.03/102.39
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.03/102.39
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.03/102.39
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.03/102.39
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.03/102.39
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.03/102.39
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.03/102.39
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.03/102.39
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.03/102.39
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.03/102.39
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.03/102.39
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.03/102.39
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.03/102.39
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.39
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.39
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.39
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.39
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.39
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.39
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.39
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.39
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.39
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.39
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.39
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.03/102.39
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.39
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.03/102.39
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.39
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.03/102.39
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.39
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.39
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.39
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.39
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.39
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.39
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.39
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.39
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.39
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.39
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.39
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.39
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.39
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.39
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.03/102.39
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.39
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.39
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.39
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.03/102.39
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.39
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.03/102.39
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.03/102.39
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.39
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.39
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.03/102.39
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1), PROPER(tt)) 334.03/102.39
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.03/102.39
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.03/102.39
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.03/102.39
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.03/102.39
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.03/102.39
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.03/102.39
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1), PROPER(0)) 334.03/102.39
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(tt), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(0), PROPER(x2)) 334.03/102.39
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(tt), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(0), PROPER(x1), PROPER(x2))
S tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.03/102.39
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.03/102.39
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.03/102.39
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.03/102.39
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.03/102.39
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.03/102.39
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.03/102.39
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.03/102.39
S(mark(z0)) → c21(S(z0)) 334.03/102.39
S(ok(z0)) → c22(S(z0)) 334.03/102.39
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.03/102.39
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.03/102.39
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.03/102.39
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.03/102.39
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.03/102.39
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.03/102.39
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.03/102.39
X(mark(z0), z1) → c30(X(z0, z1)) 334.03/102.39
X(z0, mark(z1)) → c31(X(z0, z1)) 334.03/102.39
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.03/102.39
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.39
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 334.03/102.39
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.39
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.39
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.39
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.39
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.03/102.39
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.03/102.39
ACTIVE(U11(tt, z0, z1)) → c 334.03/102.39
ACTIVE(U21(tt, z0, z1)) → c2 334.03/102.39
ACTIVE(plus(z0, s(z1))) → c5 334.03/102.39
ACTIVE(x(z0, s(z1))) → c7 334.03/102.39
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.03/102.39
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.03/102.39
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.03/102.39
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.03/102.39
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.39
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.39
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.39
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.39
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.39
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.39
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.39
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.39
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.39
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.03/102.39
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.39
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.39
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.39
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.39
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.39
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.39
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.39
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.39
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.39
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.39
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.39
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.03/102.39
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.39
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.39
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.03/102.39
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.03/102.39
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.03/102.39
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.03/102.39
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.03/102.39
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.03/102.39
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.03/102.39
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.03/102.39
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.03/102.39
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.03/102.39
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.03/102.39
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.03/102.39
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.03/102.39
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.39
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.39
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.39
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.39
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.39
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.39
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.39
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.39
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.39
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.39
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.39
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.03/102.39
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.39
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.03/102.39
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.39
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.03/102.39
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.39
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.39
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.39
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.39
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.39
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.39
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.39
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.39
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.39
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.39
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.39
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.39
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.39
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.39
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.03/102.39
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.39
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.39
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.39
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.03/102.39
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.39
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.03/102.39
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.03/102.39
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.39
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.39
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.03/102.39
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1), PROPER(tt)) 334.03/102.39
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.03/102.39
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.03/102.39
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.03/102.39
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.03/102.39
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.03/102.39
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.03/102.39
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1), PROPER(0)) 334.03/102.39
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(tt), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(0), PROPER(x2)) 334.03/102.39
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(tt), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(0), PROPER(x1), PROPER(x2))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c11, c12, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c35, c36, c37, c38, c39, c40, c42, c43, c, c2, c5, c7, c4, c8, c1, c9, c3, c10, c6, c13, c34, c14, c41, c33

334.03/102.39
334.03/102.39

(41) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 6 trailing tuple parts
334.03/102.39
334.03/102.39

(42) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.03/102.39
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.03/102.39
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.03/102.39
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.03/102.39
active(plus(z0, 0)) → mark(z0) 334.03/102.39
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.03/102.39
active(x(z0, 0)) → mark(0) 334.03/102.39
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.03/102.39
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.03/102.39
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.03/102.39
active(s(z0)) → s(active(z0)) 334.03/102.39
active(plus(z0, z1)) → plus(active(z0), z1) 334.03/102.39
active(plus(z0, z1)) → plus(z0, active(z1)) 334.03/102.39
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.03/102.39
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.03/102.39
active(x(z0, z1)) → x(active(z0), z1) 334.03/102.39
active(x(z0, z1)) → x(z0, active(z1)) 334.03/102.39
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.03/102.39
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.03/102.39
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.03/102.39
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.03/102.39
s(mark(z0)) → mark(s(z0)) 334.03/102.39
s(ok(z0)) → ok(s(z0)) 334.03/102.39
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.03/102.39
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.03/102.39
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.03/102.39
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.03/102.39
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.03/102.39
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.03/102.39
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.03/102.39
x(mark(z0), z1) → mark(x(z0, z1)) 334.03/102.39
x(z0, mark(z1)) → mark(x(z0, z1)) 334.03/102.39
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.03/102.39
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.03/102.39
proper(tt) → ok(tt) 334.03/102.39
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.03/102.39
proper(s(z0)) → s(proper(z0)) 334.03/102.39
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.03/102.39
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.03/102.39
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.03/102.39
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.03/102.39
proper(0) → ok(0) 334.03/102.39
top(mark(z0)) → top(proper(z0)) 334.03/102.39
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.03/102.39
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.03/102.39
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.03/102.39
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.03/102.39
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.03/102.39
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.03/102.39
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.03/102.39
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.03/102.39
S(mark(z0)) → c21(S(z0)) 334.03/102.39
S(ok(z0)) → c22(S(z0)) 334.03/102.39
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.03/102.39
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.03/102.39
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.03/102.39
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.03/102.39
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.03/102.39
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.03/102.39
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.03/102.39
X(mark(z0), z1) → c30(X(z0, z1)) 334.03/102.39
X(z0, mark(z1)) → c31(X(z0, z1)) 334.03/102.39
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.03/102.39
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.39
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 334.03/102.39
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.39
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.39
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.39
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.39
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.03/102.39
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.03/102.39
ACTIVE(U11(tt, z0, z1)) → c 334.03/102.39
ACTIVE(U21(tt, z0, z1)) → c2 334.03/102.39
ACTIVE(plus(z0, s(z1))) → c5 334.03/102.39
ACTIVE(x(z0, s(z1))) → c7 334.03/102.39
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.03/102.39
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.03/102.39
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.03/102.39
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.03/102.39
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.39
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.39
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.39
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.39
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.39
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.39
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.39
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.39
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.39
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.03/102.39
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.39
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.39
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.39
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.39
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.39
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.39
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.39
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.39
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.39
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.39
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.39
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.03/102.39
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.39
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.39
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.03/102.39
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.03/102.39
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.03/102.39
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.03/102.39
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.03/102.39
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.03/102.39
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.03/102.39
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.03/102.39
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.03/102.39
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.03/102.39
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.03/102.39
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.03/102.39
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.03/102.39
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.39
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.39
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.39
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.39
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.39
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.39
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.39
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.39
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.39
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.39
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.39
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.03/102.39
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.39
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.03/102.39
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.39
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.03/102.39
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.39
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.39
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.39
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.39
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.39
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.39
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.39
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.39
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.39
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.39
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.39
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.39
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.39
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.39
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.03/102.39
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.39
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.39
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.39
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.03/102.39
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.39
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.03/102.39
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.03/102.39
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.39
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.39
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.03/102.39
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.03/102.39
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.03/102.39
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.03/102.39
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.03/102.39
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.03/102.39
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.03/102.39
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.03/102.39
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.03/102.39
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.03/102.39
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.03/102.39
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
S tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.03/102.39
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.03/102.39
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.03/102.39
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.03/102.39
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.03/102.39
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.03/102.39
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.03/102.39
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.03/102.39
S(mark(z0)) → c21(S(z0)) 334.03/102.39
S(ok(z0)) → c22(S(z0)) 334.03/102.39
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.03/102.39
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.03/102.39
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.03/102.39
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.03/102.39
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.03/102.39
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.03/102.39
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.03/102.39
X(mark(z0), z1) → c30(X(z0, z1)) 334.03/102.39
X(z0, mark(z1)) → c31(X(z0, z1)) 334.03/102.39
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.03/102.39
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.39
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 334.03/102.39
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.39
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.39
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.39
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.39
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.03/102.39
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.03/102.39
ACTIVE(U11(tt, z0, z1)) → c 334.03/102.39
ACTIVE(U21(tt, z0, z1)) → c2 334.03/102.39
ACTIVE(plus(z0, s(z1))) → c5 334.03/102.39
ACTIVE(x(z0, s(z1))) → c7 334.03/102.39
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.03/102.39
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.03/102.39
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.03/102.39
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.03/102.39
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.39
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.39
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.39
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.39
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.39
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.39
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.39
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.39
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.39
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.03/102.39
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.39
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.39
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.39
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.39
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.39
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.39
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.39
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.39
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.39
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.39
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.39
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.03/102.39
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.39
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.39
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.03/102.39
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.03/102.39
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.03/102.39
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.03/102.39
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.03/102.39
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.03/102.39
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.03/102.39
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.03/102.39
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.03/102.39
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.03/102.39
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.03/102.39
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.03/102.39
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.03/102.39
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.39
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.39
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.39
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.39
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.39
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.39
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.39
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.39
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.39
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.39
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.39
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.03/102.39
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.39
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.03/102.39
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.39
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.03/102.39
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.39
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.39
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.39
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.39
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.39
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.39
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.39
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.39
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.39
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.39
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.39
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.39
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.39
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.39
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.03/102.39
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.39
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.39
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.39
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.03/102.39
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.39
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.03/102.39
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.03/102.39
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.39
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.39
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.03/102.39
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.03/102.39
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.03/102.39
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.03/102.39
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.03/102.39
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.03/102.39
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.03/102.39
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.03/102.39
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.03/102.39
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.03/102.39
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.03/102.39
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c11, c12, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c35, c36, c37, c38, c39, c40, c42, c43, c, c2, c5, c7, c4, c8, c1, c9, c3, c10, c6, c13, c34, c14, c41, c33, c33

334.03/102.39
334.03/102.39

(43) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

Removed 14 trailing nodes:

ACTIVE(x(z0, s(z1))) → c7 334.03/102.39
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.03/102.39
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.03/102.39
ACTIVE(U11(tt, z0, z1)) → c 334.03/102.39
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.03/102.39
ACTIVE(U21(tt, z0, z1)) → c2 334.03/102.39
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.03/102.39
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.03/102.39
ACTIVE(plus(z0, s(z1))) → c5 334.03/102.39
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.39
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.03/102.39
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.39
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.39
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1)))
334.03/102.39
334.03/102.39

(44) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.03/102.39
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.03/102.39
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.03/102.39
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.03/102.39
active(plus(z0, 0)) → mark(z0) 334.03/102.39
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.03/102.39
active(x(z0, 0)) → mark(0) 334.03/102.39
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.03/102.39
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.03/102.39
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.03/102.39
active(s(z0)) → s(active(z0)) 334.03/102.39
active(plus(z0, z1)) → plus(active(z0), z1) 334.03/102.39
active(plus(z0, z1)) → plus(z0, active(z1)) 334.03/102.39
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.03/102.39
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.03/102.39
active(x(z0, z1)) → x(active(z0), z1) 334.03/102.39
active(x(z0, z1)) → x(z0, active(z1)) 334.03/102.39
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.03/102.39
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.03/102.39
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.03/102.39
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.03/102.39
s(mark(z0)) → mark(s(z0)) 334.03/102.39
s(ok(z0)) → ok(s(z0)) 334.03/102.39
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.03/102.39
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.03/102.39
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.03/102.39
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.03/102.39
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.03/102.39
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.03/102.39
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.03/102.39
x(mark(z0), z1) → mark(x(z0, z1)) 334.03/102.39
x(z0, mark(z1)) → mark(x(z0, z1)) 334.03/102.39
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.03/102.39
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.03/102.39
proper(tt) → ok(tt) 334.03/102.39
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.03/102.39
proper(s(z0)) → s(proper(z0)) 334.03/102.39
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.03/102.39
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.03/102.39
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.03/102.39
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.03/102.39
proper(0) → ok(0) 334.03/102.39
top(mark(z0)) → top(proper(z0)) 334.03/102.39
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.03/102.39
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.03/102.39
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.03/102.39
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.03/102.39
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.03/102.39
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.03/102.39
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.03/102.39
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.03/102.39
S(mark(z0)) → c21(S(z0)) 334.03/102.39
S(ok(z0)) → c22(S(z0)) 334.03/102.39
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.03/102.39
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.03/102.39
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.03/102.39
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.03/102.39
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.03/102.39
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.03/102.39
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.03/102.39
X(mark(z0), z1) → c30(X(z0, z1)) 334.03/102.39
X(z0, mark(z1)) → c31(X(z0, z1)) 334.03/102.39
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.03/102.39
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.39
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 334.03/102.39
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.39
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.39
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.39
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.39
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.03/102.39
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.03/102.39
ACTIVE(U11(tt, z0, z1)) → c 334.03/102.39
ACTIVE(U21(tt, z0, z1)) → c2 334.03/102.39
ACTIVE(plus(z0, s(z1))) → c5 334.03/102.39
ACTIVE(x(z0, s(z1))) → c7 334.03/102.39
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.03/102.39
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.03/102.39
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.03/102.39
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.03/102.39
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.39
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.39
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.39
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.39
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.39
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.39
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.39
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.39
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.39
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.03/102.39
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.39
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.39
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.39
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.39
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.39
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.39
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.39
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.39
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.39
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.39
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.39
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.03/102.39
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.39
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.39
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.03/102.39
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.03/102.39
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.03/102.39
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.03/102.39
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.03/102.39
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.03/102.39
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.03/102.39
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.03/102.39
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.03/102.39
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.03/102.39
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.03/102.39
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.03/102.39
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.03/102.39
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.39
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.39
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.39
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.39
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.39
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.39
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.39
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.39
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.39
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.39
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.39
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.03/102.39
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.39
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.03/102.39
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.39
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.03/102.39
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.39
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.39
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.39
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.39
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.39
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.39
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.39
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.39
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.39
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.39
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.39
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.39
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.39
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.39
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.39
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.39
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.03/102.39
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.39
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.39
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.39
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.03/102.39
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.39
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.03/102.39
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.39
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.03/102.39
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.39
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.39
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.03/102.39
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.03/102.39
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.03/102.39
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.03/102.39
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.03/102.39
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.03/102.39
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.03/102.39
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.03/102.39
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.03/102.39
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.03/102.39
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.03/102.39
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.03/102.39
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.03/102.39
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
S tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.03/102.39
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.03/102.39
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.03/102.39
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.03/102.39
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.03/102.39
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.03/102.39
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.03/102.39
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.03/102.39
S(mark(z0)) → c21(S(z0)) 334.03/102.39
S(ok(z0)) → c22(S(z0)) 334.03/102.39
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.03/102.39
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.03/102.39
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.03/102.39
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.03/102.39
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.03/102.39
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.03/102.39
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.03/102.39
X(mark(z0), z1) → c30(X(z0, z1)) 334.03/102.39
X(z0, mark(z1)) → c31(X(z0, z1)) 334.03/102.39
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.03/102.39
PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.39
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 334.03/102.39
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.39
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.39
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.39
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.39
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.03/102.39
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.03/102.39
ACTIVE(U11(tt, z0, z1)) → c 334.03/102.39
ACTIVE(U21(tt, z0, z1)) → c2 334.03/102.39
ACTIVE(plus(z0, s(z1))) → c5 334.03/102.39
ACTIVE(x(z0, s(z1))) → c7 334.03/102.39
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.03/102.39
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.03/102.39
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.03/102.39
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.03/102.39
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.39
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.39
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.39
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.39
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.40
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.40
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.40
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.40
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.40
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.03/102.40
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.40
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.40
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.40
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.40
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.40
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.40
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.40
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.40
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.40
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.40
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.40
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.03/102.40
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.40
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.40
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.03/102.40
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.03/102.40
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.03/102.40
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.03/102.40
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.03/102.40
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.03/102.40
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.03/102.40
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.03/102.40
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.03/102.40
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.03/102.40
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.03/102.40
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.03/102.40
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.03/102.40
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.40
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.40
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.40
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.40
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.40
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.40
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.40
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.40
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.40
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.40
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.40
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.03/102.40
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.40
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.03/102.40
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.40
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.03/102.40
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.40
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.40
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.40
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.40
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.40
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.40
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.40
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.40
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.40
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.40
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.40
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.40
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.40
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.40
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.03/102.40
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.40
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.40
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.40
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.03/102.40
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.40
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.03/102.40
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.03/102.40
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.40
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.40
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.03/102.40
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.03/102.40
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.03/102.40
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.03/102.40
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.03/102.40
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.03/102.40
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.03/102.40
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.03/102.40
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.03/102.40
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.03/102.40
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.03/102.40
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c11, c12, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c35, c36, c37, c38, c39, c40, c42, c43, c, c2, c5, c7, c4, c8, c1, c9, c3, c10, c6, c13, c34, c14, c41, c33, c33

334.03/102.40
334.03/102.40

(45) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace PROPER(U12(z0, z1, z2)) → c35(U12'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) by

PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.03/102.40
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1), PROPER(tt)) 334.03/102.40
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.03/102.40
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.03/102.40
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.03/102.40
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.03/102.40
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.03/102.40
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.03/102.40
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1), PROPER(0)) 334.03/102.40
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(tt), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(0), PROPER(x2)) 334.03/102.40
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(tt), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(0), PROPER(x1), PROPER(x2))
334.03/102.40
334.03/102.40

(46) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.03/102.40
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.03/102.40
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.03/102.40
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.03/102.40
active(plus(z0, 0)) → mark(z0) 334.03/102.40
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.03/102.40
active(x(z0, 0)) → mark(0) 334.03/102.40
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.03/102.40
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.03/102.40
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.03/102.40
active(s(z0)) → s(active(z0)) 334.03/102.40
active(plus(z0, z1)) → plus(active(z0), z1) 334.03/102.40
active(plus(z0, z1)) → plus(z0, active(z1)) 334.03/102.40
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.03/102.40
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.03/102.40
active(x(z0, z1)) → x(active(z0), z1) 334.03/102.40
active(x(z0, z1)) → x(z0, active(z1)) 334.03/102.40
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.03/102.40
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.03/102.40
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.03/102.40
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.03/102.40
s(mark(z0)) → mark(s(z0)) 334.03/102.40
s(ok(z0)) → ok(s(z0)) 334.03/102.40
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.03/102.40
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.03/102.40
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.03/102.40
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.03/102.40
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.03/102.40
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.03/102.40
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.03/102.40
x(mark(z0), z1) → mark(x(z0, z1)) 334.03/102.40
x(z0, mark(z1)) → mark(x(z0, z1)) 334.03/102.40
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.03/102.40
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.03/102.40
proper(tt) → ok(tt) 334.03/102.40
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.03/102.40
proper(s(z0)) → s(proper(z0)) 334.03/102.40
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.03/102.40
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.03/102.40
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.03/102.40
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.03/102.40
proper(0) → ok(0) 334.03/102.40
top(mark(z0)) → top(proper(z0)) 334.03/102.40
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.03/102.40
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.03/102.40
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.03/102.40
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.03/102.40
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.03/102.40
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.03/102.40
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.03/102.40
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.03/102.40
S(mark(z0)) → c21(S(z0)) 334.03/102.40
S(ok(z0)) → c22(S(z0)) 334.03/102.40
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.03/102.40
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.03/102.40
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.03/102.40
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.03/102.40
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.03/102.40
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.03/102.40
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.03/102.40
X(mark(z0), z1) → c30(X(z0, z1)) 334.03/102.40
X(z0, mark(z1)) → c31(X(z0, z1)) 334.03/102.40
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.03/102.40
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 334.03/102.40
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.40
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.40
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.40
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.40
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.03/102.40
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.03/102.40
ACTIVE(U11(tt, z0, z1)) → c 334.03/102.40
ACTIVE(U21(tt, z0, z1)) → c2 334.03/102.40
ACTIVE(plus(z0, s(z1))) → c5 334.03/102.40
ACTIVE(x(z0, s(z1))) → c7 334.03/102.40
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.03/102.40
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.03/102.40
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.03/102.40
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.03/102.40
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.40
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.40
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.40
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.40
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.40
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.40
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.40
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.40
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.40
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.03/102.40
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.40
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.40
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.40
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.40
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.40
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.40
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.40
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.40
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.40
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.40
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.40
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.03/102.40
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.40
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.40
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.03/102.40
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.03/102.40
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.03/102.40
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.03/102.40
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.03/102.40
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.03/102.40
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.03/102.40
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.03/102.40
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.03/102.40
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.03/102.40
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.03/102.40
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.03/102.40
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.03/102.40
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.40
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.40
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.40
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.40
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.40
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.40
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.40
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.40
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.40
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.40
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.40
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.03/102.40
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.40
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.03/102.40
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.40
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.03/102.40
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.40
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.40
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.40
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.40
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.40
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.40
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.40
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.40
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.40
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.40
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.40
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.40
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.40
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.40
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.03/102.40
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.40
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.40
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.40
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.03/102.40
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.40
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.03/102.40
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.03/102.40
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.40
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.40
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.03/102.40
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.03/102.40
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.03/102.40
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.03/102.40
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.03/102.40
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.03/102.40
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.03/102.40
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.03/102.40
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.03/102.40
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.03/102.40
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.03/102.40
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.03/102.40
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1), PROPER(tt)) 334.03/102.40
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.03/102.40
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.03/102.40
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.03/102.40
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.03/102.40
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.03/102.40
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.03/102.40
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1), PROPER(0)) 334.03/102.40
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(tt), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(0), PROPER(x2)) 334.03/102.40
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(tt), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(0), PROPER(x1), PROPER(x2))
S tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.03/102.40
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.03/102.40
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.03/102.40
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.03/102.40
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.03/102.40
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.03/102.40
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.03/102.40
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.03/102.40
S(mark(z0)) → c21(S(z0)) 334.03/102.40
S(ok(z0)) → c22(S(z0)) 334.03/102.40
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.03/102.40
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.03/102.40
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.03/102.40
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.03/102.40
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.03/102.40
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.03/102.40
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.03/102.40
X(mark(z0), z1) → c30(X(z0, z1)) 334.03/102.40
X(z0, mark(z1)) → c31(X(z0, z1)) 334.03/102.40
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.03/102.40
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 334.03/102.40
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.40
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.40
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.40
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.40
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.03/102.40
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.03/102.40
ACTIVE(U11(tt, z0, z1)) → c 334.03/102.40
ACTIVE(U21(tt, z0, z1)) → c2 334.03/102.40
ACTIVE(plus(z0, s(z1))) → c5 334.03/102.40
ACTIVE(x(z0, s(z1))) → c7 334.03/102.40
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.03/102.40
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.03/102.40
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.03/102.40
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.03/102.40
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.40
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.40
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.40
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.40
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.40
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.40
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.40
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.40
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.40
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.03/102.40
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.40
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.40
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.40
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.40
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.40
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.40
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.40
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.40
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.40
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.40
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.40
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.03/102.40
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.40
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.40
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.03/102.40
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.03/102.40
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.03/102.40
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.03/102.40
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.03/102.40
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.03/102.40
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.03/102.40
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.03/102.40
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.03/102.40
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.03/102.40
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.03/102.40
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.03/102.40
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.03/102.40
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.40
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.40
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.40
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.40
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.40
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.40
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.40
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.40
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.40
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.40
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.40
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.03/102.40
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.40
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.03/102.40
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.40
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.03/102.40
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.40
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.40
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.40
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.40
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.40
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.40
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.40
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.40
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.40
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.40
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.40
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.40
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.40
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.40
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.03/102.40
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.40
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.40
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.40
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.03/102.40
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.40
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.03/102.40
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.03/102.40
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.40
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.40
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.03/102.40
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.03/102.40
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.03/102.40
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.03/102.40
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.03/102.40
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.03/102.40
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.03/102.40
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.03/102.40
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.03/102.40
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.03/102.40
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.03/102.40
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.03/102.40
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1), PROPER(tt)) 334.03/102.40
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.03/102.40
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.03/102.40
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.03/102.40
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.03/102.40
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.03/102.40
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.03/102.40
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1), PROPER(0)) 334.03/102.40
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(tt), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(0), PROPER(x2)) 334.03/102.40
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(tt), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(0), PROPER(x1), PROPER(x2))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c11, c12, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c36, c37, c38, c39, c40, c42, c43, c, c2, c5, c7, c4, c8, c1, c9, c3, c10, c6, c13, c34, c14, c41, c33, c33, c35

334.03/102.40
334.03/102.40

(47) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 6 trailing tuple parts
334.03/102.40
334.03/102.40

(48) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.03/102.40
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.03/102.40
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.03/102.40
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.03/102.40
active(plus(z0, 0)) → mark(z0) 334.03/102.40
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.03/102.40
active(x(z0, 0)) → mark(0) 334.03/102.40
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.03/102.40
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.03/102.40
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.03/102.40
active(s(z0)) → s(active(z0)) 334.03/102.40
active(plus(z0, z1)) → plus(active(z0), z1) 334.03/102.40
active(plus(z0, z1)) → plus(z0, active(z1)) 334.03/102.40
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.03/102.40
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.03/102.40
active(x(z0, z1)) → x(active(z0), z1) 334.03/102.40
active(x(z0, z1)) → x(z0, active(z1)) 334.03/102.40
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.03/102.40
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.03/102.40
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.03/102.40
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.03/102.40
s(mark(z0)) → mark(s(z0)) 334.03/102.40
s(ok(z0)) → ok(s(z0)) 334.03/102.40
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.03/102.40
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.03/102.40
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.03/102.40
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.03/102.40
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.03/102.40
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.03/102.40
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.03/102.40
x(mark(z0), z1) → mark(x(z0, z1)) 334.03/102.40
x(z0, mark(z1)) → mark(x(z0, z1)) 334.03/102.40
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.03/102.40
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.03/102.40
proper(tt) → ok(tt) 334.03/102.40
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.03/102.40
proper(s(z0)) → s(proper(z0)) 334.03/102.40
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.03/102.40
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.03/102.40
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.03/102.40
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.03/102.40
proper(0) → ok(0) 334.03/102.40
top(mark(z0)) → top(proper(z0)) 334.03/102.40
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.03/102.40
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.03/102.40
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.03/102.40
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.03/102.40
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.03/102.40
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.03/102.40
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.03/102.40
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.03/102.40
S(mark(z0)) → c21(S(z0)) 334.03/102.40
S(ok(z0)) → c22(S(z0)) 334.03/102.40
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.03/102.40
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.03/102.40
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.03/102.40
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.03/102.40
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.03/102.40
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.03/102.40
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.03/102.40
X(mark(z0), z1) → c30(X(z0, z1)) 334.03/102.40
X(z0, mark(z1)) → c31(X(z0, z1)) 334.03/102.40
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.03/102.40
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 334.03/102.40
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.40
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.40
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.40
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.40
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.03/102.40
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.03/102.40
ACTIVE(U11(tt, z0, z1)) → c 334.03/102.40
ACTIVE(U21(tt, z0, z1)) → c2 334.03/102.40
ACTIVE(plus(z0, s(z1))) → c5 334.03/102.40
ACTIVE(x(z0, s(z1))) → c7 334.03/102.40
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.03/102.40
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.03/102.40
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.03/102.40
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.03/102.40
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.40
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.40
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.40
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.40
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.40
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.40
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.40
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.40
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.40
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.03/102.40
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.40
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.40
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.40
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.40
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.40
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.40
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.40
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.40
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.40
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.40
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.40
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.03/102.40
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.40
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.40
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.03/102.40
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.03/102.40
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.03/102.40
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.03/102.40
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.03/102.40
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.03/102.40
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.03/102.40
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.03/102.40
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.03/102.40
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.03/102.40
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.03/102.40
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.03/102.40
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.03/102.40
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.40
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.40
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.40
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.40
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.40
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.40
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.40
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.40
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.40
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.40
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.40
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.03/102.40
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.40
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.03/102.40
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.40
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.03/102.40
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.40
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.40
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.40
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.40
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.40
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.40
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.40
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.40
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.40
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.40
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.40
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.40
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.40
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.40
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.03/102.40
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.40
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.40
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.40
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.03/102.40
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.40
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.03/102.40
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.03/102.40
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.40
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.40
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.03/102.40
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.03/102.40
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.03/102.40
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.03/102.40
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.03/102.40
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.03/102.40
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.03/102.40
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.03/102.40
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.03/102.40
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.03/102.40
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.03/102.40
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.03/102.40
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.03/102.40
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.03/102.40
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.03/102.40
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.03/102.40
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.03/102.40
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.03/102.40
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.03/102.40
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.03/102.40
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.03/102.40
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.03/102.40
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
S tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.03/102.40
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.03/102.40
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.03/102.40
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.03/102.40
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.03/102.40
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.03/102.40
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.03/102.40
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.03/102.40
S(mark(z0)) → c21(S(z0)) 334.03/102.40
S(ok(z0)) → c22(S(z0)) 334.03/102.40
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.03/102.40
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.03/102.40
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.03/102.40
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.03/102.40
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.03/102.40
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.03/102.40
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.03/102.40
X(mark(z0), z1) → c30(X(z0, z1)) 334.03/102.40
X(z0, mark(z1)) → c31(X(z0, z1)) 334.03/102.40
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.03/102.40
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 334.03/102.40
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.40
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.40
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.40
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.40
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.03/102.40
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.03/102.40
ACTIVE(U11(tt, z0, z1)) → c 334.03/102.40
ACTIVE(U21(tt, z0, z1)) → c2 334.03/102.40
ACTIVE(plus(z0, s(z1))) → c5 334.03/102.40
ACTIVE(x(z0, s(z1))) → c7 334.03/102.40
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.03/102.40
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.03/102.40
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.03/102.40
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.03/102.40
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.40
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.40
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.40
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.40
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.40
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.40
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.40
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.40
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.40
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.03/102.40
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.40
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.40
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.40
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.40
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.40
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.40
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.40
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.40
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.40
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.40
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.40
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.03/102.40
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.40
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.40
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.03/102.40
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.03/102.40
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.03/102.40
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.03/102.40
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.03/102.40
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.03/102.40
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.03/102.40
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.03/102.40
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.03/102.40
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.03/102.40
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.03/102.40
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.03/102.40
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.03/102.40
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.40
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.40
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.40
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.40
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.40
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.40
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.40
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.40
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.40
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.40
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.40
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.03/102.40
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.40
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.03/102.40
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.40
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.03/102.40
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.40
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.40
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.40
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.40
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.40
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.40
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.40
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.40
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.40
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.40
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.40
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.40
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.40
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.40
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.03/102.40
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.40
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.40
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.40
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.03/102.40
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.40
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.03/102.40
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.03/102.40
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.40
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.40
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.03/102.40
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.03/102.40
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.03/102.40
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.03/102.40
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.03/102.40
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.03/102.40
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.03/102.40
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.03/102.40
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.03/102.40
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.03/102.40
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.03/102.40
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.03/102.40
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.03/102.40
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.03/102.40
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.03/102.40
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.03/102.40
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.03/102.40
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.03/102.40
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.03/102.40
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.03/102.40
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.03/102.40
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.03/102.40
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.03/102.40
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.03/102.40
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.03/102.40
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c11, c12, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c36, c37, c38, c39, c40, c42, c43, c, c2, c5, c7, c4, c8, c1, c9, c3, c10, c6, c13, c34, c14, c41, c33, c33, c35, c35

334.03/102.40
334.03/102.40

(49) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

Removed 14 trailing nodes:

ACTIVE(x(z0, s(z1))) → c7 334.03/102.40
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.03/102.40
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.03/102.40
ACTIVE(U11(tt, z0, z1)) → c 334.03/102.40
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.03/102.40
ACTIVE(U21(tt, z0, z1)) → c2 334.03/102.40
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.03/102.40
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.03/102.40
ACTIVE(plus(z0, s(z1))) → c5 334.03/102.40
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.40
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.03/102.40
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.40
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.40
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1)))
334.03/102.40
334.03/102.40

(50) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.03/102.40
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.03/102.40
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.03/102.40
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.03/102.40
active(plus(z0, 0)) → mark(z0) 334.03/102.40
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.03/102.40
active(x(z0, 0)) → mark(0) 334.03/102.40
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.03/102.40
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.03/102.40
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.03/102.40
active(s(z0)) → s(active(z0)) 334.03/102.40
active(plus(z0, z1)) → plus(active(z0), z1) 334.03/102.40
active(plus(z0, z1)) → plus(z0, active(z1)) 334.03/102.40
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.03/102.40
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.03/102.40
active(x(z0, z1)) → x(active(z0), z1) 334.03/102.40
active(x(z0, z1)) → x(z0, active(z1)) 334.03/102.40
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.03/102.40
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.03/102.40
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.03/102.40
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.03/102.40
s(mark(z0)) → mark(s(z0)) 334.03/102.40
s(ok(z0)) → ok(s(z0)) 334.03/102.40
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.03/102.40
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.03/102.40
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.03/102.40
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.03/102.40
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.03/102.40
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.03/102.40
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.03/102.40
x(mark(z0), z1) → mark(x(z0, z1)) 334.03/102.40
x(z0, mark(z1)) → mark(x(z0, z1)) 334.03/102.40
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.03/102.40
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.03/102.40
proper(tt) → ok(tt) 334.03/102.40
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.03/102.40
proper(s(z0)) → s(proper(z0)) 334.03/102.40
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.03/102.40
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.03/102.40
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.03/102.40
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.03/102.40
proper(0) → ok(0) 334.03/102.40
top(mark(z0)) → top(proper(z0)) 334.03/102.40
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.03/102.40
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.03/102.40
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.03/102.40
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.03/102.40
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.03/102.40
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.03/102.40
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.03/102.40
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.03/102.40
S(mark(z0)) → c21(S(z0)) 334.03/102.40
S(ok(z0)) → c22(S(z0)) 334.03/102.40
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.03/102.40
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.03/102.40
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.03/102.40
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.03/102.40
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.03/102.40
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.03/102.40
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.03/102.40
X(mark(z0), z1) → c30(X(z0, z1)) 334.03/102.40
X(z0, mark(z1)) → c31(X(z0, z1)) 334.03/102.40
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.03/102.40
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 334.03/102.40
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.40
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.40
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.40
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.40
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.03/102.40
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.03/102.40
ACTIVE(U11(tt, z0, z1)) → c 334.03/102.40
ACTIVE(U21(tt, z0, z1)) → c2 334.03/102.40
ACTIVE(plus(z0, s(z1))) → c5 334.03/102.40
ACTIVE(x(z0, s(z1))) → c7 334.03/102.40
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.03/102.40
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.03/102.40
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.03/102.40
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.03/102.40
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.40
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.40
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.40
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.40
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.40
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.40
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.40
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.40
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.40
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.03/102.40
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.40
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.40
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.40
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.40
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.40
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.40
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.40
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.40
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.40
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.40
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.40
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.40
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.40
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.40
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.03/102.40
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.40
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.40
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.03/102.40
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.03/102.40
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.03/102.40
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.03/102.40
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.03/102.40
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.03/102.40
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.03/102.41
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.03/102.41
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.03/102.41
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.03/102.41
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.03/102.41
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.03/102.41
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.03/102.41
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.03/102.41
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.03/102.41
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.03/102.41
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.03/102.41
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.41
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.41
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.41
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.41
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.41
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.41
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.41
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.41
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.41
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.41
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.41
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.41
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.41
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.41
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.41
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.41
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.41
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.03/102.41
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.41
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.41
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.03/102.41
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.41
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.03/102.41
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.41
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.41
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.41
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.41
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.41
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.41
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.41
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.41
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.41
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.41
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.41
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.41
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.41
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.41
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.41
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.41
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.41
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.41
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.41
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.03/102.41
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.41
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.41
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.41
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.41
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.03/102.41
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.41
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.03/102.41
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.41
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.03/102.41
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.03/102.41
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.03/102.41
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.03/102.41
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.03/102.41
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.03/102.41
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.03/102.41
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.03/102.41
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.03/102.41
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.03/102.41
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.03/102.41
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.03/102.41
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.03/102.41
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.03/102.41
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.03/102.41
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.03/102.41
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.03/102.41
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.41
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.41
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.03/102.41
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.03/102.41
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.41
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.41
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.03/102.41
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.03/102.41
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.03/102.41
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.03/102.41
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.03/102.41
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.03/102.41
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.03/102.41
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.03/102.41
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.03/102.41
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.03/102.41
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.03/102.41
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.03/102.41
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.03/102.41
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.03/102.41
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.03/102.41
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.03/102.41
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.03/102.41
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.03/102.41
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.03/102.41
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.03/102.41
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.03/102.41
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.41
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.41
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.03/102.41
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.03/102.41
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.41
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.03/102.41
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.03/102.41
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.03/102.41
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.03/102.41
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.03/102.41
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.03/102.41
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.03/102.41
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
S tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.03/102.41
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.03/102.41
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.03/102.41
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.03/102.41
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.03/102.41
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.03/102.41
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.03/102.41
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.03/102.41
S(mark(z0)) → c21(S(z0)) 334.03/102.41
S(ok(z0)) → c22(S(z0)) 334.03/102.41
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.03/102.41
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.03/102.41
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.03/102.41
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.03/102.41
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.03/102.41
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.03/102.41
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.03/102.41
X(mark(z0), z1) → c30(X(z0, z1)) 334.03/102.41
X(z0, mark(z1)) → c31(X(z0, z1)) 334.03/102.41
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.03/102.41
PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) 334.03/102.41
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.41
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.41
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.03/102.41
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.03/102.41
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.03/102.41
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.03/102.41
ACTIVE(U11(tt, z0, z1)) → c 334.03/102.41
ACTIVE(U21(tt, z0, z1)) → c2 334.03/102.41
ACTIVE(plus(z0, s(z1))) → c5 334.03/102.41
ACTIVE(x(z0, s(z1))) → c7 334.03/102.41
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.03/102.41
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.03/102.41
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.03/102.41
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.03/102.41
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.41
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.41
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.41
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.41
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.41
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.41
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.41
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.41
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.41
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.41
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.41
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.41
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.41
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.41
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.03/102.41
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.41
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.41
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.41
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.41
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.41
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.41
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.41
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.41
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.41
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.41
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.41
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.41
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.41
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.41
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.41
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.41
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.03/102.41
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.41
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.03/102.41
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.03/102.41
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.03/102.41
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.03/102.41
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.03/102.41
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.03/102.41
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.03/102.41
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.03/102.41
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.03/102.41
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.03/102.41
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.03/102.41
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.03/102.41
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.03/102.41
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.03/102.41
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.03/102.41
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.03/102.41
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.03/102.41
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.03/102.41
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.41
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.41
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.41
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.03/102.41
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.03/102.41
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.03/102.41
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.03/102.41
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.41
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.03/102.41
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.03/102.41
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.03/102.41
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.41
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.03/102.41
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.41
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.41
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.41
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.41
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.03/102.41
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.41
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.03/102.41
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.03/102.41
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.03/102.41
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.03/102.41
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.03/102.41
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.03/102.41
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.03/102.41
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.03/102.41
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.03/102.41
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.41
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.41
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.41
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.41
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.41
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.41
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.41
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.41
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.41
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.41
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.39/102.41
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.41
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.41
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.41
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.41
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.39/102.41
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.41
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.39/102.41
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.41
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.39/102.41
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.41
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.41
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.41
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.41
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.41
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.41
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.41
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.41
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.41
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.41
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.41
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.41
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.41
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.41
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.41
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.41
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.41
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.41
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.41
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.41
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.41
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.41
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.41
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.41
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.41
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.41
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.41
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.41
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.41
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.41
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.41
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.41
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.41
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.41
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.41
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.41
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.41
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.41
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c11, c12, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c36, c37, c38, c39, c40, c42, c43, c, c2, c5, c7, c4, c8, c1, c9, c3, c10, c6, c13, c34, c14, c41, c33, c33, c35, c35

334.39/102.41
334.39/102.41

(51) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace PROPER(s(z0)) → c36(S(proper(z0)), PROPER(z0)) by

PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.39/102.41
PROPER(s(tt)) → c36(S(ok(tt)), PROPER(tt)) 334.39/102.41
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.39/102.41
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.39/102.41
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.39/102.41
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.39/102.41
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.39/102.41
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.39/102.41
PROPER(s(0)) → c36(S(ok(0)), PROPER(0))
334.39/102.41
334.39/102.41

(52) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.39/102.41
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.39/102.41
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.39/102.41
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.39/102.41
active(plus(z0, 0)) → mark(z0) 334.39/102.41
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.39/102.41
active(x(z0, 0)) → mark(0) 334.39/102.41
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.39/102.41
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.39/102.41
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.39/102.41
active(s(z0)) → s(active(z0)) 334.39/102.41
active(plus(z0, z1)) → plus(active(z0), z1) 334.39/102.41
active(plus(z0, z1)) → plus(z0, active(z1)) 334.39/102.41
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.39/102.41
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.39/102.41
active(x(z0, z1)) → x(active(z0), z1) 334.39/102.41
active(x(z0, z1)) → x(z0, active(z1)) 334.39/102.41
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.39/102.41
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.39/102.41
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.39/102.41
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.39/102.41
s(mark(z0)) → mark(s(z0)) 334.39/102.41
s(ok(z0)) → ok(s(z0)) 334.39/102.41
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.39/102.41
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.39/102.41
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.39/102.41
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.39/102.41
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.39/102.41
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.39/102.41
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.39/102.41
x(mark(z0), z1) → mark(x(z0, z1)) 334.39/102.41
x(z0, mark(z1)) → mark(x(z0, z1)) 334.39/102.41
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.39/102.41
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.39/102.41
proper(tt) → ok(tt) 334.39/102.41
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.39/102.41
proper(s(z0)) → s(proper(z0)) 334.39/102.41
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.39/102.41
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.39/102.41
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.39/102.41
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.39/102.41
proper(0) → ok(0) 334.39/102.41
top(mark(z0)) → top(proper(z0)) 334.39/102.41
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.39/102.41
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.39/102.41
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.39/102.41
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.39/102.41
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.39/102.41
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.39/102.41
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.39/102.41
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.39/102.41
S(mark(z0)) → c21(S(z0)) 334.39/102.41
S(ok(z0)) → c22(S(z0)) 334.39/102.41
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.39/102.41
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.39/102.41
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.39/102.41
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.39/102.41
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.39/102.41
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.39/102.41
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.39/102.41
X(mark(z0), z1) → c30(X(z0, z1)) 334.39/102.41
X(z0, mark(z1)) → c31(X(z0, z1)) 334.39/102.41
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.39/102.41
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.39/102.41
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.39/102.41
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.39/102.41
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.39/102.41
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.39/102.41
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.39/102.41
ACTIVE(U11(tt, z0, z1)) → c 334.39/102.41
ACTIVE(U21(tt, z0, z1)) → c2 334.39/102.41
ACTIVE(plus(z0, s(z1))) → c5 334.39/102.41
ACTIVE(x(z0, s(z1))) → c7 334.39/102.41
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.39/102.41
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.39/102.41
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.39/102.41
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.39/102.41
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.41
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.41
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.41
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.41
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.41
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.41
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.41
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.41
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.41
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.41
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.39/102.41
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.41
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.41
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.41
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.41
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.41
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.41
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.41
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.41
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.41
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.41
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.41
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.41
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.39/102.41
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.41
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.41
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.39/102.41
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.39/102.41
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.39/102.41
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.39/102.41
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.39/102.41
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.39/102.41
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.39/102.41
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.39/102.41
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.39/102.41
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.39/102.41
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.39/102.41
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.39/102.41
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.39/102.41
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.41
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.41
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.41
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.41
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.41
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.41
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.41
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.41
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.41
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.41
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.41
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.41
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.41
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.39/102.41
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.41
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.41
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.39/102.41
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.41
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.39/102.41
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.41
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.41
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.41
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.41
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.41
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.41
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.41
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.41
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.41
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.41
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.41
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.41
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.41
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.41
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.41
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.39/102.41
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.41
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.41
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.41
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.41
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.39/102.41
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.41
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.39/102.41
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.41
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.39/102.41
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.41
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.41
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.41
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.41
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.41
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.41
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.41
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.41
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.41
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.41
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.41
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.41
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.41
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.41
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.41
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.41
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.41
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.41
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.41
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.41
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.41
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.41
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.41
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.41
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.41
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.41
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.41
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.41
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.41
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.41
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.41
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.41
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.41
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.41
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.41
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.41
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.41
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.41
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.39/102.41
PROPER(s(tt)) → c36(S(ok(tt)), PROPER(tt)) 334.39/102.41
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.39/102.41
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.39/102.41
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.39/102.41
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.39/102.41
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.39/102.41
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.39/102.41
PROPER(s(0)) → c36(S(ok(0)), PROPER(0))
S tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.39/102.41
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.39/102.41
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.39/102.41
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.39/102.41
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.39/102.41
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.39/102.41
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.39/102.41
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.39/102.41
S(mark(z0)) → c21(S(z0)) 334.39/102.41
S(ok(z0)) → c22(S(z0)) 334.39/102.41
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.39/102.41
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.39/102.41
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.39/102.41
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.39/102.41
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.39/102.41
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.39/102.41
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.39/102.41
X(mark(z0), z1) → c30(X(z0, z1)) 334.39/102.41
X(z0, mark(z1)) → c31(X(z0, z1)) 334.39/102.41
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.39/102.41
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.39/102.41
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.39/102.41
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.39/102.41
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.39/102.41
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.39/102.41
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.39/102.41
ACTIVE(U11(tt, z0, z1)) → c 334.39/102.41
ACTIVE(U21(tt, z0, z1)) → c2 334.39/102.41
ACTIVE(plus(z0, s(z1))) → c5 334.39/102.41
ACTIVE(x(z0, s(z1))) → c7 334.39/102.41
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.39/102.41
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.39/102.41
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.39/102.41
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.39/102.41
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.41
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.41
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.41
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.41
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.41
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.41
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.41
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.41
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.41
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.41
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.39/102.41
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.41
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.41
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.41
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.41
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.41
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.41
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.41
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.41
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.41
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.41
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.41
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.41
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.39/102.41
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.41
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.41
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.39/102.41
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.39/102.41
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.39/102.41
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.39/102.41
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.39/102.41
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.39/102.41
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.39/102.41
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.39/102.41
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.39/102.41
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.39/102.41
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.39/102.41
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.39/102.41
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.39/102.41
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.41
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.41
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.41
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.41
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.41
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.41
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.41
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.41
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.41
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.41
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.41
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.41
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.41
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.39/102.41
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.41
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.41
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.39/102.41
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.41
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.39/102.41
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.41
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.41
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.41
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.41
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.41
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.41
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.41
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.41
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.41
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.41
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.41
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.41
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.41
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.41
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.41
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.39/102.41
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.41
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.41
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.41
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.41
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.39/102.41
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.41
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.39/102.41
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.41
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.39/102.41
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.41
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.41
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.41
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.41
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.41
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.41
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.41
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.41
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.41
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.41
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.41
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.41
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.41
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.41
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.41
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.41
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.41
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.41
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.41
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.41
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.41
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.41
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.41
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.41
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.41
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.41
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.41
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.41
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.41
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.41
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.41
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.41
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.41
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.41
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.41
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.41
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.41
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.41
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.39/102.41
PROPER(s(tt)) → c36(S(ok(tt)), PROPER(tt)) 334.39/102.41
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.39/102.41
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.39/102.41
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.39/102.41
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.39/102.41
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.39/102.41
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.39/102.41
PROPER(s(0)) → c36(S(ok(0)), PROPER(0))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c11, c12, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c37, c38, c39, c40, c42, c43, c, c2, c5, c7, c4, c8, c1, c9, c3, c10, c6, c13, c34, c14, c41, c33, c33, c35, c35, c36

334.39/102.41
334.39/102.41

(53) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 2 trailing tuple parts
334.39/102.41
334.39/102.41

(54) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.39/102.41
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.39/102.41
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.39/102.41
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.39/102.41
active(plus(z0, 0)) → mark(z0) 334.39/102.41
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.39/102.41
active(x(z0, 0)) → mark(0) 334.39/102.41
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.39/102.41
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.39/102.41
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.39/102.41
active(s(z0)) → s(active(z0)) 334.39/102.41
active(plus(z0, z1)) → plus(active(z0), z1) 334.39/102.41
active(plus(z0, z1)) → plus(z0, active(z1)) 334.39/102.41
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.39/102.41
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.39/102.41
active(x(z0, z1)) → x(active(z0), z1) 334.39/102.41
active(x(z0, z1)) → x(z0, active(z1)) 334.39/102.41
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.39/102.41
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.39/102.41
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.39/102.41
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.39/102.41
s(mark(z0)) → mark(s(z0)) 334.39/102.41
s(ok(z0)) → ok(s(z0)) 334.39/102.41
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.39/102.41
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.39/102.41
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.39/102.41
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.39/102.41
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.39/102.41
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.39/102.41
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.39/102.41
x(mark(z0), z1) → mark(x(z0, z1)) 334.39/102.41
x(z0, mark(z1)) → mark(x(z0, z1)) 334.39/102.41
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.39/102.41
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.39/102.41
proper(tt) → ok(tt) 334.39/102.41
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.39/102.41
proper(s(z0)) → s(proper(z0)) 334.39/102.41
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.39/102.41
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.39/102.41
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.39/102.41
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.39/102.41
proper(0) → ok(0) 334.39/102.41
top(mark(z0)) → top(proper(z0)) 334.39/102.41
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.39/102.41
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.39/102.41
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.39/102.41
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.39/102.41
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.39/102.41
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.39/102.41
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.39/102.41
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.39/102.41
S(mark(z0)) → c21(S(z0)) 334.39/102.41
S(ok(z0)) → c22(S(z0)) 334.39/102.41
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.39/102.41
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.39/102.41
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.39/102.41
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.39/102.41
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.39/102.41
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.39/102.41
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.39/102.41
X(mark(z0), z1) → c30(X(z0, z1)) 334.39/102.41
X(z0, mark(z1)) → c31(X(z0, z1)) 334.39/102.41
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.39/102.41
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.39/102.41
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.39/102.41
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.39/102.41
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.39/102.41
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.39/102.41
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.39/102.41
ACTIVE(U11(tt, z0, z1)) → c 334.39/102.41
ACTIVE(U21(tt, z0, z1)) → c2 334.39/102.41
ACTIVE(plus(z0, s(z1))) → c5 334.39/102.41
ACTIVE(x(z0, s(z1))) → c7 334.39/102.41
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.39/102.41
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.39/102.41
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.39/102.41
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.39/102.41
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.41
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.41
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.41
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.41
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.41
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.41
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.41
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.41
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.41
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.41
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.39/102.41
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.41
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.41
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.41
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.41
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.41
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.41
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.41
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.41
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.41
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.41
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.41
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.41
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.39/102.41
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.41
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.41
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.39/102.41
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.39/102.41
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.39/102.41
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.39/102.41
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.39/102.41
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.39/102.41
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.39/102.41
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.39/102.41
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.39/102.41
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.39/102.41
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.39/102.41
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.39/102.41
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.39/102.41
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.41
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.41
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.41
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.41
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.41
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.41
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.41
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.41
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.41
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.41
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.41
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.41
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.41
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.39/102.41
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.41
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.41
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.39/102.41
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.41
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.39/102.41
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.41
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.41
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.41
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.41
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.41
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.41
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.41
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.41
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.41
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.41
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.41
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.41
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.41
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.41
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.41
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.39/102.41
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.41
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.41
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.41
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.41
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.39/102.41
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.41
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.39/102.41
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.41
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.39/102.41
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.41
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.41
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.41
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.41
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.41
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.41
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.41
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.41
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.41
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.41
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.41
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.41
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.41
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.41
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.41
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.41
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.41
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.41
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.41
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.41
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.41
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.41
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.41
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.41
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.41
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.41
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.41
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.41
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.41
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.41
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.41
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.41
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.41
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.41
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.41
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.41
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.41
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.41
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.41
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.39/102.41
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.39/102.41
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.39/102.41
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.39/102.41
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.39/102.41
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.39/102.41
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.39/102.41
PROPER(s(tt)) → c36(S(ok(tt))) 334.39/102.41
PROPER(s(0)) → c36(S(ok(0)))
S tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.39/102.41
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.39/102.41
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.39/102.41
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.39/102.41
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.39/102.41
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.39/102.41
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.39/102.41
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.39/102.41
S(mark(z0)) → c21(S(z0)) 334.39/102.41
S(ok(z0)) → c22(S(z0)) 334.39/102.41
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.39/102.41
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.39/102.41
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.39/102.41
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.39/102.41
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.39/102.41
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.39/102.41
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.39/102.41
X(mark(z0), z1) → c30(X(z0, z1)) 334.39/102.41
X(z0, mark(z1)) → c31(X(z0, z1)) 334.39/102.41
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.39/102.41
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.39/102.41
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.39/102.41
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.39/102.41
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.39/102.41
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.39/102.41
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.39/102.41
ACTIVE(U11(tt, z0, z1)) → c 334.39/102.41
ACTIVE(U21(tt, z0, z1)) → c2 334.39/102.41
ACTIVE(plus(z0, s(z1))) → c5 334.39/102.41
ACTIVE(x(z0, s(z1))) → c7 334.39/102.41
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.39/102.41
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.39/102.41
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.39/102.41
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.39/102.41
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.41
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.41
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.41
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.41
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.41
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.41
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.41
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.41
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.41
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.41
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.39/102.41
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.41
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.41
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.41
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.41
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.41
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.41
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.41
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.41
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.41
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.41
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.41
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.41
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.39/102.41
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.41
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.41
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.39/102.41
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.39/102.41
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.39/102.41
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.39/102.41
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.39/102.41
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.39/102.41
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.39/102.41
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.39/102.41
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.39/102.41
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.39/102.41
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.39/102.41
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.39/102.41
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.39/102.41
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.41
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.41
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.41
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.41
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.41
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.41
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.41
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.41
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.41
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.41
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.41
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.41
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.41
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.39/102.41
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.41
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.41
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.39/102.41
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.41
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.39/102.41
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.41
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.41
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.41
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.41
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.41
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.41
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.41
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.41
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.41
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.41
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.41
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.41
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.41
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.41
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.41
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.41
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.41
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.39/102.41
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.41
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.41
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.41
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.41
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.39/102.41
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.41
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.39/102.41
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.41
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.39/102.41
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.41
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.41
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.41
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.41
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.41
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.41
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.42
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.42
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.42
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.42
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.42
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.42
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.42
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.42
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.42
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.42
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.42
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.42
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.42
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.42
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.42
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.42
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.42
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.42
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.42
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.42
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.42
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.42
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.42
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.42
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.42
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.42
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.42
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.42
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.42
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.42
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.42
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.42
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.39/102.42
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.39/102.42
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.39/102.42
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.39/102.42
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.39/102.42
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.39/102.42
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.39/102.42
PROPER(s(tt)) → c36(S(ok(tt))) 334.39/102.42
PROPER(s(0)) → c36(S(ok(0)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c11, c12, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c37, c38, c39, c40, c42, c43, c, c2, c5, c7, c4, c8, c1, c9, c3, c10, c6, c13, c34, c14, c41, c33, c33, c35, c35, c36, c36

334.39/102.42
334.39/102.42

(55) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

Removed 14 trailing nodes:

ACTIVE(x(z0, s(z1))) → c7 334.39/102.42
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.39/102.42
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.39/102.42
ACTIVE(U11(tt, z0, z1)) → c 334.39/102.42
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.39/102.42
ACTIVE(U21(tt, z0, z1)) → c2 334.39/102.42
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.39/102.42
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.39/102.42
ACTIVE(plus(z0, s(z1))) → c5 334.39/102.42
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.42
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.39/102.42
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.42
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.42
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1)))
334.39/102.42
334.39/102.42

(56) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.39/102.42
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.39/102.42
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.39/102.42
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.39/102.42
active(plus(z0, 0)) → mark(z0) 334.39/102.42
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.39/102.42
active(x(z0, 0)) → mark(0) 334.39/102.42
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.39/102.42
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.39/102.42
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.39/102.42
active(s(z0)) → s(active(z0)) 334.39/102.42
active(plus(z0, z1)) → plus(active(z0), z1) 334.39/102.42
active(plus(z0, z1)) → plus(z0, active(z1)) 334.39/102.42
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.39/102.42
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.39/102.42
active(x(z0, z1)) → x(active(z0), z1) 334.39/102.42
active(x(z0, z1)) → x(z0, active(z1)) 334.39/102.42
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.39/102.42
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.39/102.42
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.39/102.42
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.39/102.42
s(mark(z0)) → mark(s(z0)) 334.39/102.42
s(ok(z0)) → ok(s(z0)) 334.39/102.42
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.39/102.42
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.39/102.42
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.39/102.42
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.39/102.42
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.39/102.42
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.39/102.42
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.39/102.42
x(mark(z0), z1) → mark(x(z0, z1)) 334.39/102.42
x(z0, mark(z1)) → mark(x(z0, z1)) 334.39/102.42
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.39/102.42
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.39/102.42
proper(tt) → ok(tt) 334.39/102.42
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.39/102.42
proper(s(z0)) → s(proper(z0)) 334.39/102.42
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.39/102.42
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.39/102.42
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.39/102.42
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.39/102.42
proper(0) → ok(0) 334.39/102.42
top(mark(z0)) → top(proper(z0)) 334.39/102.42
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.39/102.42
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.39/102.42
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.39/102.42
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.39/102.42
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.39/102.42
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.39/102.42
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.39/102.42
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.39/102.42
S(mark(z0)) → c21(S(z0)) 334.39/102.42
S(ok(z0)) → c22(S(z0)) 334.39/102.42
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.39/102.42
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.39/102.42
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.39/102.42
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.39/102.42
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.39/102.42
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.39/102.42
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.39/102.42
X(mark(z0), z1) → c30(X(z0, z1)) 334.39/102.42
X(z0, mark(z1)) → c31(X(z0, z1)) 334.39/102.42
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.39/102.42
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.39/102.42
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.39/102.42
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.39/102.42
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.39/102.42
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.39/102.42
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.39/102.42
ACTIVE(U11(tt, z0, z1)) → c 334.39/102.42
ACTIVE(U21(tt, z0, z1)) → c2 334.39/102.42
ACTIVE(plus(z0, s(z1))) → c5 334.39/102.42
ACTIVE(x(z0, s(z1))) → c7 334.39/102.42
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.39/102.42
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.39/102.42
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.39/102.42
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.39/102.42
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.42
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.42
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.42
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.42
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.42
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.42
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.42
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.42
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.42
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.42
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.42
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.42
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.42
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.42
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.39/102.42
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.42
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.42
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.42
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.42
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.42
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.42
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.42
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.42
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.42
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.42
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.42
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.42
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.42
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.42
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.42
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.42
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.39/102.42
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.42
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.42
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.39/102.42
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.39/102.42
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.39/102.42
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.39/102.42
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.39/102.42
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.39/102.42
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.39/102.42
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.39/102.42
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.39/102.42
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.39/102.42
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.39/102.42
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.39/102.42
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.39/102.42
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.39/102.42
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.39/102.42
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.39/102.42
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.39/102.42
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.42
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.42
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.42
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.42
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.42
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.42
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.42
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.42
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.42
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.42
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.42
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.42
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.42
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.42
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.42
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.42
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.42
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.39/102.42
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.42
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.42
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.39/102.42
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.42
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.39/102.42
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.42
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.42
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.42
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.42
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.42
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.42
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.42
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.42
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.42
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.42
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.42
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.42
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.42
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.42
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.42
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.42
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.42
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.42
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.42
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.39/102.42
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.42
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.42
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.42
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.42
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.39/102.42
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.42
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.39/102.42
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.42
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.39/102.42
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.42
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.42
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.42
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.42
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.42
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.42
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.42
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.42
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.42
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.42
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.42
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.42
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.42
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.42
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.42
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.42
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.42
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.42
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.42
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.42
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.42
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.42
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.42
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.42
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.42
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.42
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.42
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.42
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.42
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.42
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.42
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.42
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.42
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.42
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.42
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.42
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.42
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.42
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.39/102.42
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.39/102.42
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.39/102.42
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.39/102.42
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.39/102.42
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.39/102.42
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.39/102.42
PROPER(s(tt)) → c36(S(ok(tt))) 334.39/102.42
PROPER(s(0)) → c36(S(ok(0)))
S tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.39/102.42
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.39/102.42
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.39/102.42
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.39/102.42
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.39/102.42
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.39/102.42
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.39/102.42
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.39/102.42
S(mark(z0)) → c21(S(z0)) 334.39/102.42
S(ok(z0)) → c22(S(z0)) 334.39/102.42
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.39/102.42
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.39/102.42
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.39/102.42
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.39/102.42
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.39/102.42
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.39/102.42
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.39/102.42
X(mark(z0), z1) → c30(X(z0, z1)) 334.39/102.42
X(z0, mark(z1)) → c31(X(z0, z1)) 334.39/102.42
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.39/102.42
PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.39/102.42
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.39/102.42
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.39/102.42
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.39/102.42
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.39/102.42
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.39/102.42
ACTIVE(U11(tt, z0, z1)) → c 334.39/102.42
ACTIVE(U21(tt, z0, z1)) → c2 334.39/102.42
ACTIVE(plus(z0, s(z1))) → c5 334.39/102.42
ACTIVE(x(z0, s(z1))) → c7 334.39/102.42
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.39/102.42
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.39/102.42
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.39/102.42
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.39/102.42
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.42
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.42
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.42
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.42
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.42
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.42
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.42
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.42
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.42
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.42
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.42
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.42
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.42
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.42
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.39/102.42
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.42
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.42
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.42
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.42
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.42
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.42
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.42
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.42
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.42
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.42
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.42
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.42
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.42
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.42
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.42
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.42
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.39/102.42
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.42
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.42
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.39/102.42
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.39/102.42
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.39/102.42
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.39/102.42
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.39/102.42
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.39/102.42
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.39/102.42
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.39/102.42
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.39/102.42
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.39/102.42
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.39/102.42
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.39/102.42
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.39/102.42
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.39/102.42
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.39/102.42
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.39/102.42
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.39/102.42
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.42
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.42
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.42
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.42
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.42
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.42
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.42
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.42
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.42
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.42
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.42
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.42
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.42
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.42
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.42
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.42
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.42
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.39/102.42
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.42
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.42
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.39/102.42
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.42
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.39/102.42
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.42
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.42
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.42
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.42
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.42
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.42
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.42
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.42
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.42
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.42
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.42
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.42
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.42
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.42
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.42
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.42
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.42
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.42
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.42
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.39/102.42
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.42
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.42
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.42
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.42
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.39/102.42
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.42
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.39/102.42
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.42
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.39/102.42
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.42
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.42
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.42
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.42
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.42
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.42
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.42
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.42
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.42
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.42
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.42
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.42
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.42
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.42
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.42
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.42
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.42
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.42
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.42
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.42
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.42
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.42
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.42
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.42
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.42
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.42
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.42
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.42
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.42
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.42
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.42
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.42
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.42
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.42
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.42
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.42
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.42
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.42
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.42
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.39/102.42
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.39/102.42
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.39/102.42
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.39/102.42
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.39/102.42
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.39/102.42
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.39/102.42
PROPER(s(tt)) → c36(S(ok(tt))) 334.39/102.42
PROPER(s(0)) → c36(S(ok(0)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c11, c12, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c37, c38, c39, c40, c42, c43, c, c2, c5, c7, c4, c8, c1, c9, c3, c10, c6, c13, c34, c14, c41, c33, c33, c35, c35, c36, c36

334.39/102.42
334.39/102.42

(57) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace PROPER(plus(z0, z1)) → c37(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(plus(x0, U11(z0, z1, z2))) → c37(PLUS(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.39/102.42
PROPER(plus(x0, tt)) → c37(PLUS(proper(x0), ok(tt)), PROPER(x0), PROPER(tt)) 334.39/102.42
PROPER(plus(x0, U12(z0, z1, z2))) → c37(PLUS(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.39/102.42
PROPER(plus(x0, s(z0))) → c37(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.39/102.42
PROPER(plus(x0, plus(z0, z1))) → c37(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.39/102.42
PROPER(plus(x0, U21(z0, z1, z2))) → c37(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.39/102.44
PROPER(plus(x0, U22(z0, z1, z2))) → c37(PLUS(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.39/102.44
PROPER(plus(x0, x(z0, z1))) → c37(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.39/102.44
PROPER(plus(x0, 0)) → c37(PLUS(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 334.39/102.44
PROPER(plus(U11(z0, z1, z2), x1)) → c37(PLUS(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.39/102.44
PROPER(plus(tt, x1)) → c37(PLUS(ok(tt), proper(x1)), PROPER(tt), PROPER(x1)) 334.39/102.44
PROPER(plus(U12(z0, z1, z2), x1)) → c37(PLUS(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.39/102.44
PROPER(plus(s(z0), x1)) → c37(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.39/102.44
PROPER(plus(plus(z0, z1), x1)) → c37(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.39/102.44
PROPER(plus(U21(z0, z1, z2), x1)) → c37(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.39/102.44
PROPER(plus(U22(z0, z1, z2), x1)) → c37(PLUS(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.39/102.44
PROPER(plus(x(z0, z1), x1)) → c37(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.39/102.44
PROPER(plus(0, x1)) → c37(PLUS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
334.39/102.44
334.39/102.44

(58) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.39/102.44
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.39/102.44
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.39/102.44
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.39/102.44
active(plus(z0, 0)) → mark(z0) 334.39/102.44
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.39/102.45
active(x(z0, 0)) → mark(0) 334.39/102.45
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.39/102.45
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.39/102.45
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.39/102.45
active(s(z0)) → s(active(z0)) 334.39/102.45
active(plus(z0, z1)) → plus(active(z0), z1) 334.39/102.45
active(plus(z0, z1)) → plus(z0, active(z1)) 334.39/102.45
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.39/102.45
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.39/102.45
active(x(z0, z1)) → x(active(z0), z1) 334.39/102.45
active(x(z0, z1)) → x(z0, active(z1)) 334.39/102.45
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.39/102.45
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.39/102.45
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.39/102.45
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.39/102.45
s(mark(z0)) → mark(s(z0)) 334.39/102.45
s(ok(z0)) → ok(s(z0)) 334.39/102.45
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.39/102.45
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.39/102.45
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.39/102.45
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.39/102.45
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.39/102.45
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.39/102.45
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.39/102.45
x(mark(z0), z1) → mark(x(z0, z1)) 334.39/102.45
x(z0, mark(z1)) → mark(x(z0, z1)) 334.39/102.45
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.39/102.45
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.39/102.45
proper(tt) → ok(tt) 334.39/102.45
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.39/102.45
proper(s(z0)) → s(proper(z0)) 334.39/102.45
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.39/102.45
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.39/102.45
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.39/102.45
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.39/102.45
proper(0) → ok(0) 334.39/102.45
top(mark(z0)) → top(proper(z0)) 334.39/102.45
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.39/102.45
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.39/102.45
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.39/102.45
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.39/102.45
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.39/102.45
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.39/102.45
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.39/102.45
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.39/102.45
S(mark(z0)) → c21(S(z0)) 334.39/102.45
S(ok(z0)) → c22(S(z0)) 334.39/102.45
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.39/102.45
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.39/102.45
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.39/102.45
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.39/102.45
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.39/102.45
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.39/102.45
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.39/102.45
X(mark(z0), z1) → c30(X(z0, z1)) 334.39/102.45
X(z0, mark(z1)) → c31(X(z0, z1)) 334.39/102.45
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.39/102.45
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.39/102.45
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.39/102.45
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.39/102.45
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.39/102.45
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.39/102.45
ACTIVE(U11(tt, z0, z1)) → c 334.39/102.45
ACTIVE(U21(tt, z0, z1)) → c2 334.39/102.45
ACTIVE(plus(z0, s(z1))) → c5 334.39/102.45
ACTIVE(x(z0, s(z1))) → c7 334.39/102.45
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.39/102.45
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.39/102.45
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.39/102.45
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.39/102.45
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.45
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.45
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.45
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.45
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.45
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.45
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.45
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.45
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.45
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.39/102.45
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.45
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.45
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.45
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.45
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.45
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.45
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.45
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.45
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.45
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.45
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.45
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.39/102.45
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.45
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.45
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.39/102.45
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.39/102.45
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.39/102.45
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.39/102.45
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.39/102.45
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.39/102.45
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.39/102.45
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.39/102.45
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.39/102.45
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.39/102.45
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.39/102.45
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.39/102.45
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.39/102.45
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.45
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.45
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.45
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.45
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.45
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.45
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.45
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.45
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.45
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.45
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.45
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.39/102.45
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.45
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.39/102.45
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.45
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.39/102.45
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.45
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.45
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.45
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.45
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.45
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.45
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.45
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.45
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.45
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.45
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.45
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.45
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.45
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.45
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.39/102.45
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.45
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.45
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.45
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.39/102.45
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.45
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.39/102.45
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.39/102.45
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.45
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.45
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.45
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.45
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.45
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.45
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.45
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.45
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.45
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.45
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.45
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.45
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.45
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.45
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.45
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.45
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.45
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.45
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.45
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.45
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.45
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.45
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.45
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.45
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.45
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.45
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.45
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.45
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.45
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.45
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.45
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.45
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.45
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.45
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.45
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.45
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.45
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.45
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.39/102.45
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.39/102.45
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.39/102.45
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.39/102.45
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.39/102.45
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.39/102.45
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.39/102.45
PROPER(s(tt)) → c36(S(ok(tt))) 334.39/102.45
PROPER(s(0)) → c36(S(ok(0))) 334.39/102.45
PROPER(plus(x0, U11(z0, z1, z2))) → c37(PLUS(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.39/102.45
PROPER(plus(x0, tt)) → c37(PLUS(proper(x0), ok(tt)), PROPER(x0), PROPER(tt)) 334.39/102.45
PROPER(plus(x0, U12(z0, z1, z2))) → c37(PLUS(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.39/102.45
PROPER(plus(x0, s(z0))) → c37(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.39/102.45
PROPER(plus(x0, plus(z0, z1))) → c37(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.39/102.45
PROPER(plus(x0, U21(z0, z1, z2))) → c37(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.39/102.45
PROPER(plus(x0, U22(z0, z1, z2))) → c37(PLUS(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.39/102.45
PROPER(plus(x0, x(z0, z1))) → c37(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.39/102.45
PROPER(plus(x0, 0)) → c37(PLUS(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 334.39/102.45
PROPER(plus(U11(z0, z1, z2), x1)) → c37(PLUS(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.39/102.45
PROPER(plus(tt, x1)) → c37(PLUS(ok(tt), proper(x1)), PROPER(tt), PROPER(x1)) 334.39/102.45
PROPER(plus(U12(z0, z1, z2), x1)) → c37(PLUS(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.39/102.45
PROPER(plus(s(z0), x1)) → c37(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.39/102.45
PROPER(plus(plus(z0, z1), x1)) → c37(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.39/102.45
PROPER(plus(U21(z0, z1, z2), x1)) → c37(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.39/102.45
PROPER(plus(U22(z0, z1, z2), x1)) → c37(PLUS(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.39/102.45
PROPER(plus(x(z0, z1), x1)) → c37(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.39/102.45
PROPER(plus(0, x1)) → c37(PLUS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
S tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.39/102.45
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.39/102.45
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.39/102.45
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.39/102.45
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.39/102.45
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.39/102.45
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.39/102.45
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.39/102.45
S(mark(z0)) → c21(S(z0)) 334.39/102.45
S(ok(z0)) → c22(S(z0)) 334.39/102.45
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.39/102.45
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.39/102.45
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.39/102.45
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.39/102.45
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.39/102.45
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.39/102.45
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.39/102.45
X(mark(z0), z1) → c30(X(z0, z1)) 334.39/102.45
X(z0, mark(z1)) → c31(X(z0, z1)) 334.39/102.45
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.39/102.45
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.39/102.45
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.39/102.45
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.39/102.45
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.39/102.45
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.39/102.45
ACTIVE(U11(tt, z0, z1)) → c 334.39/102.45
ACTIVE(U21(tt, z0, z1)) → c2 334.39/102.45
ACTIVE(plus(z0, s(z1))) → c5 334.39/102.45
ACTIVE(x(z0, s(z1))) → c7 334.39/102.45
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.39/102.45
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.39/102.45
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.39/102.45
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.39/102.45
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.45
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.45
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.45
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.45
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.45
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.45
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.45
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.45
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.45
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.39/102.45
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.45
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.45
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.45
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.45
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.45
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.45
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.45
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.45
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.45
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.45
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.45
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.39/102.45
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.45
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.45
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.39/102.45
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.39/102.45
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.39/102.45
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.39/102.45
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.39/102.45
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.39/102.45
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.39/102.45
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.39/102.45
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.39/102.45
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.39/102.45
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.39/102.45
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.39/102.45
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.39/102.45
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.45
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.45
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.45
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.45
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.45
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.45
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.45
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.45
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.45
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.45
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.45
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.39/102.45
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.45
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.39/102.45
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.45
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.39/102.45
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.45
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.45
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.45
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.45
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.45
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.45
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.45
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.45
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.45
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.45
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.45
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.45
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.45
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.45
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.39/102.45
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.45
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.45
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.45
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.39/102.45
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.45
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.39/102.45
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.39/102.45
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.45
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.45
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.45
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.45
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.45
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.45
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.45
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.45
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.45
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.45
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.45
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.45
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.45
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.45
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.45
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.45
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.45
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.45
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.45
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.45
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.45
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.45
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.45
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.45
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.45
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.45
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.45
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.45
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.45
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.45
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.45
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.45
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.45
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.45
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.45
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.45
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.45
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.45
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.39/102.45
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.39/102.45
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.39/102.45
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.39/102.45
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.39/102.45
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.39/102.45
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.39/102.45
PROPER(s(tt)) → c36(S(ok(tt))) 334.39/102.45
PROPER(s(0)) → c36(S(ok(0))) 334.39/102.45
PROPER(plus(x0, U11(z0, z1, z2))) → c37(PLUS(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.39/102.45
PROPER(plus(x0, tt)) → c37(PLUS(proper(x0), ok(tt)), PROPER(x0), PROPER(tt)) 334.39/102.45
PROPER(plus(x0, U12(z0, z1, z2))) → c37(PLUS(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.39/102.45
PROPER(plus(x0, s(z0))) → c37(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.39/102.45
PROPER(plus(x0, plus(z0, z1))) → c37(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.39/102.45
PROPER(plus(x0, U21(z0, z1, z2))) → c37(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.39/102.45
PROPER(plus(x0, U22(z0, z1, z2))) → c37(PLUS(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.39/102.45
PROPER(plus(x0, x(z0, z1))) → c37(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.39/102.45
PROPER(plus(x0, 0)) → c37(PLUS(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 334.39/102.45
PROPER(plus(U11(z0, z1, z2), x1)) → c37(PLUS(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.39/102.45
PROPER(plus(tt, x1)) → c37(PLUS(ok(tt), proper(x1)), PROPER(tt), PROPER(x1)) 334.39/102.45
PROPER(plus(U12(z0, z1, z2), x1)) → c37(PLUS(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.39/102.45
PROPER(plus(s(z0), x1)) → c37(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.39/102.45
PROPER(plus(plus(z0, z1), x1)) → c37(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.39/102.45
PROPER(plus(U21(z0, z1, z2), x1)) → c37(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.39/102.45
PROPER(plus(U22(z0, z1, z2), x1)) → c37(PLUS(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.39/102.45
PROPER(plus(x(z0, z1), x1)) → c37(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.39/102.45
PROPER(plus(0, x1)) → c37(PLUS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c11, c12, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c38, c39, c40, c42, c43, c, c2, c5, c7, c4, c8, c1, c9, c3, c10, c6, c13, c34, c14, c41, c33, c33, c35, c35, c36, c36, c37

334.39/102.45
334.39/102.45

(59) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 4 trailing tuple parts
334.39/102.45
334.39/102.45

(60) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.39/102.45
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.39/102.45
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.39/102.45
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.39/102.45
active(plus(z0, 0)) → mark(z0) 334.39/102.45
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.39/102.45
active(x(z0, 0)) → mark(0) 334.39/102.45
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.39/102.45
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.39/102.45
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.39/102.45
active(s(z0)) → s(active(z0)) 334.39/102.45
active(plus(z0, z1)) → plus(active(z0), z1) 334.39/102.45
active(plus(z0, z1)) → plus(z0, active(z1)) 334.39/102.45
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.39/102.45
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.39/102.45
active(x(z0, z1)) → x(active(z0), z1) 334.39/102.45
active(x(z0, z1)) → x(z0, active(z1)) 334.39/102.45
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.39/102.45
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.39/102.45
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.39/102.45
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.39/102.45
s(mark(z0)) → mark(s(z0)) 334.39/102.45
s(ok(z0)) → ok(s(z0)) 334.39/102.45
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.39/102.45
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.39/102.45
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.39/102.45
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.39/102.45
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.39/102.45
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.39/102.45
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.39/102.45
x(mark(z0), z1) → mark(x(z0, z1)) 334.39/102.45
x(z0, mark(z1)) → mark(x(z0, z1)) 334.39/102.45
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.39/102.45
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.39/102.45
proper(tt) → ok(tt) 334.39/102.45
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.39/102.45
proper(s(z0)) → s(proper(z0)) 334.39/102.45
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.39/102.45
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.39/102.45
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.39/102.45
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.39/102.45
proper(0) → ok(0) 334.39/102.45
top(mark(z0)) → top(proper(z0)) 334.39/102.45
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.39/102.45
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.39/102.45
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.39/102.45
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.39/102.45
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.39/102.45
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.39/102.45
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.39/102.45
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.39/102.45
S(mark(z0)) → c21(S(z0)) 334.39/102.45
S(ok(z0)) → c22(S(z0)) 334.39/102.45
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.39/102.45
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.39/102.45
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.39/102.45
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.39/102.45
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.39/102.45
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.39/102.45
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.39/102.45
X(mark(z0), z1) → c30(X(z0, z1)) 334.39/102.45
X(z0, mark(z1)) → c31(X(z0, z1)) 334.39/102.45
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.39/102.45
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.39/102.45
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.39/102.45
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.39/102.45
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.39/102.45
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.39/102.45
ACTIVE(U11(tt, z0, z1)) → c 334.39/102.45
ACTIVE(U21(tt, z0, z1)) → c2 334.39/102.45
ACTIVE(plus(z0, s(z1))) → c5 334.39/102.45
ACTIVE(x(z0, s(z1))) → c7 334.39/102.45
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.39/102.45
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.39/102.45
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.39/102.45
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.39/102.45
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.45
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.45
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.45
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.45
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.45
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.45
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.45
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.45
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.45
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.39/102.45
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.45
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.45
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.45
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.45
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.45
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.45
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.45
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.45
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.45
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.45
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.45
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.39/102.45
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.45
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.45
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.39/102.45
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.39/102.45
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.39/102.45
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.39/102.45
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.39/102.45
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.39/102.45
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.39/102.45
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.39/102.45
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.39/102.45
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.39/102.45
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.39/102.45
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.39/102.45
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.39/102.45
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.45
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.45
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.45
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.45
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.45
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.45
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.45
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.45
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.45
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.45
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.45
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.39/102.45
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.45
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.39/102.45
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.45
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.39/102.45
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.45
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.45
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.45
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.45
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.45
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.45
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.45
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.45
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.45
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.45
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.45
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.45
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.45
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.45
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.39/102.45
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.45
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.45
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.45
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.39/102.45
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.45
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.39/102.45
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.39/102.45
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.45
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.45
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.45
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.45
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.45
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.45
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.45
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.45
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.45
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.45
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.45
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.45
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.45
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.45
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.45
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.45
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.45
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.45
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.45
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.45
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.45
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.45
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.45
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.45
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.45
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.45
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.45
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.45
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.45
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.45
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.45
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.45
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.45
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.45
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.45
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.45
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.45
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.45
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.39/102.45
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.39/102.45
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.39/102.45
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.39/102.45
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.39/102.45
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.39/102.45
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.39/102.45
PROPER(s(tt)) → c36(S(ok(tt))) 334.39/102.45
PROPER(s(0)) → c36(S(ok(0))) 334.39/102.45
PROPER(plus(x0, U11(z0, z1, z2))) → c37(PLUS(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.39/102.45
PROPER(plus(x0, U12(z0, z1, z2))) → c37(PLUS(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.39/102.45
PROPER(plus(x0, s(z0))) → c37(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.39/102.45
PROPER(plus(x0, plus(z0, z1))) → c37(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.39/102.45
PROPER(plus(x0, U21(z0, z1, z2))) → c37(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.39/102.45
PROPER(plus(x0, U22(z0, z1, z2))) → c37(PLUS(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.39/102.45
PROPER(plus(x0, x(z0, z1))) → c37(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.39/102.45
PROPER(plus(U11(z0, z1, z2), x1)) → c37(PLUS(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.39/102.45
PROPER(plus(U12(z0, z1, z2), x1)) → c37(PLUS(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.39/102.45
PROPER(plus(s(z0), x1)) → c37(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.39/102.45
PROPER(plus(plus(z0, z1), x1)) → c37(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.39/102.45
PROPER(plus(U21(z0, z1, z2), x1)) → c37(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.39/102.45
PROPER(plus(U22(z0, z1, z2), x1)) → c37(PLUS(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.39/102.45
PROPER(plus(x(z0, z1), x1)) → c37(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.39/102.45
PROPER(plus(x0, tt)) → c37(PLUS(proper(x0), ok(tt)), PROPER(x0)) 334.39/102.45
PROPER(plus(x0, 0)) → c37(PLUS(proper(x0), ok(0)), PROPER(x0)) 334.39/102.45
PROPER(plus(tt, x1)) → c37(PLUS(ok(tt), proper(x1)), PROPER(x1)) 334.39/102.45
PROPER(plus(0, x1)) → c37(PLUS(ok(0), proper(x1)), PROPER(x1))
S tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.39/102.45
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.39/102.45
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.39/102.45
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.39/102.45
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.39/102.45
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.39/102.45
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.39/102.45
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.39/102.45
S(mark(z0)) → c21(S(z0)) 334.39/102.45
S(ok(z0)) → c22(S(z0)) 334.39/102.45
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.39/102.45
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.39/102.45
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.39/102.45
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.39/102.45
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.39/102.45
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.39/102.45
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.39/102.45
X(mark(z0), z1) → c30(X(z0, z1)) 334.39/102.45
X(z0, mark(z1)) → c31(X(z0, z1)) 334.39/102.45
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.39/102.45
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.39/102.45
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.39/102.45
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.39/102.45
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.39/102.45
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.39/102.45
ACTIVE(U11(tt, z0, z1)) → c 334.39/102.45
ACTIVE(U21(tt, z0, z1)) → c2 334.39/102.45
ACTIVE(plus(z0, s(z1))) → c5 334.39/102.45
ACTIVE(x(z0, s(z1))) → c7 334.39/102.45
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.39/102.45
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.39/102.45
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.39/102.45
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.39/102.45
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.45
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.45
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.45
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.45
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.45
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.45
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.45
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.45
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.45
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.39/102.45
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.45
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.45
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.45
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.45
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.45
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.45
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.45
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.45
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.45
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.45
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.45
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.39/102.45
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.45
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.45
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.39/102.45
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.39/102.45
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.39/102.45
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.39/102.45
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.39/102.45
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.39/102.45
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.39/102.45
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.39/102.45
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.39/102.45
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.39/102.45
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.39/102.45
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.39/102.45
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.39/102.45
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.45
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.45
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.45
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.45
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.45
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.45
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.45
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.45
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.45
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.45
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.45
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.39/102.45
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.45
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.39/102.45
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.45
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.39/102.45
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.45
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.45
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.45
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.45
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.45
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.45
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.45
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.45
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.45
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.45
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.45
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.45
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.45
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.45
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.39/102.45
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.45
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.45
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.45
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.39/102.45
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.45
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.39/102.45
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.39/102.45
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.45
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.45
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.45
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.45
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.45
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.45
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.45
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.45
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.45
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.45
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.45
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.45
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.45
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.45
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.45
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.45
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.45
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.45
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.45
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.45
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.45
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.45
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.45
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.45
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.45
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.45
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.45
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.45
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.45
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.45
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.45
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.45
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.45
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.45
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.45
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.45
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.45
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.45
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.45
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.39/102.45
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.39/102.45
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.39/102.45
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.39/102.45
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.39/102.45
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.39/102.45
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.39/102.45
PROPER(s(tt)) → c36(S(ok(tt))) 334.39/102.45
PROPER(s(0)) → c36(S(ok(0))) 334.39/102.45
PROPER(plus(x0, U11(z0, z1, z2))) → c37(PLUS(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.39/102.45
PROPER(plus(x0, U12(z0, z1, z2))) → c37(PLUS(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.39/102.45
PROPER(plus(x0, s(z0))) → c37(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.39/102.45
PROPER(plus(x0, plus(z0, z1))) → c37(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.39/102.45
PROPER(plus(x0, U21(z0, z1, z2))) → c37(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.39/102.45
PROPER(plus(x0, U22(z0, z1, z2))) → c37(PLUS(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.39/102.45
PROPER(plus(x0, x(z0, z1))) → c37(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.39/102.45
PROPER(plus(U11(z0, z1, z2), x1)) → c37(PLUS(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.39/102.45
PROPER(plus(U12(z0, z1, z2), x1)) → c37(PLUS(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.39/102.45
PROPER(plus(s(z0), x1)) → c37(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.39/102.45
PROPER(plus(plus(z0, z1), x1)) → c37(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.39/102.45
PROPER(plus(U21(z0, z1, z2), x1)) → c37(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.39/102.45
PROPER(plus(U22(z0, z1, z2), x1)) → c37(PLUS(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.39/102.45
PROPER(plus(x(z0, z1), x1)) → c37(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.39/102.45
PROPER(plus(x0, tt)) → c37(PLUS(proper(x0), ok(tt)), PROPER(x0)) 334.39/102.45
PROPER(plus(x0, 0)) → c37(PLUS(proper(x0), ok(0)), PROPER(x0)) 334.39/102.45
PROPER(plus(tt, x1)) → c37(PLUS(ok(tt), proper(x1)), PROPER(x1)) 334.39/102.45
PROPER(plus(0, x1)) → c37(PLUS(ok(0), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c11, c12, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c38, c39, c40, c42, c43, c, c2, c5, c7, c4, c8, c1, c9, c3, c10, c6, c13, c34, c14, c41, c33, c33, c35, c35, c36, c36, c37, c37

334.39/102.45
334.39/102.45

(61) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

Removed 14 trailing nodes:

ACTIVE(x(z0, s(z1))) → c7 334.39/102.45
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.39/102.45
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.39/102.45
ACTIVE(U11(tt, z0, z1)) → c 334.39/102.45
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.39/102.45
ACTIVE(U21(tt, z0, z1)) → c2 334.39/102.45
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.39/102.45
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.39/102.45
ACTIVE(plus(z0, s(z1))) → c5 334.39/102.45
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.45
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.39/102.45
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.45
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.45
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1)))
334.39/102.45
334.39/102.45

(62) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.39/102.45
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.39/102.45
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.39/102.45
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.39/102.45
active(plus(z0, 0)) → mark(z0) 334.39/102.45
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.39/102.45
active(x(z0, 0)) → mark(0) 334.39/102.45
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.39/102.45
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.39/102.45
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.39/102.45
active(s(z0)) → s(active(z0)) 334.39/102.45
active(plus(z0, z1)) → plus(active(z0), z1) 334.39/102.45
active(plus(z0, z1)) → plus(z0, active(z1)) 334.39/102.45
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.39/102.45
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.39/102.45
active(x(z0, z1)) → x(active(z0), z1) 334.39/102.45
active(x(z0, z1)) → x(z0, active(z1)) 334.39/102.45
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.39/102.45
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.39/102.45
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.39/102.45
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.39/102.45
s(mark(z0)) → mark(s(z0)) 334.39/102.45
s(ok(z0)) → ok(s(z0)) 334.39/102.45
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.39/102.45
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.39/102.45
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.39/102.45
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.39/102.45
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.39/102.45
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.39/102.45
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.39/102.45
x(mark(z0), z1) → mark(x(z0, z1)) 334.39/102.45
x(z0, mark(z1)) → mark(x(z0, z1)) 334.39/102.45
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.39/102.45
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.39/102.45
proper(tt) → ok(tt) 334.39/102.45
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.39/102.45
proper(s(z0)) → s(proper(z0)) 334.39/102.45
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.39/102.45
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.39/102.45
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.39/102.45
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.39/102.45
proper(0) → ok(0) 334.39/102.45
top(mark(z0)) → top(proper(z0)) 334.39/102.45
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.39/102.45
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.39/102.45
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.39/102.45
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.39/102.45
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.39/102.45
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.39/102.45
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.39/102.45
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.39/102.45
S(mark(z0)) → c21(S(z0)) 334.39/102.45
S(ok(z0)) → c22(S(z0)) 334.39/102.45
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.39/102.45
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.39/102.45
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.39/102.45
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.39/102.45
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.39/102.45
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.39/102.45
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.39/102.45
X(mark(z0), z1) → c30(X(z0, z1)) 334.39/102.45
X(z0, mark(z1)) → c31(X(z0, z1)) 334.39/102.45
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.39/102.45
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.39/102.45
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.39/102.45
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.39/102.45
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.39/102.45
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.39/102.45
ACTIVE(U11(tt, z0, z1)) → c 334.39/102.45
ACTIVE(U21(tt, z0, z1)) → c2 334.39/102.45
ACTIVE(plus(z0, s(z1))) → c5 334.39/102.45
ACTIVE(x(z0, s(z1))) → c7 334.39/102.45
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.39/102.45
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.39/102.45
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.39/102.45
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.39/102.45
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.45
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.45
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.45
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.45
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.45
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.45
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.45
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.45
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.45
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.39/102.45
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.45
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.45
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.45
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.45
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.45
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.45
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.45
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.45
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.45
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.45
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.45
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.39/102.45
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.45
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.45
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.39/102.45
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.39/102.45
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.39/102.45
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.39/102.45
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.39/102.45
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.39/102.45
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.39/102.45
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.39/102.45
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.39/102.45
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.39/102.45
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.39/102.45
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.39/102.45
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.39/102.45
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.45
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.45
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.45
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.45
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.45
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.45
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.45
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.45
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.45
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.45
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.45
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.39/102.45
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.45
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.39/102.45
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.45
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.39/102.45
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.45
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.45
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.45
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.45
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.45
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.45
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.45
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.45
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.45
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.45
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.45
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.45
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.45
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.45
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.45
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.45
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.39/102.45
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.45
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.45
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.45
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.39/102.45
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.45
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.39/102.45
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.45
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.39/102.45
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.45
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.45
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.45
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.45
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.45
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.46
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.46
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.46
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.46
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.46
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.46
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.46
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.46
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.46
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.46
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.46
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.46
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.46
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.46
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.46
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.46
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.46
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.46
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.46
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.46
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.46
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.46
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.46
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.46
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.46
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.46
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.46
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.46
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.46
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.46
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.46
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.46
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.46
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.46
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.46
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.46
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.46
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.46
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.46
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.46
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.46
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.46
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.46
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.46
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.46
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.46
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.46
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.46
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.46
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.46
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.46
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.39/102.46
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.39/102.46
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.39/102.46
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.39/102.46
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.39/102.46
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.39/102.46
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.39/102.46
PROPER(s(tt)) → c36(S(ok(tt))) 334.39/102.46
PROPER(s(0)) → c36(S(ok(0))) 334.39/102.46
PROPER(plus(x0, U11(z0, z1, z2))) → c37(PLUS(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.39/102.46
PROPER(plus(x0, U12(z0, z1, z2))) → c37(PLUS(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.39/102.46
PROPER(plus(x0, s(z0))) → c37(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.39/102.46
PROPER(plus(x0, plus(z0, z1))) → c37(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.39/102.46
PROPER(plus(x0, U21(z0, z1, z2))) → c37(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.39/102.46
PROPER(plus(x0, U22(z0, z1, z2))) → c37(PLUS(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.39/102.46
PROPER(plus(x0, x(z0, z1))) → c37(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.39/102.46
PROPER(plus(U11(z0, z1, z2), x1)) → c37(PLUS(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.39/102.46
PROPER(plus(U12(z0, z1, z2), x1)) → c37(PLUS(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.39/102.46
PROPER(plus(s(z0), x1)) → c37(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.39/102.46
PROPER(plus(plus(z0, z1), x1)) → c37(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.39/102.46
PROPER(plus(U21(z0, z1, z2), x1)) → c37(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.39/102.46
PROPER(plus(U22(z0, z1, z2), x1)) → c37(PLUS(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.39/102.46
PROPER(plus(x(z0, z1), x1)) → c37(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.39/102.46
PROPER(plus(x0, tt)) → c37(PLUS(proper(x0), ok(tt)), PROPER(x0)) 334.39/102.46
PROPER(plus(x0, 0)) → c37(PLUS(proper(x0), ok(0)), PROPER(x0)) 334.39/102.46
PROPER(plus(tt, x1)) → c37(PLUS(ok(tt), proper(x1)), PROPER(x1)) 334.39/102.46
PROPER(plus(0, x1)) → c37(PLUS(ok(0), proper(x1)), PROPER(x1))
S tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.39/102.46
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.39/102.46
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.39/102.46
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.39/102.46
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.39/102.46
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.39/102.46
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.39/102.46
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.39/102.46
S(mark(z0)) → c21(S(z0)) 334.39/102.46
S(ok(z0)) → c22(S(z0)) 334.39/102.46
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.39/102.46
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.39/102.46
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.39/102.46
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.39/102.46
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.39/102.46
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.39/102.46
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.39/102.46
X(mark(z0), z1) → c30(X(z0, z1)) 334.39/102.46
X(z0, mark(z1)) → c31(X(z0, z1)) 334.39/102.46
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.39/102.46
PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.39/102.46
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.39/102.46
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.39/102.46
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.39/102.46
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.39/102.46
ACTIVE(U11(tt, z0, z1)) → c 334.39/102.46
ACTIVE(U21(tt, z0, z1)) → c2 334.39/102.46
ACTIVE(plus(z0, s(z1))) → c5 334.39/102.46
ACTIVE(x(z0, s(z1))) → c7 334.39/102.46
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.39/102.46
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.39/102.46
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.39/102.46
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.39/102.46
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.46
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.46
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.46
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.46
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.46
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.46
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.46
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.46
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.46
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.46
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.46
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.46
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.46
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.46
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.39/102.46
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.46
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.46
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.46
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.46
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.46
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.46
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.46
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.46
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.46
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.46
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.46
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.46
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.46
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.46
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.46
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.46
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.39/102.46
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.46
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.46
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.39/102.46
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.39/102.46
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.39/102.46
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.39/102.46
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.39/102.46
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.39/102.46
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.39/102.46
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.39/102.46
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.39/102.46
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.39/102.46
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.39/102.46
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.39/102.46
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.39/102.46
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.39/102.46
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.39/102.46
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.39/102.46
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.39/102.46
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.46
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.46
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.46
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.46
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.46
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.46
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.46
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.46
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.46
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.46
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.46
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.46
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.46
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.46
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.46
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.46
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.46
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.39/102.46
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.46
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.46
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.39/102.46
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.46
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.39/102.46
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.46
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.46
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.46
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.46
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.46
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.46
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.46
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.46
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.46
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.46
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.46
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.46
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.46
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.46
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.46
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.46
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.46
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.46
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.46
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.39/102.46
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.46
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.46
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.46
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.46
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.39/102.46
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.46
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.39/102.46
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.46
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.39/102.46
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.46
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.46
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.46
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.46
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.46
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.46
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.46
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.46
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.46
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.46
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.46
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.46
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.46
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.46
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.46
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.46
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.46
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.46
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.46
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.46
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.46
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.46
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.46
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.46
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.46
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.46
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.46
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.46
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.46
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.46
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.46
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.46
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.46
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.46
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.46
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.46
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.46
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.46
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.46
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.46
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.46
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.46
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.46
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.46
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.46
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.46
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.46
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.46
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.46
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.46
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.46
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.46
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.46
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.46
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.46
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.46
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.39/102.46
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.39/102.46
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.39/102.46
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.39/102.46
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.39/102.46
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.39/102.46
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.39/102.46
PROPER(s(tt)) → c36(S(ok(tt))) 334.39/102.46
PROPER(s(0)) → c36(S(ok(0))) 334.39/102.46
PROPER(plus(x0, U11(z0, z1, z2))) → c37(PLUS(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.39/102.46
PROPER(plus(x0, U12(z0, z1, z2))) → c37(PLUS(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.39/102.46
PROPER(plus(x0, s(z0))) → c37(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.39/102.46
PROPER(plus(x0, plus(z0, z1))) → c37(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.39/102.46
PROPER(plus(x0, U21(z0, z1, z2))) → c37(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.39/102.46
PROPER(plus(x0, U22(z0, z1, z2))) → c37(PLUS(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.39/102.46
PROPER(plus(x0, x(z0, z1))) → c37(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.39/102.46
PROPER(plus(U11(z0, z1, z2), x1)) → c37(PLUS(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.39/102.46
PROPER(plus(U12(z0, z1, z2), x1)) → c37(PLUS(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.39/102.46
PROPER(plus(s(z0), x1)) → c37(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.39/102.46
PROPER(plus(plus(z0, z1), x1)) → c37(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.39/102.46
PROPER(plus(U21(z0, z1, z2), x1)) → c37(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.39/102.46
PROPER(plus(U22(z0, z1, z2), x1)) → c37(PLUS(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.39/102.46
PROPER(plus(x(z0, z1), x1)) → c37(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.39/102.46
PROPER(plus(x0, tt)) → c37(PLUS(proper(x0), ok(tt)), PROPER(x0)) 334.39/102.46
PROPER(plus(x0, 0)) → c37(PLUS(proper(x0), ok(0)), PROPER(x0)) 334.39/102.46
PROPER(plus(tt, x1)) → c37(PLUS(ok(tt), proper(x1)), PROPER(x1)) 334.39/102.46
PROPER(plus(0, x1)) → c37(PLUS(ok(0), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c11, c12, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c38, c39, c40, c42, c43, c, c2, c5, c7, c4, c8, c1, c9, c3, c10, c6, c13, c34, c14, c41, c33, c33, c35, c35, c36, c36, c37, c37

334.39/102.46
334.39/102.46

(63) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace PROPER(U21(z0, z1, z2)) → c38(U21'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) by

PROPER(U21(x0, x1, U11(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.46
PROPER(U21(x0, x1, tt)) → c38(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1), PROPER(tt)) 334.39/102.46
PROPER(U21(x0, x1, U12(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.46
PROPER(U21(x0, x1, s(z0))) → c38(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.46
PROPER(U21(x0, x1, plus(z0, z1))) → c38(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.46
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.46
PROPER(U21(x0, x1, U22(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.46
PROPER(U21(x0, x1, x(z0, z1))) → c38(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.46
PROPER(U21(x0, x1, 0)) → c38(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1), PROPER(0)) 334.39/102.46
PROPER(U21(x0, U11(z0, z1, z2), x2)) → c38(U21'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.46
PROPER(U21(x0, tt, x2)) → c38(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(tt), PROPER(x2)) 334.39/102.46
PROPER(U21(x0, U12(z0, z1, z2), x2)) → c38(U21'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.46
PROPER(U21(x0, s(z0), x2)) → c38(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.46
PROPER(U21(x0, plus(z0, z1), x2)) → c38(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.46
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c38(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U21(x0, U22(z0, z1, z2), x2)) → c38(U21'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U21(x0, x(z0, z1), x2)) → c38(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.47
PROPER(U21(x0, 0, x2)) → c38(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(0), PROPER(x2)) 334.39/102.47
PROPER(U21(U11(z0, z1, z2), x1, x2)) → c38(U21'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U21(tt, x1, x2)) → c38(U21'(ok(tt), proper(x1), proper(x2)), PROPER(tt), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U21(U12(z0, z1, z2), x1, x2)) → c38(U21'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U21(s(z0), x1, x2)) → c38(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U21(plus(z0, z1), x1, x2)) → c38(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c38(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U21(U22(z0, z1, z2), x1, x2)) → c38(U21'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U21(x(z0, z1), x1, x2)) → c38(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U21(0, x1, x2)) → c38(U21'(ok(0), proper(x1), proper(x2)), PROPER(0), PROPER(x1), PROPER(x2))
334.39/102.47
334.39/102.47

(64) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.39/102.47
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.39/102.47
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.39/102.47
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.39/102.47
active(plus(z0, 0)) → mark(z0) 334.39/102.47
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.39/102.47
active(x(z0, 0)) → mark(0) 334.39/102.47
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.39/102.47
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.39/102.47
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.39/102.47
active(s(z0)) → s(active(z0)) 334.39/102.47
active(plus(z0, z1)) → plus(active(z0), z1) 334.39/102.47
active(plus(z0, z1)) → plus(z0, active(z1)) 334.39/102.47
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.39/102.47
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.39/102.47
active(x(z0, z1)) → x(active(z0), z1) 334.39/102.47
active(x(z0, z1)) → x(z0, active(z1)) 334.39/102.47
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.39/102.47
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.39/102.47
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.39/102.47
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.39/102.47
s(mark(z0)) → mark(s(z0)) 334.39/102.47
s(ok(z0)) → ok(s(z0)) 334.39/102.47
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.39/102.47
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.39/102.47
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.39/102.47
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.39/102.47
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.39/102.47
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.39/102.47
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.39/102.47
x(mark(z0), z1) → mark(x(z0, z1)) 334.39/102.47
x(z0, mark(z1)) → mark(x(z0, z1)) 334.39/102.47
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.39/102.47
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.39/102.47
proper(tt) → ok(tt) 334.39/102.47
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.39/102.47
proper(s(z0)) → s(proper(z0)) 334.39/102.47
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.39/102.47
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.39/102.47
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.39/102.47
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.39/102.47
proper(0) → ok(0) 334.39/102.47
top(mark(z0)) → top(proper(z0)) 334.39/102.47
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.39/102.47
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.39/102.47
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.39/102.47
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.39/102.47
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.39/102.47
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.39/102.47
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.39/102.47
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.39/102.47
S(mark(z0)) → c21(S(z0)) 334.39/102.47
S(ok(z0)) → c22(S(z0)) 334.39/102.47
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.39/102.47
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.39/102.47
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.39/102.47
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.39/102.47
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.39/102.47
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.39/102.47
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.39/102.47
X(mark(z0), z1) → c30(X(z0, z1)) 334.39/102.47
X(z0, mark(z1)) → c31(X(z0, z1)) 334.39/102.47
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.39/102.47
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.39/102.47
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.39/102.47
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.39/102.47
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.39/102.47
ACTIVE(U11(tt, z0, z1)) → c 334.39/102.47
ACTIVE(U21(tt, z0, z1)) → c2 334.39/102.47
ACTIVE(plus(z0, s(z1))) → c5 334.39/102.47
ACTIVE(x(z0, s(z1))) → c7 334.39/102.47
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.39/102.47
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.39/102.47
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.39/102.47
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.39/102.47
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.47
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.47
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.47
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.47
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.47
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.47
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.47
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.47
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.47
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.47
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.47
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.47
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.47
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.47
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.39/102.47
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.47
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.47
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.47
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.47
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.47
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.47
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.47
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.47
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.47
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.47
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.47
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.47
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.47
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.47
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.47
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.47
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.39/102.47
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.47
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.47
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.39/102.47
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.39/102.47
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.39/102.47
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.39/102.47
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.39/102.47
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.39/102.47
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.39/102.47
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.39/102.47
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.39/102.47
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.39/102.47
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.39/102.47
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.39/102.47
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.39/102.47
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.39/102.47
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.39/102.47
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.39/102.47
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.39/102.47
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.47
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.47
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.47
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.47
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.47
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.47
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.47
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.47
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.47
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.47
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.47
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.47
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.47
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.47
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.47
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.47
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.47
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.39/102.47
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.47
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.47
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.39/102.47
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.47
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.39/102.47
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.47
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.47
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.47
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.47
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.47
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.47
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.47
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.47
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.47
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.47
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.47
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.47
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.47
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.47
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.47
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.47
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.47
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.47
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.47
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.39/102.47
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.47
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.47
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.47
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.47
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.39/102.47
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.47
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.39/102.47
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.47
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.39/102.47
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.47
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.47
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.47
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.47
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.47
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.47
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.47
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.47
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.47
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.47
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.47
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.47
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.47
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.47
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.47
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.47
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.47
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.47
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.47
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.47
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.47
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.47
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.47
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.47
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.47
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.47
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.47
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.47
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.47
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.47
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.39/102.47
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.39/102.47
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.39/102.47
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.39/102.47
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.39/102.47
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.39/102.47
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.39/102.47
PROPER(s(tt)) → c36(S(ok(tt))) 334.39/102.47
PROPER(s(0)) → c36(S(ok(0))) 334.39/102.47
PROPER(plus(x0, U11(z0, z1, z2))) → c37(PLUS(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.39/102.47
PROPER(plus(x0, U12(z0, z1, z2))) → c37(PLUS(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.39/102.47
PROPER(plus(x0, s(z0))) → c37(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.39/102.47
PROPER(plus(x0, plus(z0, z1))) → c37(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.39/102.47
PROPER(plus(x0, U21(z0, z1, z2))) → c37(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.39/102.47
PROPER(plus(x0, U22(z0, z1, z2))) → c37(PLUS(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.39/102.47
PROPER(plus(x0, x(z0, z1))) → c37(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.39/102.47
PROPER(plus(U11(z0, z1, z2), x1)) → c37(PLUS(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.39/102.47
PROPER(plus(U12(z0, z1, z2), x1)) → c37(PLUS(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.39/102.47
PROPER(plus(s(z0), x1)) → c37(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.39/102.47
PROPER(plus(plus(z0, z1), x1)) → c37(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.39/102.47
PROPER(plus(U21(z0, z1, z2), x1)) → c37(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.39/102.47
PROPER(plus(U22(z0, z1, z2), x1)) → c37(PLUS(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.39/102.47
PROPER(plus(x(z0, z1), x1)) → c37(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.39/102.47
PROPER(plus(x0, tt)) → c37(PLUS(proper(x0), ok(tt)), PROPER(x0)) 334.39/102.47
PROPER(plus(x0, 0)) → c37(PLUS(proper(x0), ok(0)), PROPER(x0)) 334.39/102.47
PROPER(plus(tt, x1)) → c37(PLUS(ok(tt), proper(x1)), PROPER(x1)) 334.39/102.47
PROPER(plus(0, x1)) → c37(PLUS(ok(0), proper(x1)), PROPER(x1)) 334.39/102.47
PROPER(U21(x0, x1, U11(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.47
PROPER(U21(x0, x1, tt)) → c38(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1), PROPER(tt)) 334.39/102.47
PROPER(U21(x0, x1, U12(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.47
PROPER(U21(x0, x1, s(z0))) → c38(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.47
PROPER(U21(x0, x1, plus(z0, z1))) → c38(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.47
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.47
PROPER(U21(x0, x1, U22(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.47
PROPER(U21(x0, x1, x(z0, z1))) → c38(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.47
PROPER(U21(x0, x1, 0)) → c38(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1), PROPER(0)) 334.39/102.47
PROPER(U21(x0, U11(z0, z1, z2), x2)) → c38(U21'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U21(x0, tt, x2)) → c38(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(tt), PROPER(x2)) 334.39/102.47
PROPER(U21(x0, U12(z0, z1, z2), x2)) → c38(U21'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U21(x0, s(z0), x2)) → c38(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.47
PROPER(U21(x0, plus(z0, z1), x2)) → c38(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.47
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c38(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U21(x0, U22(z0, z1, z2), x2)) → c38(U21'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U21(x0, x(z0, z1), x2)) → c38(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.47
PROPER(U21(x0, 0, x2)) → c38(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(0), PROPER(x2)) 334.39/102.47
PROPER(U21(U11(z0, z1, z2), x1, x2)) → c38(U21'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U21(tt, x1, x2)) → c38(U21'(ok(tt), proper(x1), proper(x2)), PROPER(tt), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U21(U12(z0, z1, z2), x1, x2)) → c38(U21'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U21(s(z0), x1, x2)) → c38(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U21(plus(z0, z1), x1, x2)) → c38(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c38(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U21(U22(z0, z1, z2), x1, x2)) → c38(U21'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U21(x(z0, z1), x1, x2)) → c38(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U21(0, x1, x2)) → c38(U21'(ok(0), proper(x1), proper(x2)), PROPER(0), PROPER(x1), PROPER(x2))
S tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.39/102.47
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.39/102.47
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.39/102.47
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.39/102.47
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.39/102.47
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.39/102.47
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.39/102.47
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.39/102.47
S(mark(z0)) → c21(S(z0)) 334.39/102.47
S(ok(z0)) → c22(S(z0)) 334.39/102.47
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.39/102.47
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.39/102.47
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.39/102.47
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.39/102.47
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.39/102.47
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.39/102.47
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.39/102.47
X(mark(z0), z1) → c30(X(z0, z1)) 334.39/102.47
X(z0, mark(z1)) → c31(X(z0, z1)) 334.39/102.47
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.39/102.47
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.39/102.47
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.39/102.47
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.39/102.47
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.39/102.47
ACTIVE(U11(tt, z0, z1)) → c 334.39/102.47
ACTIVE(U21(tt, z0, z1)) → c2 334.39/102.47
ACTIVE(plus(z0, s(z1))) → c5 334.39/102.47
ACTIVE(x(z0, s(z1))) → c7 334.39/102.47
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.39/102.47
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.39/102.47
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.39/102.47
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.39/102.47
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.47
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.47
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.47
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.47
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.47
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.47
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.47
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.47
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.47
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.47
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.47
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.47
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.47
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.47
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.39/102.47
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.47
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.47
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.47
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.47
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.47
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.47
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.47
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.47
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.47
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.47
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.47
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.47
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.47
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.47
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.47
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.47
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.39/102.47
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.47
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.47
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.39/102.47
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.39/102.47
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.39/102.47
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.39/102.47
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.39/102.47
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.39/102.47
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.39/102.47
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.39/102.47
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.39/102.47
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.39/102.47
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.39/102.47
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.39/102.47
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.39/102.47
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.39/102.47
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.39/102.47
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.39/102.47
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.39/102.47
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.47
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.47
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.47
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.47
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.47
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.47
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.47
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.47
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.47
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.47
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.47
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.47
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.47
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.47
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.47
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.47
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.47
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.39/102.47
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.47
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.47
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.39/102.47
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.47
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.39/102.47
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.47
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.47
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.47
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.47
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.47
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.47
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.47
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.47
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.47
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.47
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.47
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.47
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.47
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.47
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.47
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.47
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.47
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.47
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.47
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.39/102.47
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.47
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.47
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.47
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.47
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.39/102.47
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.47
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.39/102.47
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.47
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.39/102.47
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.47
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.47
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.47
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.47
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.47
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.47
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.47
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.47
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.47
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.47
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.47
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.47
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.47
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.47
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.47
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.47
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.47
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.47
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.47
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.47
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.47
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.47
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.47
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.47
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.47
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.47
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.47
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.47
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.47
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.47
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.39/102.47
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.39/102.47
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.39/102.47
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.39/102.47
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.39/102.47
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.39/102.47
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.39/102.47
PROPER(s(tt)) → c36(S(ok(tt))) 334.39/102.47
PROPER(s(0)) → c36(S(ok(0))) 334.39/102.47
PROPER(plus(x0, U11(z0, z1, z2))) → c37(PLUS(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.39/102.47
PROPER(plus(x0, U12(z0, z1, z2))) → c37(PLUS(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.39/102.47
PROPER(plus(x0, s(z0))) → c37(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.39/102.47
PROPER(plus(x0, plus(z0, z1))) → c37(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.39/102.47
PROPER(plus(x0, U21(z0, z1, z2))) → c37(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.39/102.47
PROPER(plus(x0, U22(z0, z1, z2))) → c37(PLUS(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.39/102.47
PROPER(plus(x0, x(z0, z1))) → c37(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.39/102.47
PROPER(plus(U11(z0, z1, z2), x1)) → c37(PLUS(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.39/102.47
PROPER(plus(U12(z0, z1, z2), x1)) → c37(PLUS(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.39/102.47
PROPER(plus(s(z0), x1)) → c37(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.39/102.47
PROPER(plus(plus(z0, z1), x1)) → c37(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.39/102.47
PROPER(plus(U21(z0, z1, z2), x1)) → c37(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.39/102.47
PROPER(plus(U22(z0, z1, z2), x1)) → c37(PLUS(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.39/102.47
PROPER(plus(x(z0, z1), x1)) → c37(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.39/102.47
PROPER(plus(x0, tt)) → c37(PLUS(proper(x0), ok(tt)), PROPER(x0)) 334.39/102.47
PROPER(plus(x0, 0)) → c37(PLUS(proper(x0), ok(0)), PROPER(x0)) 334.39/102.47
PROPER(plus(tt, x1)) → c37(PLUS(ok(tt), proper(x1)), PROPER(x1)) 334.39/102.47
PROPER(plus(0, x1)) → c37(PLUS(ok(0), proper(x1)), PROPER(x1)) 334.39/102.47
PROPER(U21(x0, x1, U11(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.47
PROPER(U21(x0, x1, tt)) → c38(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1), PROPER(tt)) 334.39/102.47
PROPER(U21(x0, x1, U12(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.47
PROPER(U21(x0, x1, s(z0))) → c38(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.47
PROPER(U21(x0, x1, plus(z0, z1))) → c38(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.47
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.47
PROPER(U21(x0, x1, U22(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.47
PROPER(U21(x0, x1, x(z0, z1))) → c38(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.47
PROPER(U21(x0, x1, 0)) → c38(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1), PROPER(0)) 334.39/102.47
PROPER(U21(x0, U11(z0, z1, z2), x2)) → c38(U21'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U21(x0, tt, x2)) → c38(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(tt), PROPER(x2)) 334.39/102.47
PROPER(U21(x0, U12(z0, z1, z2), x2)) → c38(U21'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U21(x0, s(z0), x2)) → c38(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.47
PROPER(U21(x0, plus(z0, z1), x2)) → c38(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.47
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c38(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U21(x0, U22(z0, z1, z2), x2)) → c38(U21'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U21(x0, x(z0, z1), x2)) → c38(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.47
PROPER(U21(x0, 0, x2)) → c38(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(0), PROPER(x2)) 334.39/102.47
PROPER(U21(U11(z0, z1, z2), x1, x2)) → c38(U21'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U21(tt, x1, x2)) → c38(U21'(ok(tt), proper(x1), proper(x2)), PROPER(tt), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U21(U12(z0, z1, z2), x1, x2)) → c38(U21'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U21(s(z0), x1, x2)) → c38(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U21(plus(z0, z1), x1, x2)) → c38(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c38(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U21(U22(z0, z1, z2), x1, x2)) → c38(U21'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U21(x(z0, z1), x1, x2)) → c38(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U21(0, x1, x2)) → c38(U21'(ok(0), proper(x1), proper(x2)), PROPER(0), PROPER(x1), PROPER(x2))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c11, c12, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c39, c40, c42, c43, c, c2, c5, c7, c4, c8, c1, c9, c3, c10, c6, c13, c34, c14, c41, c33, c33, c35, c35, c36, c36, c37, c37, c38

334.39/102.47
334.39/102.47

(65) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 6 trailing tuple parts
334.39/102.47
334.39/102.47

(66) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.39/102.47
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.39/102.47
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.39/102.47
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.39/102.47
active(plus(z0, 0)) → mark(z0) 334.39/102.47
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.39/102.47
active(x(z0, 0)) → mark(0) 334.39/102.47
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.39/102.47
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.39/102.47
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.39/102.47
active(s(z0)) → s(active(z0)) 334.39/102.47
active(plus(z0, z1)) → plus(active(z0), z1) 334.39/102.47
active(plus(z0, z1)) → plus(z0, active(z1)) 334.39/102.47
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.39/102.47
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.39/102.47
active(x(z0, z1)) → x(active(z0), z1) 334.39/102.47
active(x(z0, z1)) → x(z0, active(z1)) 334.39/102.47
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.39/102.47
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.39/102.47
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.39/102.47
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.39/102.47
s(mark(z0)) → mark(s(z0)) 334.39/102.47
s(ok(z0)) → ok(s(z0)) 334.39/102.47
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.39/102.47
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.39/102.47
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.39/102.47
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.39/102.47
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.39/102.47
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.39/102.47
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.39/102.47
x(mark(z0), z1) → mark(x(z0, z1)) 334.39/102.47
x(z0, mark(z1)) → mark(x(z0, z1)) 334.39/102.47
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.39/102.47
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.39/102.47
proper(tt) → ok(tt) 334.39/102.47
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.39/102.47
proper(s(z0)) → s(proper(z0)) 334.39/102.47
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.39/102.47
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.39/102.47
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.39/102.47
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.39/102.47
proper(0) → ok(0) 334.39/102.47
top(mark(z0)) → top(proper(z0)) 334.39/102.47
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.39/102.47
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.39/102.47
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.39/102.47
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.39/102.47
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.39/102.47
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.39/102.47
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.39/102.47
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.39/102.47
S(mark(z0)) → c21(S(z0)) 334.39/102.47
S(ok(z0)) → c22(S(z0)) 334.39/102.47
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.39/102.47
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.39/102.47
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.39/102.47
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.39/102.47
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.39/102.47
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.39/102.47
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.39/102.47
X(mark(z0), z1) → c30(X(z0, z1)) 334.39/102.47
X(z0, mark(z1)) → c31(X(z0, z1)) 334.39/102.47
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.39/102.47
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.39/102.47
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.39/102.47
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.39/102.47
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.39/102.47
ACTIVE(U11(tt, z0, z1)) → c 334.39/102.47
ACTIVE(U21(tt, z0, z1)) → c2 334.39/102.47
ACTIVE(plus(z0, s(z1))) → c5 334.39/102.47
ACTIVE(x(z0, s(z1))) → c7 334.39/102.47
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.39/102.47
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.39/102.47
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.39/102.47
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.39/102.47
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.47
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.47
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.47
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.47
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.47
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.47
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.47
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.47
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.47
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.47
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.47
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.47
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.47
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.47
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.39/102.47
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.47
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.47
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.47
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.47
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.47
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.47
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.47
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.47
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.47
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.47
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.47
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.47
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.47
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.47
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.47
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.47
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.39/102.47
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.47
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.47
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.39/102.47
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.39/102.47
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.39/102.47
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.39/102.47
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.39/102.47
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.39/102.47
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.39/102.47
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.39/102.47
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.39/102.47
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.39/102.47
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.39/102.47
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.39/102.47
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.39/102.47
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.39/102.47
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.39/102.47
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.39/102.47
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.39/102.47
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.47
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.47
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.47
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.47
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.47
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.47
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.47
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.47
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.47
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.47
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.47
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.47
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.47
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.47
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.47
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.47
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.47
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.39/102.47
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.47
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.47
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.39/102.47
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.47
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.39/102.47
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.47
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.47
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.47
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.47
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.47
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.47
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.47
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.47
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.47
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.47
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.47
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.47
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.47
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.47
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.47
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.47
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.47
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.47
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.47
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.39/102.47
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.47
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.47
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.47
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.47
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.39/102.47
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.47
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.39/102.47
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.47
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.39/102.47
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.47
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.47
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.47
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.47
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.47
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.47
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.47
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.47
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.47
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.47
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.47
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.47
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.47
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.47
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.47
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.47
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.47
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.47
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.47
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.47
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.47
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.47
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.47
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.47
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.47
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.47
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.47
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.47
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.47
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.47
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.39/102.47
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.39/102.47
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.39/102.47
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.39/102.47
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.39/102.47
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.39/102.47
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.39/102.47
PROPER(s(tt)) → c36(S(ok(tt))) 334.39/102.47
PROPER(s(0)) → c36(S(ok(0))) 334.39/102.47
PROPER(plus(x0, U11(z0, z1, z2))) → c37(PLUS(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.39/102.47
PROPER(plus(x0, U12(z0, z1, z2))) → c37(PLUS(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.39/102.47
PROPER(plus(x0, s(z0))) → c37(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.39/102.47
PROPER(plus(x0, plus(z0, z1))) → c37(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.39/102.47
PROPER(plus(x0, U21(z0, z1, z2))) → c37(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.39/102.47
PROPER(plus(x0, U22(z0, z1, z2))) → c37(PLUS(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.39/102.47
PROPER(plus(x0, x(z0, z1))) → c37(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.39/102.47
PROPER(plus(U11(z0, z1, z2), x1)) → c37(PLUS(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.39/102.47
PROPER(plus(U12(z0, z1, z2), x1)) → c37(PLUS(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.39/102.47
PROPER(plus(s(z0), x1)) → c37(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.39/102.47
PROPER(plus(plus(z0, z1), x1)) → c37(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.39/102.47
PROPER(plus(U21(z0, z1, z2), x1)) → c37(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.39/102.47
PROPER(plus(U22(z0, z1, z2), x1)) → c37(PLUS(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.39/102.47
PROPER(plus(x(z0, z1), x1)) → c37(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.39/102.47
PROPER(plus(x0, tt)) → c37(PLUS(proper(x0), ok(tt)), PROPER(x0)) 334.39/102.47
PROPER(plus(x0, 0)) → c37(PLUS(proper(x0), ok(0)), PROPER(x0)) 334.39/102.47
PROPER(plus(tt, x1)) → c37(PLUS(ok(tt), proper(x1)), PROPER(x1)) 334.39/102.47
PROPER(plus(0, x1)) → c37(PLUS(ok(0), proper(x1)), PROPER(x1)) 334.39/102.47
PROPER(U21(x0, x1, U11(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.47
PROPER(U21(x0, x1, U12(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.47
PROPER(U21(x0, x1, s(z0))) → c38(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.47
PROPER(U21(x0, x1, plus(z0, z1))) → c38(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.47
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.47
PROPER(U21(x0, x1, U22(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.47
PROPER(U21(x0, x1, x(z0, z1))) → c38(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.47
PROPER(U21(x0, U11(z0, z1, z2), x2)) → c38(U21'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U21(x0, U12(z0, z1, z2), x2)) → c38(U21'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U21(x0, s(z0), x2)) → c38(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.47
PROPER(U21(x0, plus(z0, z1), x2)) → c38(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.47
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c38(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U21(x0, U22(z0, z1, z2), x2)) → c38(U21'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.47
PROPER(U21(x0, x(z0, z1), x2)) → c38(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.47
PROPER(U21(U11(z0, z1, z2), x1, x2)) → c38(U21'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U21(U12(z0, z1, z2), x1, x2)) → c38(U21'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U21(s(z0), x1, x2)) → c38(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U21(plus(z0, z1), x1, x2)) → c38(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.47
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c38(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U21(U22(z0, z1, z2), x1, x2)) → c38(U21'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U21(x(z0, z1), x1, x2)) → c38(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U21(x0, x1, tt)) → c38(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.48
PROPER(U21(x0, x1, 0)) → c38(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.48
PROPER(U21(x0, tt, x2)) → c38(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.48
PROPER(U21(x0, 0, x2)) → c38(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.48
PROPER(U21(tt, x1, x2)) → c38(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U21(0, x1, x2)) → c38(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
S tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.39/102.48
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.39/102.48
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.39/102.48
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.39/102.48
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.39/102.48
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.39/102.48
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.39/102.48
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.39/102.48
S(mark(z0)) → c21(S(z0)) 334.39/102.48
S(ok(z0)) → c22(S(z0)) 334.39/102.48
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.39/102.48
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.39/102.48
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.39/102.48
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.39/102.48
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.39/102.48
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.39/102.48
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.39/102.48
X(mark(z0), z1) → c30(X(z0, z1)) 334.39/102.48
X(z0, mark(z1)) → c31(X(z0, z1)) 334.39/102.48
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.39/102.48
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.39/102.48
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.39/102.48
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.39/102.48
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.39/102.48
ACTIVE(U11(tt, z0, z1)) → c 334.39/102.48
ACTIVE(U21(tt, z0, z1)) → c2 334.39/102.48
ACTIVE(plus(z0, s(z1))) → c5 334.39/102.48
ACTIVE(x(z0, s(z1))) → c7 334.39/102.48
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.39/102.48
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.39/102.48
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.39/102.48
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.39/102.48
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.48
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.48
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.48
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.48
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.48
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.48
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.48
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.48
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.48
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.48
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.39/102.48
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.48
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.48
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.48
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.48
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.48
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.48
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.48
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.48
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.48
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.48
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.48
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.48
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.39/102.48
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.48
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.48
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.39/102.48
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.39/102.48
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.39/102.48
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.39/102.48
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.39/102.48
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.39/102.48
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.39/102.48
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.39/102.48
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.39/102.48
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.39/102.48
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.39/102.48
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.39/102.48
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.39/102.48
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.48
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.48
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.48
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.48
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.48
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.48
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.48
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.48
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.48
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.48
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.48
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.48
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.48
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.39/102.48
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.48
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.48
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.39/102.48
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.48
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.39/102.48
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.48
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.48
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.48
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.48
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.48
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.48
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.48
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.48
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.48
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.48
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.48
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.48
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.48
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.48
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.48
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.39/102.48
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.48
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.48
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.48
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.48
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.39/102.48
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.48
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.39/102.48
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.48
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.39/102.48
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.48
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.48
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.48
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.48
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.48
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.48
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.48
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.48
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.48
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.48
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.48
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.48
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.48
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.48
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.48
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.48
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.48
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.48
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.48
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.48
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.48
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.48
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.48
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.48
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.48
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.48
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.48
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.48
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.48
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.48
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.39/102.48
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.39/102.48
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.39/102.48
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.39/102.48
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.39/102.48
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.39/102.48
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.39/102.48
PROPER(s(tt)) → c36(S(ok(tt))) 334.39/102.48
PROPER(s(0)) → c36(S(ok(0))) 334.39/102.48
PROPER(plus(x0, U11(z0, z1, z2))) → c37(PLUS(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.39/102.48
PROPER(plus(x0, U12(z0, z1, z2))) → c37(PLUS(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.39/102.48
PROPER(plus(x0, s(z0))) → c37(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.39/102.48
PROPER(plus(x0, plus(z0, z1))) → c37(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.39/102.48
PROPER(plus(x0, U21(z0, z1, z2))) → c37(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.39/102.48
PROPER(plus(x0, U22(z0, z1, z2))) → c37(PLUS(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.39/102.48
PROPER(plus(x0, x(z0, z1))) → c37(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.39/102.48
PROPER(plus(U11(z0, z1, z2), x1)) → c37(PLUS(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.39/102.48
PROPER(plus(U12(z0, z1, z2), x1)) → c37(PLUS(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.39/102.48
PROPER(plus(s(z0), x1)) → c37(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.39/102.48
PROPER(plus(plus(z0, z1), x1)) → c37(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.39/102.48
PROPER(plus(U21(z0, z1, z2), x1)) → c37(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.39/102.48
PROPER(plus(U22(z0, z1, z2), x1)) → c37(PLUS(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.39/102.48
PROPER(plus(x(z0, z1), x1)) → c37(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.39/102.48
PROPER(plus(x0, tt)) → c37(PLUS(proper(x0), ok(tt)), PROPER(x0)) 334.39/102.48
PROPER(plus(x0, 0)) → c37(PLUS(proper(x0), ok(0)), PROPER(x0)) 334.39/102.48
PROPER(plus(tt, x1)) → c37(PLUS(ok(tt), proper(x1)), PROPER(x1)) 334.39/102.48
PROPER(plus(0, x1)) → c37(PLUS(ok(0), proper(x1)), PROPER(x1)) 334.39/102.48
PROPER(U21(x0, x1, U11(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.48
PROPER(U21(x0, x1, U12(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.48
PROPER(U21(x0, x1, s(z0))) → c38(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.48
PROPER(U21(x0, x1, plus(z0, z1))) → c38(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.48
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.48
PROPER(U21(x0, x1, U22(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.48
PROPER(U21(x0, x1, x(z0, z1))) → c38(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.48
PROPER(U21(x0, U11(z0, z1, z2), x2)) → c38(U21'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U21(x0, U12(z0, z1, z2), x2)) → c38(U21'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U21(x0, s(z0), x2)) → c38(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.48
PROPER(U21(x0, plus(z0, z1), x2)) → c38(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.48
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c38(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U21(x0, U22(z0, z1, z2), x2)) → c38(U21'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U21(x0, x(z0, z1), x2)) → c38(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.48
PROPER(U21(U11(z0, z1, z2), x1, x2)) → c38(U21'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U21(U12(z0, z1, z2), x1, x2)) → c38(U21'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U21(s(z0), x1, x2)) → c38(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U21(plus(z0, z1), x1, x2)) → c38(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c38(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U21(U22(z0, z1, z2), x1, x2)) → c38(U21'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U21(x(z0, z1), x1, x2)) → c38(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U21(x0, x1, tt)) → c38(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.48
PROPER(U21(x0, x1, 0)) → c38(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.48
PROPER(U21(x0, tt, x2)) → c38(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.48
PROPER(U21(x0, 0, x2)) → c38(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.48
PROPER(U21(tt, x1, x2)) → c38(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U21(0, x1, x2)) → c38(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c11, c12, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c39, c40, c42, c43, c, c2, c5, c7, c4, c8, c1, c9, c3, c10, c6, c13, c34, c14, c41, c33, c33, c35, c35, c36, c36, c37, c37, c38, c38

334.39/102.48
334.39/102.48

(67) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

Removed 14 trailing nodes:

ACTIVE(x(z0, s(z1))) → c7 334.39/102.48
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.39/102.48
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.39/102.48
ACTIVE(U11(tt, z0, z1)) → c 334.39/102.48
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.39/102.48
ACTIVE(U21(tt, z0, z1)) → c2 334.39/102.48
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.39/102.48
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.39/102.48
ACTIVE(plus(z0, s(z1))) → c5 334.39/102.48
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.48
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.39/102.48
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.48
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.48
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1)))
334.39/102.48
334.39/102.48

(68) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.39/102.48
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.39/102.48
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.39/102.48
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.39/102.48
active(plus(z0, 0)) → mark(z0) 334.39/102.48
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.39/102.48
active(x(z0, 0)) → mark(0) 334.39/102.48
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.39/102.48
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.39/102.48
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.39/102.48
active(s(z0)) → s(active(z0)) 334.39/102.48
active(plus(z0, z1)) → plus(active(z0), z1) 334.39/102.48
active(plus(z0, z1)) → plus(z0, active(z1)) 334.39/102.48
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.39/102.48
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.39/102.48
active(x(z0, z1)) → x(active(z0), z1) 334.39/102.48
active(x(z0, z1)) → x(z0, active(z1)) 334.39/102.48
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.39/102.48
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.39/102.48
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.39/102.48
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.39/102.48
s(mark(z0)) → mark(s(z0)) 334.39/102.48
s(ok(z0)) → ok(s(z0)) 334.39/102.48
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.39/102.48
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.39/102.48
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.39/102.48
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.39/102.48
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.39/102.48
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.39/102.48
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.39/102.48
x(mark(z0), z1) → mark(x(z0, z1)) 334.39/102.48
x(z0, mark(z1)) → mark(x(z0, z1)) 334.39/102.48
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.39/102.48
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.39/102.48
proper(tt) → ok(tt) 334.39/102.48
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.39/102.48
proper(s(z0)) → s(proper(z0)) 334.39/102.48
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.39/102.48
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.39/102.48
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.39/102.48
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.39/102.48
proper(0) → ok(0) 334.39/102.48
top(mark(z0)) → top(proper(z0)) 334.39/102.48
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.39/102.48
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.39/102.48
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.39/102.48
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.39/102.48
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.39/102.48
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.39/102.48
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.39/102.48
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.39/102.48
S(mark(z0)) → c21(S(z0)) 334.39/102.48
S(ok(z0)) → c22(S(z0)) 334.39/102.48
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.39/102.48
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.39/102.48
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.39/102.48
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.39/102.48
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.39/102.48
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.39/102.48
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.39/102.48
X(mark(z0), z1) → c30(X(z0, z1)) 334.39/102.48
X(z0, mark(z1)) → c31(X(z0, z1)) 334.39/102.48
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.39/102.48
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.39/102.48
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.39/102.48
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.39/102.48
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.39/102.48
ACTIVE(U11(tt, z0, z1)) → c 334.39/102.48
ACTIVE(U21(tt, z0, z1)) → c2 334.39/102.48
ACTIVE(plus(z0, s(z1))) → c5 334.39/102.48
ACTIVE(x(z0, s(z1))) → c7 334.39/102.48
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.39/102.48
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.39/102.48
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.39/102.48
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.39/102.48
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.48
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.48
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.48
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.48
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.48
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.48
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.48
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.48
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.48
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.48
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.39/102.48
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.48
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.48
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.48
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.48
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.48
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.48
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.48
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.48
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.48
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.48
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.48
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.48
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.39/102.48
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.48
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.48
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.39/102.48
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.39/102.48
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.39/102.48
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.39/102.48
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.39/102.48
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.39/102.48
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.39/102.48
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.39/102.48
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.39/102.48
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.39/102.48
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.39/102.48
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.39/102.48
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.39/102.48
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.48
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.48
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.48
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.48
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.48
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.48
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.48
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.48
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.48
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.48
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.48
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.48
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.48
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.39/102.48
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.48
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.48
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.39/102.48
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.48
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.39/102.48
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.48
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.48
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.48
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.48
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.48
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.48
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.48
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.48
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.48
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.48
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.48
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.48
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.48
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.48
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.48
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.39/102.48
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.48
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.48
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.48
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.48
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.39/102.48
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.48
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.39/102.48
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.48
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.39/102.48
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.48
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.48
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.48
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.48
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.48
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.48
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.48
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.48
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.48
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.48
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.48
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.48
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.48
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.48
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.48
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.48
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.48
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.48
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.48
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.48
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.48
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.48
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.48
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.48
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.48
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.48
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.48
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.48
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.48
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.48
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.39/102.48
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.39/102.48
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.39/102.48
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.39/102.48
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.39/102.48
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.39/102.48
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.39/102.48
PROPER(s(tt)) → c36(S(ok(tt))) 334.39/102.48
PROPER(s(0)) → c36(S(ok(0))) 334.39/102.48
PROPER(plus(x0, U11(z0, z1, z2))) → c37(PLUS(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.39/102.48
PROPER(plus(x0, U12(z0, z1, z2))) → c37(PLUS(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.39/102.48
PROPER(plus(x0, s(z0))) → c37(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.39/102.48
PROPER(plus(x0, plus(z0, z1))) → c37(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.39/102.48
PROPER(plus(x0, U21(z0, z1, z2))) → c37(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.39/102.48
PROPER(plus(x0, U22(z0, z1, z2))) → c37(PLUS(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.39/102.48
PROPER(plus(x0, x(z0, z1))) → c37(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.39/102.48
PROPER(plus(U11(z0, z1, z2), x1)) → c37(PLUS(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.39/102.48
PROPER(plus(U12(z0, z1, z2), x1)) → c37(PLUS(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.39/102.48
PROPER(plus(s(z0), x1)) → c37(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.39/102.48
PROPER(plus(plus(z0, z1), x1)) → c37(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.39/102.48
PROPER(plus(U21(z0, z1, z2), x1)) → c37(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.39/102.48
PROPER(plus(U22(z0, z1, z2), x1)) → c37(PLUS(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.39/102.48
PROPER(plus(x(z0, z1), x1)) → c37(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.39/102.48
PROPER(plus(x0, tt)) → c37(PLUS(proper(x0), ok(tt)), PROPER(x0)) 334.39/102.48
PROPER(plus(x0, 0)) → c37(PLUS(proper(x0), ok(0)), PROPER(x0)) 334.39/102.48
PROPER(plus(tt, x1)) → c37(PLUS(ok(tt), proper(x1)), PROPER(x1)) 334.39/102.48
PROPER(plus(0, x1)) → c37(PLUS(ok(0), proper(x1)), PROPER(x1)) 334.39/102.48
PROPER(U21(x0, x1, U11(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.48
PROPER(U21(x0, x1, U12(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.48
PROPER(U21(x0, x1, s(z0))) → c38(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.48
PROPER(U21(x0, x1, plus(z0, z1))) → c38(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.48
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.48
PROPER(U21(x0, x1, U22(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.48
PROPER(U21(x0, x1, x(z0, z1))) → c38(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.48
PROPER(U21(x0, U11(z0, z1, z2), x2)) → c38(U21'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U21(x0, U12(z0, z1, z2), x2)) → c38(U21'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U21(x0, s(z0), x2)) → c38(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.48
PROPER(U21(x0, plus(z0, z1), x2)) → c38(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.48
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c38(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U21(x0, U22(z0, z1, z2), x2)) → c38(U21'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U21(x0, x(z0, z1), x2)) → c38(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.48
PROPER(U21(U11(z0, z1, z2), x1, x2)) → c38(U21'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U21(U12(z0, z1, z2), x1, x2)) → c38(U21'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U21(s(z0), x1, x2)) → c38(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U21(plus(z0, z1), x1, x2)) → c38(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c38(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U21(U22(z0, z1, z2), x1, x2)) → c38(U21'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U21(x(z0, z1), x1, x2)) → c38(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U21(x0, x1, tt)) → c38(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.48
PROPER(U21(x0, x1, 0)) → c38(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.48
PROPER(U21(x0, tt, x2)) → c38(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.48
PROPER(U21(x0, 0, x2)) → c38(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.48
PROPER(U21(tt, x1, x2)) → c38(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U21(0, x1, x2)) → c38(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
S tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.39/102.48
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.39/102.48
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.39/102.48
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.39/102.48
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.39/102.48
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.39/102.48
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.39/102.48
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.39/102.48
S(mark(z0)) → c21(S(z0)) 334.39/102.48
S(ok(z0)) → c22(S(z0)) 334.39/102.48
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.39/102.48
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.39/102.48
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.39/102.48
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.39/102.48
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.39/102.48
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.39/102.48
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.39/102.48
X(mark(z0), z1) → c30(X(z0, z1)) 334.39/102.48
X(z0, mark(z1)) → c31(X(z0, z1)) 334.39/102.48
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.39/102.48
PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 334.39/102.48
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.39/102.48
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.39/102.48
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.39/102.48
ACTIVE(U11(tt, z0, z1)) → c 334.39/102.48
ACTIVE(U21(tt, z0, z1)) → c2 334.39/102.48
ACTIVE(plus(z0, s(z1))) → c5 334.39/102.48
ACTIVE(x(z0, s(z1))) → c7 334.39/102.48
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.39/102.48
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.39/102.48
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.39/102.48
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.39/102.48
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.48
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.48
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.48
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.48
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.48
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.48
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.48
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.48
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.48
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.48
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.39/102.48
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.48
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.48
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.48
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.48
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.48
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.48
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.48
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.48
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.48
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.48
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.48
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.48
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.39/102.48
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.48
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.48
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.39/102.48
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.39/102.48
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.39/102.48
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.39/102.48
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.39/102.48
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.39/102.48
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.39/102.48
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.39/102.48
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.39/102.48
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.39/102.48
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.39/102.48
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.39/102.48
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.39/102.48
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.48
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.48
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.48
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.48
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.48
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.48
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.48
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.48
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.48
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.48
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.48
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.48
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.48
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.39/102.48
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.48
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.48
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.39/102.48
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.48
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.39/102.48
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.48
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.48
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.48
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.48
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.48
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.48
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.48
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.48
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.48
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.48
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.48
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.48
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.48
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.48
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.48
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.39/102.48
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.48
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.48
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.48
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.48
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.39/102.48
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.48
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.39/102.48
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.48
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.39/102.48
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.48
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.48
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.48
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.48
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.48
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.48
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.48
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.48
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.48
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.48
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.48
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.48
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.48
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.48
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.48
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.48
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.48
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.48
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.48
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.48
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.48
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.48
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.48
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.48
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.48
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.48
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.48
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.48
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.48
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.48
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.39/102.48
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.39/102.48
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.39/102.48
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.39/102.48
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.39/102.48
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.39/102.48
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.39/102.48
PROPER(s(tt)) → c36(S(ok(tt))) 334.39/102.48
PROPER(s(0)) → c36(S(ok(0))) 334.39/102.48
PROPER(plus(x0, U11(z0, z1, z2))) → c37(PLUS(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.39/102.48
PROPER(plus(x0, U12(z0, z1, z2))) → c37(PLUS(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.39/102.48
PROPER(plus(x0, s(z0))) → c37(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.39/102.48
PROPER(plus(x0, plus(z0, z1))) → c37(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.39/102.48
PROPER(plus(x0, U21(z0, z1, z2))) → c37(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.39/102.48
PROPER(plus(x0, U22(z0, z1, z2))) → c37(PLUS(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.39/102.48
PROPER(plus(x0, x(z0, z1))) → c37(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.39/102.48
PROPER(plus(U11(z0, z1, z2), x1)) → c37(PLUS(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.39/102.48
PROPER(plus(U12(z0, z1, z2), x1)) → c37(PLUS(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.39/102.48
PROPER(plus(s(z0), x1)) → c37(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.39/102.48
PROPER(plus(plus(z0, z1), x1)) → c37(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.39/102.48
PROPER(plus(U21(z0, z1, z2), x1)) → c37(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.39/102.48
PROPER(plus(U22(z0, z1, z2), x1)) → c37(PLUS(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.39/102.48
PROPER(plus(x(z0, z1), x1)) → c37(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.39/102.48
PROPER(plus(x0, tt)) → c37(PLUS(proper(x0), ok(tt)), PROPER(x0)) 334.39/102.48
PROPER(plus(x0, 0)) → c37(PLUS(proper(x0), ok(0)), PROPER(x0)) 334.39/102.48
PROPER(plus(tt, x1)) → c37(PLUS(ok(tt), proper(x1)), PROPER(x1)) 334.39/102.48
PROPER(plus(0, x1)) → c37(PLUS(ok(0), proper(x1)), PROPER(x1)) 334.39/102.48
PROPER(U21(x0, x1, U11(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.48
PROPER(U21(x0, x1, U12(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.48
PROPER(U21(x0, x1, s(z0))) → c38(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.48
PROPER(U21(x0, x1, plus(z0, z1))) → c38(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.48
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.48
PROPER(U21(x0, x1, U22(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.48
PROPER(U21(x0, x1, x(z0, z1))) → c38(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.48
PROPER(U21(x0, U11(z0, z1, z2), x2)) → c38(U21'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U21(x0, U12(z0, z1, z2), x2)) → c38(U21'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U21(x0, s(z0), x2)) → c38(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.48
PROPER(U21(x0, plus(z0, z1), x2)) → c38(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.48
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c38(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U21(x0, U22(z0, z1, z2), x2)) → c38(U21'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U21(x0, x(z0, z1), x2)) → c38(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.48
PROPER(U21(U11(z0, z1, z2), x1, x2)) → c38(U21'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U21(U12(z0, z1, z2), x1, x2)) → c38(U21'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U21(s(z0), x1, x2)) → c38(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U21(plus(z0, z1), x1, x2)) → c38(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c38(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U21(U22(z0, z1, z2), x1, x2)) → c38(U21'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U21(x(z0, z1), x1, x2)) → c38(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U21(x0, x1, tt)) → c38(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.48
PROPER(U21(x0, x1, 0)) → c38(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.48
PROPER(U21(x0, tt, x2)) → c38(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.48
PROPER(U21(x0, 0, x2)) → c38(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.48
PROPER(U21(tt, x1, x2)) → c38(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U21(0, x1, x2)) → c38(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c11, c12, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c39, c40, c42, c43, c, c2, c5, c7, c4, c8, c1, c9, c3, c10, c6, c13, c34, c14, c41, c33, c33, c35, c35, c36, c36, c37, c37, c38, c38

334.39/102.48
334.39/102.48

(69) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace PROPER(U22(z0, z1, z2)) → c39(U22'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) by

PROPER(U22(x0, x1, U11(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.48
PROPER(U22(x0, x1, tt)) → c39(U22'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1), PROPER(tt)) 334.39/102.48
PROPER(U22(x0, x1, U12(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.48
PROPER(U22(x0, x1, s(z0))) → c39(U22'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.48
PROPER(U22(x0, x1, plus(z0, z1))) → c39(U22'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.48
PROPER(U22(x0, x1, U21(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.48
PROPER(U22(x0, x1, U22(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.48
PROPER(U22(x0, x1, x(z0, z1))) → c39(U22'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.48
PROPER(U22(x0, x1, 0)) → c39(U22'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1), PROPER(0)) 334.39/102.48
PROPER(U22(x0, U11(z0, z1, z2), x2)) → c39(U22'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U22(x0, tt, x2)) → c39(U22'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(tt), PROPER(x2)) 334.39/102.48
PROPER(U22(x0, U12(z0, z1, z2), x2)) → c39(U22'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U22(x0, s(z0), x2)) → c39(U22'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.48
PROPER(U22(x0, plus(z0, z1), x2)) → c39(U22'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.48
PROPER(U22(x0, U21(z0, z1, z2), x2)) → c39(U22'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U22(x0, U22(z0, z1, z2), x2)) → c39(U22'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U22(x0, x(z0, z1), x2)) → c39(U22'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.48
PROPER(U22(x0, 0, x2)) → c39(U22'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(0), PROPER(x2)) 334.39/102.48
PROPER(U22(U11(z0, z1, z2), x1, x2)) → c39(U22'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U22(tt, x1, x2)) → c39(U22'(ok(tt), proper(x1), proper(x2)), PROPER(tt), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U22(U12(z0, z1, z2), x1, x2)) → c39(U22'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U22(s(z0), x1, x2)) → c39(U22'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U22(plus(z0, z1), x1, x2)) → c39(U22'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U22(U21(z0, z1, z2), x1, x2)) → c39(U22'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U22(U22(z0, z1, z2), x1, x2)) → c39(U22'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U22(x(z0, z1), x1, x2)) → c39(U22'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U22(0, x1, x2)) → c39(U22'(ok(0), proper(x1), proper(x2)), PROPER(0), PROPER(x1), PROPER(x2))
334.39/102.48
334.39/102.48

(70) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.39/102.48
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.39/102.48
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.39/102.48
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.39/102.48
active(plus(z0, 0)) → mark(z0) 334.39/102.48
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.39/102.48
active(x(z0, 0)) → mark(0) 334.39/102.48
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.39/102.48
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.39/102.48
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.39/102.48
active(s(z0)) → s(active(z0)) 334.39/102.48
active(plus(z0, z1)) → plus(active(z0), z1) 334.39/102.48
active(plus(z0, z1)) → plus(z0, active(z1)) 334.39/102.48
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.39/102.48
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.39/102.48
active(x(z0, z1)) → x(active(z0), z1) 334.39/102.48
active(x(z0, z1)) → x(z0, active(z1)) 334.39/102.48
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.39/102.48
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.39/102.48
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.39/102.48
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.39/102.48
s(mark(z0)) → mark(s(z0)) 334.39/102.48
s(ok(z0)) → ok(s(z0)) 334.39/102.48
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.39/102.48
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.39/102.48
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.39/102.48
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.39/102.48
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.39/102.48
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.39/102.48
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.39/102.48
x(mark(z0), z1) → mark(x(z0, z1)) 334.39/102.48
x(z0, mark(z1)) → mark(x(z0, z1)) 334.39/102.48
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.39/102.48
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.39/102.48
proper(tt) → ok(tt) 334.39/102.48
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.39/102.48
proper(s(z0)) → s(proper(z0)) 334.39/102.48
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.39/102.48
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.39/102.48
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.39/102.48
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.39/102.48
proper(0) → ok(0) 334.39/102.48
top(mark(z0)) → top(proper(z0)) 334.39/102.48
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.39/102.48
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.39/102.48
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.39/102.48
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.39/102.48
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.39/102.48
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.39/102.48
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.39/102.48
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.39/102.48
S(mark(z0)) → c21(S(z0)) 334.39/102.48
S(ok(z0)) → c22(S(z0)) 334.39/102.48
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.39/102.48
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.39/102.48
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.39/102.48
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.39/102.48
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.39/102.48
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.39/102.48
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.39/102.48
X(mark(z0), z1) → c30(X(z0, z1)) 334.39/102.48
X(z0, mark(z1)) → c31(X(z0, z1)) 334.39/102.48
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.39/102.48
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.39/102.48
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.39/102.48
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.39/102.48
ACTIVE(U11(tt, z0, z1)) → c 334.39/102.48
ACTIVE(U21(tt, z0, z1)) → c2 334.39/102.48
ACTIVE(plus(z0, s(z1))) → c5 334.39/102.48
ACTIVE(x(z0, s(z1))) → c7 334.39/102.48
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.39/102.48
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.39/102.48
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.39/102.48
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.39/102.48
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.48
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.48
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.48
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.48
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.48
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.48
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.48
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.48
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.48
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.48
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.39/102.48
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.48
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.48
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.48
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.48
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.48
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.48
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.48
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.48
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.48
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.48
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.48
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.48
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.39/102.48
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.48
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.48
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.39/102.48
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.39/102.48
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.39/102.48
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.39/102.48
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.39/102.48
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.39/102.48
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.39/102.48
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.39/102.48
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.39/102.48
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.39/102.48
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.39/102.48
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.39/102.48
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.39/102.48
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.48
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.48
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.48
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.48
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.48
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.48
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.48
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.48
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.48
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.48
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.48
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.48
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.48
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.39/102.48
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.48
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.48
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.39/102.48
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.48
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.39/102.48
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.48
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.48
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.48
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.48
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.48
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.48
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.48
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.48
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.48
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.48
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.48
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.48
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.48
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.48
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.48
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.48
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.48
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.39/102.48
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.48
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.48
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.48
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.48
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.39/102.48
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.48
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.39/102.48
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.48
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.39/102.48
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.48
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.48
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.48
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.48
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.48
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.48
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.48
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.48
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.48
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.48
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.48
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.48
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.48
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.48
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.48
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.48
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.48
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.48
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.48
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.48
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.48
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.48
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.48
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.48
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.48
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.48
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.48
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.48
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.48
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.48
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.39/102.48
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.39/102.48
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.39/102.48
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.39/102.48
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.39/102.48
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.39/102.48
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.39/102.48
PROPER(s(tt)) → c36(S(ok(tt))) 334.39/102.48
PROPER(s(0)) → c36(S(ok(0))) 334.39/102.48
PROPER(plus(x0, U11(z0, z1, z2))) → c37(PLUS(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.39/102.48
PROPER(plus(x0, U12(z0, z1, z2))) → c37(PLUS(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.39/102.48
PROPER(plus(x0, s(z0))) → c37(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.39/102.48
PROPER(plus(x0, plus(z0, z1))) → c37(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.39/102.48
PROPER(plus(x0, U21(z0, z1, z2))) → c37(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.39/102.48
PROPER(plus(x0, U22(z0, z1, z2))) → c37(PLUS(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.39/102.48
PROPER(plus(x0, x(z0, z1))) → c37(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.39/102.48
PROPER(plus(U11(z0, z1, z2), x1)) → c37(PLUS(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.39/102.48
PROPER(plus(U12(z0, z1, z2), x1)) → c37(PLUS(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.39/102.48
PROPER(plus(s(z0), x1)) → c37(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.39/102.48
PROPER(plus(plus(z0, z1), x1)) → c37(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.39/102.48
PROPER(plus(U21(z0, z1, z2), x1)) → c37(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.39/102.48
PROPER(plus(U22(z0, z1, z2), x1)) → c37(PLUS(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.39/102.48
PROPER(plus(x(z0, z1), x1)) → c37(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.39/102.48
PROPER(plus(x0, tt)) → c37(PLUS(proper(x0), ok(tt)), PROPER(x0)) 334.39/102.48
PROPER(plus(x0, 0)) → c37(PLUS(proper(x0), ok(0)), PROPER(x0)) 334.39/102.48
PROPER(plus(tt, x1)) → c37(PLUS(ok(tt), proper(x1)), PROPER(x1)) 334.39/102.48
PROPER(plus(0, x1)) → c37(PLUS(ok(0), proper(x1)), PROPER(x1)) 334.39/102.48
PROPER(U21(x0, x1, U11(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.48
PROPER(U21(x0, x1, U12(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.48
PROPER(U21(x0, x1, s(z0))) → c38(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.48
PROPER(U21(x0, x1, plus(z0, z1))) → c38(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.48
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.48
PROPER(U21(x0, x1, U22(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.48
PROPER(U21(x0, x1, x(z0, z1))) → c38(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.48
PROPER(U21(x0, U11(z0, z1, z2), x2)) → c38(U21'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U21(x0, U12(z0, z1, z2), x2)) → c38(U21'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U21(x0, s(z0), x2)) → c38(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.48
PROPER(U21(x0, plus(z0, z1), x2)) → c38(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.48
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c38(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U21(x0, U22(z0, z1, z2), x2)) → c38(U21'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.48
PROPER(U21(x0, x(z0, z1), x2)) → c38(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.48
PROPER(U21(U11(z0, z1, z2), x1, x2)) → c38(U21'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U21(U12(z0, z1, z2), x1, x2)) → c38(U21'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U21(s(z0), x1, x2)) → c38(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U21(plus(z0, z1), x1, x2)) → c38(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c38(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U21(U22(z0, z1, z2), x1, x2)) → c38(U21'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U21(x(z0, z1), x1, x2)) → c38(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U21(x0, x1, tt)) → c38(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.48
PROPER(U21(x0, x1, 0)) → c38(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.48
PROPER(U21(x0, tt, x2)) → c38(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.48
PROPER(U21(x0, 0, x2)) → c38(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.48
PROPER(U21(tt, x1, x2)) → c38(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U21(0, x1, x2)) → c38(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.48
PROPER(U22(x0, x1, U11(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.49
PROPER(U22(x0, x1, tt)) → c39(U22'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1), PROPER(tt)) 334.39/102.49
PROPER(U22(x0, x1, U12(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.49
PROPER(U22(x0, x1, s(z0))) → c39(U22'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.49
PROPER(U22(x0, x1, plus(z0, z1))) → c39(U22'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.49
PROPER(U22(x0, x1, U21(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.49
PROPER(U22(x0, x1, U22(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.49
PROPER(U22(x0, x1, x(z0, z1))) → c39(U22'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.49
PROPER(U22(x0, x1, 0)) → c39(U22'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1), PROPER(0)) 334.39/102.49
PROPER(U22(x0, U11(z0, z1, z2), x2)) → c39(U22'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U22(x0, tt, x2)) → c39(U22'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(tt), PROPER(x2)) 334.39/102.49
PROPER(U22(x0, U12(z0, z1, z2), x2)) → c39(U22'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U22(x0, s(z0), x2)) → c39(U22'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.49
PROPER(U22(x0, plus(z0, z1), x2)) → c39(U22'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.49
PROPER(U22(x0, U21(z0, z1, z2), x2)) → c39(U22'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U22(x0, U22(z0, z1, z2), x2)) → c39(U22'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U22(x0, x(z0, z1), x2)) → c39(U22'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.49
PROPER(U22(x0, 0, x2)) → c39(U22'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(0), PROPER(x2)) 334.39/102.49
PROPER(U22(U11(z0, z1, z2), x1, x2)) → c39(U22'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U22(tt, x1, x2)) → c39(U22'(ok(tt), proper(x1), proper(x2)), PROPER(tt), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U22(U12(z0, z1, z2), x1, x2)) → c39(U22'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U22(s(z0), x1, x2)) → c39(U22'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U22(plus(z0, z1), x1, x2)) → c39(U22'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U22(U21(z0, z1, z2), x1, x2)) → c39(U22'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U22(U22(z0, z1, z2), x1, x2)) → c39(U22'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U22(x(z0, z1), x1, x2)) → c39(U22'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U22(0, x1, x2)) → c39(U22'(ok(0), proper(x1), proper(x2)), PROPER(0), PROPER(x1), PROPER(x2))
S tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.39/102.49
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.39/102.49
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.39/102.49
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.39/102.49
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.39/102.49
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.39/102.49
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.39/102.49
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.39/102.49
S(mark(z0)) → c21(S(z0)) 334.39/102.49
S(ok(z0)) → c22(S(z0)) 334.39/102.49
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.39/102.49
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.39/102.49
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.39/102.49
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.39/102.49
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.39/102.49
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.39/102.49
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.39/102.49
X(mark(z0), z1) → c30(X(z0, z1)) 334.39/102.49
X(z0, mark(z1)) → c31(X(z0, z1)) 334.39/102.49
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.39/102.49
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.39/102.49
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.39/102.49
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.39/102.49
ACTIVE(U11(tt, z0, z1)) → c 334.39/102.49
ACTIVE(U21(tt, z0, z1)) → c2 334.39/102.49
ACTIVE(plus(z0, s(z1))) → c5 334.39/102.49
ACTIVE(x(z0, s(z1))) → c7 334.39/102.49
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.39/102.49
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.39/102.49
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.39/102.49
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.39/102.49
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.49
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.49
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.49
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.49
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.49
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.49
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.49
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.49
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.49
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.49
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.39/102.49
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.49
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.49
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.49
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.49
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.49
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.49
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.49
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.49
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.49
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.49
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.49
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.49
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.39/102.49
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.49
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.49
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.39/102.49
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.39/102.49
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.39/102.49
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.39/102.49
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.39/102.49
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.39/102.49
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.39/102.49
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.39/102.49
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.39/102.49
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.39/102.49
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.39/102.49
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.39/102.49
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.39/102.49
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.49
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.49
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.49
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.49
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.49
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.49
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.49
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.49
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.49
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.49
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.49
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.49
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.49
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.39/102.49
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.49
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.49
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.39/102.49
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.49
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.39/102.49
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.49
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.49
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.49
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.49
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.49
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.49
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.49
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.49
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.49
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.49
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.49
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.49
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.49
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.49
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.49
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.39/102.49
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.49
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.49
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.49
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.49
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.39/102.49
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.49
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.39/102.49
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.49
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.39/102.49
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.49
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.49
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.49
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.49
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.49
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.49
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.49
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.49
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.49
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.49
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.49
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.49
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.49
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.49
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.49
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.49
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.49
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.49
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.49
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.49
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.49
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.49
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.49
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.49
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.49
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.49
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.49
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.49
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.49
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.49
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.39/102.49
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.39/102.49
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.39/102.49
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.39/102.49
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.39/102.49
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.39/102.49
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.39/102.49
PROPER(s(tt)) → c36(S(ok(tt))) 334.39/102.49
PROPER(s(0)) → c36(S(ok(0))) 334.39/102.49
PROPER(plus(x0, U11(z0, z1, z2))) → c37(PLUS(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.39/102.49
PROPER(plus(x0, U12(z0, z1, z2))) → c37(PLUS(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.39/102.49
PROPER(plus(x0, s(z0))) → c37(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.39/102.49
PROPER(plus(x0, plus(z0, z1))) → c37(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.39/102.49
PROPER(plus(x0, U21(z0, z1, z2))) → c37(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.39/102.49
PROPER(plus(x0, U22(z0, z1, z2))) → c37(PLUS(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.39/102.49
PROPER(plus(x0, x(z0, z1))) → c37(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.39/102.49
PROPER(plus(U11(z0, z1, z2), x1)) → c37(PLUS(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.39/102.49
PROPER(plus(U12(z0, z1, z2), x1)) → c37(PLUS(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.39/102.49
PROPER(plus(s(z0), x1)) → c37(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.39/102.49
PROPER(plus(plus(z0, z1), x1)) → c37(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.39/102.49
PROPER(plus(U21(z0, z1, z2), x1)) → c37(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.39/102.49
PROPER(plus(U22(z0, z1, z2), x1)) → c37(PLUS(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.39/102.49
PROPER(plus(x(z0, z1), x1)) → c37(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.39/102.49
PROPER(plus(x0, tt)) → c37(PLUS(proper(x0), ok(tt)), PROPER(x0)) 334.39/102.49
PROPER(plus(x0, 0)) → c37(PLUS(proper(x0), ok(0)), PROPER(x0)) 334.39/102.49
PROPER(plus(tt, x1)) → c37(PLUS(ok(tt), proper(x1)), PROPER(x1)) 334.39/102.49
PROPER(plus(0, x1)) → c37(PLUS(ok(0), proper(x1)), PROPER(x1)) 334.39/102.49
PROPER(U21(x0, x1, U11(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.49
PROPER(U21(x0, x1, U12(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.49
PROPER(U21(x0, x1, s(z0))) → c38(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.49
PROPER(U21(x0, x1, plus(z0, z1))) → c38(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.49
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.49
PROPER(U21(x0, x1, U22(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.49
PROPER(U21(x0, x1, x(z0, z1))) → c38(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.49
PROPER(U21(x0, U11(z0, z1, z2), x2)) → c38(U21'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U21(x0, U12(z0, z1, z2), x2)) → c38(U21'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U21(x0, s(z0), x2)) → c38(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.49
PROPER(U21(x0, plus(z0, z1), x2)) → c38(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.49
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c38(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U21(x0, U22(z0, z1, z2), x2)) → c38(U21'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U21(x0, x(z0, z1), x2)) → c38(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.49
PROPER(U21(U11(z0, z1, z2), x1, x2)) → c38(U21'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U21(U12(z0, z1, z2), x1, x2)) → c38(U21'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U21(s(z0), x1, x2)) → c38(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U21(plus(z0, z1), x1, x2)) → c38(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c38(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U21(U22(z0, z1, z2), x1, x2)) → c38(U21'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U21(x(z0, z1), x1, x2)) → c38(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U21(x0, x1, tt)) → c38(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.49
PROPER(U21(x0, x1, 0)) → c38(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.49
PROPER(U21(x0, tt, x2)) → c38(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.49
PROPER(U21(x0, 0, x2)) → c38(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.49
PROPER(U21(tt, x1, x2)) → c38(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U21(0, x1, x2)) → c38(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U22(x0, x1, U11(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.49
PROPER(U22(x0, x1, tt)) → c39(U22'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1), PROPER(tt)) 334.39/102.49
PROPER(U22(x0, x1, U12(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.49
PROPER(U22(x0, x1, s(z0))) → c39(U22'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.49
PROPER(U22(x0, x1, plus(z0, z1))) → c39(U22'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.49
PROPER(U22(x0, x1, U21(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.49
PROPER(U22(x0, x1, U22(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.49
PROPER(U22(x0, x1, x(z0, z1))) → c39(U22'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.49
PROPER(U22(x0, x1, 0)) → c39(U22'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1), PROPER(0)) 334.39/102.49
PROPER(U22(x0, U11(z0, z1, z2), x2)) → c39(U22'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U22(x0, tt, x2)) → c39(U22'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(tt), PROPER(x2)) 334.39/102.49
PROPER(U22(x0, U12(z0, z1, z2), x2)) → c39(U22'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U22(x0, s(z0), x2)) → c39(U22'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.49
PROPER(U22(x0, plus(z0, z1), x2)) → c39(U22'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.49
PROPER(U22(x0, U21(z0, z1, z2), x2)) → c39(U22'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U22(x0, U22(z0, z1, z2), x2)) → c39(U22'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U22(x0, x(z0, z1), x2)) → c39(U22'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.49
PROPER(U22(x0, 0, x2)) → c39(U22'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(0), PROPER(x2)) 334.39/102.49
PROPER(U22(U11(z0, z1, z2), x1, x2)) → c39(U22'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U22(tt, x1, x2)) → c39(U22'(ok(tt), proper(x1), proper(x2)), PROPER(tt), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U22(U12(z0, z1, z2), x1, x2)) → c39(U22'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U22(s(z0), x1, x2)) → c39(U22'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U22(plus(z0, z1), x1, x2)) → c39(U22'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U22(U21(z0, z1, z2), x1, x2)) → c39(U22'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U22(U22(z0, z1, z2), x1, x2)) → c39(U22'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U22(x(z0, z1), x1, x2)) → c39(U22'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U22(0, x1, x2)) → c39(U22'(ok(0), proper(x1), proper(x2)), PROPER(0), PROPER(x1), PROPER(x2))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c11, c12, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c40, c42, c43, c, c2, c5, c7, c4, c8, c1, c9, c3, c10, c6, c13, c34, c14, c41, c33, c33, c35, c35, c36, c36, c37, c37, c38, c38, c39

334.39/102.49
334.39/102.49

(71) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 6 trailing tuple parts
334.39/102.49
334.39/102.49

(72) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.39/102.49
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.39/102.49
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.39/102.49
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.39/102.49
active(plus(z0, 0)) → mark(z0) 334.39/102.49
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.39/102.49
active(x(z0, 0)) → mark(0) 334.39/102.49
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.39/102.49
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.39/102.49
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.39/102.49
active(s(z0)) → s(active(z0)) 334.39/102.49
active(plus(z0, z1)) → plus(active(z0), z1) 334.39/102.49
active(plus(z0, z1)) → plus(z0, active(z1)) 334.39/102.49
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.39/102.49
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.39/102.49
active(x(z0, z1)) → x(active(z0), z1) 334.39/102.49
active(x(z0, z1)) → x(z0, active(z1)) 334.39/102.49
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.39/102.49
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.39/102.49
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.39/102.49
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.39/102.49
s(mark(z0)) → mark(s(z0)) 334.39/102.49
s(ok(z0)) → ok(s(z0)) 334.39/102.49
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.39/102.49
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.39/102.49
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.39/102.49
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.39/102.49
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.39/102.49
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.39/102.49
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.39/102.49
x(mark(z0), z1) → mark(x(z0, z1)) 334.39/102.49
x(z0, mark(z1)) → mark(x(z0, z1)) 334.39/102.49
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.39/102.49
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.39/102.49
proper(tt) → ok(tt) 334.39/102.49
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.39/102.49
proper(s(z0)) → s(proper(z0)) 334.39/102.49
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.39/102.49
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.39/102.49
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.39/102.49
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.39/102.49
proper(0) → ok(0) 334.39/102.49
top(mark(z0)) → top(proper(z0)) 334.39/102.49
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.39/102.49
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.39/102.49
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.39/102.49
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.39/102.49
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.39/102.49
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.39/102.49
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.39/102.49
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.39/102.49
S(mark(z0)) → c21(S(z0)) 334.39/102.49
S(ok(z0)) → c22(S(z0)) 334.39/102.49
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.39/102.49
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.39/102.49
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.39/102.49
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.39/102.49
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.39/102.49
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.39/102.49
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.39/102.49
X(mark(z0), z1) → c30(X(z0, z1)) 334.39/102.49
X(z0, mark(z1)) → c31(X(z0, z1)) 334.39/102.49
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.39/102.49
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.39/102.49
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.39/102.49
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.39/102.49
ACTIVE(U11(tt, z0, z1)) → c 334.39/102.49
ACTIVE(U21(tt, z0, z1)) → c2 334.39/102.49
ACTIVE(plus(z0, s(z1))) → c5 334.39/102.49
ACTIVE(x(z0, s(z1))) → c7 334.39/102.49
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.39/102.49
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.39/102.49
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.39/102.49
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.39/102.49
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.49
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.49
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.49
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.49
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.49
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.49
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.49
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.49
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.49
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.49
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.39/102.49
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.49
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.49
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.49
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.49
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.49
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.49
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.49
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.49
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.49
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.49
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.49
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.49
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.39/102.49
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.49
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.49
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.39/102.49
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.39/102.49
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.39/102.49
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.39/102.49
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.39/102.49
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.39/102.49
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.39/102.49
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.39/102.49
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.39/102.49
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.39/102.49
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.39/102.49
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.39/102.49
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.39/102.49
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.49
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.49
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.49
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.49
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.49
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.49
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.49
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.49
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.49
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.49
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.49
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.49
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.49
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.39/102.49
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.49
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.49
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.39/102.49
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.49
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.39/102.49
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.49
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.49
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.49
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.49
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.49
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.49
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.49
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.49
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.49
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.49
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.49
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.49
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.49
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.49
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.49
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.39/102.49
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.49
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.49
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.49
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.49
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.39/102.49
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.49
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.39/102.49
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.49
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.39/102.49
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.49
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.49
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.49
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.49
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.49
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.49
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.49
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.49
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.49
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.49
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.49
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.49
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.49
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.49
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.49
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.49
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.49
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.49
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.49
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.49
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.49
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.49
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.49
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.49
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.49
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.49
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.49
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.49
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.49
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.49
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.39/102.49
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.39/102.49
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.39/102.49
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.39/102.49
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.39/102.49
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.39/102.49
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.39/102.49
PROPER(s(tt)) → c36(S(ok(tt))) 334.39/102.49
PROPER(s(0)) → c36(S(ok(0))) 334.39/102.49
PROPER(plus(x0, U11(z0, z1, z2))) → c37(PLUS(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.39/102.49
PROPER(plus(x0, U12(z0, z1, z2))) → c37(PLUS(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.39/102.49
PROPER(plus(x0, s(z0))) → c37(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.39/102.49
PROPER(plus(x0, plus(z0, z1))) → c37(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.39/102.49
PROPER(plus(x0, U21(z0, z1, z2))) → c37(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.39/102.49
PROPER(plus(x0, U22(z0, z1, z2))) → c37(PLUS(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.39/102.49
PROPER(plus(x0, x(z0, z1))) → c37(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.39/102.49
PROPER(plus(U11(z0, z1, z2), x1)) → c37(PLUS(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.39/102.49
PROPER(plus(U12(z0, z1, z2), x1)) → c37(PLUS(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.39/102.49
PROPER(plus(s(z0), x1)) → c37(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.39/102.49
PROPER(plus(plus(z0, z1), x1)) → c37(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.39/102.49
PROPER(plus(U21(z0, z1, z2), x1)) → c37(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.39/102.49
PROPER(plus(U22(z0, z1, z2), x1)) → c37(PLUS(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.39/102.49
PROPER(plus(x(z0, z1), x1)) → c37(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.39/102.49
PROPER(plus(x0, tt)) → c37(PLUS(proper(x0), ok(tt)), PROPER(x0)) 334.39/102.49
PROPER(plus(x0, 0)) → c37(PLUS(proper(x0), ok(0)), PROPER(x0)) 334.39/102.49
PROPER(plus(tt, x1)) → c37(PLUS(ok(tt), proper(x1)), PROPER(x1)) 334.39/102.49
PROPER(plus(0, x1)) → c37(PLUS(ok(0), proper(x1)), PROPER(x1)) 334.39/102.49
PROPER(U21(x0, x1, U11(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.49
PROPER(U21(x0, x1, U12(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.49
PROPER(U21(x0, x1, s(z0))) → c38(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.49
PROPER(U21(x0, x1, plus(z0, z1))) → c38(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.49
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.49
PROPER(U21(x0, x1, U22(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.49
PROPER(U21(x0, x1, x(z0, z1))) → c38(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.49
PROPER(U21(x0, U11(z0, z1, z2), x2)) → c38(U21'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U21(x0, U12(z0, z1, z2), x2)) → c38(U21'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U21(x0, s(z0), x2)) → c38(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.49
PROPER(U21(x0, plus(z0, z1), x2)) → c38(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.49
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c38(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U21(x0, U22(z0, z1, z2), x2)) → c38(U21'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U21(x0, x(z0, z1), x2)) → c38(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.49
PROPER(U21(U11(z0, z1, z2), x1, x2)) → c38(U21'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U21(U12(z0, z1, z2), x1, x2)) → c38(U21'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U21(s(z0), x1, x2)) → c38(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U21(plus(z0, z1), x1, x2)) → c38(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c38(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U21(U22(z0, z1, z2), x1, x2)) → c38(U21'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U21(x(z0, z1), x1, x2)) → c38(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U21(x0, x1, tt)) → c38(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.49
PROPER(U21(x0, x1, 0)) → c38(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.49
PROPER(U21(x0, tt, x2)) → c38(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.49
PROPER(U21(x0, 0, x2)) → c38(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.49
PROPER(U21(tt, x1, x2)) → c38(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U21(0, x1, x2)) → c38(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U22(x0, x1, U11(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.49
PROPER(U22(x0, x1, U12(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.49
PROPER(U22(x0, x1, s(z0))) → c39(U22'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.49
PROPER(U22(x0, x1, plus(z0, z1))) → c39(U22'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.49
PROPER(U22(x0, x1, U21(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.49
PROPER(U22(x0, x1, U22(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.49
PROPER(U22(x0, x1, x(z0, z1))) → c39(U22'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.49
PROPER(U22(x0, U11(z0, z1, z2), x2)) → c39(U22'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U22(x0, U12(z0, z1, z2), x2)) → c39(U22'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U22(x0, s(z0), x2)) → c39(U22'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.49
PROPER(U22(x0, plus(z0, z1), x2)) → c39(U22'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.49
PROPER(U22(x0, U21(z0, z1, z2), x2)) → c39(U22'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U22(x0, U22(z0, z1, z2), x2)) → c39(U22'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U22(x0, x(z0, z1), x2)) → c39(U22'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.49
PROPER(U22(U11(z0, z1, z2), x1, x2)) → c39(U22'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U22(U12(z0, z1, z2), x1, x2)) → c39(U22'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U22(s(z0), x1, x2)) → c39(U22'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U22(plus(z0, z1), x1, x2)) → c39(U22'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U22(U21(z0, z1, z2), x1, x2)) → c39(U22'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U22(U22(z0, z1, z2), x1, x2)) → c39(U22'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U22(x(z0, z1), x1, x2)) → c39(U22'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U22(x0, x1, tt)) → c39(U22'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.49
PROPER(U22(x0, x1, 0)) → c39(U22'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.49
PROPER(U22(x0, tt, x2)) → c39(U22'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.49
PROPER(U22(x0, 0, x2)) → c39(U22'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.49
PROPER(U22(tt, x1, x2)) → c39(U22'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U22(0, x1, x2)) → c39(U22'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
S tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.39/102.49
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.39/102.49
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.39/102.49
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.39/102.49
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.39/102.49
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.39/102.49
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.39/102.49
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.39/102.49
S(mark(z0)) → c21(S(z0)) 334.39/102.49
S(ok(z0)) → c22(S(z0)) 334.39/102.49
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.39/102.49
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.39/102.49
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.39/102.49
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.39/102.49
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.39/102.49
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.39/102.49
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.39/102.49
X(mark(z0), z1) → c30(X(z0, z1)) 334.39/102.49
X(z0, mark(z1)) → c31(X(z0, z1)) 334.39/102.49
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.39/102.49
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.39/102.49
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.39/102.49
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.39/102.49
ACTIVE(U11(tt, z0, z1)) → c 334.39/102.49
ACTIVE(U21(tt, z0, z1)) → c2 334.39/102.49
ACTIVE(plus(z0, s(z1))) → c5 334.39/102.49
ACTIVE(x(z0, s(z1))) → c7 334.39/102.49
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.39/102.49
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.39/102.49
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.39/102.49
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.39/102.49
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.49
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.49
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.49
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.49
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.49
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.49
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.49
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.49
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.49
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.49
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.39/102.49
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.49
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.49
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.49
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.49
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.49
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.49
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.49
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.49
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.49
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.49
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.49
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.49
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.39/102.49
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.49
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.49
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.39/102.49
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.39/102.49
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.39/102.49
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.39/102.49
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.39/102.49
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.39/102.49
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.39/102.49
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.39/102.49
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.39/102.49
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.39/102.49
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.39/102.49
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.39/102.49
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.39/102.49
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.49
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.49
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.49
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.49
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.49
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.49
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.49
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.49
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.49
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.49
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.49
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.49
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.49
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.39/102.49
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.49
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.49
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.39/102.49
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.49
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.39/102.49
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.49
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.49
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.49
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.49
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.49
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.49
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.49
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.49
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.49
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.49
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.49
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.49
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.49
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.49
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.49
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.39/102.49
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.49
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.49
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.49
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.49
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.39/102.49
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.49
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.39/102.49
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.49
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.39/102.49
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.49
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.49
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.49
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.49
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.49
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.49
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.49
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.49
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.49
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.49
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.49
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.49
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.49
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.49
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.49
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.49
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.49
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.49
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.49
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.49
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.49
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.49
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.49
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.49
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.49
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.49
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.49
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.49
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.49
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.49
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.39/102.49
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.39/102.49
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.39/102.49
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.39/102.49
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.39/102.49
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.39/102.49
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.39/102.49
PROPER(s(tt)) → c36(S(ok(tt))) 334.39/102.49
PROPER(s(0)) → c36(S(ok(0))) 334.39/102.49
PROPER(plus(x0, U11(z0, z1, z2))) → c37(PLUS(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.39/102.49
PROPER(plus(x0, U12(z0, z1, z2))) → c37(PLUS(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.39/102.49
PROPER(plus(x0, s(z0))) → c37(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.39/102.49
PROPER(plus(x0, plus(z0, z1))) → c37(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.39/102.49
PROPER(plus(x0, U21(z0, z1, z2))) → c37(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.39/102.49
PROPER(plus(x0, U22(z0, z1, z2))) → c37(PLUS(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.39/102.49
PROPER(plus(x0, x(z0, z1))) → c37(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.39/102.49
PROPER(plus(U11(z0, z1, z2), x1)) → c37(PLUS(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.39/102.49
PROPER(plus(U12(z0, z1, z2), x1)) → c37(PLUS(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.39/102.49
PROPER(plus(s(z0), x1)) → c37(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.39/102.49
PROPER(plus(plus(z0, z1), x1)) → c37(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.39/102.49
PROPER(plus(U21(z0, z1, z2), x1)) → c37(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.39/102.49
PROPER(plus(U22(z0, z1, z2), x1)) → c37(PLUS(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.39/102.49
PROPER(plus(x(z0, z1), x1)) → c37(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.39/102.49
PROPER(plus(x0, tt)) → c37(PLUS(proper(x0), ok(tt)), PROPER(x0)) 334.39/102.49
PROPER(plus(x0, 0)) → c37(PLUS(proper(x0), ok(0)), PROPER(x0)) 334.39/102.49
PROPER(plus(tt, x1)) → c37(PLUS(ok(tt), proper(x1)), PROPER(x1)) 334.39/102.49
PROPER(plus(0, x1)) → c37(PLUS(ok(0), proper(x1)), PROPER(x1)) 334.39/102.49
PROPER(U21(x0, x1, U11(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.49
PROPER(U21(x0, x1, U12(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.49
PROPER(U21(x0, x1, s(z0))) → c38(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.49
PROPER(U21(x0, x1, plus(z0, z1))) → c38(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.49
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.49
PROPER(U21(x0, x1, U22(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.49
PROPER(U21(x0, x1, x(z0, z1))) → c38(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.49
PROPER(U21(x0, U11(z0, z1, z2), x2)) → c38(U21'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U21(x0, U12(z0, z1, z2), x2)) → c38(U21'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U21(x0, s(z0), x2)) → c38(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.49
PROPER(U21(x0, plus(z0, z1), x2)) → c38(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.49
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c38(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U21(x0, U22(z0, z1, z2), x2)) → c38(U21'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U21(x0, x(z0, z1), x2)) → c38(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.49
PROPER(U21(U11(z0, z1, z2), x1, x2)) → c38(U21'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U21(U12(z0, z1, z2), x1, x2)) → c38(U21'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U21(s(z0), x1, x2)) → c38(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U21(plus(z0, z1), x1, x2)) → c38(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c38(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U21(U22(z0, z1, z2), x1, x2)) → c38(U21'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U21(x(z0, z1), x1, x2)) → c38(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U21(x0, x1, tt)) → c38(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.49
PROPER(U21(x0, x1, 0)) → c38(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.49
PROPER(U21(x0, tt, x2)) → c38(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.49
PROPER(U21(x0, 0, x2)) → c38(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.49
PROPER(U21(tt, x1, x2)) → c38(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U21(0, x1, x2)) → c38(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U22(x0, x1, U11(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.49
PROPER(U22(x0, x1, U12(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.49
PROPER(U22(x0, x1, s(z0))) → c39(U22'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.49
PROPER(U22(x0, x1, plus(z0, z1))) → c39(U22'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.49
PROPER(U22(x0, x1, U21(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.49
PROPER(U22(x0, x1, U22(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.49
PROPER(U22(x0, x1, x(z0, z1))) → c39(U22'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.49
PROPER(U22(x0, U11(z0, z1, z2), x2)) → c39(U22'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U22(x0, U12(z0, z1, z2), x2)) → c39(U22'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U22(x0, s(z0), x2)) → c39(U22'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.49
PROPER(U22(x0, plus(z0, z1), x2)) → c39(U22'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.49
PROPER(U22(x0, U21(z0, z1, z2), x2)) → c39(U22'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U22(x0, U22(z0, z1, z2), x2)) → c39(U22'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U22(x0, x(z0, z1), x2)) → c39(U22'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.49
PROPER(U22(U11(z0, z1, z2), x1, x2)) → c39(U22'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U22(U12(z0, z1, z2), x1, x2)) → c39(U22'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U22(s(z0), x1, x2)) → c39(U22'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U22(plus(z0, z1), x1, x2)) → c39(U22'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U22(U21(z0, z1, z2), x1, x2)) → c39(U22'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U22(U22(z0, z1, z2), x1, x2)) → c39(U22'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U22(x(z0, z1), x1, x2)) → c39(U22'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U22(x0, x1, tt)) → c39(U22'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.49
PROPER(U22(x0, x1, 0)) → c39(U22'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.49
PROPER(U22(x0, tt, x2)) → c39(U22'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.49
PROPER(U22(x0, 0, x2)) → c39(U22'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.49
PROPER(U22(tt, x1, x2)) → c39(U22'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U22(0, x1, x2)) → c39(U22'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c11, c12, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c40, c42, c43, c, c2, c5, c7, c4, c8, c1, c9, c3, c10, c6, c13, c34, c14, c41, c33, c33, c35, c35, c36, c36, c37, c37, c38, c38, c39, c39

334.39/102.49
334.39/102.49

(73) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

Removed 14 trailing nodes:

ACTIVE(x(z0, s(z1))) → c7 334.39/102.49
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.39/102.49
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.39/102.49
ACTIVE(U11(tt, z0, z1)) → c 334.39/102.49
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.39/102.49
ACTIVE(U21(tt, z0, z1)) → c2 334.39/102.49
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.39/102.49
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.39/102.49
ACTIVE(plus(z0, s(z1))) → c5 334.39/102.49
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.49
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.39/102.49
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.49
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.49
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1)))
334.39/102.49
334.39/102.49

(74) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.39/102.49
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.39/102.49
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.39/102.49
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.39/102.49
active(plus(z0, 0)) → mark(z0) 334.39/102.49
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.39/102.49
active(x(z0, 0)) → mark(0) 334.39/102.49
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.39/102.49
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.39/102.49
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.39/102.49
active(s(z0)) → s(active(z0)) 334.39/102.49
active(plus(z0, z1)) → plus(active(z0), z1) 334.39/102.49
active(plus(z0, z1)) → plus(z0, active(z1)) 334.39/102.49
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.39/102.49
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.39/102.49
active(x(z0, z1)) → x(active(z0), z1) 334.39/102.49
active(x(z0, z1)) → x(z0, active(z1)) 334.39/102.49
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.39/102.49
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.39/102.49
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.39/102.49
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.39/102.49
s(mark(z0)) → mark(s(z0)) 334.39/102.49
s(ok(z0)) → ok(s(z0)) 334.39/102.49
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.39/102.49
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.39/102.49
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.39/102.49
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.39/102.49
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.39/102.49
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.39/102.49
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.39/102.49
x(mark(z0), z1) → mark(x(z0, z1)) 334.39/102.49
x(z0, mark(z1)) → mark(x(z0, z1)) 334.39/102.49
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.39/102.49
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.39/102.49
proper(tt) → ok(tt) 334.39/102.49
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.39/102.49
proper(s(z0)) → s(proper(z0)) 334.39/102.49
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.39/102.49
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.39/102.49
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.39/102.49
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.39/102.49
proper(0) → ok(0) 334.39/102.49
top(mark(z0)) → top(proper(z0)) 334.39/102.49
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.39/102.49
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.39/102.49
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.39/102.49
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.39/102.49
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.39/102.49
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.39/102.49
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.39/102.49
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.39/102.49
S(mark(z0)) → c21(S(z0)) 334.39/102.49
S(ok(z0)) → c22(S(z0)) 334.39/102.49
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.39/102.49
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.39/102.49
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.39/102.49
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.39/102.49
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.39/102.49
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.39/102.49
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.39/102.49
X(mark(z0), z1) → c30(X(z0, z1)) 334.39/102.49
X(z0, mark(z1)) → c31(X(z0, z1)) 334.39/102.49
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.39/102.49
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.39/102.49
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.39/102.49
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.39/102.49
ACTIVE(U11(tt, z0, z1)) → c 334.39/102.49
ACTIVE(U21(tt, z0, z1)) → c2 334.39/102.49
ACTIVE(plus(z0, s(z1))) → c5 334.39/102.49
ACTIVE(x(z0, s(z1))) → c7 334.39/102.49
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.39/102.49
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.39/102.49
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.39/102.49
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.39/102.49
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.49
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.49
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.49
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.49
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.49
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.49
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.49
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.49
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.49
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.49
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.39/102.49
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.49
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.49
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.49
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.49
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.49
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.49
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.49
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.49
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.49
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.49
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.49
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.49
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.39/102.49
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.49
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.49
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.39/102.49
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.39/102.49
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.39/102.49
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.39/102.49
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.39/102.49
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.39/102.49
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.39/102.49
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.39/102.49
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.39/102.49
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.39/102.49
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.39/102.49
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.39/102.49
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.39/102.49
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.49
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.49
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.49
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.49
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.49
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.49
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.49
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.49
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.49
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.49
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.49
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.49
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.49
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.39/102.49
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.49
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.49
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.39/102.49
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.49
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.39/102.49
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.49
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.49
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.49
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.49
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.49
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.49
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.49
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.49
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.49
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.49
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.49
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.49
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.49
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.49
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.49
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.49
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.49
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.39/102.49
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.49
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.49
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.49
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.49
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.39/102.49
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.49
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.39/102.49
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.49
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.39/102.49
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.49
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.49
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.49
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.49
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.49
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.49
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.49
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.49
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.49
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.49
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.49
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.49
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.49
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.49
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.49
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.49
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.49
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.49
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.49
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.49
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.49
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.49
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.49
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.49
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.50
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.50
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.50
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.50
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.50
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.50
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.50
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.50
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.39/102.50
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.39/102.50
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.39/102.50
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.39/102.50
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.39/102.50
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.39/102.50
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.39/102.50
PROPER(s(tt)) → c36(S(ok(tt))) 334.39/102.50
PROPER(s(0)) → c36(S(ok(0))) 334.39/102.50
PROPER(plus(x0, U11(z0, z1, z2))) → c37(PLUS(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.39/102.50
PROPER(plus(x0, U12(z0, z1, z2))) → c37(PLUS(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.39/102.50
PROPER(plus(x0, s(z0))) → c37(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.39/102.50
PROPER(plus(x0, plus(z0, z1))) → c37(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.39/102.50
PROPER(plus(x0, U21(z0, z1, z2))) → c37(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.39/102.50
PROPER(plus(x0, U22(z0, z1, z2))) → c37(PLUS(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.39/102.50
PROPER(plus(x0, x(z0, z1))) → c37(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.39/102.50
PROPER(plus(U11(z0, z1, z2), x1)) → c37(PLUS(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.39/102.50
PROPER(plus(U12(z0, z1, z2), x1)) → c37(PLUS(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.39/102.50
PROPER(plus(s(z0), x1)) → c37(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.39/102.50
PROPER(plus(plus(z0, z1), x1)) → c37(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.39/102.50
PROPER(plus(U21(z0, z1, z2), x1)) → c37(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.39/102.50
PROPER(plus(U22(z0, z1, z2), x1)) → c37(PLUS(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.39/102.50
PROPER(plus(x(z0, z1), x1)) → c37(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.39/102.50
PROPER(plus(x0, tt)) → c37(PLUS(proper(x0), ok(tt)), PROPER(x0)) 334.39/102.50
PROPER(plus(x0, 0)) → c37(PLUS(proper(x0), ok(0)), PROPER(x0)) 334.39/102.50
PROPER(plus(tt, x1)) → c37(PLUS(ok(tt), proper(x1)), PROPER(x1)) 334.39/102.50
PROPER(plus(0, x1)) → c37(PLUS(ok(0), proper(x1)), PROPER(x1)) 334.39/102.50
PROPER(U21(x0, x1, U11(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.50
PROPER(U21(x0, x1, U12(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.50
PROPER(U21(x0, x1, s(z0))) → c38(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.50
PROPER(U21(x0, x1, plus(z0, z1))) → c38(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.50
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.50
PROPER(U21(x0, x1, U22(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.50
PROPER(U21(x0, x1, x(z0, z1))) → c38(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.50
PROPER(U21(x0, U11(z0, z1, z2), x2)) → c38(U21'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U21(x0, U12(z0, z1, z2), x2)) → c38(U21'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U21(x0, s(z0), x2)) → c38(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.50
PROPER(U21(x0, plus(z0, z1), x2)) → c38(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.50
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c38(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U21(x0, U22(z0, z1, z2), x2)) → c38(U21'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U21(x0, x(z0, z1), x2)) → c38(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.50
PROPER(U21(U11(z0, z1, z2), x1, x2)) → c38(U21'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U21(U12(z0, z1, z2), x1, x2)) → c38(U21'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U21(s(z0), x1, x2)) → c38(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U21(plus(z0, z1), x1, x2)) → c38(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c38(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U21(U22(z0, z1, z2), x1, x2)) → c38(U21'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U21(x(z0, z1), x1, x2)) → c38(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U21(x0, x1, tt)) → c38(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.50
PROPER(U21(x0, x1, 0)) → c38(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.50
PROPER(U21(x0, tt, x2)) → c38(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.50
PROPER(U21(x0, 0, x2)) → c38(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.50
PROPER(U21(tt, x1, x2)) → c38(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U21(0, x1, x2)) → c38(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U22(x0, x1, U11(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.50
PROPER(U22(x0, x1, U12(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.50
PROPER(U22(x0, x1, s(z0))) → c39(U22'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.50
PROPER(U22(x0, x1, plus(z0, z1))) → c39(U22'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.50
PROPER(U22(x0, x1, U21(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.50
PROPER(U22(x0, x1, U22(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.50
PROPER(U22(x0, x1, x(z0, z1))) → c39(U22'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.50
PROPER(U22(x0, U11(z0, z1, z2), x2)) → c39(U22'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U22(x0, U12(z0, z1, z2), x2)) → c39(U22'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U22(x0, s(z0), x2)) → c39(U22'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.50
PROPER(U22(x0, plus(z0, z1), x2)) → c39(U22'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.50
PROPER(U22(x0, U21(z0, z1, z2), x2)) → c39(U22'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U22(x0, U22(z0, z1, z2), x2)) → c39(U22'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U22(x0, x(z0, z1), x2)) → c39(U22'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.50
PROPER(U22(U11(z0, z1, z2), x1, x2)) → c39(U22'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U22(U12(z0, z1, z2), x1, x2)) → c39(U22'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U22(s(z0), x1, x2)) → c39(U22'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U22(plus(z0, z1), x1, x2)) → c39(U22'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U22(U21(z0, z1, z2), x1, x2)) → c39(U22'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U22(U22(z0, z1, z2), x1, x2)) → c39(U22'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U22(x(z0, z1), x1, x2)) → c39(U22'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U22(x0, x1, tt)) → c39(U22'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.50
PROPER(U22(x0, x1, 0)) → c39(U22'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.50
PROPER(U22(x0, tt, x2)) → c39(U22'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.50
PROPER(U22(x0, 0, x2)) → c39(U22'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.50
PROPER(U22(tt, x1, x2)) → c39(U22'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U22(0, x1, x2)) → c39(U22'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
S tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.39/102.50
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.39/102.50
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.39/102.50
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.39/102.50
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.39/102.50
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.39/102.50
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.39/102.50
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.39/102.50
S(mark(z0)) → c21(S(z0)) 334.39/102.50
S(ok(z0)) → c22(S(z0)) 334.39/102.50
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.39/102.50
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.39/102.50
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.39/102.50
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.39/102.50
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.39/102.50
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.39/102.50
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.39/102.50
X(mark(z0), z1) → c30(X(z0, z1)) 334.39/102.50
X(z0, mark(z1)) → c31(X(z0, z1)) 334.39/102.50
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.39/102.50
PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.39/102.50
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.39/102.50
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.39/102.50
ACTIVE(U11(tt, z0, z1)) → c 334.39/102.50
ACTIVE(U21(tt, z0, z1)) → c2 334.39/102.50
ACTIVE(plus(z0, s(z1))) → c5 334.39/102.50
ACTIVE(x(z0, s(z1))) → c7 334.39/102.50
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.39/102.50
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.39/102.50
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.39/102.50
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.39/102.50
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.50
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.50
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.50
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.50
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.50
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.50
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.50
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.50
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.50
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.50
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.50
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.50
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.50
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.50
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.39/102.50
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.50
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.50
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.50
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.50
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.50
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.50
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.50
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.50
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.50
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.50
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.50
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.50
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.50
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.50
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.50
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.50
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.39/102.50
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.50
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.50
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.39/102.50
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.39/102.50
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.39/102.50
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.39/102.50
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.39/102.50
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.39/102.50
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.39/102.50
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.39/102.50
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.39/102.50
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.39/102.50
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.39/102.50
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.39/102.50
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.39/102.50
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.39/102.50
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.39/102.50
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.39/102.50
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.39/102.50
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.50
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.50
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.50
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.50
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.50
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.50
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.50
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.50
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.50
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.50
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.50
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.50
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.50
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.50
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.50
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.50
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.50
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.39/102.50
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.50
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.50
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.39/102.50
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.50
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.39/102.50
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.50
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.50
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.50
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.50
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.50
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.50
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.50
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.50
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.50
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.50
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.50
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.50
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.50
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.50
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.50
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.50
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.50
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.50
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.50
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.39/102.50
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.50
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.50
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.50
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.50
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.39/102.50
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.50
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.39/102.50
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.50
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.39/102.50
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.50
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.50
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.50
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.50
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.50
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.50
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.50
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.50
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.50
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.50
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.50
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.50
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.50
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.50
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.50
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.50
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.50
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.50
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.50
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.50
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.50
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.50
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.50
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.50
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.50
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.50
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.50
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.50
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.50
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.50
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.39/102.50
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.39/102.50
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.39/102.50
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.39/102.50
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.39/102.50
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.39/102.50
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.39/102.50
PROPER(s(tt)) → c36(S(ok(tt))) 334.39/102.50
PROPER(s(0)) → c36(S(ok(0))) 334.39/102.50
PROPER(plus(x0, U11(z0, z1, z2))) → c37(PLUS(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.39/102.50
PROPER(plus(x0, U12(z0, z1, z2))) → c37(PLUS(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.39/102.50
PROPER(plus(x0, s(z0))) → c37(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.39/102.50
PROPER(plus(x0, plus(z0, z1))) → c37(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.39/102.50
PROPER(plus(x0, U21(z0, z1, z2))) → c37(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.39/102.50
PROPER(plus(x0, U22(z0, z1, z2))) → c37(PLUS(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.39/102.50
PROPER(plus(x0, x(z0, z1))) → c37(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.39/102.50
PROPER(plus(U11(z0, z1, z2), x1)) → c37(PLUS(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.39/102.50
PROPER(plus(U12(z0, z1, z2), x1)) → c37(PLUS(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.39/102.50
PROPER(plus(s(z0), x1)) → c37(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.39/102.50
PROPER(plus(plus(z0, z1), x1)) → c37(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.39/102.50
PROPER(plus(U21(z0, z1, z2), x1)) → c37(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.39/102.50
PROPER(plus(U22(z0, z1, z2), x1)) → c37(PLUS(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.39/102.50
PROPER(plus(x(z0, z1), x1)) → c37(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.39/102.50
PROPER(plus(x0, tt)) → c37(PLUS(proper(x0), ok(tt)), PROPER(x0)) 334.39/102.50
PROPER(plus(x0, 0)) → c37(PLUS(proper(x0), ok(0)), PROPER(x0)) 334.39/102.50
PROPER(plus(tt, x1)) → c37(PLUS(ok(tt), proper(x1)), PROPER(x1)) 334.39/102.50
PROPER(plus(0, x1)) → c37(PLUS(ok(0), proper(x1)), PROPER(x1)) 334.39/102.50
PROPER(U21(x0, x1, U11(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.50
PROPER(U21(x0, x1, U12(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.50
PROPER(U21(x0, x1, s(z0))) → c38(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.50
PROPER(U21(x0, x1, plus(z0, z1))) → c38(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.50
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.50
PROPER(U21(x0, x1, U22(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.50
PROPER(U21(x0, x1, x(z0, z1))) → c38(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.50
PROPER(U21(x0, U11(z0, z1, z2), x2)) → c38(U21'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U21(x0, U12(z0, z1, z2), x2)) → c38(U21'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U21(x0, s(z0), x2)) → c38(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.50
PROPER(U21(x0, plus(z0, z1), x2)) → c38(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.50
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c38(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U21(x0, U22(z0, z1, z2), x2)) → c38(U21'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U21(x0, x(z0, z1), x2)) → c38(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.50
PROPER(U21(U11(z0, z1, z2), x1, x2)) → c38(U21'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U21(U12(z0, z1, z2), x1, x2)) → c38(U21'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U21(s(z0), x1, x2)) → c38(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U21(plus(z0, z1), x1, x2)) → c38(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c38(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U21(U22(z0, z1, z2), x1, x2)) → c38(U21'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U21(x(z0, z1), x1, x2)) → c38(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U21(x0, x1, tt)) → c38(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.50
PROPER(U21(x0, x1, 0)) → c38(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.50
PROPER(U21(x0, tt, x2)) → c38(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.50
PROPER(U21(x0, 0, x2)) → c38(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.50
PROPER(U21(tt, x1, x2)) → c38(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U21(0, x1, x2)) → c38(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U22(x0, x1, U11(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.50
PROPER(U22(x0, x1, U12(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.50
PROPER(U22(x0, x1, s(z0))) → c39(U22'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.50
PROPER(U22(x0, x1, plus(z0, z1))) → c39(U22'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.50
PROPER(U22(x0, x1, U21(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.50
PROPER(U22(x0, x1, U22(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.50
PROPER(U22(x0, x1, x(z0, z1))) → c39(U22'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.50
PROPER(U22(x0, U11(z0, z1, z2), x2)) → c39(U22'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U22(x0, U12(z0, z1, z2), x2)) → c39(U22'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U22(x0, s(z0), x2)) → c39(U22'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.50
PROPER(U22(x0, plus(z0, z1), x2)) → c39(U22'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.50
PROPER(U22(x0, U21(z0, z1, z2), x2)) → c39(U22'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U22(x0, U22(z0, z1, z2), x2)) → c39(U22'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U22(x0, x(z0, z1), x2)) → c39(U22'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.50
PROPER(U22(U11(z0, z1, z2), x1, x2)) → c39(U22'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U22(U12(z0, z1, z2), x1, x2)) → c39(U22'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U22(s(z0), x1, x2)) → c39(U22'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U22(plus(z0, z1), x1, x2)) → c39(U22'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U22(U21(z0, z1, z2), x1, x2)) → c39(U22'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U22(U22(z0, z1, z2), x1, x2)) → c39(U22'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U22(x(z0, z1), x1, x2)) → c39(U22'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U22(x0, x1, tt)) → c39(U22'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.50
PROPER(U22(x0, x1, 0)) → c39(U22'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.50
PROPER(U22(x0, tt, x2)) → c39(U22'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.50
PROPER(U22(x0, 0, x2)) → c39(U22'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.50
PROPER(U22(tt, x1, x2)) → c39(U22'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U22(0, x1, x2)) → c39(U22'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c11, c12, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c40, c42, c43, c, c2, c5, c7, c4, c8, c1, c9, c3, c10, c6, c13, c34, c14, c41, c33, c33, c35, c35, c36, c36, c37, c37, c38, c38, c39, c39

334.39/102.50
334.39/102.50

(75) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace PROPER(x(z0, z1)) → c40(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(x(x0, U11(z0, z1, z2))) → c40(X(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.39/102.50
PROPER(x(x0, tt)) → c40(X(proper(x0), ok(tt)), PROPER(x0), PROPER(tt)) 334.39/102.50
PROPER(x(x0, U12(z0, z1, z2))) → c40(X(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.39/102.50
PROPER(x(x0, s(z0))) → c40(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.39/102.50
PROPER(x(x0, plus(z0, z1))) → c40(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.39/102.50
PROPER(x(x0, U21(z0, z1, z2))) → c40(X(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.39/102.50
PROPER(x(x0, U22(z0, z1, z2))) → c40(X(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.39/102.50
PROPER(x(x0, x(z0, z1))) → c40(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.39/102.50
PROPER(x(x0, 0)) → c40(X(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 334.39/102.50
PROPER(x(U11(z0, z1, z2), x1)) → c40(X(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.39/102.50
PROPER(x(tt, x1)) → c40(X(ok(tt), proper(x1)), PROPER(tt), PROPER(x1)) 334.39/102.50
PROPER(x(U12(z0, z1, z2), x1)) → c40(X(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.39/102.50
PROPER(x(s(z0), x1)) → c40(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.39/102.50
PROPER(x(plus(z0, z1), x1)) → c40(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.39/102.50
PROPER(x(U21(z0, z1, z2), x1)) → c40(X(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.39/102.50
PROPER(x(U22(z0, z1, z2), x1)) → c40(X(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.39/102.50
PROPER(x(x(z0, z1), x1)) → c40(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.39/102.50
PROPER(x(0, x1)) → c40(X(ok(0), proper(x1)), PROPER(0), PROPER(x1))
334.39/102.50
334.39/102.50

(76) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.39/102.50
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.39/102.50
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.39/102.50
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.39/102.50
active(plus(z0, 0)) → mark(z0) 334.39/102.50
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.39/102.50
active(x(z0, 0)) → mark(0) 334.39/102.50
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.39/102.50
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.39/102.50
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.39/102.50
active(s(z0)) → s(active(z0)) 334.39/102.50
active(plus(z0, z1)) → plus(active(z0), z1) 334.39/102.50
active(plus(z0, z1)) → plus(z0, active(z1)) 334.39/102.50
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.39/102.50
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.39/102.50
active(x(z0, z1)) → x(active(z0), z1) 334.39/102.50
active(x(z0, z1)) → x(z0, active(z1)) 334.39/102.50
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.39/102.50
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.39/102.50
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.39/102.50
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.39/102.50
s(mark(z0)) → mark(s(z0)) 334.39/102.50
s(ok(z0)) → ok(s(z0)) 334.39/102.50
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.39/102.50
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.39/102.50
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.39/102.50
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.39/102.50
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.39/102.50
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.39/102.50
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.39/102.50
x(mark(z0), z1) → mark(x(z0, z1)) 334.39/102.50
x(z0, mark(z1)) → mark(x(z0, z1)) 334.39/102.50
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.39/102.50
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.39/102.50
proper(tt) → ok(tt) 334.39/102.50
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.39/102.50
proper(s(z0)) → s(proper(z0)) 334.39/102.50
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.39/102.50
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.39/102.50
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.39/102.50
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.39/102.50
proper(0) → ok(0) 334.39/102.50
top(mark(z0)) → top(proper(z0)) 334.39/102.50
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.39/102.50
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.39/102.50
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.39/102.50
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.39/102.50
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.39/102.50
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.39/102.50
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.39/102.50
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.39/102.50
S(mark(z0)) → c21(S(z0)) 334.39/102.50
S(ok(z0)) → c22(S(z0)) 334.39/102.50
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.39/102.50
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.39/102.50
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.39/102.50
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.39/102.50
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.39/102.50
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.39/102.50
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.39/102.50
X(mark(z0), z1) → c30(X(z0, z1)) 334.39/102.50
X(z0, mark(z1)) → c31(X(z0, z1)) 334.39/102.50
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.39/102.50
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.39/102.50
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.39/102.50
ACTIVE(U11(tt, z0, z1)) → c 334.39/102.50
ACTIVE(U21(tt, z0, z1)) → c2 334.39/102.50
ACTIVE(plus(z0, s(z1))) → c5 334.39/102.50
ACTIVE(x(z0, s(z1))) → c7 334.39/102.50
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.39/102.50
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.39/102.50
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.39/102.50
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.39/102.50
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.50
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.50
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.50
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.50
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.50
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.50
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.50
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.50
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.50
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.50
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.50
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.50
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.50
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.50
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.39/102.50
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.50
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.50
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.50
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.50
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.50
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.50
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.50
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.50
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.50
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.50
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.50
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.50
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.50
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.50
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.50
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.50
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.39/102.50
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.50
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.50
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.39/102.50
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.39/102.50
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.39/102.50
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.39/102.50
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.39/102.50
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.39/102.50
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.39/102.50
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.39/102.50
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.39/102.50
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.39/102.50
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.39/102.50
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.39/102.50
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.39/102.50
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.39/102.50
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.39/102.50
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.39/102.50
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.39/102.50
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.50
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.50
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.50
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.50
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.50
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.50
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.50
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.50
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.50
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.50
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.50
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.50
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.50
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.50
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.50
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.50
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.50
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.39/102.50
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.50
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.50
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.39/102.50
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.50
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.39/102.50
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.50
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.50
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.50
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.50
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.50
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.50
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.50
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.50
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.50
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.50
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.50
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.50
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.50
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.50
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.50
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.50
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.50
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.50
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.50
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.39/102.50
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.50
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.50
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.50
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.50
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.39/102.50
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.50
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.39/102.50
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.50
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.39/102.50
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.50
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.50
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.50
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.50
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.50
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.50
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.50
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.50
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.50
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.50
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.50
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.50
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.50
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.50
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.50
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.50
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.50
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.50
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.50
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.50
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.50
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.50
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.50
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.50
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.50
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.50
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.50
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.50
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.50
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.50
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.39/102.50
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.39/102.50
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.39/102.50
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.39/102.50
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.39/102.50
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.39/102.50
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.39/102.50
PROPER(s(tt)) → c36(S(ok(tt))) 334.39/102.50
PROPER(s(0)) → c36(S(ok(0))) 334.39/102.50
PROPER(plus(x0, U11(z0, z1, z2))) → c37(PLUS(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.39/102.50
PROPER(plus(x0, U12(z0, z1, z2))) → c37(PLUS(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.39/102.50
PROPER(plus(x0, s(z0))) → c37(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.39/102.50
PROPER(plus(x0, plus(z0, z1))) → c37(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.39/102.50
PROPER(plus(x0, U21(z0, z1, z2))) → c37(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.39/102.50
PROPER(plus(x0, U22(z0, z1, z2))) → c37(PLUS(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.39/102.50
PROPER(plus(x0, x(z0, z1))) → c37(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.39/102.50
PROPER(plus(U11(z0, z1, z2), x1)) → c37(PLUS(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.39/102.50
PROPER(plus(U12(z0, z1, z2), x1)) → c37(PLUS(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.39/102.50
PROPER(plus(s(z0), x1)) → c37(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.39/102.50
PROPER(plus(plus(z0, z1), x1)) → c37(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.39/102.50
PROPER(plus(U21(z0, z1, z2), x1)) → c37(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.39/102.50
PROPER(plus(U22(z0, z1, z2), x1)) → c37(PLUS(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.39/102.50
PROPER(plus(x(z0, z1), x1)) → c37(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.39/102.50
PROPER(plus(x0, tt)) → c37(PLUS(proper(x0), ok(tt)), PROPER(x0)) 334.39/102.50
PROPER(plus(x0, 0)) → c37(PLUS(proper(x0), ok(0)), PROPER(x0)) 334.39/102.50
PROPER(plus(tt, x1)) → c37(PLUS(ok(tt), proper(x1)), PROPER(x1)) 334.39/102.50
PROPER(plus(0, x1)) → c37(PLUS(ok(0), proper(x1)), PROPER(x1)) 334.39/102.50
PROPER(U21(x0, x1, U11(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.50
PROPER(U21(x0, x1, U12(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.50
PROPER(U21(x0, x1, s(z0))) → c38(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.50
PROPER(U21(x0, x1, plus(z0, z1))) → c38(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.50
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.50
PROPER(U21(x0, x1, U22(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.50
PROPER(U21(x0, x1, x(z0, z1))) → c38(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.50
PROPER(U21(x0, U11(z0, z1, z2), x2)) → c38(U21'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U21(x0, U12(z0, z1, z2), x2)) → c38(U21'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U21(x0, s(z0), x2)) → c38(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.50
PROPER(U21(x0, plus(z0, z1), x2)) → c38(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.50
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c38(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U21(x0, U22(z0, z1, z2), x2)) → c38(U21'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U21(x0, x(z0, z1), x2)) → c38(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.50
PROPER(U21(U11(z0, z1, z2), x1, x2)) → c38(U21'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U21(U12(z0, z1, z2), x1, x2)) → c38(U21'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U21(s(z0), x1, x2)) → c38(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U21(plus(z0, z1), x1, x2)) → c38(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c38(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U21(U22(z0, z1, z2), x1, x2)) → c38(U21'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U21(x(z0, z1), x1, x2)) → c38(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U21(x0, x1, tt)) → c38(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.50
PROPER(U21(x0, x1, 0)) → c38(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.50
PROPER(U21(x0, tt, x2)) → c38(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.50
PROPER(U21(x0, 0, x2)) → c38(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.50
PROPER(U21(tt, x1, x2)) → c38(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U21(0, x1, x2)) → c38(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U22(x0, x1, U11(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.50
PROPER(U22(x0, x1, U12(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.50
PROPER(U22(x0, x1, s(z0))) → c39(U22'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.50
PROPER(U22(x0, x1, plus(z0, z1))) → c39(U22'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.50
PROPER(U22(x0, x1, U21(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.50
PROPER(U22(x0, x1, U22(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.50
PROPER(U22(x0, x1, x(z0, z1))) → c39(U22'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.50
PROPER(U22(x0, U11(z0, z1, z2), x2)) → c39(U22'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U22(x0, U12(z0, z1, z2), x2)) → c39(U22'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U22(x0, s(z0), x2)) → c39(U22'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.50
PROPER(U22(x0, plus(z0, z1), x2)) → c39(U22'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.50
PROPER(U22(x0, U21(z0, z1, z2), x2)) → c39(U22'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U22(x0, U22(z0, z1, z2), x2)) → c39(U22'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U22(x0, x(z0, z1), x2)) → c39(U22'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.50
PROPER(U22(U11(z0, z1, z2), x1, x2)) → c39(U22'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U22(U12(z0, z1, z2), x1, x2)) → c39(U22'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U22(s(z0), x1, x2)) → c39(U22'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U22(plus(z0, z1), x1, x2)) → c39(U22'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U22(U21(z0, z1, z2), x1, x2)) → c39(U22'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U22(U22(z0, z1, z2), x1, x2)) → c39(U22'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U22(x(z0, z1), x1, x2)) → c39(U22'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U22(x0, x1, tt)) → c39(U22'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.50
PROPER(U22(x0, x1, 0)) → c39(U22'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.50
PROPER(U22(x0, tt, x2)) → c39(U22'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.50
PROPER(U22(x0, 0, x2)) → c39(U22'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.50
PROPER(U22(tt, x1, x2)) → c39(U22'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U22(0, x1, x2)) → c39(U22'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(x(x0, U11(z0, z1, z2))) → c40(X(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.39/102.50
PROPER(x(x0, tt)) → c40(X(proper(x0), ok(tt)), PROPER(x0), PROPER(tt)) 334.39/102.50
PROPER(x(x0, U12(z0, z1, z2))) → c40(X(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.39/102.50
PROPER(x(x0, s(z0))) → c40(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.39/102.50
PROPER(x(x0, plus(z0, z1))) → c40(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.39/102.50
PROPER(x(x0, U21(z0, z1, z2))) → c40(X(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.39/102.50
PROPER(x(x0, U22(z0, z1, z2))) → c40(X(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.39/102.50
PROPER(x(x0, x(z0, z1))) → c40(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.39/102.50
PROPER(x(x0, 0)) → c40(X(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 334.39/102.50
PROPER(x(U11(z0, z1, z2), x1)) → c40(X(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.39/102.50
PROPER(x(tt, x1)) → c40(X(ok(tt), proper(x1)), PROPER(tt), PROPER(x1)) 334.39/102.50
PROPER(x(U12(z0, z1, z2), x1)) → c40(X(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.39/102.50
PROPER(x(s(z0), x1)) → c40(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.39/102.50
PROPER(x(plus(z0, z1), x1)) → c40(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.39/102.50
PROPER(x(U21(z0, z1, z2), x1)) → c40(X(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.39/102.50
PROPER(x(U22(z0, z1, z2), x1)) → c40(X(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.39/102.50
PROPER(x(x(z0, z1), x1)) → c40(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.39/102.50
PROPER(x(0, x1)) → c40(X(ok(0), proper(x1)), PROPER(0), PROPER(x1))
S tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.39/102.50
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.39/102.50
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.39/102.50
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.39/102.50
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.39/102.50
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.39/102.50
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.39/102.50
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.39/102.50
S(mark(z0)) → c21(S(z0)) 334.39/102.50
S(ok(z0)) → c22(S(z0)) 334.39/102.50
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.39/102.50
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.39/102.50
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.39/102.50
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.39/102.50
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.39/102.50
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.39/102.50
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.39/102.50
X(mark(z0), z1) → c30(X(z0, z1)) 334.39/102.50
X(z0, mark(z1)) → c31(X(z0, z1)) 334.39/102.50
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.39/102.50
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.39/102.50
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.39/102.50
ACTIVE(U11(tt, z0, z1)) → c 334.39/102.50
ACTIVE(U21(tt, z0, z1)) → c2 334.39/102.50
ACTIVE(plus(z0, s(z1))) → c5 334.39/102.50
ACTIVE(x(z0, s(z1))) → c7 334.39/102.50
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.39/102.50
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.39/102.50
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.39/102.50
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.39/102.50
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.50
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.50
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.50
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.50
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.50
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.50
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.50
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.50
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.50
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.50
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.50
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.50
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.50
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.50
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.39/102.50
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.50
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.50
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.50
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.50
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.50
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.50
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.50
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.50
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.50
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.50
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.50
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.50
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.50
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.50
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.50
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.50
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.39/102.50
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.50
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.39/102.50
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.39/102.50
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.39/102.50
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.39/102.50
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.39/102.50
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.39/102.50
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.39/102.50
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.39/102.50
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.39/102.50
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.39/102.50
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.39/102.50
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.39/102.50
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.39/102.50
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.39/102.50
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.39/102.50
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.39/102.50
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.39/102.50
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.39/102.50
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.50
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.50
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.50
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.50
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.50
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.50
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.50
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.50
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.50
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.50
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.50
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.50
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.50
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.50
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.50
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.50
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.50
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.39/102.50
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.50
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.50
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.39/102.50
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.50
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.39/102.50
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.50
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.39/102.50
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.39/102.50
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.39/102.50
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.39/102.50
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.39/102.50
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.39/102.50
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.39/102.50
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.39/102.50
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.50
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.39/102.50
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.39/102.50
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.39/102.50
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.50
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.39/102.50
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.50
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.50
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.50
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.50
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.39/102.50
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.50
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.50
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.50
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.39/102.50
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.39/102.50
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.39/102.50
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.39/102.50
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.39/102.50
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.39/102.50
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.39/102.50
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.39/102.50
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.50
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.50
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.50
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.50
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.50
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.50
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.50
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.50
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.50
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.50
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.50
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.50
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.50
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.50
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.39/102.50
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.39/102.50
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.39/102.50
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.39/102.50
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.39/102.50
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.39/102.50
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.39/102.50
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.39/102.50
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.39/102.50
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.39/102.50
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.39/102.50
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.39/102.50
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.39/102.50
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.50
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.39/102.50
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.39/102.50
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.39/102.50
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.39/102.50
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.39/102.50
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.39/102.50
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.39/102.50
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.39/102.50
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.39/102.50
PROPER(s(tt)) → c36(S(ok(tt))) 334.39/102.50
PROPER(s(0)) → c36(S(ok(0))) 334.39/102.50
PROPER(plus(x0, U11(z0, z1, z2))) → c37(PLUS(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.71/102.50
PROPER(plus(x0, U12(z0, z1, z2))) → c37(PLUS(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.71/102.50
PROPER(plus(x0, s(z0))) → c37(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.71/102.50
PROPER(plus(x0, plus(z0, z1))) → c37(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.71/102.50
PROPER(plus(x0, U21(z0, z1, z2))) → c37(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.71/102.50
PROPER(plus(x0, U22(z0, z1, z2))) → c37(PLUS(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.71/102.50
PROPER(plus(x0, x(z0, z1))) → c37(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.71/102.50
PROPER(plus(U11(z0, z1, z2), x1)) → c37(PLUS(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.71/102.50
PROPER(plus(U12(z0, z1, z2), x1)) → c37(PLUS(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.71/102.50
PROPER(plus(s(z0), x1)) → c37(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.71/102.50
PROPER(plus(plus(z0, z1), x1)) → c37(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.71/102.50
PROPER(plus(U21(z0, z1, z2), x1)) → c37(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.71/102.50
PROPER(plus(U22(z0, z1, z2), x1)) → c37(PLUS(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.71/102.50
PROPER(plus(x(z0, z1), x1)) → c37(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.71/102.50
PROPER(plus(x0, tt)) → c37(PLUS(proper(x0), ok(tt)), PROPER(x0)) 334.71/102.50
PROPER(plus(x0, 0)) → c37(PLUS(proper(x0), ok(0)), PROPER(x0)) 334.71/102.50
PROPER(plus(tt, x1)) → c37(PLUS(ok(tt), proper(x1)), PROPER(x1)) 334.71/102.50
PROPER(plus(0, x1)) → c37(PLUS(ok(0), proper(x1)), PROPER(x1)) 334.71/102.50
PROPER(U21(x0, x1, U11(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.50
PROPER(U21(x0, x1, U12(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.50
PROPER(U21(x0, x1, s(z0))) → c38(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.50
PROPER(U21(x0, x1, plus(z0, z1))) → c38(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.50
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.50
PROPER(U21(x0, x1, U22(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.50
PROPER(U21(x0, x1, x(z0, z1))) → c38(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.50
PROPER(U21(x0, U11(z0, z1, z2), x2)) → c38(U21'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.50
PROPER(U21(x0, U12(z0, z1, z2), x2)) → c38(U21'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.50
PROPER(U21(x0, s(z0), x2)) → c38(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.50
PROPER(U21(x0, plus(z0, z1), x2)) → c38(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.50
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c38(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.50
PROPER(U21(x0, U22(z0, z1, z2), x2)) → c38(U21'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.50
PROPER(U21(x0, x(z0, z1), x2)) → c38(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.50
PROPER(U21(U11(z0, z1, z2), x1, x2)) → c38(U21'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U21(U12(z0, z1, z2), x1, x2)) → c38(U21'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U21(s(z0), x1, x2)) → c38(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U21(plus(z0, z1), x1, x2)) → c38(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c38(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U21(U22(z0, z1, z2), x1, x2)) → c38(U21'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U21(x(z0, z1), x1, x2)) → c38(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U21(x0, x1, tt)) → c38(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.50
PROPER(U21(x0, x1, 0)) → c38(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.50
PROPER(U21(x0, tt, x2)) → c38(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.50
PROPER(U21(x0, 0, x2)) → c38(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.50
PROPER(U21(tt, x1, x2)) → c38(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U21(0, x1, x2)) → c38(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U22(x0, x1, U11(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.50
PROPER(U22(x0, x1, U12(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.50
PROPER(U22(x0, x1, s(z0))) → c39(U22'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.50
PROPER(U22(x0, x1, plus(z0, z1))) → c39(U22'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.50
PROPER(U22(x0, x1, U21(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.50
PROPER(U22(x0, x1, U22(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.50
PROPER(U22(x0, x1, x(z0, z1))) → c39(U22'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.50
PROPER(U22(x0, U11(z0, z1, z2), x2)) → c39(U22'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.50
PROPER(U22(x0, U12(z0, z1, z2), x2)) → c39(U22'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.50
PROPER(U22(x0, s(z0), x2)) → c39(U22'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.50
PROPER(U22(x0, plus(z0, z1), x2)) → c39(U22'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.50
PROPER(U22(x0, U21(z0, z1, z2), x2)) → c39(U22'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.50
PROPER(U22(x0, U22(z0, z1, z2), x2)) → c39(U22'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.50
PROPER(U22(x0, x(z0, z1), x2)) → c39(U22'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.50
PROPER(U22(U11(z0, z1, z2), x1, x2)) → c39(U22'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U22(U12(z0, z1, z2), x1, x2)) → c39(U22'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U22(s(z0), x1, x2)) → c39(U22'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U22(plus(z0, z1), x1, x2)) → c39(U22'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U22(U21(z0, z1, z2), x1, x2)) → c39(U22'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U22(U22(z0, z1, z2), x1, x2)) → c39(U22'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U22(x(z0, z1), x1, x2)) → c39(U22'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U22(x0, x1, tt)) → c39(U22'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.50
PROPER(U22(x0, x1, 0)) → c39(U22'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.50
PROPER(U22(x0, tt, x2)) → c39(U22'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.50
PROPER(U22(x0, 0, x2)) → c39(U22'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.50
PROPER(U22(tt, x1, x2)) → c39(U22'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U22(0, x1, x2)) → c39(U22'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(x(x0, U11(z0, z1, z2))) → c40(X(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.71/102.50
PROPER(x(x0, tt)) → c40(X(proper(x0), ok(tt)), PROPER(x0), PROPER(tt)) 334.71/102.50
PROPER(x(x0, U12(z0, z1, z2))) → c40(X(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.71/102.50
PROPER(x(x0, s(z0))) → c40(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.71/102.50
PROPER(x(x0, plus(z0, z1))) → c40(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.71/102.50
PROPER(x(x0, U21(z0, z1, z2))) → c40(X(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.71/102.50
PROPER(x(x0, U22(z0, z1, z2))) → c40(X(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.71/102.50
PROPER(x(x0, x(z0, z1))) → c40(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.71/102.50
PROPER(x(x0, 0)) → c40(X(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 334.71/102.50
PROPER(x(U11(z0, z1, z2), x1)) → c40(X(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.71/102.50
PROPER(x(tt, x1)) → c40(X(ok(tt), proper(x1)), PROPER(tt), PROPER(x1)) 334.71/102.50
PROPER(x(U12(z0, z1, z2), x1)) → c40(X(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.71/102.50
PROPER(x(s(z0), x1)) → c40(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.71/102.50
PROPER(x(plus(z0, z1), x1)) → c40(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.71/102.50
PROPER(x(U21(z0, z1, z2), x1)) → c40(X(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.71/102.50
PROPER(x(U22(z0, z1, z2), x1)) → c40(X(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.71/102.50
PROPER(x(x(z0, z1), x1)) → c40(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.71/102.50
PROPER(x(0, x1)) → c40(X(ok(0), proper(x1)), PROPER(0), PROPER(x1))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, TOP, PROPER

Compound Symbols:

c11, c12, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c42, c43, c, c2, c5, c7, c4, c8, c1, c9, c3, c10, c6, c13, c34, c14, c41, c33, c33, c35, c35, c36, c36, c37, c37, c38, c38, c39, c39, c40

334.71/102.50
334.71/102.50

(77) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 4 trailing tuple parts
334.71/102.50
334.71/102.50

(78) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.71/102.50
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.71/102.50
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.71/102.50
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.71/102.50
active(plus(z0, 0)) → mark(z0) 334.71/102.50
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.71/102.50
active(x(z0, 0)) → mark(0) 334.71/102.50
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.71/102.50
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.71/102.50
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.71/102.50
active(s(z0)) → s(active(z0)) 334.71/102.50
active(plus(z0, z1)) → plus(active(z0), z1) 334.71/102.50
active(plus(z0, z1)) → plus(z0, active(z1)) 334.71/102.50
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.71/102.50
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.71/102.50
active(x(z0, z1)) → x(active(z0), z1) 334.71/102.50
active(x(z0, z1)) → x(z0, active(z1)) 334.71/102.50
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.71/102.50
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.71/102.50
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.71/102.50
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.71/102.50
s(mark(z0)) → mark(s(z0)) 334.71/102.50
s(ok(z0)) → ok(s(z0)) 334.71/102.50
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.71/102.50
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.71/102.50
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.71/102.50
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.71/102.50
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.71/102.50
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.71/102.50
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.71/102.50
x(mark(z0), z1) → mark(x(z0, z1)) 334.71/102.50
x(z0, mark(z1)) → mark(x(z0, z1)) 334.71/102.50
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.71/102.50
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.71/102.50
proper(tt) → ok(tt) 334.71/102.50
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.71/102.50
proper(s(z0)) → s(proper(z0)) 334.71/102.50
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.71/102.50
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.71/102.50
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.71/102.50
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.71/102.50
proper(0) → ok(0) 334.71/102.50
top(mark(z0)) → top(proper(z0)) 334.71/102.50
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.71/102.50
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.71/102.50
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.71/102.50
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.71/102.50
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.50
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.50
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.50
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.50
S(mark(z0)) → c21(S(z0)) 334.71/102.50
S(ok(z0)) → c22(S(z0)) 334.71/102.50
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.50
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.50
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.50
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.50
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.50
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.50
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.50
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.50
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.50
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.71/102.50
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.71/102.50
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.71/102.50
ACTIVE(U11(tt, z0, z1)) → c 334.71/102.50
ACTIVE(U21(tt, z0, z1)) → c2 334.71/102.50
ACTIVE(plus(z0, s(z1))) → c5 334.71/102.50
ACTIVE(x(z0, s(z1))) → c7 334.71/102.50
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.71/102.50
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.71/102.50
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.71/102.50
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.71/102.50
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.50
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.50
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.50
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.50
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.50
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.50
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.50
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.50
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.50
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.50
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.50
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.50
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.50
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.50
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.71/102.50
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.50
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.50
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.50
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.50
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.50
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.50
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.50
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.50
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.50
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.50
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.50
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.50
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.50
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.50
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.71/102.50
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.50
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.71/102.50
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.50
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.71/102.50
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.71/102.50
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.71/102.50
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.71/102.50
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.71/102.50
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.71/102.50
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.71/102.50
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.71/102.50
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.71/102.50
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.71/102.50
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.71/102.50
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.71/102.50
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.71/102.50
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.71/102.50
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.71/102.50
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.71/102.50
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.71/102.50
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.71/102.50
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.50
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.50
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.50
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.50
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.50
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.50
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.50
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.50
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.50
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.50
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.50
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.50
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.50
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.50
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.50
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.50
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.50
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.71/102.50
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.50
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.50
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.71/102.50
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.50
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.71/102.50
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.50
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.50
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.50
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.50
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.50
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.50
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.50
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.50
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.50
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.50
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.50
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.50
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.50
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.50
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.50
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.50
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.50
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.50
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.50
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.71/102.50
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.50
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.50
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.50
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.50
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.71/102.50
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.50
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.71/102.50
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.50
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.71/102.50
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.50
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.50
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.50
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.50
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.50
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.50
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.50
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.50
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.50
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.50
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.50
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.50
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.50
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.50
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.50
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.50
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.50
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.50
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.50
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.50
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.50
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.50
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.50
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.50
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.50
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.50
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.50
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.50
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.50
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.50
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.50
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.50
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.50
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.50
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.50
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.50
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.50
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.50
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.71/102.50
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.71/102.50
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.71/102.50
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.71/102.50
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.71/102.50
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.71/102.50
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.71/102.50
PROPER(s(tt)) → c36(S(ok(tt))) 334.71/102.50
PROPER(s(0)) → c36(S(ok(0))) 334.71/102.50
PROPER(plus(x0, U11(z0, z1, z2))) → c37(PLUS(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.71/102.50
PROPER(plus(x0, U12(z0, z1, z2))) → c37(PLUS(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.71/102.50
PROPER(plus(x0, s(z0))) → c37(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.71/102.50
PROPER(plus(x0, plus(z0, z1))) → c37(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.71/102.50
PROPER(plus(x0, U21(z0, z1, z2))) → c37(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.71/102.50
PROPER(plus(x0, U22(z0, z1, z2))) → c37(PLUS(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.71/102.50
PROPER(plus(x0, x(z0, z1))) → c37(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.71/102.50
PROPER(plus(U11(z0, z1, z2), x1)) → c37(PLUS(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.71/102.50
PROPER(plus(U12(z0, z1, z2), x1)) → c37(PLUS(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.71/102.50
PROPER(plus(s(z0), x1)) → c37(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.71/102.50
PROPER(plus(plus(z0, z1), x1)) → c37(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.71/102.50
PROPER(plus(U21(z0, z1, z2), x1)) → c37(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.71/102.50
PROPER(plus(U22(z0, z1, z2), x1)) → c37(PLUS(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.71/102.50
PROPER(plus(x(z0, z1), x1)) → c37(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.71/102.50
PROPER(plus(x0, tt)) → c37(PLUS(proper(x0), ok(tt)), PROPER(x0)) 334.71/102.50
PROPER(plus(x0, 0)) → c37(PLUS(proper(x0), ok(0)), PROPER(x0)) 334.71/102.50
PROPER(plus(tt, x1)) → c37(PLUS(ok(tt), proper(x1)), PROPER(x1)) 334.71/102.50
PROPER(plus(0, x1)) → c37(PLUS(ok(0), proper(x1)), PROPER(x1)) 334.71/102.50
PROPER(U21(x0, x1, U11(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.50
PROPER(U21(x0, x1, U12(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.50
PROPER(U21(x0, x1, s(z0))) → c38(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.50
PROPER(U21(x0, x1, plus(z0, z1))) → c38(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.50
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.50
PROPER(U21(x0, x1, U22(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.50
PROPER(U21(x0, x1, x(z0, z1))) → c38(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.50
PROPER(U21(x0, U11(z0, z1, z2), x2)) → c38(U21'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.50
PROPER(U21(x0, U12(z0, z1, z2), x2)) → c38(U21'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.50
PROPER(U21(x0, s(z0), x2)) → c38(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.50
PROPER(U21(x0, plus(z0, z1), x2)) → c38(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.50
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c38(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.50
PROPER(U21(x0, U22(z0, z1, z2), x2)) → c38(U21'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.50
PROPER(U21(x0, x(z0, z1), x2)) → c38(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.50
PROPER(U21(U11(z0, z1, z2), x1, x2)) → c38(U21'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U21(U12(z0, z1, z2), x1, x2)) → c38(U21'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U21(s(z0), x1, x2)) → c38(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U21(plus(z0, z1), x1, x2)) → c38(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c38(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U21(U22(z0, z1, z2), x1, x2)) → c38(U21'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U21(x(z0, z1), x1, x2)) → c38(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U21(x0, x1, tt)) → c38(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.50
PROPER(U21(x0, x1, 0)) → c38(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.50
PROPER(U21(x0, tt, x2)) → c38(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.50
PROPER(U21(x0, 0, x2)) → c38(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.50
PROPER(U21(tt, x1, x2)) → c38(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U21(0, x1, x2)) → c38(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U22(x0, x1, U11(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.50
PROPER(U22(x0, x1, U12(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.50
PROPER(U22(x0, x1, s(z0))) → c39(U22'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.50
PROPER(U22(x0, x1, plus(z0, z1))) → c39(U22'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.50
PROPER(U22(x0, x1, U21(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.50
PROPER(U22(x0, x1, U22(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.50
PROPER(U22(x0, x1, x(z0, z1))) → c39(U22'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.50
PROPER(U22(x0, U11(z0, z1, z2), x2)) → c39(U22'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.50
PROPER(U22(x0, U12(z0, z1, z2), x2)) → c39(U22'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.50
PROPER(U22(x0, s(z0), x2)) → c39(U22'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.50
PROPER(U22(x0, plus(z0, z1), x2)) → c39(U22'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.50
PROPER(U22(x0, U21(z0, z1, z2), x2)) → c39(U22'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.50
PROPER(U22(x0, U22(z0, z1, z2), x2)) → c39(U22'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.50
PROPER(U22(x0, x(z0, z1), x2)) → c39(U22'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.50
PROPER(U22(U11(z0, z1, z2), x1, x2)) → c39(U22'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.50
PROPER(U22(U12(z0, z1, z2), x1, x2)) → c39(U22'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(s(z0), x1, x2)) → c39(U22'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(plus(z0, z1), x1, x2)) → c39(U22'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(U21(z0, z1, z2), x1, x2)) → c39(U22'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(U22(z0, z1, z2), x1, x2)) → c39(U22'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(x(z0, z1), x1, x2)) → c39(U22'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, x1, tt)) → c39(U22'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.51
PROPER(U22(x0, x1, 0)) → c39(U22'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.51
PROPER(U22(x0, tt, x2)) → c39(U22'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, 0, x2)) → c39(U22'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.51
PROPER(U22(tt, x1, x2)) → c39(U22'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(0, x1, x2)) → c39(U22'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(x(x0, U11(z0, z1, z2))) → c40(X(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.71/102.51
PROPER(x(x0, U12(z0, z1, z2))) → c40(X(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.71/102.51
PROPER(x(x0, s(z0))) → c40(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.71/102.51
PROPER(x(x0, plus(z0, z1))) → c40(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.71/102.51
PROPER(x(x0, U21(z0, z1, z2))) → c40(X(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.71/102.51
PROPER(x(x0, U22(z0, z1, z2))) → c40(X(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.71/102.51
PROPER(x(x0, x(z0, z1))) → c40(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.71/102.51
PROPER(x(U11(z0, z1, z2), x1)) → c40(X(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.71/102.51
PROPER(x(U12(z0, z1, z2), x1)) → c40(X(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.71/102.51
PROPER(x(s(z0), x1)) → c40(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.71/102.51
PROPER(x(plus(z0, z1), x1)) → c40(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.71/102.51
PROPER(x(U21(z0, z1, z2), x1)) → c40(X(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.71/102.51
PROPER(x(U22(z0, z1, z2), x1)) → c40(X(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.71/102.51
PROPER(x(x(z0, z1), x1)) → c40(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.71/102.51
PROPER(x(x0, tt)) → c40(X(proper(x0), ok(tt)), PROPER(x0)) 334.71/102.51
PROPER(x(x0, 0)) → c40(X(proper(x0), ok(0)), PROPER(x0)) 334.71/102.51
PROPER(x(tt, x1)) → c40(X(ok(tt), proper(x1)), PROPER(x1)) 334.71/102.51
PROPER(x(0, x1)) → c40(X(ok(0), proper(x1)), PROPER(x1))
S tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.71/102.51
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.71/102.51
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.71/102.51
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.71/102.51
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.51
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.51
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.51
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.51
S(mark(z0)) → c21(S(z0)) 334.71/102.51
S(ok(z0)) → c22(S(z0)) 334.71/102.51
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.51
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.51
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.51
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.51
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.51
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.51
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.51
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.51
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.51
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.71/102.51
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.71/102.51
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.71/102.51
ACTIVE(U11(tt, z0, z1)) → c 334.71/102.51
ACTIVE(U21(tt, z0, z1)) → c2 334.71/102.51
ACTIVE(plus(z0, s(z1))) → c5 334.71/102.51
ACTIVE(x(z0, s(z1))) → c7 334.71/102.51
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.71/102.51
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.71/102.51
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.71/102.51
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.71/102.51
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.51
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.51
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.51
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.51
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.51
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.51
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.51
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.51
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.51
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.51
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.71/102.51
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.51
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.51
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.51
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.51
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.51
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.51
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.51
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.51
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.51
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.51
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.71/102.51
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.51
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.71/102.51
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.51
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.71/102.51
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.71/102.51
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.71/102.51
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.71/102.51
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.71/102.51
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.71/102.51
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.71/102.51
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.71/102.51
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.71/102.51
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.71/102.51
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.71/102.51
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.71/102.51
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.71/102.51
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.71/102.51
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.51
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.51
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.51
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.51
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.51
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.51
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.51
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.51
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.51
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.51
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.51
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.51
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.51
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.71/102.51
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.51
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.51
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.71/102.51
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.51
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.71/102.51
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.51
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.51
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.51
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.51
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.51
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.51
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.51
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.51
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.51
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.51
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.51
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.51
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.51
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.51
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.51
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.71/102.51
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.51
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.51
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.51
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.51
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.71/102.51
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.51
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.71/102.51
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.51
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.71/102.51
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.51
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.51
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.51
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.51
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.51
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.51
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.51
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.51
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.51
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.51
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.51
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.51
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.51
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.51
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.51
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.51
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.51
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.51
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.51
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.51
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.51
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.51
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.51
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.51
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.51
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.51
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.51
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.51
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.51
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.51
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.71/102.51
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.71/102.51
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.71/102.51
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.71/102.51
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.71/102.51
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.71/102.51
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.71/102.51
PROPER(s(tt)) → c36(S(ok(tt))) 334.71/102.51
PROPER(s(0)) → c36(S(ok(0))) 334.71/102.51
PROPER(plus(x0, U11(z0, z1, z2))) → c37(PLUS(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.71/102.51
PROPER(plus(x0, U12(z0, z1, z2))) → c37(PLUS(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.71/102.51
PROPER(plus(x0, s(z0))) → c37(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.71/102.51
PROPER(plus(x0, plus(z0, z1))) → c37(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.71/102.51
PROPER(plus(x0, U21(z0, z1, z2))) → c37(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.71/102.51
PROPER(plus(x0, U22(z0, z1, z2))) → c37(PLUS(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.71/102.51
PROPER(plus(x0, x(z0, z1))) → c37(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.71/102.51
PROPER(plus(U11(z0, z1, z2), x1)) → c37(PLUS(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.71/102.51
PROPER(plus(U12(z0, z1, z2), x1)) → c37(PLUS(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.71/102.51
PROPER(plus(s(z0), x1)) → c37(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.71/102.51
PROPER(plus(plus(z0, z1), x1)) → c37(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.71/102.51
PROPER(plus(U21(z0, z1, z2), x1)) → c37(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.71/102.51
PROPER(plus(U22(z0, z1, z2), x1)) → c37(PLUS(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.71/102.51
PROPER(plus(x(z0, z1), x1)) → c37(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.71/102.51
PROPER(plus(x0, tt)) → c37(PLUS(proper(x0), ok(tt)), PROPER(x0)) 334.71/102.51
PROPER(plus(x0, 0)) → c37(PLUS(proper(x0), ok(0)), PROPER(x0)) 334.71/102.51
PROPER(plus(tt, x1)) → c37(PLUS(ok(tt), proper(x1)), PROPER(x1)) 334.71/102.51
PROPER(plus(0, x1)) → c37(PLUS(ok(0), proper(x1)), PROPER(x1)) 334.71/102.51
PROPER(U21(x0, x1, U11(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.51
PROPER(U21(x0, x1, U12(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.51
PROPER(U21(x0, x1, s(z0))) → c38(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.51
PROPER(U21(x0, x1, plus(z0, z1))) → c38(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.51
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.51
PROPER(U21(x0, x1, U22(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.51
PROPER(U21(x0, x1, x(z0, z1))) → c38(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.51
PROPER(U21(x0, U11(z0, z1, z2), x2)) → c38(U21'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U21(x0, U12(z0, z1, z2), x2)) → c38(U21'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U21(x0, s(z0), x2)) → c38(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.51
PROPER(U21(x0, plus(z0, z1), x2)) → c38(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.51
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c38(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U21(x0, U22(z0, z1, z2), x2)) → c38(U21'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U21(x0, x(z0, z1), x2)) → c38(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.51
PROPER(U21(U11(z0, z1, z2), x1, x2)) → c38(U21'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U21(U12(z0, z1, z2), x1, x2)) → c38(U21'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U21(s(z0), x1, x2)) → c38(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U21(plus(z0, z1), x1, x2)) → c38(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c38(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U21(U22(z0, z1, z2), x1, x2)) → c38(U21'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U21(x(z0, z1), x1, x2)) → c38(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U21(x0, x1, tt)) → c38(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.51
PROPER(U21(x0, x1, 0)) → c38(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.51
PROPER(U21(x0, tt, x2)) → c38(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.51
PROPER(U21(x0, 0, x2)) → c38(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.51
PROPER(U21(tt, x1, x2)) → c38(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U21(0, x1, x2)) → c38(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, x1, U11(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.51
PROPER(U22(x0, x1, U12(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.51
PROPER(U22(x0, x1, s(z0))) → c39(U22'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.51
PROPER(U22(x0, x1, plus(z0, z1))) → c39(U22'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.51
PROPER(U22(x0, x1, U21(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.51
PROPER(U22(x0, x1, U22(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.51
PROPER(U22(x0, x1, x(z0, z1))) → c39(U22'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.51
PROPER(U22(x0, U11(z0, z1, z2), x2)) → c39(U22'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, U12(z0, z1, z2), x2)) → c39(U22'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, s(z0), x2)) → c39(U22'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, plus(z0, z1), x2)) → c39(U22'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, U21(z0, z1, z2), x2)) → c39(U22'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, U22(z0, z1, z2), x2)) → c39(U22'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, x(z0, z1), x2)) → c39(U22'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.51
PROPER(U22(U11(z0, z1, z2), x1, x2)) → c39(U22'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(U12(z0, z1, z2), x1, x2)) → c39(U22'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(s(z0), x1, x2)) → c39(U22'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(plus(z0, z1), x1, x2)) → c39(U22'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(U21(z0, z1, z2), x1, x2)) → c39(U22'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(U22(z0, z1, z2), x1, x2)) → c39(U22'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(x(z0, z1), x1, x2)) → c39(U22'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, x1, tt)) → c39(U22'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.51
PROPER(U22(x0, x1, 0)) → c39(U22'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.51
PROPER(U22(x0, tt, x2)) → c39(U22'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, 0, x2)) → c39(U22'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.51
PROPER(U22(tt, x1, x2)) → c39(U22'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(0, x1, x2)) → c39(U22'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(x(x0, U11(z0, z1, z2))) → c40(X(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.71/102.51
PROPER(x(x0, U12(z0, z1, z2))) → c40(X(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.71/102.51
PROPER(x(x0, s(z0))) → c40(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.71/102.51
PROPER(x(x0, plus(z0, z1))) → c40(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.71/102.51
PROPER(x(x0, U21(z0, z1, z2))) → c40(X(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.71/102.51
PROPER(x(x0, U22(z0, z1, z2))) → c40(X(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.71/102.51
PROPER(x(x0, x(z0, z1))) → c40(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.71/102.51
PROPER(x(U11(z0, z1, z2), x1)) → c40(X(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.71/102.51
PROPER(x(U12(z0, z1, z2), x1)) → c40(X(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.71/102.51
PROPER(x(s(z0), x1)) → c40(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.71/102.51
PROPER(x(plus(z0, z1), x1)) → c40(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.71/102.51
PROPER(x(U21(z0, z1, z2), x1)) → c40(X(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.71/102.51
PROPER(x(U22(z0, z1, z2), x1)) → c40(X(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.71/102.51
PROPER(x(x(z0, z1), x1)) → c40(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.71/102.51
PROPER(x(x0, tt)) → c40(X(proper(x0), ok(tt)), PROPER(x0)) 334.71/102.51
PROPER(x(x0, 0)) → c40(X(proper(x0), ok(0)), PROPER(x0)) 334.71/102.51
PROPER(x(tt, x1)) → c40(X(ok(tt), proper(x1)), PROPER(x1)) 334.71/102.51
PROPER(x(0, x1)) → c40(X(ok(0), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, TOP, PROPER

Compound Symbols:

c11, c12, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c42, c43, c, c2, c5, c7, c4, c8, c1, c9, c3, c10, c6, c13, c34, c14, c41, c33, c33, c35, c35, c36, c36, c37, c37, c38, c38, c39, c39, c40, c40

334.71/102.51
334.71/102.51

(79) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

Removed 14 trailing nodes:

ACTIVE(x(z0, s(z1))) → c7 334.71/102.51
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.71/102.51
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.71/102.51
ACTIVE(U11(tt, z0, z1)) → c 334.71/102.51
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.71/102.51
ACTIVE(U21(tt, z0, z1)) → c2 334.71/102.51
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.71/102.51
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.71/102.51
ACTIVE(plus(z0, s(z1))) → c5 334.71/102.51
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.51
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.71/102.51
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.51
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.51
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1)))
334.71/102.51
334.71/102.51

(80) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.71/102.51
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.71/102.51
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.71/102.51
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.71/102.51
active(plus(z0, 0)) → mark(z0) 334.71/102.51
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.71/102.51
active(x(z0, 0)) → mark(0) 334.71/102.51
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.71/102.51
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.71/102.51
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.71/102.51
active(s(z0)) → s(active(z0)) 334.71/102.51
active(plus(z0, z1)) → plus(active(z0), z1) 334.71/102.51
active(plus(z0, z1)) → plus(z0, active(z1)) 334.71/102.51
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.71/102.51
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.71/102.51
active(x(z0, z1)) → x(active(z0), z1) 334.71/102.51
active(x(z0, z1)) → x(z0, active(z1)) 334.71/102.51
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.71/102.51
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.71/102.51
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.71/102.51
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.71/102.51
s(mark(z0)) → mark(s(z0)) 334.71/102.51
s(ok(z0)) → ok(s(z0)) 334.71/102.51
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.71/102.51
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.71/102.51
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.71/102.51
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.71/102.51
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.71/102.51
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.71/102.51
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.71/102.51
x(mark(z0), z1) → mark(x(z0, z1)) 334.71/102.51
x(z0, mark(z1)) → mark(x(z0, z1)) 334.71/102.51
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.71/102.51
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.71/102.51
proper(tt) → ok(tt) 334.71/102.51
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.71/102.51
proper(s(z0)) → s(proper(z0)) 334.71/102.51
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.71/102.51
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.71/102.51
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.71/102.51
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.71/102.51
proper(0) → ok(0) 334.71/102.51
top(mark(z0)) → top(proper(z0)) 334.71/102.51
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.71/102.51
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.71/102.51
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.71/102.51
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.71/102.51
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.51
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.51
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.51
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.51
S(mark(z0)) → c21(S(z0)) 334.71/102.51
S(ok(z0)) → c22(S(z0)) 334.71/102.51
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.51
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.51
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.51
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.51
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.51
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.51
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.51
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.51
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.51
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.71/102.51
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.71/102.51
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.71/102.51
ACTIVE(U11(tt, z0, z1)) → c 334.71/102.51
ACTIVE(U21(tt, z0, z1)) → c2 334.71/102.51
ACTIVE(plus(z0, s(z1))) → c5 334.71/102.51
ACTIVE(x(z0, s(z1))) → c7 334.71/102.51
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.71/102.51
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.71/102.51
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.71/102.51
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.71/102.51
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.51
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.51
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.51
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.51
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.51
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.51
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.51
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.51
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.51
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.51
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.71/102.51
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.51
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.51
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.51
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.51
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.51
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.51
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.51
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.51
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.51
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.51
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.71/102.51
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.51
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.71/102.51
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.51
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.71/102.51
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.71/102.51
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.71/102.51
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.71/102.51
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.71/102.51
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.71/102.51
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.71/102.51
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.71/102.51
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.71/102.51
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.71/102.51
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.71/102.51
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.71/102.51
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.71/102.51
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.71/102.51
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.51
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.51
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.51
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.51
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.51
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.51
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.51
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.51
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.51
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.51
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.51
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.51
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.51
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.71/102.51
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.51
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.51
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.71/102.51
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.51
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.71/102.51
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.51
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.51
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.51
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.51
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.51
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.51
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.51
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.51
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.51
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.51
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.51
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.51
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.51
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.51
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.51
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.71/102.51
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.51
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.51
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.51
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.51
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.71/102.51
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.51
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.71/102.51
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.51
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.71/102.51
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.51
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.51
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.51
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.51
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.51
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.51
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.51
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.51
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.51
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.51
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.51
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.51
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.51
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.51
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.51
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.51
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.51
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.51
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.51
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.51
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.51
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.51
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.51
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.51
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.51
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.51
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.51
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.51
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.51
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.51
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.71/102.51
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.71/102.51
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.71/102.51
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.71/102.51
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.71/102.51
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.71/102.51
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.71/102.51
PROPER(s(tt)) → c36(S(ok(tt))) 334.71/102.51
PROPER(s(0)) → c36(S(ok(0))) 334.71/102.51
PROPER(plus(x0, U11(z0, z1, z2))) → c37(PLUS(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.71/102.51
PROPER(plus(x0, U12(z0, z1, z2))) → c37(PLUS(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.71/102.51
PROPER(plus(x0, s(z0))) → c37(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.71/102.51
PROPER(plus(x0, plus(z0, z1))) → c37(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.71/102.51
PROPER(plus(x0, U21(z0, z1, z2))) → c37(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.71/102.51
PROPER(plus(x0, U22(z0, z1, z2))) → c37(PLUS(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.71/102.51
PROPER(plus(x0, x(z0, z1))) → c37(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.71/102.51
PROPER(plus(U11(z0, z1, z2), x1)) → c37(PLUS(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.71/102.51
PROPER(plus(U12(z0, z1, z2), x1)) → c37(PLUS(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.71/102.51
PROPER(plus(s(z0), x1)) → c37(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.71/102.51
PROPER(plus(plus(z0, z1), x1)) → c37(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.71/102.51
PROPER(plus(U21(z0, z1, z2), x1)) → c37(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.71/102.51
PROPER(plus(U22(z0, z1, z2), x1)) → c37(PLUS(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.71/102.51
PROPER(plus(x(z0, z1), x1)) → c37(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.71/102.51
PROPER(plus(x0, tt)) → c37(PLUS(proper(x0), ok(tt)), PROPER(x0)) 334.71/102.51
PROPER(plus(x0, 0)) → c37(PLUS(proper(x0), ok(0)), PROPER(x0)) 334.71/102.51
PROPER(plus(tt, x1)) → c37(PLUS(ok(tt), proper(x1)), PROPER(x1)) 334.71/102.51
PROPER(plus(0, x1)) → c37(PLUS(ok(0), proper(x1)), PROPER(x1)) 334.71/102.51
PROPER(U21(x0, x1, U11(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.51
PROPER(U21(x0, x1, U12(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.51
PROPER(U21(x0, x1, s(z0))) → c38(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.51
PROPER(U21(x0, x1, plus(z0, z1))) → c38(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.51
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.51
PROPER(U21(x0, x1, U22(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.51
PROPER(U21(x0, x1, x(z0, z1))) → c38(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.51
PROPER(U21(x0, U11(z0, z1, z2), x2)) → c38(U21'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U21(x0, U12(z0, z1, z2), x2)) → c38(U21'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U21(x0, s(z0), x2)) → c38(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.51
PROPER(U21(x0, plus(z0, z1), x2)) → c38(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.51
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c38(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U21(x0, U22(z0, z1, z2), x2)) → c38(U21'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U21(x0, x(z0, z1), x2)) → c38(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.51
PROPER(U21(U11(z0, z1, z2), x1, x2)) → c38(U21'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U21(U12(z0, z1, z2), x1, x2)) → c38(U21'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U21(s(z0), x1, x2)) → c38(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U21(plus(z0, z1), x1, x2)) → c38(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c38(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U21(U22(z0, z1, z2), x1, x2)) → c38(U21'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U21(x(z0, z1), x1, x2)) → c38(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U21(x0, x1, tt)) → c38(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.51
PROPER(U21(x0, x1, 0)) → c38(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.51
PROPER(U21(x0, tt, x2)) → c38(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.51
PROPER(U21(x0, 0, x2)) → c38(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.51
PROPER(U21(tt, x1, x2)) → c38(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U21(0, x1, x2)) → c38(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, x1, U11(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.51
PROPER(U22(x0, x1, U12(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.51
PROPER(U22(x0, x1, s(z0))) → c39(U22'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.51
PROPER(U22(x0, x1, plus(z0, z1))) → c39(U22'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.51
PROPER(U22(x0, x1, U21(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.51
PROPER(U22(x0, x1, U22(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.51
PROPER(U22(x0, x1, x(z0, z1))) → c39(U22'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.51
PROPER(U22(x0, U11(z0, z1, z2), x2)) → c39(U22'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, U12(z0, z1, z2), x2)) → c39(U22'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, s(z0), x2)) → c39(U22'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, plus(z0, z1), x2)) → c39(U22'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, U21(z0, z1, z2), x2)) → c39(U22'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, U22(z0, z1, z2), x2)) → c39(U22'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, x(z0, z1), x2)) → c39(U22'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.51
PROPER(U22(U11(z0, z1, z2), x1, x2)) → c39(U22'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(U12(z0, z1, z2), x1, x2)) → c39(U22'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(s(z0), x1, x2)) → c39(U22'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(plus(z0, z1), x1, x2)) → c39(U22'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(U21(z0, z1, z2), x1, x2)) → c39(U22'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(U22(z0, z1, z2), x1, x2)) → c39(U22'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(x(z0, z1), x1, x2)) → c39(U22'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, x1, tt)) → c39(U22'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.51
PROPER(U22(x0, x1, 0)) → c39(U22'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.51
PROPER(U22(x0, tt, x2)) → c39(U22'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, 0, x2)) → c39(U22'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.51
PROPER(U22(tt, x1, x2)) → c39(U22'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(0, x1, x2)) → c39(U22'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(x(x0, U11(z0, z1, z2))) → c40(X(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.71/102.51
PROPER(x(x0, U12(z0, z1, z2))) → c40(X(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.71/102.51
PROPER(x(x0, s(z0))) → c40(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.71/102.51
PROPER(x(x0, plus(z0, z1))) → c40(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.71/102.51
PROPER(x(x0, U21(z0, z1, z2))) → c40(X(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.71/102.51
PROPER(x(x0, U22(z0, z1, z2))) → c40(X(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.71/102.51
PROPER(x(x0, x(z0, z1))) → c40(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.71/102.51
PROPER(x(U11(z0, z1, z2), x1)) → c40(X(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.71/102.51
PROPER(x(U12(z0, z1, z2), x1)) → c40(X(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.71/102.51
PROPER(x(s(z0), x1)) → c40(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.71/102.51
PROPER(x(plus(z0, z1), x1)) → c40(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.71/102.51
PROPER(x(U21(z0, z1, z2), x1)) → c40(X(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.71/102.51
PROPER(x(U22(z0, z1, z2), x1)) → c40(X(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.71/102.51
PROPER(x(x(z0, z1), x1)) → c40(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.71/102.51
PROPER(x(x0, tt)) → c40(X(proper(x0), ok(tt)), PROPER(x0)) 334.71/102.51
PROPER(x(x0, 0)) → c40(X(proper(x0), ok(0)), PROPER(x0)) 334.71/102.51
PROPER(x(tt, x1)) → c40(X(ok(tt), proper(x1)), PROPER(x1)) 334.71/102.51
PROPER(x(0, x1)) → c40(X(ok(0), proper(x1)), PROPER(x1))
S tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.71/102.51
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.71/102.51
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.71/102.51
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.71/102.51
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.51
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.51
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.51
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.51
S(mark(z0)) → c21(S(z0)) 334.71/102.51
S(ok(z0)) → c22(S(z0)) 334.71/102.51
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.51
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.51
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.51
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.51
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.51
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.51
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.51
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.51
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.51
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.71/102.51
TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) 334.71/102.51
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.71/102.51
ACTIVE(U11(tt, z0, z1)) → c 334.71/102.51
ACTIVE(U21(tt, z0, z1)) → c2 334.71/102.51
ACTIVE(plus(z0, s(z1))) → c5 334.71/102.51
ACTIVE(x(z0, s(z1))) → c7 334.71/102.51
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.71/102.51
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.71/102.51
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.71/102.51
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.71/102.51
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.51
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.51
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.51
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.51
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.51
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.51
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.51
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.51
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.51
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.51
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.71/102.51
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.51
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.51
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.51
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.51
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.51
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.51
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.51
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.51
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.51
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.51
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.71/102.51
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.51
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.71/102.51
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.51
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.71/102.51
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.71/102.51
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.71/102.51
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.71/102.51
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.71/102.51
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.71/102.51
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.71/102.51
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.71/102.51
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.71/102.51
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.71/102.51
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.71/102.51
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.71/102.51
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.71/102.51
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.71/102.51
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.51
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.51
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.51
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.51
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.51
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.51
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.51
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.51
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.51
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.51
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.51
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.51
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.51
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.71/102.51
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.51
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.51
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.71/102.51
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.51
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.71/102.51
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.51
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.51
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.51
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.51
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.51
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.51
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.51
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.51
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.51
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.51
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.51
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.51
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.51
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.51
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.51
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.71/102.51
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.51
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.51
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.51
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.51
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.71/102.51
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.51
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.71/102.51
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.51
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.71/102.51
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.51
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.51
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.51
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.51
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.51
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.51
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.51
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.51
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.51
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.51
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.51
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.51
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.51
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.51
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.51
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.51
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.51
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.51
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.51
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.51
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.51
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.51
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.51
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.51
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.51
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.51
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.51
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.51
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.51
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.51
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.71/102.51
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.71/102.51
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.71/102.51
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.71/102.51
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.71/102.51
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.71/102.51
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.71/102.51
PROPER(s(tt)) → c36(S(ok(tt))) 334.71/102.51
PROPER(s(0)) → c36(S(ok(0))) 334.71/102.51
PROPER(plus(x0, U11(z0, z1, z2))) → c37(PLUS(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.71/102.51
PROPER(plus(x0, U12(z0, z1, z2))) → c37(PLUS(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.71/102.51
PROPER(plus(x0, s(z0))) → c37(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.71/102.51
PROPER(plus(x0, plus(z0, z1))) → c37(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.71/102.51
PROPER(plus(x0, U21(z0, z1, z2))) → c37(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.71/102.51
PROPER(plus(x0, U22(z0, z1, z2))) → c37(PLUS(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.71/102.51
PROPER(plus(x0, x(z0, z1))) → c37(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.71/102.51
PROPER(plus(U11(z0, z1, z2), x1)) → c37(PLUS(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.71/102.51
PROPER(plus(U12(z0, z1, z2), x1)) → c37(PLUS(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.71/102.51
PROPER(plus(s(z0), x1)) → c37(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.71/102.51
PROPER(plus(plus(z0, z1), x1)) → c37(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.71/102.51
PROPER(plus(U21(z0, z1, z2), x1)) → c37(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.71/102.51
PROPER(plus(U22(z0, z1, z2), x1)) → c37(PLUS(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.71/102.51
PROPER(plus(x(z0, z1), x1)) → c37(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.71/102.51
PROPER(plus(x0, tt)) → c37(PLUS(proper(x0), ok(tt)), PROPER(x0)) 334.71/102.51
PROPER(plus(x0, 0)) → c37(PLUS(proper(x0), ok(0)), PROPER(x0)) 334.71/102.51
PROPER(plus(tt, x1)) → c37(PLUS(ok(tt), proper(x1)), PROPER(x1)) 334.71/102.51
PROPER(plus(0, x1)) → c37(PLUS(ok(0), proper(x1)), PROPER(x1)) 334.71/102.51
PROPER(U21(x0, x1, U11(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.51
PROPER(U21(x0, x1, U12(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.51
PROPER(U21(x0, x1, s(z0))) → c38(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.51
PROPER(U21(x0, x1, plus(z0, z1))) → c38(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.51
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.51
PROPER(U21(x0, x1, U22(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.51
PROPER(U21(x0, x1, x(z0, z1))) → c38(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.51
PROPER(U21(x0, U11(z0, z1, z2), x2)) → c38(U21'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U21(x0, U12(z0, z1, z2), x2)) → c38(U21'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U21(x0, s(z0), x2)) → c38(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.51
PROPER(U21(x0, plus(z0, z1), x2)) → c38(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.51
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c38(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U21(x0, U22(z0, z1, z2), x2)) → c38(U21'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U21(x0, x(z0, z1), x2)) → c38(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.51
PROPER(U21(U11(z0, z1, z2), x1, x2)) → c38(U21'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U21(U12(z0, z1, z2), x1, x2)) → c38(U21'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U21(s(z0), x1, x2)) → c38(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U21(plus(z0, z1), x1, x2)) → c38(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c38(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U21(U22(z0, z1, z2), x1, x2)) → c38(U21'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U21(x(z0, z1), x1, x2)) → c38(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U21(x0, x1, tt)) → c38(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.51
PROPER(U21(x0, x1, 0)) → c38(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.51
PROPER(U21(x0, tt, x2)) → c38(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.51
PROPER(U21(x0, 0, x2)) → c38(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.51
PROPER(U21(tt, x1, x2)) → c38(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U21(0, x1, x2)) → c38(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, x1, U11(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.51
PROPER(U22(x0, x1, U12(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.51
PROPER(U22(x0, x1, s(z0))) → c39(U22'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.51
PROPER(U22(x0, x1, plus(z0, z1))) → c39(U22'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.51
PROPER(U22(x0, x1, U21(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.51
PROPER(U22(x0, x1, U22(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.51
PROPER(U22(x0, x1, x(z0, z1))) → c39(U22'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.51
PROPER(U22(x0, U11(z0, z1, z2), x2)) → c39(U22'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, U12(z0, z1, z2), x2)) → c39(U22'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, s(z0), x2)) → c39(U22'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, plus(z0, z1), x2)) → c39(U22'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, U21(z0, z1, z2), x2)) → c39(U22'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, U22(z0, z1, z2), x2)) → c39(U22'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, x(z0, z1), x2)) → c39(U22'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.51
PROPER(U22(U11(z0, z1, z2), x1, x2)) → c39(U22'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(U12(z0, z1, z2), x1, x2)) → c39(U22'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(s(z0), x1, x2)) → c39(U22'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(plus(z0, z1), x1, x2)) → c39(U22'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(U21(z0, z1, z2), x1, x2)) → c39(U22'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(U22(z0, z1, z2), x1, x2)) → c39(U22'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(x(z0, z1), x1, x2)) → c39(U22'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, x1, tt)) → c39(U22'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.51
PROPER(U22(x0, x1, 0)) → c39(U22'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.51
PROPER(U22(x0, tt, x2)) → c39(U22'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, 0, x2)) → c39(U22'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.51
PROPER(U22(tt, x1, x2)) → c39(U22'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(0, x1, x2)) → c39(U22'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(x(x0, U11(z0, z1, z2))) → c40(X(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.71/102.51
PROPER(x(x0, U12(z0, z1, z2))) → c40(X(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.71/102.51
PROPER(x(x0, s(z0))) → c40(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.71/102.51
PROPER(x(x0, plus(z0, z1))) → c40(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.71/102.51
PROPER(x(x0, U21(z0, z1, z2))) → c40(X(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.71/102.51
PROPER(x(x0, U22(z0, z1, z2))) → c40(X(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.71/102.51
PROPER(x(x0, x(z0, z1))) → c40(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.71/102.51
PROPER(x(U11(z0, z1, z2), x1)) → c40(X(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.71/102.51
PROPER(x(U12(z0, z1, z2), x1)) → c40(X(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.71/102.51
PROPER(x(s(z0), x1)) → c40(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.71/102.51
PROPER(x(plus(z0, z1), x1)) → c40(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.71/102.51
PROPER(x(U21(z0, z1, z2), x1)) → c40(X(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.71/102.51
PROPER(x(U22(z0, z1, z2), x1)) → c40(X(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.71/102.51
PROPER(x(x(z0, z1), x1)) → c40(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.71/102.51
PROPER(x(x0, tt)) → c40(X(proper(x0), ok(tt)), PROPER(x0)) 334.71/102.51
PROPER(x(x0, 0)) → c40(X(proper(x0), ok(0)), PROPER(x0)) 334.71/102.51
PROPER(x(tt, x1)) → c40(X(ok(tt), proper(x1)), PROPER(x1)) 334.71/102.51
PROPER(x(0, x1)) → c40(X(ok(0), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, TOP, PROPER

Compound Symbols:

c11, c12, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c42, c43, c, c2, c5, c7, c4, c8, c1, c9, c3, c10, c6, c13, c34, c14, c41, c33, c33, c35, c35, c36, c36, c37, c37, c38, c38, c39, c39, c40, c40

334.71/102.51
334.71/102.51

(81) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace TOP(mark(z0)) → c42(TOP(proper(z0)), PROPER(z0)) by

TOP(mark(U11(z0, z1, z2))) → c42(TOP(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.71/102.51
TOP(mark(tt)) → c42(TOP(ok(tt)), PROPER(tt)) 334.71/102.51
TOP(mark(U12(z0, z1, z2))) → c42(TOP(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.71/102.51
TOP(mark(s(z0))) → c42(TOP(s(proper(z0))), PROPER(s(z0))) 334.71/102.51
TOP(mark(plus(z0, z1))) → c42(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.71/102.51
TOP(mark(U21(z0, z1, z2))) → c42(TOP(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.71/102.51
TOP(mark(U22(z0, z1, z2))) → c42(TOP(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.71/102.51
TOP(mark(x(z0, z1))) → c42(TOP(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.71/102.51
TOP(mark(0)) → c42(TOP(ok(0)), PROPER(0))
334.71/102.51
334.71/102.51

(82) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.71/102.51
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.71/102.51
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.71/102.51
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.71/102.51
active(plus(z0, 0)) → mark(z0) 334.71/102.51
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.71/102.51
active(x(z0, 0)) → mark(0) 334.71/102.51
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.71/102.51
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.71/102.51
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.71/102.51
active(s(z0)) → s(active(z0)) 334.71/102.51
active(plus(z0, z1)) → plus(active(z0), z1) 334.71/102.51
active(plus(z0, z1)) → plus(z0, active(z1)) 334.71/102.51
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.71/102.51
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.71/102.51
active(x(z0, z1)) → x(active(z0), z1) 334.71/102.51
active(x(z0, z1)) → x(z0, active(z1)) 334.71/102.51
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.71/102.51
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.71/102.51
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.71/102.51
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.71/102.51
s(mark(z0)) → mark(s(z0)) 334.71/102.51
s(ok(z0)) → ok(s(z0)) 334.71/102.51
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.71/102.51
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.71/102.51
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.71/102.51
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.71/102.51
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.71/102.51
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.71/102.51
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.71/102.51
x(mark(z0), z1) → mark(x(z0, z1)) 334.71/102.51
x(z0, mark(z1)) → mark(x(z0, z1)) 334.71/102.51
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.71/102.51
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.71/102.51
proper(tt) → ok(tt) 334.71/102.51
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.71/102.51
proper(s(z0)) → s(proper(z0)) 334.71/102.51
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.71/102.51
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.71/102.51
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.71/102.51
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.71/102.51
proper(0) → ok(0) 334.71/102.51
top(mark(z0)) → top(proper(z0)) 334.71/102.51
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.71/102.51
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.71/102.51
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.71/102.51
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.71/102.51
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.51
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.51
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.51
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.51
S(mark(z0)) → c21(S(z0)) 334.71/102.51
S(ok(z0)) → c22(S(z0)) 334.71/102.51
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.51
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.51
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.51
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.51
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.51
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.51
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.51
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.51
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.51
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.71/102.51
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.71/102.51
ACTIVE(U11(tt, z0, z1)) → c 334.71/102.51
ACTIVE(U21(tt, z0, z1)) → c2 334.71/102.51
ACTIVE(plus(z0, s(z1))) → c5 334.71/102.51
ACTIVE(x(z0, s(z1))) → c7 334.71/102.51
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.71/102.51
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.71/102.51
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.71/102.51
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.71/102.51
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.51
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.51
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.51
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.51
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.51
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.51
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.51
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.51
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.51
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.51
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.71/102.51
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.51
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.51
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.51
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.51
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.51
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.51
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.51
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.51
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.51
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.51
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.71/102.51
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.51
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.71/102.51
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.51
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.71/102.51
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.71/102.51
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.71/102.51
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.71/102.51
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.71/102.51
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.71/102.51
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.71/102.51
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.71/102.51
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.71/102.51
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.71/102.51
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.71/102.51
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.71/102.51
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.71/102.51
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.71/102.51
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.51
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.51
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.51
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.51
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.51
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.51
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.51
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.51
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.51
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.51
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.51
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.51
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.51
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.71/102.51
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.51
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.51
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.71/102.51
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.51
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.71/102.51
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.51
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.51
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.51
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.51
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.51
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.51
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.51
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.51
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.51
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.51
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.51
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.51
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.51
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.51
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.51
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.71/102.51
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.51
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.51
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.51
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.51
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.71/102.51
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.51
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.71/102.51
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.51
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.71/102.51
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.51
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.51
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.51
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.51
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.51
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.51
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.51
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.51
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.51
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.51
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.51
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.51
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.51
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.51
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.51
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.51
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.51
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.51
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.51
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.51
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.51
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.51
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.51
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.51
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.51
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.51
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.51
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.51
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.51
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.51
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.71/102.51
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.71/102.51
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.71/102.51
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.71/102.51
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.71/102.51
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.71/102.51
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.71/102.51
PROPER(s(tt)) → c36(S(ok(tt))) 334.71/102.51
PROPER(s(0)) → c36(S(ok(0))) 334.71/102.51
PROPER(plus(x0, U11(z0, z1, z2))) → c37(PLUS(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.71/102.51
PROPER(plus(x0, U12(z0, z1, z2))) → c37(PLUS(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.71/102.51
PROPER(plus(x0, s(z0))) → c37(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.71/102.51
PROPER(plus(x0, plus(z0, z1))) → c37(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.71/102.51
PROPER(plus(x0, U21(z0, z1, z2))) → c37(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.71/102.51
PROPER(plus(x0, U22(z0, z1, z2))) → c37(PLUS(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.71/102.51
PROPER(plus(x0, x(z0, z1))) → c37(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.71/102.51
PROPER(plus(U11(z0, z1, z2), x1)) → c37(PLUS(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.71/102.51
PROPER(plus(U12(z0, z1, z2), x1)) → c37(PLUS(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.71/102.51
PROPER(plus(s(z0), x1)) → c37(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.71/102.51
PROPER(plus(plus(z0, z1), x1)) → c37(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.71/102.51
PROPER(plus(U21(z0, z1, z2), x1)) → c37(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.71/102.51
PROPER(plus(U22(z0, z1, z2), x1)) → c37(PLUS(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.71/102.51
PROPER(plus(x(z0, z1), x1)) → c37(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.71/102.51
PROPER(plus(x0, tt)) → c37(PLUS(proper(x0), ok(tt)), PROPER(x0)) 334.71/102.51
PROPER(plus(x0, 0)) → c37(PLUS(proper(x0), ok(0)), PROPER(x0)) 334.71/102.51
PROPER(plus(tt, x1)) → c37(PLUS(ok(tt), proper(x1)), PROPER(x1)) 334.71/102.51
PROPER(plus(0, x1)) → c37(PLUS(ok(0), proper(x1)), PROPER(x1)) 334.71/102.51
PROPER(U21(x0, x1, U11(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.51
PROPER(U21(x0, x1, U12(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.51
PROPER(U21(x0, x1, s(z0))) → c38(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.51
PROPER(U21(x0, x1, plus(z0, z1))) → c38(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.51
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.51
PROPER(U21(x0, x1, U22(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.51
PROPER(U21(x0, x1, x(z0, z1))) → c38(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.51
PROPER(U21(x0, U11(z0, z1, z2), x2)) → c38(U21'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U21(x0, U12(z0, z1, z2), x2)) → c38(U21'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U21(x0, s(z0), x2)) → c38(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.51
PROPER(U21(x0, plus(z0, z1), x2)) → c38(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.51
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c38(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U21(x0, U22(z0, z1, z2), x2)) → c38(U21'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U21(x0, x(z0, z1), x2)) → c38(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.51
PROPER(U21(U11(z0, z1, z2), x1, x2)) → c38(U21'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U21(U12(z0, z1, z2), x1, x2)) → c38(U21'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U21(s(z0), x1, x2)) → c38(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U21(plus(z0, z1), x1, x2)) → c38(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c38(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U21(U22(z0, z1, z2), x1, x2)) → c38(U21'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U21(x(z0, z1), x1, x2)) → c38(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U21(x0, x1, tt)) → c38(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.51
PROPER(U21(x0, x1, 0)) → c38(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.51
PROPER(U21(x0, tt, x2)) → c38(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.51
PROPER(U21(x0, 0, x2)) → c38(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.51
PROPER(U21(tt, x1, x2)) → c38(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U21(0, x1, x2)) → c38(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, x1, U11(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.51
PROPER(U22(x0, x1, U12(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.51
PROPER(U22(x0, x1, s(z0))) → c39(U22'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.51
PROPER(U22(x0, x1, plus(z0, z1))) → c39(U22'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.51
PROPER(U22(x0, x1, U21(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.51
PROPER(U22(x0, x1, U22(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.51
PROPER(U22(x0, x1, x(z0, z1))) → c39(U22'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.51
PROPER(U22(x0, U11(z0, z1, z2), x2)) → c39(U22'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, U12(z0, z1, z2), x2)) → c39(U22'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, s(z0), x2)) → c39(U22'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, plus(z0, z1), x2)) → c39(U22'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, U21(z0, z1, z2), x2)) → c39(U22'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, U22(z0, z1, z2), x2)) → c39(U22'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, x(z0, z1), x2)) → c39(U22'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.51
PROPER(U22(U11(z0, z1, z2), x1, x2)) → c39(U22'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(U12(z0, z1, z2), x1, x2)) → c39(U22'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(s(z0), x1, x2)) → c39(U22'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(plus(z0, z1), x1, x2)) → c39(U22'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(U21(z0, z1, z2), x1, x2)) → c39(U22'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(U22(z0, z1, z2), x1, x2)) → c39(U22'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(x(z0, z1), x1, x2)) → c39(U22'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, x1, tt)) → c39(U22'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.51
PROPER(U22(x0, x1, 0)) → c39(U22'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.51
PROPER(U22(x0, tt, x2)) → c39(U22'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.51
PROPER(U22(x0, 0, x2)) → c39(U22'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.51
PROPER(U22(tt, x1, x2)) → c39(U22'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(U22(0, x1, x2)) → c39(U22'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.51
PROPER(x(x0, U11(z0, z1, z2))) → c40(X(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.71/102.51
PROPER(x(x0, U12(z0, z1, z2))) → c40(X(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.71/102.51
PROPER(x(x0, s(z0))) → c40(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.71/102.51
PROPER(x(x0, plus(z0, z1))) → c40(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.71/102.51
PROPER(x(x0, U21(z0, z1, z2))) → c40(X(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.71/102.51
PROPER(x(x0, U22(z0, z1, z2))) → c40(X(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.71/102.51
PROPER(x(x0, x(z0, z1))) → c40(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.71/102.51
PROPER(x(U11(z0, z1, z2), x1)) → c40(X(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.71/102.51
PROPER(x(U12(z0, z1, z2), x1)) → c40(X(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.71/102.51
PROPER(x(s(z0), x1)) → c40(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.71/102.51
PROPER(x(plus(z0, z1), x1)) → c40(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.71/102.51
PROPER(x(U21(z0, z1, z2), x1)) → c40(X(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.71/102.51
PROPER(x(U22(z0, z1, z2), x1)) → c40(X(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.71/102.51
PROPER(x(x(z0, z1), x1)) → c40(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.71/102.51
PROPER(x(x0, tt)) → c40(X(proper(x0), ok(tt)), PROPER(x0)) 334.71/102.51
PROPER(x(x0, 0)) → c40(X(proper(x0), ok(0)), PROPER(x0)) 334.71/102.51
PROPER(x(tt, x1)) → c40(X(ok(tt), proper(x1)), PROPER(x1)) 334.71/102.51
PROPER(x(0, x1)) → c40(X(ok(0), proper(x1)), PROPER(x1)) 334.71/102.51
TOP(mark(U11(z0, z1, z2))) → c42(TOP(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.71/102.51
TOP(mark(tt)) → c42(TOP(ok(tt)), PROPER(tt)) 334.71/102.51
TOP(mark(U12(z0, z1, z2))) → c42(TOP(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.71/102.51
TOP(mark(s(z0))) → c42(TOP(s(proper(z0))), PROPER(s(z0))) 334.71/102.51
TOP(mark(plus(z0, z1))) → c42(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.71/102.51
TOP(mark(U21(z0, z1, z2))) → c42(TOP(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.71/102.51
TOP(mark(U22(z0, z1, z2))) → c42(TOP(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.71/102.51
TOP(mark(x(z0, z1))) → c42(TOP(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.71/102.51
TOP(mark(0)) → c42(TOP(ok(0)), PROPER(0))
S tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.71/102.51
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.71/102.51
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.71/102.51
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.71/102.51
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.51
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.51
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.51
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.51
S(mark(z0)) → c21(S(z0)) 334.71/102.51
S(ok(z0)) → c22(S(z0)) 334.71/102.51
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.51
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.51
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.51
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.51
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.51
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.51
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.51
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.51
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.51
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.71/102.51
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.71/102.51
ACTIVE(U11(tt, z0, z1)) → c 334.71/102.51
ACTIVE(U21(tt, z0, z1)) → c2 334.71/102.51
ACTIVE(plus(z0, s(z1))) → c5 334.71/102.51
ACTIVE(x(z0, s(z1))) → c7 334.71/102.51
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.71/102.51
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.71/102.51
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.71/102.51
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.71/102.51
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.51
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.51
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.51
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.51
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.51
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.51
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.51
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.51
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.51
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.51
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.51
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.51
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.71/102.51
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.51
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.51
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.51
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.51
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.52
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.52
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.52
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.52
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.52
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.52
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.71/102.52
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.71/102.52
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.52
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.71/102.52
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.71/102.52
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.71/102.52
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.71/102.52
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.71/102.52
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.71/102.52
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.71/102.52
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.71/102.52
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.71/102.52
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.71/102.52
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.71/102.52
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.71/102.52
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.71/102.52
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.71/102.52
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.52
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.52
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.52
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.52
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.52
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.52
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.52
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.52
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.52
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.52
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.52
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.71/102.52
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.52
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.71/102.52
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.52
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.71/102.52
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.52
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.52
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.52
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.52
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.52
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.52
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.52
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.52
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.52
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.52
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.52
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.52
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.52
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.52
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.71/102.52
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.52
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.52
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.52
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.71/102.52
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.52
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.71/102.52
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.71/102.52
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.52
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.52
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.52
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.52
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.52
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.52
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.52
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.52
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.52
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.52
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.52
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.52
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.52
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.52
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.52
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.52
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.52
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.52
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.52
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.52
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.52
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.52
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.52
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.52
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.52
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.52
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.52
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.52
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.52
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.52
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.71/102.52
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.71/102.52
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.71/102.52
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.71/102.52
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.71/102.52
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.71/102.52
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.71/102.52
PROPER(s(tt)) → c36(S(ok(tt))) 334.71/102.52
PROPER(s(0)) → c36(S(ok(0))) 334.71/102.52
PROPER(plus(x0, U11(z0, z1, z2))) → c37(PLUS(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.71/102.52
PROPER(plus(x0, U12(z0, z1, z2))) → c37(PLUS(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.71/102.52
PROPER(plus(x0, s(z0))) → c37(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.71/102.52
PROPER(plus(x0, plus(z0, z1))) → c37(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.71/102.52
PROPER(plus(x0, U21(z0, z1, z2))) → c37(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.71/102.52
PROPER(plus(x0, U22(z0, z1, z2))) → c37(PLUS(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.71/102.52
PROPER(plus(x0, x(z0, z1))) → c37(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.71/102.52
PROPER(plus(U11(z0, z1, z2), x1)) → c37(PLUS(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.71/102.52
PROPER(plus(U12(z0, z1, z2), x1)) → c37(PLUS(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.71/102.52
PROPER(plus(s(z0), x1)) → c37(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.71/102.52
PROPER(plus(plus(z0, z1), x1)) → c37(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.71/102.52
PROPER(plus(U21(z0, z1, z2), x1)) → c37(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.71/102.52
PROPER(plus(U22(z0, z1, z2), x1)) → c37(PLUS(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.71/102.52
PROPER(plus(x(z0, z1), x1)) → c37(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.71/102.52
PROPER(plus(x0, tt)) → c37(PLUS(proper(x0), ok(tt)), PROPER(x0)) 334.71/102.52
PROPER(plus(x0, 0)) → c37(PLUS(proper(x0), ok(0)), PROPER(x0)) 334.71/102.52
PROPER(plus(tt, x1)) → c37(PLUS(ok(tt), proper(x1)), PROPER(x1)) 334.71/102.52
PROPER(plus(0, x1)) → c37(PLUS(ok(0), proper(x1)), PROPER(x1)) 334.71/102.52
PROPER(U21(x0, x1, U11(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.52
PROPER(U21(x0, x1, U12(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.52
PROPER(U21(x0, x1, s(z0))) → c38(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.52
PROPER(U21(x0, x1, plus(z0, z1))) → c38(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.52
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.52
PROPER(U21(x0, x1, U22(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.52
PROPER(U21(x0, x1, x(z0, z1))) → c38(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.52
PROPER(U21(x0, U11(z0, z1, z2), x2)) → c38(U21'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U21(x0, U12(z0, z1, z2), x2)) → c38(U21'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U21(x0, s(z0), x2)) → c38(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.52
PROPER(U21(x0, plus(z0, z1), x2)) → c38(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.52
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c38(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U21(x0, U22(z0, z1, z2), x2)) → c38(U21'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U21(x0, x(z0, z1), x2)) → c38(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.52
PROPER(U21(U11(z0, z1, z2), x1, x2)) → c38(U21'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U21(U12(z0, z1, z2), x1, x2)) → c38(U21'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U21(s(z0), x1, x2)) → c38(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U21(plus(z0, z1), x1, x2)) → c38(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c38(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U21(U22(z0, z1, z2), x1, x2)) → c38(U21'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U21(x(z0, z1), x1, x2)) → c38(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U21(x0, x1, tt)) → c38(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.52
PROPER(U21(x0, x1, 0)) → c38(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.52
PROPER(U21(x0, tt, x2)) → c38(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.52
PROPER(U21(x0, 0, x2)) → c38(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.52
PROPER(U21(tt, x1, x2)) → c38(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U21(0, x1, x2)) → c38(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U22(x0, x1, U11(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.52
PROPER(U22(x0, x1, U12(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.52
PROPER(U22(x0, x1, s(z0))) → c39(U22'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.52
PROPER(U22(x0, x1, plus(z0, z1))) → c39(U22'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.52
PROPER(U22(x0, x1, U21(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.52
PROPER(U22(x0, x1, U22(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.52
PROPER(U22(x0, x1, x(z0, z1))) → c39(U22'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.52
PROPER(U22(x0, U11(z0, z1, z2), x2)) → c39(U22'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U22(x0, U12(z0, z1, z2), x2)) → c39(U22'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U22(x0, s(z0), x2)) → c39(U22'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.52
PROPER(U22(x0, plus(z0, z1), x2)) → c39(U22'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.52
PROPER(U22(x0, U21(z0, z1, z2), x2)) → c39(U22'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U22(x0, U22(z0, z1, z2), x2)) → c39(U22'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U22(x0, x(z0, z1), x2)) → c39(U22'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.52
PROPER(U22(U11(z0, z1, z2), x1, x2)) → c39(U22'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U22(U12(z0, z1, z2), x1, x2)) → c39(U22'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U22(s(z0), x1, x2)) → c39(U22'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U22(plus(z0, z1), x1, x2)) → c39(U22'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U22(U21(z0, z1, z2), x1, x2)) → c39(U22'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U22(U22(z0, z1, z2), x1, x2)) → c39(U22'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U22(x(z0, z1), x1, x2)) → c39(U22'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U22(x0, x1, tt)) → c39(U22'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.52
PROPER(U22(x0, x1, 0)) → c39(U22'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.52
PROPER(U22(x0, tt, x2)) → c39(U22'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.52
PROPER(U22(x0, 0, x2)) → c39(U22'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.52
PROPER(U22(tt, x1, x2)) → c39(U22'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U22(0, x1, x2)) → c39(U22'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(x(x0, U11(z0, z1, z2))) → c40(X(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.71/102.52
PROPER(x(x0, U12(z0, z1, z2))) → c40(X(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.71/102.52
PROPER(x(x0, s(z0))) → c40(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.71/102.52
PROPER(x(x0, plus(z0, z1))) → c40(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.71/102.52
PROPER(x(x0, U21(z0, z1, z2))) → c40(X(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.71/102.52
PROPER(x(x0, U22(z0, z1, z2))) → c40(X(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.71/102.52
PROPER(x(x0, x(z0, z1))) → c40(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.71/102.52
PROPER(x(U11(z0, z1, z2), x1)) → c40(X(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.71/102.52
PROPER(x(U12(z0, z1, z2), x1)) → c40(X(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.71/102.52
PROPER(x(s(z0), x1)) → c40(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.71/102.52
PROPER(x(plus(z0, z1), x1)) → c40(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.71/102.52
PROPER(x(U21(z0, z1, z2), x1)) → c40(X(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.71/102.52
PROPER(x(U22(z0, z1, z2), x1)) → c40(X(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.71/102.52
PROPER(x(x(z0, z1), x1)) → c40(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.71/102.52
PROPER(x(x0, tt)) → c40(X(proper(x0), ok(tt)), PROPER(x0)) 334.71/102.52
PROPER(x(x0, 0)) → c40(X(proper(x0), ok(0)), PROPER(x0)) 334.71/102.52
PROPER(x(tt, x1)) → c40(X(ok(tt), proper(x1)), PROPER(x1)) 334.71/102.52
PROPER(x(0, x1)) → c40(X(ok(0), proper(x1)), PROPER(x1)) 334.71/102.52
TOP(mark(U11(z0, z1, z2))) → c42(TOP(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.71/102.52
TOP(mark(tt)) → c42(TOP(ok(tt)), PROPER(tt)) 334.71/102.52
TOP(mark(U12(z0, z1, z2))) → c42(TOP(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.71/102.52
TOP(mark(s(z0))) → c42(TOP(s(proper(z0))), PROPER(s(z0))) 334.71/102.52
TOP(mark(plus(z0, z1))) → c42(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.71/102.52
TOP(mark(U21(z0, z1, z2))) → c42(TOP(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.71/102.52
TOP(mark(U22(z0, z1, z2))) → c42(TOP(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.71/102.52
TOP(mark(x(z0, z1))) → c42(TOP(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.71/102.52
TOP(mark(0)) → c42(TOP(ok(0)), PROPER(0))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, TOP, PROPER

Compound Symbols:

c11, c12, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c43, c, c2, c5, c7, c4, c8, c1, c9, c3, c10, c6, c13, c34, c14, c41, c33, c33, c35, c35, c36, c36, c37, c37, c38, c38, c39, c39, c40, c40, c42

334.71/102.52
334.71/102.52

(83) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 2 trailing tuple parts
334.71/102.52
334.71/102.52

(84) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.71/102.52
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.71/102.52
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.71/102.52
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.71/102.52
active(plus(z0, 0)) → mark(z0) 334.71/102.52
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.71/102.52
active(x(z0, 0)) → mark(0) 334.71/102.52
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.71/102.52
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.71/102.52
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.71/102.52
active(s(z0)) → s(active(z0)) 334.71/102.52
active(plus(z0, z1)) → plus(active(z0), z1) 334.71/102.52
active(plus(z0, z1)) → plus(z0, active(z1)) 334.71/102.52
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.71/102.52
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.71/102.52
active(x(z0, z1)) → x(active(z0), z1) 334.71/102.52
active(x(z0, z1)) → x(z0, active(z1)) 334.71/102.52
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.71/102.52
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.71/102.52
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.71/102.52
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.71/102.52
s(mark(z0)) → mark(s(z0)) 334.71/102.52
s(ok(z0)) → ok(s(z0)) 334.71/102.52
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.71/102.52
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.71/102.52
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.71/102.52
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.71/102.52
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.71/102.52
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.71/102.52
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.71/102.52
x(mark(z0), z1) → mark(x(z0, z1)) 334.71/102.52
x(z0, mark(z1)) → mark(x(z0, z1)) 334.71/102.52
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.71/102.52
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.71/102.52
proper(tt) → ok(tt) 334.71/102.52
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.71/102.52
proper(s(z0)) → s(proper(z0)) 334.71/102.52
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.71/102.52
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.71/102.52
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.71/102.52
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.71/102.52
proper(0) → ok(0) 334.71/102.52
top(mark(z0)) → top(proper(z0)) 334.71/102.52
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.71/102.52
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.71/102.52
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.71/102.52
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.71/102.52
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.52
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.52
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.52
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.52
S(mark(z0)) → c21(S(z0)) 334.71/102.52
S(ok(z0)) → c22(S(z0)) 334.71/102.52
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.52
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.52
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.52
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.52
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.52
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.52
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.52
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.52
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.52
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.71/102.52
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.71/102.52
ACTIVE(U11(tt, z0, z1)) → c 334.71/102.52
ACTIVE(U21(tt, z0, z1)) → c2 334.71/102.52
ACTIVE(plus(z0, s(z1))) → c5 334.71/102.52
ACTIVE(x(z0, s(z1))) → c7 334.71/102.52
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.71/102.52
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.71/102.52
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.71/102.52
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.71/102.52
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.52
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.52
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.52
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.52
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.52
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.52
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.52
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.52
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.52
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.71/102.52
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.52
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.52
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.52
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.52
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.52
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.52
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.52
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.52
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.52
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.52
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.71/102.52
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.71/102.52
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.52
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.71/102.52
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.71/102.52
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.71/102.52
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.71/102.52
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.71/102.52
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.71/102.52
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.71/102.52
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.71/102.52
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.71/102.52
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.71/102.52
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.71/102.52
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.71/102.52
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.71/102.52
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.71/102.52
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.52
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.52
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.52
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.52
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.52
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.52
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.52
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.52
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.52
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.52
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.52
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.71/102.52
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.52
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.71/102.52
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.52
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.71/102.52
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.52
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.52
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.52
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.52
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.52
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.52
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.52
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.52
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.52
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.52
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.52
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.52
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.52
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.52
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.71/102.52
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.52
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.52
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.52
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.71/102.52
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.52
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.71/102.52
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.71/102.52
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.52
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.52
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.52
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.52
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.52
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.52
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.52
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.52
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.52
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.52
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.52
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.52
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.52
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.52
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.52
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.52
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.52
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.52
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.52
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.52
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.52
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.52
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.52
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.52
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.52
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.52
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.52
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.52
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.52
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.52
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.71/102.52
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.71/102.52
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.71/102.52
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.71/102.52
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.71/102.52
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.71/102.52
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.71/102.52
PROPER(s(tt)) → c36(S(ok(tt))) 334.71/102.52
PROPER(s(0)) → c36(S(ok(0))) 334.71/102.52
PROPER(plus(x0, U11(z0, z1, z2))) → c37(PLUS(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.71/102.52
PROPER(plus(x0, U12(z0, z1, z2))) → c37(PLUS(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.71/102.52
PROPER(plus(x0, s(z0))) → c37(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.71/102.52
PROPER(plus(x0, plus(z0, z1))) → c37(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.71/102.52
PROPER(plus(x0, U21(z0, z1, z2))) → c37(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.71/102.52
PROPER(plus(x0, U22(z0, z1, z2))) → c37(PLUS(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.71/102.52
PROPER(plus(x0, x(z0, z1))) → c37(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.71/102.52
PROPER(plus(U11(z0, z1, z2), x1)) → c37(PLUS(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.71/102.52
PROPER(plus(U12(z0, z1, z2), x1)) → c37(PLUS(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.71/102.52
PROPER(plus(s(z0), x1)) → c37(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.71/102.52
PROPER(plus(plus(z0, z1), x1)) → c37(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.71/102.52
PROPER(plus(U21(z0, z1, z2), x1)) → c37(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.71/102.52
PROPER(plus(U22(z0, z1, z2), x1)) → c37(PLUS(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.71/102.52
PROPER(plus(x(z0, z1), x1)) → c37(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.71/102.52
PROPER(plus(x0, tt)) → c37(PLUS(proper(x0), ok(tt)), PROPER(x0)) 334.71/102.52
PROPER(plus(x0, 0)) → c37(PLUS(proper(x0), ok(0)), PROPER(x0)) 334.71/102.52
PROPER(plus(tt, x1)) → c37(PLUS(ok(tt), proper(x1)), PROPER(x1)) 334.71/102.52
PROPER(plus(0, x1)) → c37(PLUS(ok(0), proper(x1)), PROPER(x1)) 334.71/102.52
PROPER(U21(x0, x1, U11(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.52
PROPER(U21(x0, x1, U12(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.52
PROPER(U21(x0, x1, s(z0))) → c38(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.52
PROPER(U21(x0, x1, plus(z0, z1))) → c38(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.52
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.52
PROPER(U21(x0, x1, U22(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.52
PROPER(U21(x0, x1, x(z0, z1))) → c38(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.52
PROPER(U21(x0, U11(z0, z1, z2), x2)) → c38(U21'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U21(x0, U12(z0, z1, z2), x2)) → c38(U21'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U21(x0, s(z0), x2)) → c38(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.52
PROPER(U21(x0, plus(z0, z1), x2)) → c38(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.52
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c38(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U21(x0, U22(z0, z1, z2), x2)) → c38(U21'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U21(x0, x(z0, z1), x2)) → c38(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.52
PROPER(U21(U11(z0, z1, z2), x1, x2)) → c38(U21'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U21(U12(z0, z1, z2), x1, x2)) → c38(U21'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U21(s(z0), x1, x2)) → c38(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U21(plus(z0, z1), x1, x2)) → c38(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c38(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U21(U22(z0, z1, z2), x1, x2)) → c38(U21'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U21(x(z0, z1), x1, x2)) → c38(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U21(x0, x1, tt)) → c38(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.52
PROPER(U21(x0, x1, 0)) → c38(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.52
PROPER(U21(x0, tt, x2)) → c38(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.52
PROPER(U21(x0, 0, x2)) → c38(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.52
PROPER(U21(tt, x1, x2)) → c38(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U21(0, x1, x2)) → c38(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U22(x0, x1, U11(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.52
PROPER(U22(x0, x1, U12(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.52
PROPER(U22(x0, x1, s(z0))) → c39(U22'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.52
PROPER(U22(x0, x1, plus(z0, z1))) → c39(U22'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.52
PROPER(U22(x0, x1, U21(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.52
PROPER(U22(x0, x1, U22(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.52
PROPER(U22(x0, x1, x(z0, z1))) → c39(U22'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.52
PROPER(U22(x0, U11(z0, z1, z2), x2)) → c39(U22'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U22(x0, U12(z0, z1, z2), x2)) → c39(U22'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U22(x0, s(z0), x2)) → c39(U22'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.52
PROPER(U22(x0, plus(z0, z1), x2)) → c39(U22'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.52
PROPER(U22(x0, U21(z0, z1, z2), x2)) → c39(U22'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U22(x0, U22(z0, z1, z2), x2)) → c39(U22'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U22(x0, x(z0, z1), x2)) → c39(U22'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.52
PROPER(U22(U11(z0, z1, z2), x1, x2)) → c39(U22'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U22(U12(z0, z1, z2), x1, x2)) → c39(U22'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U22(s(z0), x1, x2)) → c39(U22'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U22(plus(z0, z1), x1, x2)) → c39(U22'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U22(U21(z0, z1, z2), x1, x2)) → c39(U22'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U22(U22(z0, z1, z2), x1, x2)) → c39(U22'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U22(x(z0, z1), x1, x2)) → c39(U22'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U22(x0, x1, tt)) → c39(U22'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.52
PROPER(U22(x0, x1, 0)) → c39(U22'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.52
PROPER(U22(x0, tt, x2)) → c39(U22'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.52
PROPER(U22(x0, 0, x2)) → c39(U22'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.52
PROPER(U22(tt, x1, x2)) → c39(U22'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U22(0, x1, x2)) → c39(U22'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(x(x0, U11(z0, z1, z2))) → c40(X(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.71/102.52
PROPER(x(x0, U12(z0, z1, z2))) → c40(X(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.71/102.52
PROPER(x(x0, s(z0))) → c40(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.71/102.52
PROPER(x(x0, plus(z0, z1))) → c40(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.71/102.52
PROPER(x(x0, U21(z0, z1, z2))) → c40(X(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.71/102.52
PROPER(x(x0, U22(z0, z1, z2))) → c40(X(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.71/102.52
PROPER(x(x0, x(z0, z1))) → c40(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.71/102.52
PROPER(x(U11(z0, z1, z2), x1)) → c40(X(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.71/102.52
PROPER(x(U12(z0, z1, z2), x1)) → c40(X(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.71/102.52
PROPER(x(s(z0), x1)) → c40(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.71/102.52
PROPER(x(plus(z0, z1), x1)) → c40(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.71/102.52
PROPER(x(U21(z0, z1, z2), x1)) → c40(X(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.71/102.52
PROPER(x(U22(z0, z1, z2), x1)) → c40(X(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.71/102.52
PROPER(x(x(z0, z1), x1)) → c40(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.71/102.52
PROPER(x(x0, tt)) → c40(X(proper(x0), ok(tt)), PROPER(x0)) 334.71/102.52
PROPER(x(x0, 0)) → c40(X(proper(x0), ok(0)), PROPER(x0)) 334.71/102.52
PROPER(x(tt, x1)) → c40(X(ok(tt), proper(x1)), PROPER(x1)) 334.71/102.52
PROPER(x(0, x1)) → c40(X(ok(0), proper(x1)), PROPER(x1)) 334.71/102.52
TOP(mark(U11(z0, z1, z2))) → c42(TOP(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.71/102.52
TOP(mark(U12(z0, z1, z2))) → c42(TOP(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.71/102.52
TOP(mark(s(z0))) → c42(TOP(s(proper(z0))), PROPER(s(z0))) 334.71/102.52
TOP(mark(plus(z0, z1))) → c42(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.71/102.52
TOP(mark(U21(z0, z1, z2))) → c42(TOP(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.71/102.52
TOP(mark(U22(z0, z1, z2))) → c42(TOP(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.71/102.52
TOP(mark(x(z0, z1))) → c42(TOP(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.71/102.52
TOP(mark(tt)) → c42(TOP(ok(tt))) 334.71/102.52
TOP(mark(0)) → c42(TOP(ok(0)))
S tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.71/102.52
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.71/102.52
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.71/102.52
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.71/102.52
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.52
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.52
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.52
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.52
S(mark(z0)) → c21(S(z0)) 334.71/102.52
S(ok(z0)) → c22(S(z0)) 334.71/102.52
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.52
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.52
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.52
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.52
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.52
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.52
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.52
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.52
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.52
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.71/102.52
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.71/102.52
ACTIVE(U11(tt, z0, z1)) → c 334.71/102.52
ACTIVE(U21(tt, z0, z1)) → c2 334.71/102.52
ACTIVE(plus(z0, s(z1))) → c5 334.71/102.52
ACTIVE(x(z0, s(z1))) → c7 334.71/102.52
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.71/102.52
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.71/102.52
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.71/102.52
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.71/102.52
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.52
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.52
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.52
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.52
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.52
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.52
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.52
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.52
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.52
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.71/102.52
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.52
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.52
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.52
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.52
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.52
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.52
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.52
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.52
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.52
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.52
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.71/102.52
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.71/102.52
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.52
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.71/102.52
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.71/102.52
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.71/102.52
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.71/102.52
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.71/102.52
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.71/102.52
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.71/102.52
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.71/102.52
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.71/102.52
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.71/102.52
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.71/102.52
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.71/102.52
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.71/102.52
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.71/102.52
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.52
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.52
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.52
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.52
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.52
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.52
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.52
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.52
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.52
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.52
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.52
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.71/102.52
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.52
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.71/102.52
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.52
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.71/102.52
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.52
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.52
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.52
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.52
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.52
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.52
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.52
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.52
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.52
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.52
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.52
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.52
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.52
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.52
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.71/102.52
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.52
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.52
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.52
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.71/102.52
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.52
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.71/102.52
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.71/102.52
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.52
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.52
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.52
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.52
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.52
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.52
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.52
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.52
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.52
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.52
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.52
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.52
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.52
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.52
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.52
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.52
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.52
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.52
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.52
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.52
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.52
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.52
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.52
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.52
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.52
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.52
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.52
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.52
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.52
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.52
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.71/102.52
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.71/102.52
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.71/102.52
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.71/102.52
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.71/102.52
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.71/102.52
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.71/102.52
PROPER(s(tt)) → c36(S(ok(tt))) 334.71/102.52
PROPER(s(0)) → c36(S(ok(0))) 334.71/102.52
PROPER(plus(x0, U11(z0, z1, z2))) → c37(PLUS(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.71/102.52
PROPER(plus(x0, U12(z0, z1, z2))) → c37(PLUS(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.71/102.52
PROPER(plus(x0, s(z0))) → c37(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.71/102.52
PROPER(plus(x0, plus(z0, z1))) → c37(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.71/102.52
PROPER(plus(x0, U21(z0, z1, z2))) → c37(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.71/102.52
PROPER(plus(x0, U22(z0, z1, z2))) → c37(PLUS(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.71/102.52
PROPER(plus(x0, x(z0, z1))) → c37(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.71/102.52
PROPER(plus(U11(z0, z1, z2), x1)) → c37(PLUS(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.71/102.52
PROPER(plus(U12(z0, z1, z2), x1)) → c37(PLUS(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.71/102.52
PROPER(plus(s(z0), x1)) → c37(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.71/102.52
PROPER(plus(plus(z0, z1), x1)) → c37(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.71/102.52
PROPER(plus(U21(z0, z1, z2), x1)) → c37(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.71/102.52
PROPER(plus(U22(z0, z1, z2), x1)) → c37(PLUS(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.71/102.52
PROPER(plus(x(z0, z1), x1)) → c37(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.71/102.52
PROPER(plus(x0, tt)) → c37(PLUS(proper(x0), ok(tt)), PROPER(x0)) 334.71/102.52
PROPER(plus(x0, 0)) → c37(PLUS(proper(x0), ok(0)), PROPER(x0)) 334.71/102.52
PROPER(plus(tt, x1)) → c37(PLUS(ok(tt), proper(x1)), PROPER(x1)) 334.71/102.52
PROPER(plus(0, x1)) → c37(PLUS(ok(0), proper(x1)), PROPER(x1)) 334.71/102.52
PROPER(U21(x0, x1, U11(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.52
PROPER(U21(x0, x1, U12(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.52
PROPER(U21(x0, x1, s(z0))) → c38(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.52
PROPER(U21(x0, x1, plus(z0, z1))) → c38(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.52
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.52
PROPER(U21(x0, x1, U22(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.52
PROPER(U21(x0, x1, x(z0, z1))) → c38(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.52
PROPER(U21(x0, U11(z0, z1, z2), x2)) → c38(U21'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U21(x0, U12(z0, z1, z2), x2)) → c38(U21'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U21(x0, s(z0), x2)) → c38(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.52
PROPER(U21(x0, plus(z0, z1), x2)) → c38(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.52
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c38(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U21(x0, U22(z0, z1, z2), x2)) → c38(U21'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U21(x0, x(z0, z1), x2)) → c38(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.52
PROPER(U21(U11(z0, z1, z2), x1, x2)) → c38(U21'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U21(U12(z0, z1, z2), x1, x2)) → c38(U21'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U21(s(z0), x1, x2)) → c38(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U21(plus(z0, z1), x1, x2)) → c38(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c38(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U21(U22(z0, z1, z2), x1, x2)) → c38(U21'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U21(x(z0, z1), x1, x2)) → c38(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U21(x0, x1, tt)) → c38(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.52
PROPER(U21(x0, x1, 0)) → c38(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.52
PROPER(U21(x0, tt, x2)) → c38(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.52
PROPER(U21(x0, 0, x2)) → c38(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.52
PROPER(U21(tt, x1, x2)) → c38(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U21(0, x1, x2)) → c38(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U22(x0, x1, U11(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.52
PROPER(U22(x0, x1, U12(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.52
PROPER(U22(x0, x1, s(z0))) → c39(U22'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.52
PROPER(U22(x0, x1, plus(z0, z1))) → c39(U22'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.52
PROPER(U22(x0, x1, U21(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.52
PROPER(U22(x0, x1, U22(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.52
PROPER(U22(x0, x1, x(z0, z1))) → c39(U22'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.52
PROPER(U22(x0, U11(z0, z1, z2), x2)) → c39(U22'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U22(x0, U12(z0, z1, z2), x2)) → c39(U22'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U22(x0, s(z0), x2)) → c39(U22'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.52
PROPER(U22(x0, plus(z0, z1), x2)) → c39(U22'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.52
PROPER(U22(x0, U21(z0, z1, z2), x2)) → c39(U22'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U22(x0, U22(z0, z1, z2), x2)) → c39(U22'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U22(x0, x(z0, z1), x2)) → c39(U22'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.52
PROPER(U22(U11(z0, z1, z2), x1, x2)) → c39(U22'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U22(U12(z0, z1, z2), x1, x2)) → c39(U22'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U22(s(z0), x1, x2)) → c39(U22'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U22(plus(z0, z1), x1, x2)) → c39(U22'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U22(U21(z0, z1, z2), x1, x2)) → c39(U22'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U22(U22(z0, z1, z2), x1, x2)) → c39(U22'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U22(x(z0, z1), x1, x2)) → c39(U22'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U22(x0, x1, tt)) → c39(U22'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.52
PROPER(U22(x0, x1, 0)) → c39(U22'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.52
PROPER(U22(x0, tt, x2)) → c39(U22'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.52
PROPER(U22(x0, 0, x2)) → c39(U22'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.52
PROPER(U22(tt, x1, x2)) → c39(U22'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U22(0, x1, x2)) → c39(U22'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(x(x0, U11(z0, z1, z2))) → c40(X(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.71/102.52
PROPER(x(x0, U12(z0, z1, z2))) → c40(X(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.71/102.52
PROPER(x(x0, s(z0))) → c40(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.71/102.52
PROPER(x(x0, plus(z0, z1))) → c40(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.71/102.52
PROPER(x(x0, U21(z0, z1, z2))) → c40(X(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.71/102.52
PROPER(x(x0, U22(z0, z1, z2))) → c40(X(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.71/102.52
PROPER(x(x0, x(z0, z1))) → c40(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.71/102.52
PROPER(x(U11(z0, z1, z2), x1)) → c40(X(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.71/102.52
PROPER(x(U12(z0, z1, z2), x1)) → c40(X(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.71/102.52
PROPER(x(s(z0), x1)) → c40(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.71/102.52
PROPER(x(plus(z0, z1), x1)) → c40(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.71/102.52
PROPER(x(U21(z0, z1, z2), x1)) → c40(X(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.71/102.52
PROPER(x(U22(z0, z1, z2), x1)) → c40(X(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.71/102.52
PROPER(x(x(z0, z1), x1)) → c40(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.71/102.52
PROPER(x(x0, tt)) → c40(X(proper(x0), ok(tt)), PROPER(x0)) 334.71/102.52
PROPER(x(x0, 0)) → c40(X(proper(x0), ok(0)), PROPER(x0)) 334.71/102.52
PROPER(x(tt, x1)) → c40(X(ok(tt), proper(x1)), PROPER(x1)) 334.71/102.52
PROPER(x(0, x1)) → c40(X(ok(0), proper(x1)), PROPER(x1)) 334.71/102.52
TOP(mark(U11(z0, z1, z2))) → c42(TOP(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.71/102.52
TOP(mark(U12(z0, z1, z2))) → c42(TOP(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.71/102.52
TOP(mark(s(z0))) → c42(TOP(s(proper(z0))), PROPER(s(z0))) 334.71/102.52
TOP(mark(plus(z0, z1))) → c42(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.71/102.52
TOP(mark(U21(z0, z1, z2))) → c42(TOP(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.71/102.52
TOP(mark(U22(z0, z1, z2))) → c42(TOP(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.71/102.52
TOP(mark(x(z0, z1))) → c42(TOP(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.71/102.52
TOP(mark(tt)) → c42(TOP(ok(tt))) 334.71/102.52
TOP(mark(0)) → c42(TOP(ok(0)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, TOP, PROPER

Compound Symbols:

c11, c12, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c43, c, c2, c5, c7, c4, c8, c1, c9, c3, c10, c6, c13, c34, c14, c41, c33, c33, c35, c35, c36, c36, c37, c37, c38, c38, c39, c39, c40, c40, c42, c42

334.71/102.52
334.71/102.52

(85) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

Removed 14 trailing nodes:

ACTIVE(x(z0, s(z1))) → c7 334.71/102.52
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.71/102.52
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.71/102.52
ACTIVE(U11(tt, z0, z1)) → c 334.71/102.52
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.71/102.52
ACTIVE(U21(tt, z0, z1)) → c2 334.71/102.52
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.71/102.52
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.71/102.52
ACTIVE(plus(z0, s(z1))) → c5 334.71/102.52
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.52
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.71/102.52
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.52
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.52
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1)))
334.71/102.52
334.71/102.52

(86) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.71/102.52
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.71/102.52
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.71/102.52
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.71/102.52
active(plus(z0, 0)) → mark(z0) 334.71/102.52
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.71/102.52
active(x(z0, 0)) → mark(0) 334.71/102.52
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.71/102.52
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.71/102.52
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.71/102.52
active(s(z0)) → s(active(z0)) 334.71/102.52
active(plus(z0, z1)) → plus(active(z0), z1) 334.71/102.52
active(plus(z0, z1)) → plus(z0, active(z1)) 334.71/102.52
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.71/102.52
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.71/102.52
active(x(z0, z1)) → x(active(z0), z1) 334.71/102.52
active(x(z0, z1)) → x(z0, active(z1)) 334.71/102.52
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.71/102.52
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.71/102.52
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.71/102.52
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.71/102.52
s(mark(z0)) → mark(s(z0)) 334.71/102.52
s(ok(z0)) → ok(s(z0)) 334.71/102.52
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.71/102.52
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.71/102.52
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.71/102.52
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.71/102.52
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.71/102.52
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.71/102.52
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.71/102.52
x(mark(z0), z1) → mark(x(z0, z1)) 334.71/102.52
x(z0, mark(z1)) → mark(x(z0, z1)) 334.71/102.52
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.71/102.52
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.71/102.52
proper(tt) → ok(tt) 334.71/102.52
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.71/102.52
proper(s(z0)) → s(proper(z0)) 334.71/102.52
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.71/102.52
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.71/102.52
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.71/102.52
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.71/102.52
proper(0) → ok(0) 334.71/102.52
top(mark(z0)) → top(proper(z0)) 334.71/102.52
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.71/102.52
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.71/102.52
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.71/102.52
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.71/102.52
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.52
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.52
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.52
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.52
S(mark(z0)) → c21(S(z0)) 334.71/102.52
S(ok(z0)) → c22(S(z0)) 334.71/102.52
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.52
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.52
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.52
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.52
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.52
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.52
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.52
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.52
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.52
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.71/102.52
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.71/102.52
ACTIVE(U11(tt, z0, z1)) → c 334.71/102.52
ACTIVE(U21(tt, z0, z1)) → c2 334.71/102.52
ACTIVE(plus(z0, s(z1))) → c5 334.71/102.52
ACTIVE(x(z0, s(z1))) → c7 334.71/102.52
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.71/102.52
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.71/102.52
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.71/102.52
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.71/102.52
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.52
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.52
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.52
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.52
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.52
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.52
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.52
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.52
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.52
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.71/102.52
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.52
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.52
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.52
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.52
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.52
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.52
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.52
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.52
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.52
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.52
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.71/102.52
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.71/102.52
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.52
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.71/102.52
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.71/102.52
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.71/102.52
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.71/102.52
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.71/102.52
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.71/102.52
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.71/102.52
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.71/102.52
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.71/102.52
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.71/102.52
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.71/102.52
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.71/102.52
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.71/102.52
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.71/102.52
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.52
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.52
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.52
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.52
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.52
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.52
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.52
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.52
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.52
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.52
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.52
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.71/102.52
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.52
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.71/102.52
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.52
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.71/102.52
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.52
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.52
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.52
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.52
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.52
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.52
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.52
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.52
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.52
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.52
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.52
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.52
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.52
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.52
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.71/102.52
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.52
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.52
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.52
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.71/102.52
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.52
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.71/102.52
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.71/102.52
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.52
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.52
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.52
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.52
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.52
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.52
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.52
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.52
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.52
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.52
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.52
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.52
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.52
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.52
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.52
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.52
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.52
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.52
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.52
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.52
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.52
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.52
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.52
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.52
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.52
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.52
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.52
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.52
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.52
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.52
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.71/102.52
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.71/102.52
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.71/102.52
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.71/102.52
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.71/102.52
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.71/102.52
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.71/102.52
PROPER(s(tt)) → c36(S(ok(tt))) 334.71/102.52
PROPER(s(0)) → c36(S(ok(0))) 334.71/102.52
PROPER(plus(x0, U11(z0, z1, z2))) → c37(PLUS(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.71/102.52
PROPER(plus(x0, U12(z0, z1, z2))) → c37(PLUS(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.71/102.52
PROPER(plus(x0, s(z0))) → c37(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.71/102.52
PROPER(plus(x0, plus(z0, z1))) → c37(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.71/102.52
PROPER(plus(x0, U21(z0, z1, z2))) → c37(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.71/102.52
PROPER(plus(x0, U22(z0, z1, z2))) → c37(PLUS(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.71/102.52
PROPER(plus(x0, x(z0, z1))) → c37(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.71/102.52
PROPER(plus(U11(z0, z1, z2), x1)) → c37(PLUS(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.71/102.52
PROPER(plus(U12(z0, z1, z2), x1)) → c37(PLUS(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.71/102.52
PROPER(plus(s(z0), x1)) → c37(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.71/102.52
PROPER(plus(plus(z0, z1), x1)) → c37(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.71/102.52
PROPER(plus(U21(z0, z1, z2), x1)) → c37(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.71/102.52
PROPER(plus(U22(z0, z1, z2), x1)) → c37(PLUS(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.71/102.52
PROPER(plus(x(z0, z1), x1)) → c37(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.71/102.52
PROPER(plus(x0, tt)) → c37(PLUS(proper(x0), ok(tt)), PROPER(x0)) 334.71/102.52
PROPER(plus(x0, 0)) → c37(PLUS(proper(x0), ok(0)), PROPER(x0)) 334.71/102.52
PROPER(plus(tt, x1)) → c37(PLUS(ok(tt), proper(x1)), PROPER(x1)) 334.71/102.52
PROPER(plus(0, x1)) → c37(PLUS(ok(0), proper(x1)), PROPER(x1)) 334.71/102.52
PROPER(U21(x0, x1, U11(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.52
PROPER(U21(x0, x1, U12(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.52
PROPER(U21(x0, x1, s(z0))) → c38(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.52
PROPER(U21(x0, x1, plus(z0, z1))) → c38(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.52
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.52
PROPER(U21(x0, x1, U22(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.52
PROPER(U21(x0, x1, x(z0, z1))) → c38(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.52
PROPER(U21(x0, U11(z0, z1, z2), x2)) → c38(U21'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U21(x0, U12(z0, z1, z2), x2)) → c38(U21'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U21(x0, s(z0), x2)) → c38(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.52
PROPER(U21(x0, plus(z0, z1), x2)) → c38(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.52
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c38(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U21(x0, U22(z0, z1, z2), x2)) → c38(U21'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U21(x0, x(z0, z1), x2)) → c38(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.52
PROPER(U21(U11(z0, z1, z2), x1, x2)) → c38(U21'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U21(U12(z0, z1, z2), x1, x2)) → c38(U21'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U21(s(z0), x1, x2)) → c38(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U21(plus(z0, z1), x1, x2)) → c38(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c38(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U21(U22(z0, z1, z2), x1, x2)) → c38(U21'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U21(x(z0, z1), x1, x2)) → c38(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U21(x0, x1, tt)) → c38(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.52
PROPER(U21(x0, x1, 0)) → c38(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.52
PROPER(U21(x0, tt, x2)) → c38(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.52
PROPER(U21(x0, 0, x2)) → c38(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.52
PROPER(U21(tt, x1, x2)) → c38(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U21(0, x1, x2)) → c38(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U22(x0, x1, U11(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.52
PROPER(U22(x0, x1, U12(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.52
PROPER(U22(x0, x1, s(z0))) → c39(U22'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.52
PROPER(U22(x0, x1, plus(z0, z1))) → c39(U22'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.52
PROPER(U22(x0, x1, U21(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.52
PROPER(U22(x0, x1, U22(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.52
PROPER(U22(x0, x1, x(z0, z1))) → c39(U22'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.52
PROPER(U22(x0, U11(z0, z1, z2), x2)) → c39(U22'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U22(x0, U12(z0, z1, z2), x2)) → c39(U22'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U22(x0, s(z0), x2)) → c39(U22'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.52
PROPER(U22(x0, plus(z0, z1), x2)) → c39(U22'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.52
PROPER(U22(x0, U21(z0, z1, z2), x2)) → c39(U22'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U22(x0, U22(z0, z1, z2), x2)) → c39(U22'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.52
PROPER(U22(x0, x(z0, z1), x2)) → c39(U22'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.52
PROPER(U22(U11(z0, z1, z2), x1, x2)) → c39(U22'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U22(U12(z0, z1, z2), x1, x2)) → c39(U22'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U22(s(z0), x1, x2)) → c39(U22'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U22(plus(z0, z1), x1, x2)) → c39(U22'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U22(U21(z0, z1, z2), x1, x2)) → c39(U22'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U22(U22(z0, z1, z2), x1, x2)) → c39(U22'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U22(x(z0, z1), x1, x2)) → c39(U22'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U22(x0, x1, tt)) → c39(U22'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.52
PROPER(U22(x0, x1, 0)) → c39(U22'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.52
PROPER(U22(x0, tt, x2)) → c39(U22'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.52
PROPER(U22(x0, 0, x2)) → c39(U22'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.52
PROPER(U22(tt, x1, x2)) → c39(U22'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(U22(0, x1, x2)) → c39(U22'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.52
PROPER(x(x0, U11(z0, z1, z2))) → c40(X(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.71/102.52
PROPER(x(x0, U12(z0, z1, z2))) → c40(X(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.71/102.52
PROPER(x(x0, s(z0))) → c40(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.71/102.52
PROPER(x(x0, plus(z0, z1))) → c40(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.71/102.52
PROPER(x(x0, U21(z0, z1, z2))) → c40(X(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.71/102.52
PROPER(x(x0, U22(z0, z1, z2))) → c40(X(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.71/102.52
PROPER(x(x0, x(z0, z1))) → c40(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.71/102.52
PROPER(x(U11(z0, z1, z2), x1)) → c40(X(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.71/102.52
PROPER(x(U12(z0, z1, z2), x1)) → c40(X(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.71/102.52
PROPER(x(s(z0), x1)) → c40(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.71/102.52
PROPER(x(plus(z0, z1), x1)) → c40(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.71/102.52
PROPER(x(U21(z0, z1, z2), x1)) → c40(X(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.71/102.52
PROPER(x(U22(z0, z1, z2), x1)) → c40(X(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.71/102.52
PROPER(x(x(z0, z1), x1)) → c40(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.71/102.52
PROPER(x(x0, tt)) → c40(X(proper(x0), ok(tt)), PROPER(x0)) 334.71/102.52
PROPER(x(x0, 0)) → c40(X(proper(x0), ok(0)), PROPER(x0)) 334.71/102.52
PROPER(x(tt, x1)) → c40(X(ok(tt), proper(x1)), PROPER(x1)) 334.71/102.52
PROPER(x(0, x1)) → c40(X(ok(0), proper(x1)), PROPER(x1)) 334.71/102.52
TOP(mark(U11(z0, z1, z2))) → c42(TOP(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.71/102.52
TOP(mark(U12(z0, z1, z2))) → c42(TOP(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.71/102.52
TOP(mark(s(z0))) → c42(TOP(s(proper(z0))), PROPER(s(z0))) 334.71/102.52
TOP(mark(plus(z0, z1))) → c42(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.71/102.52
TOP(mark(U21(z0, z1, z2))) → c42(TOP(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.71/102.52
TOP(mark(U22(z0, z1, z2))) → c42(TOP(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.71/102.52
TOP(mark(x(z0, z1))) → c42(TOP(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.71/102.52
TOP(mark(tt)) → c42(TOP(ok(tt))) 334.71/102.52
TOP(mark(0)) → c42(TOP(ok(0)))
S tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.71/102.52
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.71/102.52
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.71/102.52
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.71/102.52
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.52
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.52
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.52
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.52
S(mark(z0)) → c21(S(z0)) 334.71/102.52
S(ok(z0)) → c22(S(z0)) 334.71/102.52
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.52
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.52
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.52
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.52
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.52
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.52
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.52
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.52
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.52
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.71/102.52
TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) 334.71/102.52
ACTIVE(U11(tt, z0, z1)) → c 334.71/102.52
ACTIVE(U21(tt, z0, z1)) → c2 334.71/102.52
ACTIVE(plus(z0, s(z1))) → c5 334.71/102.52
ACTIVE(x(z0, s(z1))) → c7 334.71/102.52
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.71/102.52
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.71/102.52
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.71/102.52
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.71/102.52
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.52
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.52
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.52
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.52
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.52
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.52
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.52
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.52
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.52
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.71/102.52
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.52
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.52
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.52
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.52
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.52
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.52
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.52
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.52
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.52
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.52
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.71/102.52
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.71/102.52
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.52
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.71/102.52
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.71/102.52
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.71/102.52
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.71/102.52
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.71/102.52
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.71/102.52
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.71/102.52
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.71/102.52
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.71/102.52
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.71/102.52
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.71/102.52
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.71/102.52
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.71/102.52
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.71/102.52
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.52
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.52
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.52
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.52
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.52
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.52
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.52
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.52
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.52
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.52
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.52
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.52
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.71/102.52
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.52
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.71/102.52
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.52
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.71/102.52
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.52
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.52
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.52
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.52
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.52
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.52
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.52
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.52
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.52
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.52
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.52
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.53
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.53
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.53
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.53
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.53
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.53
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.53
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.71/102.53
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.53
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.53
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.53
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.53
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.71/102.53
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.53
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.71/102.53
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.53
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.71/102.53
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.53
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.53
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.53
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.53
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.53
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.53
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.53
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.53
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.53
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.53
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.53
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.53
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.53
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.53
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.53
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.53
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.53
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.53
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.53
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.53
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.53
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.53
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.53
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.53
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.53
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.53
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.53
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.53
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.53
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.53
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.71/102.53
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.71/102.53
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.71/102.53
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.71/102.53
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.71/102.53
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.71/102.53
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.71/102.53
PROPER(s(tt)) → c36(S(ok(tt))) 334.71/102.53
PROPER(s(0)) → c36(S(ok(0))) 334.71/102.53
PROPER(plus(x0, U11(z0, z1, z2))) → c37(PLUS(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.71/102.53
PROPER(plus(x0, U12(z0, z1, z2))) → c37(PLUS(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.71/102.53
PROPER(plus(x0, s(z0))) → c37(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.71/102.53
PROPER(plus(x0, plus(z0, z1))) → c37(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.71/102.53
PROPER(plus(x0, U21(z0, z1, z2))) → c37(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.71/102.53
PROPER(plus(x0, U22(z0, z1, z2))) → c37(PLUS(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.71/102.53
PROPER(plus(x0, x(z0, z1))) → c37(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.71/102.53
PROPER(plus(U11(z0, z1, z2), x1)) → c37(PLUS(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.71/102.53
PROPER(plus(U12(z0, z1, z2), x1)) → c37(PLUS(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.71/102.53
PROPER(plus(s(z0), x1)) → c37(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.71/102.53
PROPER(plus(plus(z0, z1), x1)) → c37(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.71/102.53
PROPER(plus(U21(z0, z1, z2), x1)) → c37(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.71/102.53
PROPER(plus(U22(z0, z1, z2), x1)) → c37(PLUS(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.71/102.53
PROPER(plus(x(z0, z1), x1)) → c37(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.71/102.53
PROPER(plus(x0, tt)) → c37(PLUS(proper(x0), ok(tt)), PROPER(x0)) 334.71/102.53
PROPER(plus(x0, 0)) → c37(PLUS(proper(x0), ok(0)), PROPER(x0)) 334.71/102.53
PROPER(plus(tt, x1)) → c37(PLUS(ok(tt), proper(x1)), PROPER(x1)) 334.71/102.53
PROPER(plus(0, x1)) → c37(PLUS(ok(0), proper(x1)), PROPER(x1)) 334.71/102.53
PROPER(U21(x0, x1, U11(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.53
PROPER(U21(x0, x1, U12(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.53
PROPER(U21(x0, x1, s(z0))) → c38(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.53
PROPER(U21(x0, x1, plus(z0, z1))) → c38(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.53
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.53
PROPER(U21(x0, x1, U22(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.53
PROPER(U21(x0, x1, x(z0, z1))) → c38(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.53
PROPER(U21(x0, U11(z0, z1, z2), x2)) → c38(U21'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U21(x0, U12(z0, z1, z2), x2)) → c38(U21'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U21(x0, s(z0), x2)) → c38(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.53
PROPER(U21(x0, plus(z0, z1), x2)) → c38(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.53
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c38(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U21(x0, U22(z0, z1, z2), x2)) → c38(U21'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U21(x0, x(z0, z1), x2)) → c38(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.53
PROPER(U21(U11(z0, z1, z2), x1, x2)) → c38(U21'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U21(U12(z0, z1, z2), x1, x2)) → c38(U21'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U21(s(z0), x1, x2)) → c38(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U21(plus(z0, z1), x1, x2)) → c38(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c38(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U21(U22(z0, z1, z2), x1, x2)) → c38(U21'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U21(x(z0, z1), x1, x2)) → c38(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U21(x0, x1, tt)) → c38(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.53
PROPER(U21(x0, x1, 0)) → c38(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.53
PROPER(U21(x0, tt, x2)) → c38(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.53
PROPER(U21(x0, 0, x2)) → c38(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.53
PROPER(U21(tt, x1, x2)) → c38(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U21(0, x1, x2)) → c38(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U22(x0, x1, U11(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.53
PROPER(U22(x0, x1, U12(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.53
PROPER(U22(x0, x1, s(z0))) → c39(U22'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.53
PROPER(U22(x0, x1, plus(z0, z1))) → c39(U22'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.53
PROPER(U22(x0, x1, U21(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.53
PROPER(U22(x0, x1, U22(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.53
PROPER(U22(x0, x1, x(z0, z1))) → c39(U22'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.53
PROPER(U22(x0, U11(z0, z1, z2), x2)) → c39(U22'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U22(x0, U12(z0, z1, z2), x2)) → c39(U22'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U22(x0, s(z0), x2)) → c39(U22'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.53
PROPER(U22(x0, plus(z0, z1), x2)) → c39(U22'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.53
PROPER(U22(x0, U21(z0, z1, z2), x2)) → c39(U22'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U22(x0, U22(z0, z1, z2), x2)) → c39(U22'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U22(x0, x(z0, z1), x2)) → c39(U22'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.53
PROPER(U22(U11(z0, z1, z2), x1, x2)) → c39(U22'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U22(U12(z0, z1, z2), x1, x2)) → c39(U22'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U22(s(z0), x1, x2)) → c39(U22'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U22(plus(z0, z1), x1, x2)) → c39(U22'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U22(U21(z0, z1, z2), x1, x2)) → c39(U22'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U22(U22(z0, z1, z2), x1, x2)) → c39(U22'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U22(x(z0, z1), x1, x2)) → c39(U22'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U22(x0, x1, tt)) → c39(U22'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.53
PROPER(U22(x0, x1, 0)) → c39(U22'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.53
PROPER(U22(x0, tt, x2)) → c39(U22'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.53
PROPER(U22(x0, 0, x2)) → c39(U22'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.53
PROPER(U22(tt, x1, x2)) → c39(U22'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U22(0, x1, x2)) → c39(U22'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(x(x0, U11(z0, z1, z2))) → c40(X(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.71/102.53
PROPER(x(x0, U12(z0, z1, z2))) → c40(X(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.71/102.53
PROPER(x(x0, s(z0))) → c40(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.71/102.53
PROPER(x(x0, plus(z0, z1))) → c40(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.71/102.53
PROPER(x(x0, U21(z0, z1, z2))) → c40(X(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.71/102.53
PROPER(x(x0, U22(z0, z1, z2))) → c40(X(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.71/102.53
PROPER(x(x0, x(z0, z1))) → c40(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.71/102.53
PROPER(x(U11(z0, z1, z2), x1)) → c40(X(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.71/102.53
PROPER(x(U12(z0, z1, z2), x1)) → c40(X(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.71/102.53
PROPER(x(s(z0), x1)) → c40(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.71/102.53
PROPER(x(plus(z0, z1), x1)) → c40(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.71/102.53
PROPER(x(U21(z0, z1, z2), x1)) → c40(X(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.71/102.53
PROPER(x(U22(z0, z1, z2), x1)) → c40(X(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.71/102.53
PROPER(x(x(z0, z1), x1)) → c40(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.71/102.53
PROPER(x(x0, tt)) → c40(X(proper(x0), ok(tt)), PROPER(x0)) 334.71/102.53
PROPER(x(x0, 0)) → c40(X(proper(x0), ok(0)), PROPER(x0)) 334.71/102.53
PROPER(x(tt, x1)) → c40(X(ok(tt), proper(x1)), PROPER(x1)) 334.71/102.53
PROPER(x(0, x1)) → c40(X(ok(0), proper(x1)), PROPER(x1)) 334.71/102.53
TOP(mark(U11(z0, z1, z2))) → c42(TOP(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.71/102.53
TOP(mark(U12(z0, z1, z2))) → c42(TOP(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.71/102.53
TOP(mark(s(z0))) → c42(TOP(s(proper(z0))), PROPER(s(z0))) 334.71/102.53
TOP(mark(plus(z0, z1))) → c42(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.71/102.53
TOP(mark(U21(z0, z1, z2))) → c42(TOP(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.71/102.53
TOP(mark(U22(z0, z1, z2))) → c42(TOP(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.71/102.53
TOP(mark(x(z0, z1))) → c42(TOP(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.71/102.53
TOP(mark(tt)) → c42(TOP(ok(tt))) 334.71/102.53
TOP(mark(0)) → c42(TOP(ok(0)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, TOP, PROPER

Compound Symbols:

c11, c12, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c43, c, c2, c5, c7, c4, c8, c1, c9, c3, c10, c6, c13, c34, c14, c41, c33, c33, c35, c35, c36, c36, c37, c37, c38, c38, c39, c39, c40, c40, c42, c42

334.71/102.53
334.71/102.53

(87) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace TOP(ok(z0)) → c43(TOP(active(z0)), ACTIVE(z0)) by

TOP(ok(U11(tt, z0, z1))) → c43(TOP(mark(U12(tt, z0, z1))), ACTIVE(U11(tt, z0, z1))) 334.71/102.53
TOP(ok(U12(tt, z0, z1))) → c43(TOP(mark(s(plus(z1, z0)))), ACTIVE(U12(tt, z0, z1))) 334.71/102.53
TOP(ok(U21(tt, z0, z1))) → c43(TOP(mark(U22(tt, z0, z1))), ACTIVE(U21(tt, z0, z1))) 334.71/102.53
TOP(ok(U22(tt, z0, z1))) → c43(TOP(mark(plus(x(z1, z0), z1))), ACTIVE(U22(tt, z0, z1))) 334.71/102.53
TOP(ok(plus(z0, 0))) → c43(TOP(mark(z0)), ACTIVE(plus(z0, 0))) 334.71/102.53
TOP(ok(plus(z0, s(z1)))) → c43(TOP(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.71/102.53
TOP(ok(x(z0, 0))) → c43(TOP(mark(0)), ACTIVE(x(z0, 0))) 334.71/102.53
TOP(ok(x(z0, s(z1)))) → c43(TOP(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.71/102.53
TOP(ok(U11(z0, z1, z2))) → c43(TOP(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.71/102.53
TOP(ok(U12(z0, z1, z2))) → c43(TOP(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.71/102.53
TOP(ok(s(z0))) → c43(TOP(s(active(z0))), ACTIVE(s(z0))) 334.71/102.53
TOP(ok(plus(z0, z1))) → c43(TOP(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.71/102.53
TOP(ok(plus(z0, z1))) → c43(TOP(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.71/102.53
TOP(ok(U21(z0, z1, z2))) → c43(TOP(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.71/102.53
TOP(ok(U22(z0, z1, z2))) → c43(TOP(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.71/102.53
TOP(ok(x(z0, z1))) → c43(TOP(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.71/102.53
TOP(ok(x(z0, z1))) → c43(TOP(x(z0, active(z1))), ACTIVE(x(z0, z1)))
334.71/102.53
334.71/102.53

(88) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.71/102.53
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.71/102.53
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.71/102.53
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.71/102.53
active(plus(z0, 0)) → mark(z0) 334.71/102.53
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.71/102.53
active(x(z0, 0)) → mark(0) 334.71/102.53
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.71/102.53
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.71/102.53
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.71/102.53
active(s(z0)) → s(active(z0)) 334.71/102.53
active(plus(z0, z1)) → plus(active(z0), z1) 334.71/102.53
active(plus(z0, z1)) → plus(z0, active(z1)) 334.71/102.53
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.71/102.53
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.71/102.53
active(x(z0, z1)) → x(active(z0), z1) 334.71/102.53
active(x(z0, z1)) → x(z0, active(z1)) 334.71/102.53
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.71/102.53
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.71/102.53
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.71/102.53
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.71/102.53
s(mark(z0)) → mark(s(z0)) 334.71/102.53
s(ok(z0)) → ok(s(z0)) 334.71/102.53
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.71/102.53
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.71/102.53
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.71/102.53
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.71/102.53
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.71/102.53
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.71/102.53
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.71/102.53
x(mark(z0), z1) → mark(x(z0, z1)) 334.71/102.53
x(z0, mark(z1)) → mark(x(z0, z1)) 334.71/102.53
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.71/102.53
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.71/102.53
proper(tt) → ok(tt) 334.71/102.53
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.71/102.53
proper(s(z0)) → s(proper(z0)) 334.71/102.53
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.71/102.53
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.71/102.53
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.71/102.53
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.71/102.53
proper(0) → ok(0) 334.71/102.53
top(mark(z0)) → top(proper(z0)) 334.71/102.53
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.71/102.53
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.71/102.53
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.71/102.53
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.71/102.53
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.53
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.53
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.53
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.53
S(mark(z0)) → c21(S(z0)) 334.71/102.53
S(ok(z0)) → c22(S(z0)) 334.71/102.53
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.53
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.53
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.53
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.53
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.53
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.53
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.53
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.53
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.53
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.71/102.53
ACTIVE(U11(tt, z0, z1)) → c 334.71/102.53
ACTIVE(U21(tt, z0, z1)) → c2 334.71/102.53
ACTIVE(plus(z0, s(z1))) → c5 334.71/102.53
ACTIVE(x(z0, s(z1))) → c7 334.71/102.53
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.71/102.53
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.71/102.53
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.71/102.53
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.71/102.53
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.53
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.53
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.53
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.53
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.53
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.53
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.53
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.53
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.53
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.53
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.53
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.53
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.53
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.53
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.71/102.53
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.53
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.53
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.53
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.53
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.53
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.53
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.53
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.53
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.53
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.53
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.53
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.53
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.53
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.53
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.71/102.53
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.53
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.71/102.53
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.53
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.71/102.53
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.71/102.53
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.71/102.53
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.71/102.53
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.71/102.53
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.71/102.53
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.71/102.53
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.71/102.53
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.71/102.53
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.71/102.53
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.71/102.53
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.71/102.53
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.71/102.53
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.71/102.53
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.71/102.53
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.71/102.53
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.71/102.53
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.71/102.53
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.53
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.53
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.53
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.53
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.53
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.53
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.53
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.53
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.53
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.53
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.53
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.53
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.53
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.53
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.53
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.53
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.53
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.71/102.53
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.53
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.53
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.71/102.53
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.53
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.71/102.53
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.53
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.53
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.53
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.53
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.53
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.53
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.53
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.53
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.53
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.53
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.53
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.53
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.53
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.53
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.53
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.53
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.53
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.53
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.53
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.71/102.53
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.53
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.53
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.53
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.53
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.71/102.53
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.53
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.71/102.53
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.53
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.71/102.53
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.53
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.53
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.53
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.53
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.53
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.53
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.53
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.53
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.53
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.53
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.53
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.53
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.53
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.53
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.53
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.53
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.53
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.53
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.53
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.53
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.53
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.53
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.53
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.53
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.53
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.53
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.53
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.53
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.53
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.53
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.71/102.53
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.71/102.53
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.71/102.53
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.71/102.53
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.71/102.53
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.71/102.53
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.71/102.53
PROPER(s(tt)) → c36(S(ok(tt))) 334.71/102.53
PROPER(s(0)) → c36(S(ok(0))) 334.71/102.53
PROPER(plus(x0, U11(z0, z1, z2))) → c37(PLUS(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.71/102.53
PROPER(plus(x0, U12(z0, z1, z2))) → c37(PLUS(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.71/102.53
PROPER(plus(x0, s(z0))) → c37(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.71/102.53
PROPER(plus(x0, plus(z0, z1))) → c37(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.71/102.53
PROPER(plus(x0, U21(z0, z1, z2))) → c37(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.71/102.53
PROPER(plus(x0, U22(z0, z1, z2))) → c37(PLUS(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.71/102.53
PROPER(plus(x0, x(z0, z1))) → c37(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.71/102.53
PROPER(plus(U11(z0, z1, z2), x1)) → c37(PLUS(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.71/102.53
PROPER(plus(U12(z0, z1, z2), x1)) → c37(PLUS(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.71/102.53
PROPER(plus(s(z0), x1)) → c37(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.71/102.53
PROPER(plus(plus(z0, z1), x1)) → c37(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.71/102.53
PROPER(plus(U21(z0, z1, z2), x1)) → c37(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.71/102.53
PROPER(plus(U22(z0, z1, z2), x1)) → c37(PLUS(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.71/102.53
PROPER(plus(x(z0, z1), x1)) → c37(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.71/102.53
PROPER(plus(x0, tt)) → c37(PLUS(proper(x0), ok(tt)), PROPER(x0)) 334.71/102.53
PROPER(plus(x0, 0)) → c37(PLUS(proper(x0), ok(0)), PROPER(x0)) 334.71/102.53
PROPER(plus(tt, x1)) → c37(PLUS(ok(tt), proper(x1)), PROPER(x1)) 334.71/102.53
PROPER(plus(0, x1)) → c37(PLUS(ok(0), proper(x1)), PROPER(x1)) 334.71/102.53
PROPER(U21(x0, x1, U11(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.53
PROPER(U21(x0, x1, U12(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.53
PROPER(U21(x0, x1, s(z0))) → c38(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.53
PROPER(U21(x0, x1, plus(z0, z1))) → c38(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.53
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.53
PROPER(U21(x0, x1, U22(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.53
PROPER(U21(x0, x1, x(z0, z1))) → c38(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.53
PROPER(U21(x0, U11(z0, z1, z2), x2)) → c38(U21'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U21(x0, U12(z0, z1, z2), x2)) → c38(U21'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U21(x0, s(z0), x2)) → c38(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.53
PROPER(U21(x0, plus(z0, z1), x2)) → c38(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.53
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c38(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U21(x0, U22(z0, z1, z2), x2)) → c38(U21'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U21(x0, x(z0, z1), x2)) → c38(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.53
PROPER(U21(U11(z0, z1, z2), x1, x2)) → c38(U21'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U21(U12(z0, z1, z2), x1, x2)) → c38(U21'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U21(s(z0), x1, x2)) → c38(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U21(plus(z0, z1), x1, x2)) → c38(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c38(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U21(U22(z0, z1, z2), x1, x2)) → c38(U21'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U21(x(z0, z1), x1, x2)) → c38(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U21(x0, x1, tt)) → c38(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.53
PROPER(U21(x0, x1, 0)) → c38(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.53
PROPER(U21(x0, tt, x2)) → c38(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.53
PROPER(U21(x0, 0, x2)) → c38(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.53
PROPER(U21(tt, x1, x2)) → c38(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U21(0, x1, x2)) → c38(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U22(x0, x1, U11(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.53
PROPER(U22(x0, x1, U12(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.53
PROPER(U22(x0, x1, s(z0))) → c39(U22'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.53
PROPER(U22(x0, x1, plus(z0, z1))) → c39(U22'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.53
PROPER(U22(x0, x1, U21(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.53
PROPER(U22(x0, x1, U22(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.53
PROPER(U22(x0, x1, x(z0, z1))) → c39(U22'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.53
PROPER(U22(x0, U11(z0, z1, z2), x2)) → c39(U22'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U22(x0, U12(z0, z1, z2), x2)) → c39(U22'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U22(x0, s(z0), x2)) → c39(U22'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.53
PROPER(U22(x0, plus(z0, z1), x2)) → c39(U22'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.53
PROPER(U22(x0, U21(z0, z1, z2), x2)) → c39(U22'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U22(x0, U22(z0, z1, z2), x2)) → c39(U22'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U22(x0, x(z0, z1), x2)) → c39(U22'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.53
PROPER(U22(U11(z0, z1, z2), x1, x2)) → c39(U22'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U22(U12(z0, z1, z2), x1, x2)) → c39(U22'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U22(s(z0), x1, x2)) → c39(U22'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U22(plus(z0, z1), x1, x2)) → c39(U22'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U22(U21(z0, z1, z2), x1, x2)) → c39(U22'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U22(U22(z0, z1, z2), x1, x2)) → c39(U22'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U22(x(z0, z1), x1, x2)) → c39(U22'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U22(x0, x1, tt)) → c39(U22'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.53
PROPER(U22(x0, x1, 0)) → c39(U22'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.53
PROPER(U22(x0, tt, x2)) → c39(U22'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.53
PROPER(U22(x0, 0, x2)) → c39(U22'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.53
PROPER(U22(tt, x1, x2)) → c39(U22'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U22(0, x1, x2)) → c39(U22'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(x(x0, U11(z0, z1, z2))) → c40(X(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.71/102.53
PROPER(x(x0, U12(z0, z1, z2))) → c40(X(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.71/102.53
PROPER(x(x0, s(z0))) → c40(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.71/102.53
PROPER(x(x0, plus(z0, z1))) → c40(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.71/102.53
PROPER(x(x0, U21(z0, z1, z2))) → c40(X(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.71/102.53
PROPER(x(x0, U22(z0, z1, z2))) → c40(X(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.71/102.53
PROPER(x(x0, x(z0, z1))) → c40(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.71/102.53
PROPER(x(U11(z0, z1, z2), x1)) → c40(X(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.71/102.53
PROPER(x(U12(z0, z1, z2), x1)) → c40(X(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.71/102.53
PROPER(x(s(z0), x1)) → c40(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.71/102.53
PROPER(x(plus(z0, z1), x1)) → c40(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.71/102.53
PROPER(x(U21(z0, z1, z2), x1)) → c40(X(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.71/102.53
PROPER(x(U22(z0, z1, z2), x1)) → c40(X(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.71/102.53
PROPER(x(x(z0, z1), x1)) → c40(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.71/102.53
PROPER(x(x0, tt)) → c40(X(proper(x0), ok(tt)), PROPER(x0)) 334.71/102.53
PROPER(x(x0, 0)) → c40(X(proper(x0), ok(0)), PROPER(x0)) 334.71/102.53
PROPER(x(tt, x1)) → c40(X(ok(tt), proper(x1)), PROPER(x1)) 334.71/102.53
PROPER(x(0, x1)) → c40(X(ok(0), proper(x1)), PROPER(x1)) 334.71/102.53
TOP(mark(U11(z0, z1, z2))) → c42(TOP(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.71/102.53
TOP(mark(U12(z0, z1, z2))) → c42(TOP(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.71/102.53
TOP(mark(s(z0))) → c42(TOP(s(proper(z0))), PROPER(s(z0))) 334.71/102.53
TOP(mark(plus(z0, z1))) → c42(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.71/102.53
TOP(mark(U21(z0, z1, z2))) → c42(TOP(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.71/102.53
TOP(mark(U22(z0, z1, z2))) → c42(TOP(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.71/102.53
TOP(mark(x(z0, z1))) → c42(TOP(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.71/102.53
TOP(mark(tt)) → c42(TOP(ok(tt))) 334.71/102.53
TOP(mark(0)) → c42(TOP(ok(0))) 334.71/102.53
TOP(ok(U11(tt, z0, z1))) → c43(TOP(mark(U12(tt, z0, z1))), ACTIVE(U11(tt, z0, z1))) 334.71/102.53
TOP(ok(U12(tt, z0, z1))) → c43(TOP(mark(s(plus(z1, z0)))), ACTIVE(U12(tt, z0, z1))) 334.71/102.53
TOP(ok(U21(tt, z0, z1))) → c43(TOP(mark(U22(tt, z0, z1))), ACTIVE(U21(tt, z0, z1))) 334.71/102.53
TOP(ok(U22(tt, z0, z1))) → c43(TOP(mark(plus(x(z1, z0), z1))), ACTIVE(U22(tt, z0, z1))) 334.71/102.53
TOP(ok(plus(z0, 0))) → c43(TOP(mark(z0)), ACTIVE(plus(z0, 0))) 334.71/102.53
TOP(ok(plus(z0, s(z1)))) → c43(TOP(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.71/102.53
TOP(ok(x(z0, 0))) → c43(TOP(mark(0)), ACTIVE(x(z0, 0))) 334.71/102.53
TOP(ok(x(z0, s(z1)))) → c43(TOP(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.71/102.53
TOP(ok(U11(z0, z1, z2))) → c43(TOP(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.71/102.53
TOP(ok(U12(z0, z1, z2))) → c43(TOP(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.71/102.53
TOP(ok(s(z0))) → c43(TOP(s(active(z0))), ACTIVE(s(z0))) 334.71/102.53
TOP(ok(plus(z0, z1))) → c43(TOP(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.71/102.53
TOP(ok(plus(z0, z1))) → c43(TOP(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.71/102.53
TOP(ok(U21(z0, z1, z2))) → c43(TOP(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.71/102.53
TOP(ok(U22(z0, z1, z2))) → c43(TOP(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.71/102.53
TOP(ok(x(z0, z1))) → c43(TOP(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.71/102.53
TOP(ok(x(z0, z1))) → c43(TOP(x(z0, active(z1))), ACTIVE(x(z0, z1)))
S tuples:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.71/102.53
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.71/102.53
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.71/102.53
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.71/102.53
U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.53
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.53
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.53
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.53
S(mark(z0)) → c21(S(z0)) 334.71/102.53
S(ok(z0)) → c22(S(z0)) 334.71/102.53
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.53
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.53
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.53
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.53
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.53
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.53
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.53
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.53
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.53
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.71/102.53
ACTIVE(U11(tt, z0, z1)) → c 334.71/102.53
ACTIVE(U21(tt, z0, z1)) → c2 334.71/102.53
ACTIVE(plus(z0, s(z1))) → c5 334.71/102.53
ACTIVE(x(z0, s(z1))) → c7 334.71/102.53
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.71/102.53
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.71/102.53
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.71/102.53
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.71/102.53
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.53
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.53
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.53
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.53
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.53
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.53
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.53
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.53
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.53
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.53
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.53
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.53
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.53
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.53
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.71/102.53
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.53
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.53
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.53
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.53
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.53
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.53
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.53
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.53
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.53
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.53
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.53
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.53
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.53
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.53
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.71/102.53
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.53
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.71/102.53
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.53
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.71/102.53
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.71/102.53
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.71/102.53
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.71/102.53
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.71/102.53
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.71/102.53
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.71/102.53
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.71/102.53
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.71/102.53
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.71/102.53
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.71/102.53
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.71/102.53
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.71/102.53
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.71/102.53
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.71/102.53
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.71/102.53
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.71/102.53
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.71/102.53
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.53
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.53
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.53
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.53
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.53
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.53
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.53
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.53
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.53
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.53
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.53
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.53
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.53
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.53
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.53
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.53
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.53
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.71/102.53
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.53
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.53
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.71/102.53
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.53
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.71/102.53
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.53
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.53
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.53
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.53
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.53
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.53
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.53
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.53
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.53
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.53
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.53
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.53
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.53
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.53
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.53
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.53
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.53
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.53
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.53
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.71/102.53
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.53
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.53
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.53
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.53
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.71/102.53
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.53
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.71/102.53
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.53
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.71/102.53
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.53
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.53
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.53
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.53
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.53
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.53
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.53
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.53
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.53
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.53
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.53
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.53
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.53
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.53
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.53
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.53
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.53
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.53
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.53
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.53
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.53
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.53
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.53
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.53
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.53
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.53
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.53
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.53
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.53
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.53
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.71/102.53
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.71/102.53
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.71/102.53
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.71/102.53
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.71/102.53
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.71/102.53
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.71/102.53
PROPER(s(tt)) → c36(S(ok(tt))) 334.71/102.53
PROPER(s(0)) → c36(S(ok(0))) 334.71/102.53
PROPER(plus(x0, U11(z0, z1, z2))) → c37(PLUS(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.71/102.53
PROPER(plus(x0, U12(z0, z1, z2))) → c37(PLUS(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.71/102.53
PROPER(plus(x0, s(z0))) → c37(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.71/102.53
PROPER(plus(x0, plus(z0, z1))) → c37(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.71/102.53
PROPER(plus(x0, U21(z0, z1, z2))) → c37(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.71/102.53
PROPER(plus(x0, U22(z0, z1, z2))) → c37(PLUS(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.71/102.53
PROPER(plus(x0, x(z0, z1))) → c37(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.71/102.53
PROPER(plus(U11(z0, z1, z2), x1)) → c37(PLUS(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.71/102.53
PROPER(plus(U12(z0, z1, z2), x1)) → c37(PLUS(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.71/102.53
PROPER(plus(s(z0), x1)) → c37(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.71/102.53
PROPER(plus(plus(z0, z1), x1)) → c37(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.71/102.53
PROPER(plus(U21(z0, z1, z2), x1)) → c37(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.71/102.53
PROPER(plus(U22(z0, z1, z2), x1)) → c37(PLUS(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.71/102.53
PROPER(plus(x(z0, z1), x1)) → c37(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.71/102.53
PROPER(plus(x0, tt)) → c37(PLUS(proper(x0), ok(tt)), PROPER(x0)) 334.71/102.53
PROPER(plus(x0, 0)) → c37(PLUS(proper(x0), ok(0)), PROPER(x0)) 334.71/102.53
PROPER(plus(tt, x1)) → c37(PLUS(ok(tt), proper(x1)), PROPER(x1)) 334.71/102.53
PROPER(plus(0, x1)) → c37(PLUS(ok(0), proper(x1)), PROPER(x1)) 334.71/102.53
PROPER(U21(x0, x1, U11(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.53
PROPER(U21(x0, x1, U12(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.53
PROPER(U21(x0, x1, s(z0))) → c38(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.53
PROPER(U21(x0, x1, plus(z0, z1))) → c38(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.53
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.53
PROPER(U21(x0, x1, U22(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.53
PROPER(U21(x0, x1, x(z0, z1))) → c38(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.53
PROPER(U21(x0, U11(z0, z1, z2), x2)) → c38(U21'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U21(x0, U12(z0, z1, z2), x2)) → c38(U21'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U21(x0, s(z0), x2)) → c38(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.53
PROPER(U21(x0, plus(z0, z1), x2)) → c38(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.53
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c38(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U21(x0, U22(z0, z1, z2), x2)) → c38(U21'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U21(x0, x(z0, z1), x2)) → c38(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.53
PROPER(U21(U11(z0, z1, z2), x1, x2)) → c38(U21'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U21(U12(z0, z1, z2), x1, x2)) → c38(U21'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U21(s(z0), x1, x2)) → c38(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U21(plus(z0, z1), x1, x2)) → c38(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c38(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U21(U22(z0, z1, z2), x1, x2)) → c38(U21'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U21(x(z0, z1), x1, x2)) → c38(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U21(x0, x1, tt)) → c38(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.53
PROPER(U21(x0, x1, 0)) → c38(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.53
PROPER(U21(x0, tt, x2)) → c38(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.53
PROPER(U21(x0, 0, x2)) → c38(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.53
PROPER(U21(tt, x1, x2)) → c38(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U21(0, x1, x2)) → c38(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U22(x0, x1, U11(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.53
PROPER(U22(x0, x1, U12(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.53
PROPER(U22(x0, x1, s(z0))) → c39(U22'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.53
PROPER(U22(x0, x1, plus(z0, z1))) → c39(U22'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.53
PROPER(U22(x0, x1, U21(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.53
PROPER(U22(x0, x1, U22(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.53
PROPER(U22(x0, x1, x(z0, z1))) → c39(U22'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.53
PROPER(U22(x0, U11(z0, z1, z2), x2)) → c39(U22'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U22(x0, U12(z0, z1, z2), x2)) → c39(U22'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U22(x0, s(z0), x2)) → c39(U22'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.53
PROPER(U22(x0, plus(z0, z1), x2)) → c39(U22'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.53
PROPER(U22(x0, U21(z0, z1, z2), x2)) → c39(U22'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U22(x0, U22(z0, z1, z2), x2)) → c39(U22'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U22(x0, x(z0, z1), x2)) → c39(U22'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.53
PROPER(U22(U11(z0, z1, z2), x1, x2)) → c39(U22'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U22(U12(z0, z1, z2), x1, x2)) → c39(U22'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U22(s(z0), x1, x2)) → c39(U22'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U22(plus(z0, z1), x1, x2)) → c39(U22'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U22(U21(z0, z1, z2), x1, x2)) → c39(U22'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U22(U22(z0, z1, z2), x1, x2)) → c39(U22'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U22(x(z0, z1), x1, x2)) → c39(U22'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U22(x0, x1, tt)) → c39(U22'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.53
PROPER(U22(x0, x1, 0)) → c39(U22'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.53
PROPER(U22(x0, tt, x2)) → c39(U22'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.53
PROPER(U22(x0, 0, x2)) → c39(U22'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.53
PROPER(U22(tt, x1, x2)) → c39(U22'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U22(0, x1, x2)) → c39(U22'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(x(x0, U11(z0, z1, z2))) → c40(X(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.71/102.53
PROPER(x(x0, U12(z0, z1, z2))) → c40(X(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.71/102.53
PROPER(x(x0, s(z0))) → c40(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.71/102.53
PROPER(x(x0, plus(z0, z1))) → c40(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.71/102.53
PROPER(x(x0, U21(z0, z1, z2))) → c40(X(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.71/102.53
PROPER(x(x0, U22(z0, z1, z2))) → c40(X(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.71/102.53
PROPER(x(x0, x(z0, z1))) → c40(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.71/102.53
PROPER(x(U11(z0, z1, z2), x1)) → c40(X(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.71/102.53
PROPER(x(U12(z0, z1, z2), x1)) → c40(X(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.71/102.53
PROPER(x(s(z0), x1)) → c40(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.71/102.53
PROPER(x(plus(z0, z1), x1)) → c40(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.71/102.53
PROPER(x(U21(z0, z1, z2), x1)) → c40(X(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.71/102.53
PROPER(x(U22(z0, z1, z2), x1)) → c40(X(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.71/102.53
PROPER(x(x(z0, z1), x1)) → c40(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.71/102.53
PROPER(x(x0, tt)) → c40(X(proper(x0), ok(tt)), PROPER(x0)) 334.71/102.53
PROPER(x(x0, 0)) → c40(X(proper(x0), ok(0)), PROPER(x0)) 334.71/102.53
PROPER(x(tt, x1)) → c40(X(ok(tt), proper(x1)), PROPER(x1)) 334.71/102.53
PROPER(x(0, x1)) → c40(X(ok(0), proper(x1)), PROPER(x1)) 334.71/102.53
TOP(mark(U11(z0, z1, z2))) → c42(TOP(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.71/102.53
TOP(mark(U12(z0, z1, z2))) → c42(TOP(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.71/102.53
TOP(mark(s(z0))) → c42(TOP(s(proper(z0))), PROPER(s(z0))) 334.71/102.53
TOP(mark(plus(z0, z1))) → c42(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.71/102.53
TOP(mark(U21(z0, z1, z2))) → c42(TOP(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.71/102.53
TOP(mark(U22(z0, z1, z2))) → c42(TOP(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.71/102.53
TOP(mark(x(z0, z1))) → c42(TOP(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.71/102.53
TOP(mark(tt)) → c42(TOP(ok(tt))) 334.71/102.53
TOP(mark(0)) → c42(TOP(ok(0))) 334.71/102.53
TOP(ok(U11(tt, z0, z1))) → c43(TOP(mark(U12(tt, z0, z1))), ACTIVE(U11(tt, z0, z1))) 334.71/102.53
TOP(ok(U12(tt, z0, z1))) → c43(TOP(mark(s(plus(z1, z0)))), ACTIVE(U12(tt, z0, z1))) 334.71/102.53
TOP(ok(U21(tt, z0, z1))) → c43(TOP(mark(U22(tt, z0, z1))), ACTIVE(U21(tt, z0, z1))) 334.71/102.53
TOP(ok(U22(tt, z0, z1))) → c43(TOP(mark(plus(x(z1, z0), z1))), ACTIVE(U22(tt, z0, z1))) 334.71/102.53
TOP(ok(plus(z0, 0))) → c43(TOP(mark(z0)), ACTIVE(plus(z0, 0))) 334.71/102.53
TOP(ok(plus(z0, s(z1)))) → c43(TOP(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.71/102.53
TOP(ok(x(z0, 0))) → c43(TOP(mark(0)), ACTIVE(x(z0, 0))) 334.71/102.53
TOP(ok(x(z0, s(z1)))) → c43(TOP(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.71/102.53
TOP(ok(U11(z0, z1, z2))) → c43(TOP(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.71/102.53
TOP(ok(U12(z0, z1, z2))) → c43(TOP(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.71/102.53
TOP(ok(s(z0))) → c43(TOP(s(active(z0))), ACTIVE(s(z0))) 334.71/102.53
TOP(ok(plus(z0, z1))) → c43(TOP(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.71/102.53
TOP(ok(plus(z0, z1))) → c43(TOP(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.71/102.53
TOP(ok(U21(z0, z1, z2))) → c43(TOP(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.71/102.53
TOP(ok(U22(z0, z1, z2))) → c43(TOP(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.71/102.53
TOP(ok(x(z0, z1))) → c43(TOP(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.71/102.53
TOP(ok(x(z0, z1))) → c43(TOP(x(z0, active(z1))), ACTIVE(x(z0, z1)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

ACTIVE, U11', U12', S, PLUS, U21', U22', X, PROPER, TOP

Compound Symbols:

c11, c12, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c, c2, c5, c7, c4, c8, c1, c9, c3, c10, c6, c13, c34, c14, c41, c33, c33, c35, c35, c36, c36, c37, c37, c38, c38, c39, c39, c40, c40, c42, c42, c43

334.71/102.53
334.71/102.53

(89) CdtUnreachableProof (EQUIVALENT transformation)

The following tuples could be removed as they are not reachable from basic start terms:

ACTIVE(plus(z0, z1)) → c11(PLUS(active(z0), z1), ACTIVE(z0)) 334.71/102.53
ACTIVE(plus(z0, z1)) → c12(PLUS(z0, active(z1)), ACTIVE(z1)) 334.71/102.53
ACTIVE(x(z0, z1)) → c15(X(active(z0), z1), ACTIVE(z0)) 334.71/102.53
ACTIVE(x(z0, z1)) → c16(X(z0, active(z1)), ACTIVE(z1)) 334.71/102.53
ACTIVE(U11(tt, z0, z1)) → c 334.71/102.53
ACTIVE(U21(tt, z0, z1)) → c2 334.71/102.53
ACTIVE(plus(z0, s(z1))) → c5 334.71/102.53
ACTIVE(x(z0, s(z1))) → c7 334.71/102.53
ACTIVE(U12(tt, z0, z1)) → c4(S(plus(z1, z0))) 334.71/102.53
ACTIVE(U12(tt, z0, z1)) → c4(PLUS(z1, z0)) 334.71/102.53
ACTIVE(U22(tt, z0, z1)) → c4(PLUS(x(z1, z0), z1)) 334.71/102.53
ACTIVE(U22(tt, z0, z1)) → c4(X(z1, z0)) 334.71/102.53
ACTIVE(U11(plus(z0, 0), x1, x2)) → c8(U11'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.53
ACTIVE(U11(plus(z0, s(z1)), x1, x2)) → c8(U11'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.53
ACTIVE(U11(x(z0, 0), x1, x2)) → c8(U11'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.53
ACTIVE(U11(x(z0, s(z1)), x1, x2)) → c8(U11'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.53
ACTIVE(U11(U11(z0, z1, z2), x1, x2)) → c8(U11'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.53
ACTIVE(U11(U12(z0, z1, z2), x1, x2)) → c8(U11'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.53
ACTIVE(U11(s(z0), x1, x2)) → c8(U11'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.53
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.53
ACTIVE(U11(plus(z0, z1), x1, x2)) → c8(U11'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.53
ACTIVE(U11(U21(z0, z1, z2), x1, x2)) → c8(U11'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.53
ACTIVE(U11(U22(z0, z1, z2), x1, x2)) → c8(U11'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.53
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.53
ACTIVE(U11(x(z0, z1), x1, x2)) → c8(U11'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.53
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(U11'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.53
ACTIVE(U11(U11(tt, z0, z1), x1, x2)) → c1(ACTIVE(U11(tt, z0, z1))) 334.71/102.53
ACTIVE(U12(plus(z0, 0), x1, x2)) → c9(U12'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.53
ACTIVE(U12(plus(z0, s(z1)), x1, x2)) → c9(U12'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.53
ACTIVE(U12(x(z0, 0), x1, x2)) → c9(U12'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.53
ACTIVE(U12(x(z0, s(z1)), x1, x2)) → c9(U12'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.53
ACTIVE(U12(U11(z0, z1, z2), x1, x2)) → c9(U12'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.53
ACTIVE(U12(U12(z0, z1, z2), x1, x2)) → c9(U12'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.53
ACTIVE(U12(s(z0), x1, x2)) → c9(U12'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.53
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.53
ACTIVE(U12(plus(z0, z1), x1, x2)) → c9(U12'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.53
ACTIVE(U12(U21(z0, z1, z2), x1, x2)) → c9(U12'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.53
ACTIVE(U12(U22(z0, z1, z2), x1, x2)) → c9(U12'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.53
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.53
ACTIVE(U12(x(z0, z1), x1, x2)) → c9(U12'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.53
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(U11'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.53
ACTIVE(U11(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.71/102.53
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(U12'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.53
ACTIVE(U12(U11(tt, z0, z1), x1, x2)) → c3(ACTIVE(U11(tt, z0, z1))) 334.71/102.53
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(U12'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.53
ACTIVE(U12(U12(tt, z0, z1), x1, x2)) → c3(ACTIVE(U12(tt, z0, z1))) 334.71/102.53
ACTIVE(s(plus(z0, 0))) → c10(S(mark(z0)), ACTIVE(plus(z0, 0))) 334.71/102.53
ACTIVE(s(plus(z0, s(z1)))) → c10(S(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.71/102.53
ACTIVE(s(x(z0, 0))) → c10(S(mark(0)), ACTIVE(x(z0, 0))) 334.71/102.53
ACTIVE(s(x(z0, s(z1)))) → c10(S(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.71/102.53
ACTIVE(s(U11(z0, z1, z2))) → c10(S(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.71/102.53
ACTIVE(s(U12(z0, z1, z2))) → c10(S(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.71/102.53
ACTIVE(s(s(z0))) → c10(S(s(active(z0))), ACTIVE(s(z0))) 334.71/102.53
ACTIVE(s(plus(z0, z1))) → c10(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.71/102.53
ACTIVE(s(plus(z0, z1))) → c10(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.71/102.53
ACTIVE(s(U21(z0, z1, z2))) → c10(S(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.71/102.53
ACTIVE(s(U22(z0, z1, z2))) → c10(S(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.71/102.53
ACTIVE(s(x(z0, z1))) → c10(S(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.71/102.53
ACTIVE(s(x(z0, z1))) → c10(S(x(z0, active(z1))), ACTIVE(x(z0, z1))) 334.71/102.53
ACTIVE(s(U11(tt, z0, z1))) → c6(S(mark(U12(tt, z0, z1)))) 334.71/102.53
ACTIVE(s(U11(tt, z0, z1))) → c6(ACTIVE(U11(tt, z0, z1))) 334.71/102.53
ACTIVE(s(U12(tt, z0, z1))) → c6(S(mark(s(plus(z1, z0))))) 334.71/102.53
ACTIVE(s(U12(tt, z0, z1))) → c6(ACTIVE(U12(tt, z0, z1))) 334.71/102.53
ACTIVE(U21(plus(z0, 0), x1, x2)) → c13(U21'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.53
ACTIVE(U21(plus(z0, s(z1)), x1, x2)) → c13(U21'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.53
ACTIVE(U21(x(z0, 0), x1, x2)) → c13(U21'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.53
ACTIVE(U21(x(z0, s(z1)), x1, x2)) → c13(U21'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.53
ACTIVE(U21(U11(z0, z1, z2), x1, x2)) → c13(U21'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.53
ACTIVE(U21(U12(z0, z1, z2), x1, x2)) → c13(U21'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.53
ACTIVE(U21(s(z0), x1, x2)) → c13(U21'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.53
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.53
ACTIVE(U21(plus(z0, z1), x1, x2)) → c13(U21'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.53
ACTIVE(U21(U21(z0, z1, z2), x1, x2)) → c13(U21'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.53
ACTIVE(U21(U22(z0, z1, z2), x1, x2)) → c13(U21'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.53
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.53
ACTIVE(U21(x(z0, z1), x1, x2)) → c13(U21'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.53
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(U11'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.53
ACTIVE(U11(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.53
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(U12'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.53
ACTIVE(U12(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.53
ACTIVE(s(U21(tt, z0, z1))) → c34(S(mark(U22(tt, z0, z1)))) 334.71/102.53
ACTIVE(s(U21(tt, z0, z1))) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.53
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(U21'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.53
ACTIVE(U21(U11(tt, z0, z1), x1, x2)) → c34(ACTIVE(U11(tt, z0, z1))) 334.71/102.53
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(U21'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.53
ACTIVE(U21(U12(tt, z0, z1), x1, x2)) → c34(ACTIVE(U12(tt, z0, z1))) 334.71/102.53
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(U21'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.53
ACTIVE(U21(U21(tt, z0, z1), x1, x2)) → c34(ACTIVE(U21(tt, z0, z1))) 334.71/102.53
ACTIVE(U22(plus(z0, 0), x1, x2)) → c14(U22'(mark(z0), x1, x2), ACTIVE(plus(z0, 0))) 334.71/102.53
ACTIVE(U22(plus(z0, s(z1)), x1, x2)) → c14(U22'(mark(U11(tt, z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 334.71/102.53
ACTIVE(U22(x(z0, 0), x1, x2)) → c14(U22'(mark(0), x1, x2), ACTIVE(x(z0, 0))) 334.71/102.53
ACTIVE(U22(x(z0, s(z1)), x1, x2)) → c14(U22'(mark(U21(tt, z1, z0)), x1, x2), ACTIVE(x(z0, s(z1)))) 334.71/102.53
ACTIVE(U22(U11(z0, z1, z2), x1, x2)) → c14(U22'(U11(active(z0), z1, z2), x1, x2), ACTIVE(U11(z0, z1, z2))) 334.71/102.53
ACTIVE(U22(U12(z0, z1, z2), x1, x2)) → c14(U22'(U12(active(z0), z1, z2), x1, x2), ACTIVE(U12(z0, z1, z2))) 334.71/102.53
ACTIVE(U22(s(z0), x1, x2)) → c14(U22'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 334.71/102.53
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.53
ACTIVE(U22(plus(z0, z1), x1, x2)) → c14(U22'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 334.71/102.53
ACTIVE(U22(U21(z0, z1, z2), x1, x2)) → c14(U22'(U21(active(z0), z1, z2), x1, x2), ACTIVE(U21(z0, z1, z2))) 334.71/102.53
ACTIVE(U22(U22(z0, z1, z2), x1, x2)) → c14(U22'(U22(active(z0), z1, z2), x1, x2), ACTIVE(U22(z0, z1, z2))) 334.71/102.53
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.53
ACTIVE(U22(x(z0, z1), x1, x2)) → c14(U22'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1))) 334.71/102.53
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(U11'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.53
ACTIVE(U11(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.53
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(U12'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.53
ACTIVE(U12(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.53
ACTIVE(s(U22(tt, z0, z1))) → c41(S(mark(plus(x(z1, z0), z1)))) 334.71/102.53
ACTIVE(s(U22(tt, z0, z1))) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.53
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(U21'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.53
ACTIVE(U21(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.53
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(U22'(mark(U12(tt, z0, z1)), x1, x2)) 334.71/102.53
ACTIVE(U22(U11(tt, z0, z1), x1, x2)) → c41(ACTIVE(U11(tt, z0, z1))) 334.71/102.53
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(U22'(mark(s(plus(z1, z0))), x1, x2)) 334.71/102.53
ACTIVE(U22(U12(tt, z0, z1), x1, x2)) → c41(ACTIVE(U12(tt, z0, z1))) 334.71/102.53
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(U22'(mark(U22(tt, z0, z1)), x1, x2)) 334.71/102.53
ACTIVE(U22(U21(tt, z0, z1), x1, x2)) → c41(ACTIVE(U21(tt, z0, z1))) 334.71/102.53
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(U22'(mark(plus(x(z1, z0), z1)), x1, x2)) 334.71/102.53
ACTIVE(U22(U22(tt, z0, z1), x1, x2)) → c41(ACTIVE(U22(tt, z0, z1))) 334.71/102.53
PROPER(U11(x0, x1, U11(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.53
PROPER(U11(x0, x1, U12(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.53
PROPER(U11(x0, x1, s(z0))) → c33(U11'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.53
PROPER(U11(x0, x1, plus(z0, z1))) → c33(U11'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.53
PROPER(U11(x0, x1, U21(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.53
PROPER(U11(x0, x1, U22(z0, z1, z2))) → c33(U11'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.53
PROPER(U11(x0, x1, x(z0, z1))) → c33(U11'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.53
PROPER(U11(x0, U11(z0, z1, z2), x2)) → c33(U11'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U11(x0, U12(z0, z1, z2), x2)) → c33(U11'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U11(x0, s(z0), x2)) → c33(U11'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.53
PROPER(U11(x0, plus(z0, z1), x2)) → c33(U11'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.53
PROPER(U11(x0, U21(z0, z1, z2), x2)) → c33(U11'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U11(x0, U22(z0, z1, z2), x2)) → c33(U11'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U11(x0, x(z0, z1), x2)) → c33(U11'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.53
PROPER(U11(U11(z0, z1, z2), x1, x2)) → c33(U11'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U11(U12(z0, z1, z2), x1, x2)) → c33(U11'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U11(s(z0), x1, x2)) → c33(U11'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U11(plus(z0, z1), x1, x2)) → c33(U11'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U11(U21(z0, z1, z2), x1, x2)) → c33(U11'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U11(U22(z0, z1, z2), x1, x2)) → c33(U11'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U11(x(z0, z1), x1, x2)) → c33(U11'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U11(x0, x1, tt)) → c33(U11'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.53
PROPER(U11(x0, x1, 0)) → c33(U11'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.53
PROPER(U11(x0, tt, x2)) → c33(U11'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.53
PROPER(U11(x0, 0, x2)) → c33(U11'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.53
PROPER(U11(tt, x1, x2)) → c33(U11'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U11(0, x1, x2)) → c33(U11'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U12(x0, x1, U11(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.53
PROPER(U12(x0, x1, U12(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.53
PROPER(U12(x0, x1, s(z0))) → c35(U12'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.53
PROPER(U12(x0, x1, plus(z0, z1))) → c35(U12'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.53
PROPER(U12(x0, x1, U21(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.53
PROPER(U12(x0, x1, U22(z0, z1, z2))) → c35(U12'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.53
PROPER(U12(x0, x1, x(z0, z1))) → c35(U12'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.53
PROPER(U12(x0, U11(z0, z1, z2), x2)) → c35(U12'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U12(x0, U12(z0, z1, z2), x2)) → c35(U12'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U12(x0, s(z0), x2)) → c35(U12'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.53
PROPER(U12(x0, plus(z0, z1), x2)) → c35(U12'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.53
PROPER(U12(x0, U21(z0, z1, z2), x2)) → c35(U12'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U12(x0, U22(z0, z1, z2), x2)) → c35(U12'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U12(x0, x(z0, z1), x2)) → c35(U12'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.53
PROPER(U12(U11(z0, z1, z2), x1, x2)) → c35(U12'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U12(U12(z0, z1, z2), x1, x2)) → c35(U12'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U12(s(z0), x1, x2)) → c35(U12'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U12(plus(z0, z1), x1, x2)) → c35(U12'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U12(U21(z0, z1, z2), x1, x2)) → c35(U12'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U12(U22(z0, z1, z2), x1, x2)) → c35(U12'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U12(x(z0, z1), x1, x2)) → c35(U12'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U12(x0, x1, tt)) → c35(U12'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.53
PROPER(U12(x0, x1, 0)) → c35(U12'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.53
PROPER(U12(x0, tt, x2)) → c35(U12'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.53
PROPER(U12(x0, 0, x2)) → c35(U12'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.53
PROPER(U12(tt, x1, x2)) → c35(U12'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U12(0, x1, x2)) → c35(U12'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(s(U11(z0, z1, z2))) → c36(S(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.71/102.53
PROPER(s(U12(z0, z1, z2))) → c36(S(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.71/102.53
PROPER(s(s(z0))) → c36(S(s(proper(z0))), PROPER(s(z0))) 334.71/102.53
PROPER(s(plus(z0, z1))) → c36(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.71/102.53
PROPER(s(U21(z0, z1, z2))) → c36(S(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.71/102.53
PROPER(s(U22(z0, z1, z2))) → c36(S(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.71/102.53
PROPER(s(x(z0, z1))) → c36(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.71/102.53
PROPER(s(tt)) → c36(S(ok(tt))) 334.71/102.53
PROPER(s(0)) → c36(S(ok(0))) 334.71/102.53
PROPER(plus(x0, U11(z0, z1, z2))) → c37(PLUS(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.71/102.53
PROPER(plus(x0, U12(z0, z1, z2))) → c37(PLUS(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.71/102.53
PROPER(plus(x0, s(z0))) → c37(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.71/102.53
PROPER(plus(x0, plus(z0, z1))) → c37(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.71/102.53
PROPER(plus(x0, U21(z0, z1, z2))) → c37(PLUS(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.71/102.53
PROPER(plus(x0, U22(z0, z1, z2))) → c37(PLUS(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.71/102.53
PROPER(plus(x0, x(z0, z1))) → c37(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.71/102.53
PROPER(plus(U11(z0, z1, z2), x1)) → c37(PLUS(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.71/102.53
PROPER(plus(U12(z0, z1, z2), x1)) → c37(PLUS(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.71/102.53
PROPER(plus(s(z0), x1)) → c37(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.71/102.53
PROPER(plus(plus(z0, z1), x1)) → c37(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.71/102.53
PROPER(plus(U21(z0, z1, z2), x1)) → c37(PLUS(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.71/102.53
PROPER(plus(U22(z0, z1, z2), x1)) → c37(PLUS(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.71/102.53
PROPER(plus(x(z0, z1), x1)) → c37(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.71/102.53
PROPER(plus(x0, tt)) → c37(PLUS(proper(x0), ok(tt)), PROPER(x0)) 334.71/102.53
PROPER(plus(x0, 0)) → c37(PLUS(proper(x0), ok(0)), PROPER(x0)) 334.71/102.53
PROPER(plus(tt, x1)) → c37(PLUS(ok(tt), proper(x1)), PROPER(x1)) 334.71/102.53
PROPER(plus(0, x1)) → c37(PLUS(ok(0), proper(x1)), PROPER(x1)) 334.71/102.53
PROPER(U21(x0, x1, U11(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.53
PROPER(U21(x0, x1, U12(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.53
PROPER(U21(x0, x1, s(z0))) → c38(U21'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.53
PROPER(U21(x0, x1, plus(z0, z1))) → c38(U21'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.53
PROPER(U21(x0, x1, U21(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.53
PROPER(U21(x0, x1, U22(z0, z1, z2))) → c38(U21'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.53
PROPER(U21(x0, x1, x(z0, z1))) → c38(U21'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.53
PROPER(U21(x0, U11(z0, z1, z2), x2)) → c38(U21'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U21(x0, U12(z0, z1, z2), x2)) → c38(U21'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U21(x0, s(z0), x2)) → c38(U21'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.53
PROPER(U21(x0, plus(z0, z1), x2)) → c38(U21'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.53
PROPER(U21(x0, U21(z0, z1, z2), x2)) → c38(U21'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U21(x0, U22(z0, z1, z2), x2)) → c38(U21'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U21(x0, x(z0, z1), x2)) → c38(U21'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.53
PROPER(U21(U11(z0, z1, z2), x1, x2)) → c38(U21'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U21(U12(z0, z1, z2), x1, x2)) → c38(U21'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U21(s(z0), x1, x2)) → c38(U21'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U21(plus(z0, z1), x1, x2)) → c38(U21'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U21(U21(z0, z1, z2), x1, x2)) → c38(U21'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U21(U22(z0, z1, z2), x1, x2)) → c38(U21'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U21(x(z0, z1), x1, x2)) → c38(U21'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U21(x0, x1, tt)) → c38(U21'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.53
PROPER(U21(x0, x1, 0)) → c38(U21'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.53
PROPER(U21(x0, tt, x2)) → c38(U21'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.53
PROPER(U21(x0, 0, x2)) → c38(U21'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.53
PROPER(U21(tt, x1, x2)) → c38(U21'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U21(0, x1, x2)) → c38(U21'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U22(x0, x1, U11(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1, z2))) 334.71/102.53
PROPER(U22(x0, x1, U12(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U12(z0, z1, z2))) 334.71/102.53
PROPER(U22(x0, x1, s(z0))) → c39(U22'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 334.71/102.53
PROPER(U22(x0, x1, plus(z0, z1))) → c39(U22'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 334.71/102.53
PROPER(U22(x0, x1, U21(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U21(z0, z1, z2))) 334.71/102.53
PROPER(U22(x0, x1, U22(z0, z1, z2))) → c39(U22'(proper(x0), proper(x1), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U22(z0, z1, z2))) 334.71/102.53
PROPER(U22(x0, x1, x(z0, z1))) → c39(U22'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1))) 334.71/102.53
PROPER(U22(x0, U11(z0, z1, z2), x2)) → c39(U22'(proper(x0), U11(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U22(x0, U12(z0, z1, z2), x2)) → c39(U22'(proper(x0), U12(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U12(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U22(x0, s(z0), x2)) → c39(U22'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 334.71/102.53
PROPER(U22(x0, plus(z0, z1), x2)) → c39(U22'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 334.71/102.53
PROPER(U22(x0, U21(z0, z1, z2), x2)) → c39(U22'(proper(x0), U21(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U21(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U22(x0, U22(z0, z1, z2), x2)) → c39(U22'(proper(x0), U22(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U22(z0, z1, z2)), PROPER(x2)) 334.71/102.53
PROPER(U22(x0, x(z0, z1), x2)) → c39(U22'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2)) 334.71/102.53
PROPER(U22(U11(z0, z1, z2), x1, x2)) → c39(U22'(U11(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U11(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U22(U12(z0, z1, z2), x1, x2)) → c39(U22'(U12(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U12(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U22(s(z0), x1, x2)) → c39(U22'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U22(plus(z0, z1), x1, x2)) → c39(U22'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U22(U21(z0, z1, z2), x1, x2)) → c39(U22'(U21(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U21(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U22(U22(z0, z1, z2), x1, x2)) → c39(U22'(U22(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U22(z0, z1, z2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U22(x(z0, z1), x1, x2)) → c39(U22'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U22(x0, x1, tt)) → c39(U22'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 334.71/102.53
PROPER(U22(x0, x1, 0)) → c39(U22'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 334.71/102.53
PROPER(U22(x0, tt, x2)) → c39(U22'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.53
PROPER(U22(x0, 0, x2)) → c39(U22'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 334.71/102.53
PROPER(U22(tt, x1, x2)) → c39(U22'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(U22(0, x1, x2)) → c39(U22'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 334.71/102.53
PROPER(x(x0, U11(z0, z1, z2))) → c40(X(proper(x0), U11(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U11(z0, z1, z2))) 334.71/102.53
PROPER(x(x0, U12(z0, z1, z2))) → c40(X(proper(x0), U12(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U12(z0, z1, z2))) 334.71/102.53
PROPER(x(x0, s(z0))) → c40(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.71/102.53
PROPER(x(x0, plus(z0, z1))) → c40(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 334.71/102.53
PROPER(x(x0, U21(z0, z1, z2))) → c40(X(proper(x0), U21(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U21(z0, z1, z2))) 334.71/102.53
PROPER(x(x0, U22(z0, z1, z2))) → c40(X(proper(x0), U22(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U22(z0, z1, z2))) 334.71/102.53
PROPER(x(x0, x(z0, z1))) → c40(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1))) 334.71/102.53
PROPER(x(U11(z0, z1, z2), x1)) → c40(X(U11(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U11(z0, z1, z2)), PROPER(x1)) 334.71/102.53
PROPER(x(U12(z0, z1, z2), x1)) → c40(X(U12(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U12(z0, z1, z2)), PROPER(x1)) 334.71/102.53
PROPER(x(s(z0), x1)) → c40(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.71/102.53
PROPER(x(plus(z0, z1), x1)) → c40(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 334.71/102.53
PROPER(x(U21(z0, z1, z2), x1)) → c40(X(U21(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U21(z0, z1, z2)), PROPER(x1)) 334.71/102.53
PROPER(x(U22(z0, z1, z2), x1)) → c40(X(U22(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U22(z0, z1, z2)), PROPER(x1)) 334.71/102.53
PROPER(x(x(z0, z1), x1)) → c40(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1)) 334.71/102.53
PROPER(x(x0, tt)) → c40(X(proper(x0), ok(tt)), PROPER(x0)) 334.71/102.53
PROPER(x(x0, 0)) → c40(X(proper(x0), ok(0)), PROPER(x0)) 334.71/102.53
PROPER(x(tt, x1)) → c40(X(ok(tt), proper(x1)), PROPER(x1)) 334.71/102.53
PROPER(x(0, x1)) → c40(X(ok(0), proper(x1)), PROPER(x1)) 334.71/102.53
TOP(mark(U11(z0, z1, z2))) → c42(TOP(U11(proper(z0), proper(z1), proper(z2))), PROPER(U11(z0, z1, z2))) 334.71/102.53
TOP(mark(U12(z0, z1, z2))) → c42(TOP(U12(proper(z0), proper(z1), proper(z2))), PROPER(U12(z0, z1, z2))) 334.71/102.53
TOP(mark(s(z0))) → c42(TOP(s(proper(z0))), PROPER(s(z0))) 334.71/102.53
TOP(mark(plus(z0, z1))) → c42(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 334.71/102.53
TOP(mark(U21(z0, z1, z2))) → c42(TOP(U21(proper(z0), proper(z1), proper(z2))), PROPER(U21(z0, z1, z2))) 334.71/102.53
TOP(mark(U22(z0, z1, z2))) → c42(TOP(U22(proper(z0), proper(z1), proper(z2))), PROPER(U22(z0, z1, z2))) 334.71/102.53
TOP(mark(x(z0, z1))) → c42(TOP(x(proper(z0), proper(z1))), PROPER(x(z0, z1))) 334.71/102.53
TOP(ok(U11(tt, z0, z1))) → c43(TOP(mark(U12(tt, z0, z1))), ACTIVE(U11(tt, z0, z1))) 334.71/102.53
TOP(ok(U12(tt, z0, z1))) → c43(TOP(mark(s(plus(z1, z0)))), ACTIVE(U12(tt, z0, z1))) 334.71/102.53
TOP(ok(U21(tt, z0, z1))) → c43(TOP(mark(U22(tt, z0, z1))), ACTIVE(U21(tt, z0, z1))) 334.71/102.53
TOP(ok(U22(tt, z0, z1))) → c43(TOP(mark(plus(x(z1, z0), z1))), ACTIVE(U22(tt, z0, z1))) 334.71/102.53
TOP(ok(plus(z0, 0))) → c43(TOP(mark(z0)), ACTIVE(plus(z0, 0))) 334.71/102.53
TOP(ok(plus(z0, s(z1)))) → c43(TOP(mark(U11(tt, z1, z0))), ACTIVE(plus(z0, s(z1)))) 334.71/102.53
TOP(ok(x(z0, 0))) → c43(TOP(mark(0)), ACTIVE(x(z0, 0))) 334.71/102.53
TOP(ok(x(z0, s(z1)))) → c43(TOP(mark(U21(tt, z1, z0))), ACTIVE(x(z0, s(z1)))) 334.71/102.53
TOP(ok(U11(z0, z1, z2))) → c43(TOP(U11(active(z0), z1, z2)), ACTIVE(U11(z0, z1, z2))) 334.71/102.53
TOP(ok(U12(z0, z1, z2))) → c43(TOP(U12(active(z0), z1, z2)), ACTIVE(U12(z0, z1, z2))) 334.71/102.53
TOP(ok(s(z0))) → c43(TOP(s(active(z0))), ACTIVE(s(z0))) 334.71/102.53
TOP(ok(plus(z0, z1))) → c43(TOP(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 334.71/102.53
TOP(ok(plus(z0, z1))) → c43(TOP(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 334.71/102.53
TOP(ok(U21(z0, z1, z2))) → c43(TOP(U21(active(z0), z1, z2)), ACTIVE(U21(z0, z1, z2))) 334.71/102.53
TOP(ok(U22(z0, z1, z2))) → c43(TOP(U22(active(z0), z1, z2)), ACTIVE(U22(z0, z1, z2))) 334.71/102.53
TOP(ok(x(z0, z1))) → c43(TOP(x(active(z0), z1)), ACTIVE(x(z0, z1))) 334.71/102.53
TOP(ok(x(z0, z1))) → c43(TOP(x(z0, active(z1))), ACTIVE(x(z0, z1)))
334.71/102.53
334.71/102.53

(90) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.71/102.53
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.71/102.53
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.71/102.53
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.71/102.53
active(plus(z0, 0)) → mark(z0) 334.71/102.53
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.71/102.53
active(x(z0, 0)) → mark(0) 334.71/102.53
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.71/102.53
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.71/102.53
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.71/102.53
active(s(z0)) → s(active(z0)) 334.71/102.53
active(plus(z0, z1)) → plus(active(z0), z1) 334.71/102.53
active(plus(z0, z1)) → plus(z0, active(z1)) 334.71/102.53
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.71/102.53
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.71/102.53
active(x(z0, z1)) → x(active(z0), z1) 334.71/102.53
active(x(z0, z1)) → x(z0, active(z1)) 334.71/102.53
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.71/102.53
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.71/102.53
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.71/102.53
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.71/102.53
s(mark(z0)) → mark(s(z0)) 334.71/102.53
s(ok(z0)) → ok(s(z0)) 334.71/102.53
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.71/102.53
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.71/102.53
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.71/102.53
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.71/102.53
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.71/102.53
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.71/102.53
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.71/102.53
x(mark(z0), z1) → mark(x(z0, z1)) 334.71/102.53
x(z0, mark(z1)) → mark(x(z0, z1)) 334.71/102.53
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.71/102.53
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.71/102.53
proper(tt) → ok(tt) 334.71/102.53
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.71/102.53
proper(s(z0)) → s(proper(z0)) 334.71/102.53
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.71/102.53
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.71/102.53
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.71/102.53
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.71/102.53
proper(0) → ok(0) 334.71/102.53
top(mark(z0)) → top(proper(z0)) 334.71/102.53
top(ok(z0)) → top(active(z0))
Tuples:

U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.53
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.53
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.53
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.53
S(mark(z0)) → c21(S(z0)) 334.71/102.53
S(ok(z0)) → c22(S(z0)) 334.71/102.53
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.53
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.53
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.53
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.53
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.53
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.53
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.53
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.53
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.53
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.71/102.53
TOP(mark(tt)) → c42(TOP(ok(tt))) 334.71/102.53
TOP(mark(0)) → c42(TOP(ok(0)))
S tuples:

U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.53
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.53
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.53
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.53
S(mark(z0)) → c21(S(z0)) 334.71/102.53
S(ok(z0)) → c22(S(z0)) 334.71/102.53
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.53
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.53
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.53
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.53
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.53
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.53
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.53
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.53
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.53
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.71/102.53
TOP(mark(tt)) → c42(TOP(ok(tt))) 334.71/102.53
TOP(mark(0)) → c42(TOP(ok(0)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

U11', U12', S, PLUS, U21', U22', X, TOP

Compound Symbols:

c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c42

334.71/102.53
334.71/102.53

(91) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 2 trailing tuple parts
334.71/102.53
334.71/102.53

(92) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.71/102.53
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.71/102.53
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.71/102.53
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.71/102.53
active(plus(z0, 0)) → mark(z0) 334.71/102.53
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.71/102.53
active(x(z0, 0)) → mark(0) 334.71/102.53
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.71/102.53
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.71/102.53
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.71/102.53
active(s(z0)) → s(active(z0)) 334.71/102.53
active(plus(z0, z1)) → plus(active(z0), z1) 334.71/102.53
active(plus(z0, z1)) → plus(z0, active(z1)) 334.71/102.53
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.71/102.53
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.71/102.53
active(x(z0, z1)) → x(active(z0), z1) 334.71/102.53
active(x(z0, z1)) → x(z0, active(z1)) 334.71/102.53
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.71/102.53
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.71/102.53
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.71/102.53
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.71/102.53
s(mark(z0)) → mark(s(z0)) 334.71/102.53
s(ok(z0)) → ok(s(z0)) 334.71/102.53
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.71/102.53
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.71/102.53
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.71/102.53
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.71/102.53
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.71/102.53
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.71/102.53
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.71/102.53
x(mark(z0), z1) → mark(x(z0, z1)) 334.71/102.53
x(z0, mark(z1)) → mark(x(z0, z1)) 334.71/102.53
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.71/102.53
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.71/102.53
proper(tt) → ok(tt) 334.71/102.53
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.71/102.53
proper(s(z0)) → s(proper(z0)) 334.71/102.53
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.71/102.53
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.71/102.53
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.71/102.53
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.71/102.53
proper(0) → ok(0) 334.71/102.53
top(mark(z0)) → top(proper(z0)) 334.71/102.53
top(ok(z0)) → top(active(z0))
Tuples:

U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.53
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.53
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.53
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.53
S(mark(z0)) → c21(S(z0)) 334.71/102.53
S(ok(z0)) → c22(S(z0)) 334.71/102.53
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.53
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.53
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.53
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.53
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.53
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.53
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.53
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.53
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.53
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.71/102.53
TOP(mark(tt)) → c42 334.71/102.53
TOP(mark(0)) → c42
S tuples:

U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.53
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.53
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.53
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.53
S(mark(z0)) → c21(S(z0)) 334.71/102.53
S(ok(z0)) → c22(S(z0)) 334.71/102.53
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.53
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.53
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.53
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.53
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.53
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.53
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.53
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.53
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.53
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.71/102.53
TOP(mark(tt)) → c42 334.71/102.53
TOP(mark(0)) → c42
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

U11', U12', S, PLUS, U21', U22', X, TOP

Compound Symbols:

c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c42

334.71/102.53
334.71/102.53

(93) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

Removed 2 trailing nodes:

TOP(mark(tt)) → c42 334.71/102.53
TOP(mark(0)) → c42
334.71/102.53
334.71/102.53

(94) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.71/102.53
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.71/102.53
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.71/102.53
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.71/102.53
active(plus(z0, 0)) → mark(z0) 334.71/102.53
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.71/102.53
active(x(z0, 0)) → mark(0) 334.71/102.53
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.71/102.53
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.71/102.53
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.71/102.53
active(s(z0)) → s(active(z0)) 334.71/102.53
active(plus(z0, z1)) → plus(active(z0), z1) 334.71/102.53
active(plus(z0, z1)) → plus(z0, active(z1)) 334.71/102.53
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.71/102.53
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.71/102.53
active(x(z0, z1)) → x(active(z0), z1) 334.71/102.53
active(x(z0, z1)) → x(z0, active(z1)) 334.71/102.53
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.71/102.53
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.71/102.53
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.71/102.53
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.71/102.53
s(mark(z0)) → mark(s(z0)) 334.71/102.53
s(ok(z0)) → ok(s(z0)) 334.71/102.53
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.71/102.53
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.71/102.53
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.71/102.53
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.71/102.53
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.71/102.53
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.71/102.53
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.71/102.53
x(mark(z0), z1) → mark(x(z0, z1)) 334.71/102.53
x(z0, mark(z1)) → mark(x(z0, z1)) 334.71/102.53
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.71/102.53
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.71/102.53
proper(tt) → ok(tt) 334.71/102.53
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.71/102.53
proper(s(z0)) → s(proper(z0)) 334.71/102.53
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.71/102.53
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.71/102.53
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.71/102.53
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.71/102.53
proper(0) → ok(0) 334.71/102.53
top(mark(z0)) → top(proper(z0)) 334.71/102.53
top(ok(z0)) → top(active(z0))
Tuples:

U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.53
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.53
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.53
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.53
S(mark(z0)) → c21(S(z0)) 334.71/102.53
S(ok(z0)) → c22(S(z0)) 334.71/102.53
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.53
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.53
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.53
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.53
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.53
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.53
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.53
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.53
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.53
X(ok(z0), ok(z1)) → c32(X(z0, z1))
S tuples:

U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.54
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.54
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.54
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.54
S(mark(z0)) → c21(S(z0)) 334.71/102.54
S(ok(z0)) → c22(S(z0)) 334.71/102.54
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.54
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.54
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.54
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.54
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.54
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.54
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.54
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.54
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.54
X(ok(z0), ok(z1)) → c32(X(z0, z1))
K tuples:none
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

U11', U12', S, PLUS, U21', U22', X

Compound Symbols:

c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32

334.71/102.54
334.71/102.54

(95) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2))
We considered the (Usable) Rules:none
And the Tuples:

U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.54
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.54
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.54
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.54
S(mark(z0)) → c21(S(z0)) 334.71/102.54
S(ok(z0)) → c22(S(z0)) 334.71/102.54
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.54
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.54
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.54
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.54
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.54
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.54
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.54
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.54
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.54
X(ok(z0), ok(z1)) → c32(X(z0, z1))
The order we found is given by the following interpretation:
Polynomial interpretation : 334.71/102.54

POL(PLUS(x1, x2)) = 0    334.71/102.54
POL(S(x1)) = 0    334.71/102.54
POL(U11'(x1, x2, x3)) = [4]x1    334.71/102.54
POL(U12'(x1, x2, x3)) = 0    334.71/102.54
POL(U21'(x1, x2, x3)) = 0    334.71/102.54
POL(U22'(x1, x2, x3)) = 0    334.71/102.54
POL(X(x1, x2)) = 0    334.71/102.54
POL(c17(x1)) = x1    334.71/102.54
POL(c18(x1)) = x1    334.71/102.54
POL(c19(x1)) = x1    334.71/102.54
POL(c20(x1)) = x1    334.71/102.54
POL(c21(x1)) = x1    334.71/102.54
POL(c22(x1)) = x1    334.71/102.54
POL(c23(x1)) = x1    334.71/102.54
POL(c24(x1)) = x1    334.71/102.54
POL(c25(x1)) = x1    334.71/102.54
POL(c26(x1)) = x1    334.71/102.54
POL(c27(x1)) = x1    334.71/102.54
POL(c28(x1)) = x1    334.71/102.54
POL(c29(x1)) = x1    334.71/102.54
POL(c30(x1)) = x1    334.71/102.54
POL(c31(x1)) = x1    334.71/102.54
POL(c32(x1)) = x1    334.71/102.54
POL(mark(x1)) = [4] + x1    334.71/102.54
POL(ok(x1)) = x1   
334.71/102.54
334.71/102.54

(96) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.71/102.54
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.71/102.54
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.71/102.54
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.71/102.54
active(plus(z0, 0)) → mark(z0) 334.71/102.54
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.71/102.54
active(x(z0, 0)) → mark(0) 334.71/102.54
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.71/102.54
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.71/102.54
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.71/102.54
active(s(z0)) → s(active(z0)) 334.71/102.54
active(plus(z0, z1)) → plus(active(z0), z1) 334.71/102.54
active(plus(z0, z1)) → plus(z0, active(z1)) 334.71/102.54
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.71/102.54
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.71/102.54
active(x(z0, z1)) → x(active(z0), z1) 334.71/102.54
active(x(z0, z1)) → x(z0, active(z1)) 334.71/102.54
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.71/102.54
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.71/102.54
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.71/102.54
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.71/102.54
s(mark(z0)) → mark(s(z0)) 334.71/102.54
s(ok(z0)) → ok(s(z0)) 334.71/102.54
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.71/102.54
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.71/102.54
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.71/102.54
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.71/102.54
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.71/102.54
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.71/102.54
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.71/102.54
x(mark(z0), z1) → mark(x(z0, z1)) 334.71/102.54
x(z0, mark(z1)) → mark(x(z0, z1)) 334.71/102.54
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.71/102.54
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.71/102.54
proper(tt) → ok(tt) 334.71/102.54
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.71/102.54
proper(s(z0)) → s(proper(z0)) 334.71/102.54
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.71/102.54
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.71/102.54
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.71/102.54
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.71/102.54
proper(0) → ok(0) 334.71/102.54
top(mark(z0)) → top(proper(z0)) 334.71/102.54
top(ok(z0)) → top(active(z0))
Tuples:

U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.54
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.54
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.54
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.54
S(mark(z0)) → c21(S(z0)) 334.71/102.54
S(ok(z0)) → c22(S(z0)) 334.71/102.54
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.54
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.54
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.54
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.54
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.54
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.54
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.54
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.54
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.54
X(ok(z0), ok(z1)) → c32(X(z0, z1))
S tuples:

U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.54
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.54
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.54
S(mark(z0)) → c21(S(z0)) 334.71/102.54
S(ok(z0)) → c22(S(z0)) 334.71/102.54
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.54
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.54
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.54
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.54
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.54
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.54
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.54
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.54
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.54
X(ok(z0), ok(z1)) → c32(X(z0, z1))
K tuples:

U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2))
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

U11', U12', S, PLUS, U21', U22', X

Compound Symbols:

c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32

334.71/102.54
334.71/102.54

(97) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.54
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.54
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2))
We considered the (Usable) Rules:none
And the Tuples:

U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.54
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.54
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.54
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.54
S(mark(z0)) → c21(S(z0)) 334.71/102.54
S(ok(z0)) → c22(S(z0)) 334.71/102.54
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.54
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.54
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.54
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.54
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.54
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.54
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.54
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.54
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.54
X(ok(z0), ok(z1)) → c32(X(z0, z1))
The order we found is given by the following interpretation:
Polynomial interpretation : 334.71/102.54

POL(PLUS(x1, x2)) = 0    334.71/102.54
POL(S(x1)) = 0    334.71/102.54
POL(U11'(x1, x2, x3)) = x3    334.71/102.54
POL(U12'(x1, x2, x3)) = x1    334.71/102.54
POL(U21'(x1, x2, x3)) = 0    334.71/102.54
POL(U22'(x1, x2, x3)) = 0    334.71/102.54
POL(X(x1, x2)) = 0    334.71/102.54
POL(c17(x1)) = x1    334.71/102.54
POL(c18(x1)) = x1    334.71/102.54
POL(c19(x1)) = x1    334.71/102.54
POL(c20(x1)) = x1    334.71/102.54
POL(c21(x1)) = x1    334.71/102.54
POL(c22(x1)) = x1    334.71/102.54
POL(c23(x1)) = x1    334.71/102.54
POL(c24(x1)) = x1    334.71/102.54
POL(c25(x1)) = x1    334.71/102.54
POL(c26(x1)) = x1    334.71/102.54
POL(c27(x1)) = x1    334.71/102.54
POL(c28(x1)) = x1    334.71/102.54
POL(c29(x1)) = x1    334.71/102.54
POL(c30(x1)) = x1    334.71/102.54
POL(c31(x1)) = x1    334.71/102.54
POL(c32(x1)) = x1    334.71/102.54
POL(mark(x1)) = [4] + x1    334.71/102.54
POL(ok(x1)) = [1] + x1   
334.71/102.54
334.71/102.54

(98) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.71/102.54
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.71/102.54
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.71/102.54
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.71/102.54
active(plus(z0, 0)) → mark(z0) 334.71/102.54
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.71/102.54
active(x(z0, 0)) → mark(0) 334.71/102.54
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.71/102.54
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.71/102.54
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.71/102.54
active(s(z0)) → s(active(z0)) 334.71/102.54
active(plus(z0, z1)) → plus(active(z0), z1) 334.71/102.54
active(plus(z0, z1)) → plus(z0, active(z1)) 334.71/102.54
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.71/102.54
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.71/102.54
active(x(z0, z1)) → x(active(z0), z1) 334.71/102.54
active(x(z0, z1)) → x(z0, active(z1)) 334.71/102.54
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.71/102.54
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.71/102.54
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.71/102.54
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.71/102.54
s(mark(z0)) → mark(s(z0)) 334.71/102.54
s(ok(z0)) → ok(s(z0)) 334.71/102.54
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.71/102.54
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.71/102.54
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.71/102.54
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.71/102.54
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.71/102.54
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.71/102.54
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.71/102.54
x(mark(z0), z1) → mark(x(z0, z1)) 334.71/102.54
x(z0, mark(z1)) → mark(x(z0, z1)) 334.71/102.54
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.71/102.54
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.71/102.54
proper(tt) → ok(tt) 334.71/102.54
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.71/102.54
proper(s(z0)) → s(proper(z0)) 334.71/102.54
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.71/102.54
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.71/102.54
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.71/102.54
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.71/102.54
proper(0) → ok(0) 334.71/102.54
top(mark(z0)) → top(proper(z0)) 334.71/102.54
top(ok(z0)) → top(active(z0))
Tuples:

U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.54
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.54
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.54
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.54
S(mark(z0)) → c21(S(z0)) 334.71/102.54
S(ok(z0)) → c22(S(z0)) 334.71/102.54
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.54
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.54
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.54
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.54
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.54
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.54
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.54
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.54
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.54
X(ok(z0), ok(z1)) → c32(X(z0, z1))
S tuples:

S(mark(z0)) → c21(S(z0)) 334.71/102.54
S(ok(z0)) → c22(S(z0)) 334.71/102.54
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.54
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.54
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.54
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.54
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.54
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.54
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.54
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.54
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.54
X(ok(z0), ok(z1)) → c32(X(z0, z1))
K tuples:

U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.54
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.54
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.54
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2))
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

U11', U12', S, PLUS, U21', U22', X

Compound Symbols:

c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32

334.71/102.54
334.71/102.54

(99) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2))
We considered the (Usable) Rules:none
And the Tuples:

U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.54
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.54
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.54
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.54
S(mark(z0)) → c21(S(z0)) 334.71/102.54
S(ok(z0)) → c22(S(z0)) 334.71/102.54
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.54
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.54
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.54
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.54
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.54
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.54
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.54
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.54
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.54
X(ok(z0), ok(z1)) → c32(X(z0, z1))
The order we found is given by the following interpretation:
Polynomial interpretation : 334.71/102.54

POL(PLUS(x1, x2)) = 0    334.71/102.54
POL(S(x1)) = 0    334.71/102.54
POL(U11'(x1, x2, x3)) = [3]x2 + [5]x3    334.71/102.54
POL(U12'(x1, x2, x3)) = [5]x2 + [5]x3    334.71/102.54
POL(U21'(x1, x2, x3)) = 0    334.71/102.54
POL(U22'(x1, x2, x3)) = x3    334.71/102.54
POL(X(x1, x2)) = 0    334.71/102.54
POL(c17(x1)) = x1    334.71/102.54
POL(c18(x1)) = x1    334.71/102.54
POL(c19(x1)) = x1    334.71/102.54
POL(c20(x1)) = x1    334.71/102.54
POL(c21(x1)) = x1    334.71/102.54
POL(c22(x1)) = x1    334.71/102.54
POL(c23(x1)) = x1    334.71/102.54
POL(c24(x1)) = x1    334.71/102.54
POL(c25(x1)) = x1    334.71/102.54
POL(c26(x1)) = x1    334.71/102.54
POL(c27(x1)) = x1    334.71/102.54
POL(c28(x1)) = x1    334.71/102.54
POL(c29(x1)) = x1    334.71/102.54
POL(c30(x1)) = x1    334.71/102.54
POL(c31(x1)) = x1    334.71/102.54
POL(c32(x1)) = x1    334.71/102.54
POL(mark(x1)) = 0    334.71/102.54
POL(ok(x1)) = [1] + x1   
334.71/102.54
334.71/102.54

(100) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.71/102.54
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.71/102.54
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.71/102.54
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.71/102.54
active(plus(z0, 0)) → mark(z0) 334.71/102.54
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.71/102.54
active(x(z0, 0)) → mark(0) 334.71/102.54
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.71/102.54
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.71/102.54
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.71/102.54
active(s(z0)) → s(active(z0)) 334.71/102.54
active(plus(z0, z1)) → plus(active(z0), z1) 334.71/102.54
active(plus(z0, z1)) → plus(z0, active(z1)) 334.71/102.54
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.71/102.54
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.71/102.54
active(x(z0, z1)) → x(active(z0), z1) 334.71/102.54
active(x(z0, z1)) → x(z0, active(z1)) 334.71/102.54
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.71/102.54
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.71/102.54
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.71/102.54
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.71/102.54
s(mark(z0)) → mark(s(z0)) 334.71/102.54
s(ok(z0)) → ok(s(z0)) 334.71/102.54
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.71/102.54
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.71/102.54
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.71/102.54
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.71/102.54
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.71/102.54
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.71/102.54
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.71/102.54
x(mark(z0), z1) → mark(x(z0, z1)) 334.71/102.54
x(z0, mark(z1)) → mark(x(z0, z1)) 334.71/102.54
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.71/102.54
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.71/102.54
proper(tt) → ok(tt) 334.71/102.54
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.71/102.54
proper(s(z0)) → s(proper(z0)) 334.71/102.54
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.71/102.54
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.71/102.54
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.71/102.54
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.71/102.54
proper(0) → ok(0) 334.71/102.54
top(mark(z0)) → top(proper(z0)) 334.71/102.54
top(ok(z0)) → top(active(z0))
Tuples:

U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.54
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.54
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.54
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.54
S(mark(z0)) → c21(S(z0)) 334.71/102.54
S(ok(z0)) → c22(S(z0)) 334.71/102.54
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.54
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.54
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.54
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.54
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.54
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.54
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.54
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.54
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.54
X(ok(z0), ok(z1)) → c32(X(z0, z1))
S tuples:

S(mark(z0)) → c21(S(z0)) 334.71/102.54
S(ok(z0)) → c22(S(z0)) 334.71/102.54
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.54
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.54
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.54
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.54
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.54
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.54
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.54
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.54
X(ok(z0), ok(z1)) → c32(X(z0, z1))
K tuples:

U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.54
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.54
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.54
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.54
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2))
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

U11', U12', S, PLUS, U21', U22', X

Compound Symbols:

c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32

334.71/102.54
334.71/102.54

(101) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:

U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.54
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.54
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.54
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.54
S(mark(z0)) → c21(S(z0)) 334.71/102.54
S(ok(z0)) → c22(S(z0)) 334.71/102.54
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.54
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.54
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.54
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.54
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.54
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.54
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.54
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.54
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.54
X(ok(z0), ok(z1)) → c32(X(z0, z1))
The order we found is given by the following interpretation:
Polynomial interpretation : 334.71/102.54

POL(PLUS(x1, x2)) = x1    334.71/102.54
POL(S(x1)) = 0    334.71/102.54
POL(U11'(x1, x2, x3)) = [3]x1 + [5]x2 + [5]x3    334.71/102.54
POL(U12'(x1, x2, x3)) = [5]x1 + [5]x2 + [3]x3    334.71/102.54
POL(U21'(x1, x2, x3)) = 0    334.71/102.54
POL(U22'(x1, x2, x3)) = [3]x2 + [5]x3    334.71/102.54
POL(X(x1, x2)) = 0    334.71/102.54
POL(c17(x1)) = x1    334.71/102.54
POL(c18(x1)) = x1    334.71/102.54
POL(c19(x1)) = x1    334.71/102.54
POL(c20(x1)) = x1    334.71/102.54
POL(c21(x1)) = x1    334.71/102.54
POL(c22(x1)) = x1    334.71/102.54
POL(c23(x1)) = x1    334.71/102.54
POL(c24(x1)) = x1    334.71/102.54
POL(c25(x1)) = x1    334.71/102.54
POL(c26(x1)) = x1    334.71/102.54
POL(c27(x1)) = x1    334.71/102.54
POL(c28(x1)) = x1    334.71/102.54
POL(c29(x1)) = x1    334.71/102.54
POL(c30(x1)) = x1    334.71/102.54
POL(c31(x1)) = x1    334.71/102.54
POL(c32(x1)) = x1    334.71/102.54
POL(mark(x1)) = x1    334.71/102.54
POL(ok(x1)) = [2] + x1   
334.71/102.54
334.71/102.54

(102) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.71/102.54
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.71/102.54
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.71/102.54
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.71/102.54
active(plus(z0, 0)) → mark(z0) 334.71/102.54
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.71/102.54
active(x(z0, 0)) → mark(0) 334.71/102.54
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.71/102.54
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.71/102.54
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.71/102.54
active(s(z0)) → s(active(z0)) 334.71/102.54
active(plus(z0, z1)) → plus(active(z0), z1) 334.71/102.54
active(plus(z0, z1)) → plus(z0, active(z1)) 334.71/102.54
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.71/102.54
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.71/102.54
active(x(z0, z1)) → x(active(z0), z1) 334.71/102.54
active(x(z0, z1)) → x(z0, active(z1)) 334.71/102.54
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.71/102.54
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.71/102.54
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.71/102.54
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.71/102.54
s(mark(z0)) → mark(s(z0)) 334.71/102.54
s(ok(z0)) → ok(s(z0)) 334.71/102.54
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.71/102.54
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.71/102.54
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.71/102.54
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.71/102.54
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.71/102.54
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.71/102.54
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.71/102.54
x(mark(z0), z1) → mark(x(z0, z1)) 334.71/102.54
x(z0, mark(z1)) → mark(x(z0, z1)) 334.71/102.54
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.71/102.54
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.71/102.54
proper(tt) → ok(tt) 334.71/102.54
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.71/102.54
proper(s(z0)) → s(proper(z0)) 334.71/102.54
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.71/102.54
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.71/102.54
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.71/102.54
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.71/102.54
proper(0) → ok(0) 334.71/102.54
top(mark(z0)) → top(proper(z0)) 334.71/102.54
top(ok(z0)) → top(active(z0))
Tuples:

U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.54
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.54
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.54
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.54
S(mark(z0)) → c21(S(z0)) 334.71/102.54
S(ok(z0)) → c22(S(z0)) 334.71/102.54
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.54
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.54
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.54
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.54
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.54
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.54
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.54
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.54
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.54
X(ok(z0), ok(z1)) → c32(X(z0, z1))
S tuples:

S(mark(z0)) → c21(S(z0)) 334.71/102.54
S(ok(z0)) → c22(S(z0)) 334.71/102.54
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.54
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.54
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.54
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.54
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.54
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.54
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.54
X(ok(z0), ok(z1)) → c32(X(z0, z1))
K tuples:

U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.54
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.54
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.54
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.54
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.54
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1))
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

U11', U12', S, PLUS, U21', U22', X

Compound Symbols:

c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32

334.71/102.54
334.71/102.54

(103) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2))
We considered the (Usable) Rules:none
And the Tuples:

U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.54
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.54
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.54
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.54
S(mark(z0)) → c21(S(z0)) 334.71/102.54
S(ok(z0)) → c22(S(z0)) 334.71/102.54
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.54
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.54
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.54
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.54
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.54
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.54
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.54
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.54
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.54
X(ok(z0), ok(z1)) → c32(X(z0, z1))
The order we found is given by the following interpretation:
Polynomial interpretation : 334.71/102.54

POL(PLUS(x1, x2)) = 0    334.71/102.54
POL(S(x1)) = 0    334.71/102.54
POL(U11'(x1, x2, x3)) = [3]x1 + [5]x2 + [3]x3    334.71/102.54
POL(U12'(x1, x2, x3)) = [5]x1 + [5]x2 + [3]x3    334.71/102.54
POL(U21'(x1, x2, x3)) = 0    334.71/102.54
POL(U22'(x1, x2, x3)) = x1 + [5]x2 + [5]x3    334.71/102.54
POL(X(x1, x2)) = 0    334.71/102.54
POL(c17(x1)) = x1    334.71/102.54
POL(c18(x1)) = x1    334.71/102.54
POL(c19(x1)) = x1    334.71/102.54
POL(c20(x1)) = x1    334.71/102.54
POL(c21(x1)) = x1    334.71/102.54
POL(c22(x1)) = x1    334.71/102.54
POL(c23(x1)) = x1    334.71/102.54
POL(c24(x1)) = x1    334.71/102.54
POL(c25(x1)) = x1    334.71/102.54
POL(c26(x1)) = x1    334.71/102.54
POL(c27(x1)) = x1    334.71/102.54
POL(c28(x1)) = x1    334.71/102.54
POL(c29(x1)) = x1    334.71/102.54
POL(c30(x1)) = x1    334.71/102.54
POL(c31(x1)) = x1    334.71/102.54
POL(c32(x1)) = x1    334.71/102.54
POL(mark(x1)) = [1] + x1    334.71/102.54
POL(ok(x1)) = x1   
334.71/102.54
334.71/102.54

(104) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.71/102.54
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.71/102.54
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.71/102.54
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.71/102.54
active(plus(z0, 0)) → mark(z0) 334.71/102.54
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.71/102.54
active(x(z0, 0)) → mark(0) 334.71/102.54
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.71/102.54
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.71/102.54
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.71/102.54
active(s(z0)) → s(active(z0)) 334.71/102.54
active(plus(z0, z1)) → plus(active(z0), z1) 334.71/102.54
active(plus(z0, z1)) → plus(z0, active(z1)) 334.71/102.54
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.71/102.54
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.71/102.54
active(x(z0, z1)) → x(active(z0), z1) 334.71/102.54
active(x(z0, z1)) → x(z0, active(z1)) 334.71/102.54
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.71/102.54
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.71/102.54
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.71/102.54
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.71/102.54
s(mark(z0)) → mark(s(z0)) 334.71/102.54
s(ok(z0)) → ok(s(z0)) 334.71/102.54
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.71/102.54
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.71/102.54
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.71/102.54
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.71/102.54
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.71/102.54
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.71/102.54
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.71/102.54
x(mark(z0), z1) → mark(x(z0, z1)) 334.71/102.54
x(z0, mark(z1)) → mark(x(z0, z1)) 334.71/102.54
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.71/102.54
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.71/102.54
proper(tt) → ok(tt) 334.71/102.54
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.71/102.54
proper(s(z0)) → s(proper(z0)) 334.71/102.54
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.71/102.54
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.71/102.54
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.71/102.54
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.71/102.54
proper(0) → ok(0) 334.71/102.54
top(mark(z0)) → top(proper(z0)) 334.71/102.54
top(ok(z0)) → top(active(z0))
Tuples:

U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.54
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.54
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.54
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.54
S(mark(z0)) → c21(S(z0)) 334.71/102.54
S(ok(z0)) → c22(S(z0)) 334.71/102.54
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.54
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.54
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.54
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.54
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.54
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.54
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.54
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.54
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.54
X(ok(z0), ok(z1)) → c32(X(z0, z1))
S tuples:

S(mark(z0)) → c21(S(z0)) 334.71/102.54
S(ok(z0)) → c22(S(z0)) 334.71/102.54
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.54
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.54
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.54
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.54
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.54
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.54
X(ok(z0), ok(z1)) → c32(X(z0, z1))
K tuples:

U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.54
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.54
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.54
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.54
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.54
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.54
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2))
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

U11', U12', S, PLUS, U21', U22', X

Compound Symbols:

c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32

334.71/102.54
334.71/102.54

(105) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.54
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.54
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.54
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.54
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.54
X(ok(z0), ok(z1)) → c32(X(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:

U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.54
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.54
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.54
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.54
S(mark(z0)) → c21(S(z0)) 334.71/102.54
S(ok(z0)) → c22(S(z0)) 334.71/102.54
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.54
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.54
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.54
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.54
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.54
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.54
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.54
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.54
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.54
X(ok(z0), ok(z1)) → c32(X(z0, z1))
The order we found is given by the following interpretation:
Polynomial interpretation : 334.71/102.54

POL(PLUS(x1, x2)) = x2    334.71/102.54
POL(S(x1)) = 0    334.71/102.54
POL(U11'(x1, x2, x3)) = [5]x1 + [5]x2 + [5]x3    334.71/102.54
POL(U12'(x1, x2, x3)) = [5]x1 + [5]x2 + [5]x3    334.71/102.54
POL(U21'(x1, x2, x3)) = x1 + x2 + [2]x3    334.71/102.54
POL(U22'(x1, x2, x3)) = [5]x1 + [5]x2 + [5]x3    334.71/102.54
POL(X(x1, x2)) = [2]x1 + x2    334.71/102.54
POL(c17(x1)) = x1    334.71/102.54
POL(c18(x1)) = x1    334.71/102.54
POL(c19(x1)) = x1    334.71/102.54
POL(c20(x1)) = x1    334.71/102.54
POL(c21(x1)) = x1    334.71/102.54
POL(c22(x1)) = x1    334.71/102.54
POL(c23(x1)) = x1    334.71/102.54
POL(c24(x1)) = x1    334.71/102.54
POL(c25(x1)) = x1    334.71/102.54
POL(c26(x1)) = x1    334.71/102.54
POL(c27(x1)) = x1    334.71/102.54
POL(c28(x1)) = x1    334.71/102.54
POL(c29(x1)) = x1    334.71/102.54
POL(c30(x1)) = x1    334.71/102.54
POL(c31(x1)) = x1    334.71/102.54
POL(c32(x1)) = x1    334.71/102.54
POL(mark(x1)) = [1] + x1    334.71/102.54
POL(ok(x1)) = [1] + x1   
334.71/102.54
334.71/102.54

(106) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.71/102.54
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.71/102.54
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.71/102.54
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.71/102.54
active(plus(z0, 0)) → mark(z0) 334.71/102.54
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.71/102.54
active(x(z0, 0)) → mark(0) 334.71/102.54
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.71/102.54
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.71/102.54
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.71/102.54
active(s(z0)) → s(active(z0)) 334.71/102.54
active(plus(z0, z1)) → plus(active(z0), z1) 334.71/102.54
active(plus(z0, z1)) → plus(z0, active(z1)) 334.71/102.54
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.71/102.54
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.71/102.54
active(x(z0, z1)) → x(active(z0), z1) 334.71/102.54
active(x(z0, z1)) → x(z0, active(z1)) 334.71/102.54
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.71/102.54
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.71/102.54
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.71/102.54
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.71/102.54
s(mark(z0)) → mark(s(z0)) 334.71/102.54
s(ok(z0)) → ok(s(z0)) 334.71/102.54
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.71/102.54
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.71/102.54
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.71/102.54
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.71/102.54
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.71/102.54
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.71/102.54
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.71/102.54
x(mark(z0), z1) → mark(x(z0, z1)) 334.71/102.54
x(z0, mark(z1)) → mark(x(z0, z1)) 334.71/102.54
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.71/102.54
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.71/102.54
proper(tt) → ok(tt) 334.71/102.54
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.71/102.54
proper(s(z0)) → s(proper(z0)) 334.71/102.54
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.71/102.54
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.71/102.54
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.71/102.54
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.71/102.54
proper(0) → ok(0) 334.71/102.54
top(mark(z0)) → top(proper(z0)) 334.71/102.54
top(ok(z0)) → top(active(z0))
Tuples:

U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.54
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.54
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.54
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.54
S(mark(z0)) → c21(S(z0)) 334.71/102.54
S(ok(z0)) → c22(S(z0)) 334.71/102.54
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.54
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.54
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.54
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.54
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.54
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.54
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.54
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.54
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.54
X(ok(z0), ok(z1)) → c32(X(z0, z1))
S tuples:

S(mark(z0)) → c21(S(z0)) 334.71/102.54
S(ok(z0)) → c22(S(z0)) 334.71/102.54
PLUS(mark(z0), z1) → c23(PLUS(z0, z1))
K tuples:

U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.54
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.54
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.54
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.54
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.54
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.54
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.54
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.54
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.54
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.54
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.54
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.54
X(ok(z0), ok(z1)) → c32(X(z0, z1))
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

U11', U12', S, PLUS, U21', U22', X

Compound Symbols:

c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32

334.71/102.54
334.71/102.54

(107) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

S(mark(z0)) → c21(S(z0))
We considered the (Usable) Rules:none
And the Tuples:

U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.54
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.54
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.54
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.54
S(mark(z0)) → c21(S(z0)) 334.71/102.54
S(ok(z0)) → c22(S(z0)) 334.71/102.54
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.54
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.54
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.54
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.54
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.54
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.54
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.54
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.54
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.54
X(ok(z0), ok(z1)) → c32(X(z0, z1))
The order we found is given by the following interpretation:
Polynomial interpretation : 334.71/102.54

POL(PLUS(x1, x2)) = [5]x2    334.71/102.54
POL(S(x1)) = [4]x1    334.71/102.54
POL(U11'(x1, x2, x3)) = [5]x1 + [5]x2 + [5]x3    334.71/102.54
POL(U12'(x1, x2, x3)) = [3]x1 + [5]x2 + [5]x3    334.71/102.54
POL(U21'(x1, x2, x3)) = [5]x1 + [5]x2 + [3]x3    334.71/102.54
POL(U22'(x1, x2, x3)) = [3]x1 + [5]x2 + [5]x3    334.71/102.54
POL(X(x1, x2)) = [3]x1 + [3]x2    334.71/102.54
POL(c17(x1)) = x1    334.71/102.54
POL(c18(x1)) = x1    334.71/102.54
POL(c19(x1)) = x1    334.71/102.54
POL(c20(x1)) = x1    334.71/102.54
POL(c21(x1)) = x1    334.71/102.54
POL(c22(x1)) = x1    334.71/102.54
POL(c23(x1)) = x1    334.71/102.54
POL(c24(x1)) = x1    334.71/102.54
POL(c25(x1)) = x1    334.71/102.54
POL(c26(x1)) = x1    334.71/102.54
POL(c27(x1)) = x1    334.71/102.54
POL(c28(x1)) = x1    334.71/102.54
POL(c29(x1)) = x1    334.71/102.54
POL(c30(x1)) = x1    334.71/102.54
POL(c31(x1)) = x1    334.71/102.54
POL(c32(x1)) = x1    334.71/102.54
POL(mark(x1)) = [4] + x1    334.71/102.54
POL(ok(x1)) = x1   
334.71/102.54
334.71/102.54

(108) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.71/102.54
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.71/102.54
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.71/102.54
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.71/102.54
active(plus(z0, 0)) → mark(z0) 334.71/102.54
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.71/102.54
active(x(z0, 0)) → mark(0) 334.71/102.54
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.71/102.54
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.71/102.54
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.71/102.54
active(s(z0)) → s(active(z0)) 334.71/102.54
active(plus(z0, z1)) → plus(active(z0), z1) 334.71/102.54
active(plus(z0, z1)) → plus(z0, active(z1)) 334.71/102.54
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.71/102.54
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.71/102.54
active(x(z0, z1)) → x(active(z0), z1) 334.71/102.54
active(x(z0, z1)) → x(z0, active(z1)) 334.71/102.54
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.71/102.54
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.71/102.54
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.71/102.54
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.71/102.54
s(mark(z0)) → mark(s(z0)) 334.71/102.54
s(ok(z0)) → ok(s(z0)) 334.71/102.54
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.71/102.54
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.71/102.54
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.71/102.54
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.71/102.54
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.71/102.54
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.71/102.54
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.71/102.54
x(mark(z0), z1) → mark(x(z0, z1)) 334.71/102.54
x(z0, mark(z1)) → mark(x(z0, z1)) 334.71/102.54
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.71/102.54
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.71/102.54
proper(tt) → ok(tt) 334.71/102.54
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.71/102.54
proper(s(z0)) → s(proper(z0)) 334.71/102.54
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.71/102.54
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.71/102.54
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.71/102.54
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.71/102.54
proper(0) → ok(0) 334.71/102.54
top(mark(z0)) → top(proper(z0)) 334.71/102.54
top(ok(z0)) → top(active(z0))
Tuples:

U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.54
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.54
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.54
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.54
S(mark(z0)) → c21(S(z0)) 334.71/102.54
S(ok(z0)) → c22(S(z0)) 334.71/102.54
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.54
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.54
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.54
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.54
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.54
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.54
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.54
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.54
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.54
X(ok(z0), ok(z1)) → c32(X(z0, z1))
S tuples:

S(ok(z0)) → c22(S(z0)) 334.71/102.54
PLUS(mark(z0), z1) → c23(PLUS(z0, z1))
K tuples:

U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.54
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.54
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.54
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.54
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.54
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.54
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.54
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.54
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.54
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.54
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.54
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.54
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.71/102.54
S(mark(z0)) → c21(S(z0))
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

U11', U12', S, PLUS, U21', U22', X

Compound Symbols:

c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32

334.71/102.54
334.71/102.54

(109) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

PLUS(mark(z0), z1) → c23(PLUS(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:

U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.54
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.54
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.54
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.54
S(mark(z0)) → c21(S(z0)) 334.71/102.54
S(ok(z0)) → c22(S(z0)) 334.71/102.54
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.54
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.54
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.54
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.54
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.54
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.54
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.54
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.54
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.54
X(ok(z0), ok(z1)) → c32(X(z0, z1))
The order we found is given by the following interpretation:
Polynomial interpretation : 334.71/102.54

POL(PLUS(x1, x2)) = x1 + [5]x2    334.71/102.54
POL(S(x1)) = 0    334.71/102.54
POL(U11'(x1, x2, x3)) = [5]x1 + [5]x2 + [3]x3    334.71/102.54
POL(U12'(x1, x2, x3)) = [3]x1 + [5]x2 + [5]x3    334.71/102.54
POL(U21'(x1, x2, x3)) = [3]x1 + [3]x2 + [5]x3    334.71/102.54
POL(U22'(x1, x2, x3)) = [3]x1 + [5]x2 + [5]x3    334.71/102.54
POL(X(x1, x2)) = [5]x1 + [5]x2    334.71/102.54
POL(c17(x1)) = x1    334.71/102.54
POL(c18(x1)) = x1    334.71/102.54
POL(c19(x1)) = x1    334.71/102.54
POL(c20(x1)) = x1    334.71/102.54
POL(c21(x1)) = x1    334.71/102.54
POL(c22(x1)) = x1    334.71/102.54
POL(c23(x1)) = x1    334.71/102.54
POL(c24(x1)) = x1    334.71/102.54
POL(c25(x1)) = x1    334.71/102.54
POL(c26(x1)) = x1    334.71/102.54
POL(c27(x1)) = x1    334.71/102.54
POL(c28(x1)) = x1    334.71/102.54
POL(c29(x1)) = x1    334.71/102.54
POL(c30(x1)) = x1    334.71/102.54
POL(c31(x1)) = x1    334.71/102.54
POL(c32(x1)) = x1    334.71/102.54
POL(mark(x1)) = [1] + x1    334.71/102.54
POL(ok(x1)) = [1] + x1   
334.71/102.54
334.71/102.54

(110) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.71/102.54
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.71/102.54
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.71/102.54
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.71/102.54
active(plus(z0, 0)) → mark(z0) 334.71/102.54
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.71/102.54
active(x(z0, 0)) → mark(0) 334.71/102.54
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.71/102.54
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.71/102.54
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.71/102.54
active(s(z0)) → s(active(z0)) 334.71/102.54
active(plus(z0, z1)) → plus(active(z0), z1) 334.71/102.54
active(plus(z0, z1)) → plus(z0, active(z1)) 334.71/102.54
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.71/102.54
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.71/102.54
active(x(z0, z1)) → x(active(z0), z1) 334.71/102.54
active(x(z0, z1)) → x(z0, active(z1)) 334.71/102.54
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.71/102.54
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.71/102.54
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.71/102.54
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.71/102.54
s(mark(z0)) → mark(s(z0)) 334.71/102.54
s(ok(z0)) → ok(s(z0)) 334.71/102.54
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.71/102.54
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.71/102.54
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.71/102.54
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.71/102.54
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.71/102.54
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.71/102.54
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.71/102.54
x(mark(z0), z1) → mark(x(z0, z1)) 334.71/102.54
x(z0, mark(z1)) → mark(x(z0, z1)) 334.71/102.54
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.71/102.54
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.71/102.54
proper(tt) → ok(tt) 334.71/102.54
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.71/102.54
proper(s(z0)) → s(proper(z0)) 334.71/102.54
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.71/102.54
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.71/102.54
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.71/102.54
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.71/102.54
proper(0) → ok(0) 334.71/102.54
top(mark(z0)) → top(proper(z0)) 334.71/102.54
top(ok(z0)) → top(active(z0))
Tuples:

U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.54
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.54
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.54
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.54
S(mark(z0)) → c21(S(z0)) 334.71/102.54
S(ok(z0)) → c22(S(z0)) 334.71/102.54
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.54
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.54
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.54
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.54
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.54
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.54
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.54
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.54
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.54
X(ok(z0), ok(z1)) → c32(X(z0, z1))
S tuples:

S(ok(z0)) → c22(S(z0))
K tuples:

U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.54
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.54
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.54
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.54
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.54
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.54
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.54
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.54
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.54
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.54
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.54
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.54
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.71/102.54
S(mark(z0)) → c21(S(z0)) 334.71/102.54
PLUS(mark(z0), z1) → c23(PLUS(z0, z1))
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

U11', U12', S, PLUS, U21', U22', X

Compound Symbols:

c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32

334.71/102.54
334.71/102.54

(111) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

S(ok(z0)) → c22(S(z0))
We considered the (Usable) Rules:none
And the Tuples:

U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.54
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.54
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.54
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.54
S(mark(z0)) → c21(S(z0)) 334.71/102.54
S(ok(z0)) → c22(S(z0)) 334.71/102.54
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.54
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.54
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.54
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.54
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.54
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.54
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.54
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.54
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.54
X(ok(z0), ok(z1)) → c32(X(z0, z1))
The order we found is given by the following interpretation:
Polynomial interpretation : 334.71/102.54

POL(PLUS(x1, x2)) = [3]x1 + [3]x2    334.71/102.54
POL(S(x1)) = [5]x1    334.71/102.54
POL(U11'(x1, x2, x3)) = [3]x1 + [5]x2 + [5]x3    334.71/102.54
POL(U12'(x1, x2, x3)) = [3]x1 + [5]x2 + [5]x3    334.71/102.54
POL(U21'(x1, x2, x3)) = [5]x1 + [5]x2 + [5]x3    334.71/102.54
POL(U22'(x1, x2, x3)) = [3]x1 + [5]x2 + [3]x3    334.71/102.54
POL(X(x1, x2)) = [3]x1 + [5]x2    334.71/102.54
POL(c17(x1)) = x1    334.71/102.54
POL(c18(x1)) = x1    334.71/102.54
POL(c19(x1)) = x1    334.71/102.54
POL(c20(x1)) = x1    334.71/102.54
POL(c21(x1)) = x1    334.71/102.54
POL(c22(x1)) = x1    334.71/102.54
POL(c23(x1)) = x1    334.71/102.54
POL(c24(x1)) = x1    334.71/102.54
POL(c25(x1)) = x1    334.71/102.54
POL(c26(x1)) = x1    334.71/102.54
POL(c27(x1)) = x1    334.71/102.54
POL(c28(x1)) = x1    334.71/102.54
POL(c29(x1)) = x1    334.71/102.54
POL(c30(x1)) = x1    334.71/102.54
POL(c31(x1)) = x1    334.71/102.54
POL(c32(x1)) = x1    334.71/102.54
POL(mark(x1)) = x1    334.71/102.54
POL(ok(x1)) = [1] + x1   
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(112) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1)) 334.71/102.54
active(U12(tt, z0, z1)) → mark(s(plus(z1, z0))) 334.71/102.54
active(U21(tt, z0, z1)) → mark(U22(tt, z0, z1)) 334.71/102.54
active(U22(tt, z0, z1)) → mark(plus(x(z1, z0), z1)) 334.71/102.54
active(plus(z0, 0)) → mark(z0) 334.71/102.54
active(plus(z0, s(z1))) → mark(U11(tt, z1, z0)) 334.71/102.54
active(x(z0, 0)) → mark(0) 334.71/102.54
active(x(z0, s(z1))) → mark(U21(tt, z1, z0)) 334.71/102.54
active(U11(z0, z1, z2)) → U11(active(z0), z1, z2) 334.71/102.54
active(U12(z0, z1, z2)) → U12(active(z0), z1, z2) 334.71/102.54
active(s(z0)) → s(active(z0)) 334.71/102.54
active(plus(z0, z1)) → plus(active(z0), z1) 334.71/102.54
active(plus(z0, z1)) → plus(z0, active(z1)) 334.71/102.54
active(U21(z0, z1, z2)) → U21(active(z0), z1, z2) 334.71/102.54
active(U22(z0, z1, z2)) → U22(active(z0), z1, z2) 334.71/102.54
active(x(z0, z1)) → x(active(z0), z1) 334.71/102.54
active(x(z0, z1)) → x(z0, active(z1)) 334.71/102.54
U11(mark(z0), z1, z2) → mark(U11(z0, z1, z2)) 334.71/102.54
U11(ok(z0), ok(z1), ok(z2)) → ok(U11(z0, z1, z2)) 334.71/102.54
U12(mark(z0), z1, z2) → mark(U12(z0, z1, z2)) 334.71/102.54
U12(ok(z0), ok(z1), ok(z2)) → ok(U12(z0, z1, z2)) 334.71/102.54
s(mark(z0)) → mark(s(z0)) 334.71/102.54
s(ok(z0)) → ok(s(z0)) 334.71/102.54
plus(mark(z0), z1) → mark(plus(z0, z1)) 334.71/102.54
plus(z0, mark(z1)) → mark(plus(z0, z1)) 334.71/102.54
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 334.71/102.54
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2)) 334.71/102.54
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2)) 334.71/102.54
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2)) 334.71/102.54
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2)) 334.71/102.54
x(mark(z0), z1) → mark(x(z0, z1)) 334.71/102.54
x(z0, mark(z1)) → mark(x(z0, z1)) 334.71/102.54
x(ok(z0), ok(z1)) → ok(x(z0, z1)) 334.71/102.54
proper(U11(z0, z1, z2)) → U11(proper(z0), proper(z1), proper(z2)) 334.71/102.54
proper(tt) → ok(tt) 334.71/102.54
proper(U12(z0, z1, z2)) → U12(proper(z0), proper(z1), proper(z2)) 334.71/102.54
proper(s(z0)) → s(proper(z0)) 334.71/102.54
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 334.71/102.54
proper(U21(z0, z1, z2)) → U21(proper(z0), proper(z1), proper(z2)) 334.71/102.54
proper(U22(z0, z1, z2)) → U22(proper(z0), proper(z1), proper(z2)) 334.71/102.54
proper(x(z0, z1)) → x(proper(z0), proper(z1)) 334.71/102.54
proper(0) → ok(0) 334.71/102.54
top(mark(z0)) → top(proper(z0)) 334.71/102.54
top(ok(z0)) → top(active(z0))
Tuples:

U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.54
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.54
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.54
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.54
S(mark(z0)) → c21(S(z0)) 334.71/102.54
S(ok(z0)) → c22(S(z0)) 334.71/102.54
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.54
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.54
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.54
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.54
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.54
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.54
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.54
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.54
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.54
X(ok(z0), ok(z1)) → c32(X(z0, z1))
S tuples:none
K tuples:

U11'(mark(z0), z1, z2) → c17(U11'(z0, z1, z2)) 334.71/102.54
U11'(ok(z0), ok(z1), ok(z2)) → c18(U11'(z0, z1, z2)) 334.71/102.54
U12'(mark(z0), z1, z2) → c19(U12'(z0, z1, z2)) 334.71/102.54
U12'(ok(z0), ok(z1), ok(z2)) → c20(U12'(z0, z1, z2)) 334.71/102.54
U22'(ok(z0), ok(z1), ok(z2)) → c29(U22'(z0, z1, z2)) 334.71/102.54
PLUS(ok(z0), ok(z1)) → c25(PLUS(z0, z1)) 334.71/102.54
U22'(mark(z0), z1, z2) → c28(U22'(z0, z1, z2)) 334.71/102.54
PLUS(z0, mark(z1)) → c24(PLUS(z0, z1)) 334.71/102.54
U21'(mark(z0), z1, z2) → c26(U21'(z0, z1, z2)) 334.71/102.54
U21'(ok(z0), ok(z1), ok(z2)) → c27(U21'(z0, z1, z2)) 334.71/102.54
X(mark(z0), z1) → c30(X(z0, z1)) 334.71/102.54
X(z0, mark(z1)) → c31(X(z0, z1)) 334.71/102.54
X(ok(z0), ok(z1)) → c32(X(z0, z1)) 334.71/102.54
S(mark(z0)) → c21(S(z0)) 334.71/102.54
PLUS(mark(z0), z1) → c23(PLUS(z0, z1)) 334.71/102.54
S(ok(z0)) → c22(S(z0))
Defined Rule Symbols:

active, U11, U12, s, plus, U21, U22, x, proper, top

Defined Pair Symbols:

U11', U12', S, PLUS, U21', U22', X

Compound Symbols:

c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32

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334.71/102.54

(113) SIsEmptyProof (BOTH BOUNDS(ID, ID) transformation)

The set S is empty
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(114) BOUNDS(O(1), O(1))

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334.80/102.61 EOF