YES(O(1), O(n^2)) 148.09/48.50 YES(O(1), O(n^2)) 148.09/48.53 148.09/48.53 148.09/48.53
148.09/48.53 148.09/48.530 CpxTRS148.09/48.53
↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))148.09/48.53
↳2 CdtProblem148.09/48.53
↳3 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))148.09/48.53
↳4 CdtProblem148.09/48.53
↳5 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))148.09/48.53
↳6 CdtProblem148.09/48.53
↳7 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))148.09/48.53
↳8 CdtProblem148.09/48.53
↳9 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^2))))148.09/48.53
↳10 CdtProblem148.09/48.53
↳11 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^2))))148.09/48.53
↳12 CdtProblem148.09/48.53
↳13 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^2))))148.09/48.53
↳14 CdtProblem148.09/48.53
↳15 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^2))))148.09/48.53
↳16 CdtProblem148.09/48.53
↳17 CdtNarrowingProof (BOTH BOUNDS(ID, ID))148.09/48.53
↳18 CdtProblem148.09/48.53
↳19 CdtNarrowingProof (BOTH BOUNDS(ID, ID))148.09/48.53
↳20 CdtProblem148.09/48.53
↳21 CdtNarrowingProof (BOTH BOUNDS(ID, ID))148.09/48.53
↳22 CdtProblem148.09/48.53
↳23 CdtNarrowingProof (BOTH BOUNDS(ID, ID))148.09/48.53
↳24 CdtProblem148.09/48.53
↳25 CdtNarrowingProof (BOTH BOUNDS(ID, ID))148.09/48.53
↳26 CdtProblem148.09/48.53
↳27 CdtNarrowingProof (BOTH BOUNDS(ID, ID))148.09/48.53
↳28 CdtProblem148.09/48.53
↳29 CdtUnreachableProof (⇔)148.09/48.53
↳30 CdtProblem148.09/48.53
↳31 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))148.09/48.53
↳32 CdtProblem148.09/48.53
↳33 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))148.09/48.53
↳34 CdtProblem148.09/48.53
↳35 SIsEmptyProof (BOTH BOUNDS(ID, ID))148.09/48.53
↳36 BOUNDS(O(1), O(1))148.09/48.53
active(f(g(X), Y)) → mark(f(X, f(g(X), Y))) 148.09/48.53
active(f(X1, X2)) → f(active(X1), X2) 148.09/48.53
active(g(X)) → g(active(X)) 148.09/48.53
f(mark(X1), X2) → mark(f(X1, X2)) 148.09/48.53
g(mark(X)) → mark(g(X)) 148.09/48.53
proper(f(X1, X2)) → f(proper(X1), proper(X2)) 148.09/48.53
proper(g(X)) → g(proper(X)) 148.09/48.53
f(ok(X1), ok(X2)) → ok(f(X1, X2)) 148.09/48.53
g(ok(X)) → ok(g(X)) 148.09/48.53
top(mark(X)) → top(proper(X)) 148.09/48.53
top(ok(X)) → top(active(X))
Tuples:
active(f(g(z0), z1)) → mark(f(z0, f(g(z0), z1))) 148.09/48.57
active(f(z0, z1)) → f(active(z0), z1) 148.09/48.57
active(g(z0)) → g(active(z0)) 148.09/48.57
f(mark(z0), z1) → mark(f(z0, z1)) 148.09/48.57
f(ok(z0), ok(z1)) → ok(f(z0, z1)) 148.09/48.57
g(mark(z0)) → mark(g(z0)) 148.09/48.57
g(ok(z0)) → ok(g(z0)) 148.09/48.57
proper(f(z0, z1)) → f(proper(z0), proper(z1)) 148.09/48.57
proper(g(z0)) → g(proper(z0)) 148.09/48.57
top(mark(z0)) → top(proper(z0)) 148.09/48.57
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(f(g(z0), z1)) → c(F(z0, f(g(z0), z1)), F(g(z0), z1), G(z0)) 148.09/48.57
ACTIVE(f(z0, z1)) → c1(F(active(z0), z1), ACTIVE(z0)) 148.09/48.57
ACTIVE(g(z0)) → c2(G(active(z0)), ACTIVE(z0)) 148.09/48.57
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.57
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.57
G(mark(z0)) → c5(G(z0)) 148.09/48.57
G(ok(z0)) → c6(G(z0)) 148.09/48.57
PROPER(f(z0, z1)) → c7(F(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 148.09/48.57
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0)) 148.09/48.57
TOP(mark(z0)) → c9(TOP(proper(z0)), PROPER(z0)) 148.09/48.57
TOP(ok(z0)) → c10(TOP(active(z0)), ACTIVE(z0))
K tuples:none
ACTIVE(f(g(z0), z1)) → c(F(z0, f(g(z0), z1)), F(g(z0), z1), G(z0)) 148.09/48.57
ACTIVE(f(z0, z1)) → c1(F(active(z0), z1), ACTIVE(z0)) 148.09/48.57
ACTIVE(g(z0)) → c2(G(active(z0)), ACTIVE(z0)) 148.09/48.57
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.57
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.57
G(mark(z0)) → c5(G(z0)) 148.09/48.57
G(ok(z0)) → c6(G(z0)) 148.09/48.57
PROPER(f(z0, z1)) → c7(F(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 148.09/48.57
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0)) 148.09/48.57
TOP(mark(z0)) → c9(TOP(proper(z0)), PROPER(z0)) 148.09/48.57
TOP(ok(z0)) → c10(TOP(active(z0)), ACTIVE(z0))
active, f, g, proper, top
ACTIVE, F, G, PROPER, TOP
c, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10
Tuples:
active(f(g(z0), z1)) → mark(f(z0, f(g(z0), z1))) 148.09/48.57
active(f(z0, z1)) → f(active(z0), z1) 148.09/48.57
active(g(z0)) → g(active(z0)) 148.09/48.57
f(mark(z0), z1) → mark(f(z0, z1)) 148.09/48.57
f(ok(z0), ok(z1)) → ok(f(z0, z1)) 148.09/48.57
g(mark(z0)) → mark(g(z0)) 148.09/48.57
g(ok(z0)) → ok(g(z0)) 148.09/48.57
proper(f(z0, z1)) → f(proper(z0), proper(z1)) 148.09/48.57
proper(g(z0)) → g(proper(z0)) 148.09/48.57
top(mark(z0)) → top(proper(z0)) 148.09/48.57
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(f(z0, z1)) → c1(F(active(z0), z1), ACTIVE(z0)) 148.09/48.57
ACTIVE(g(z0)) → c2(G(active(z0)), ACTIVE(z0)) 148.09/48.57
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.57
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.57
G(mark(z0)) → c5(G(z0)) 148.09/48.57
G(ok(z0)) → c6(G(z0)) 148.09/48.57
PROPER(f(z0, z1)) → c7(F(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 148.09/48.57
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0)) 148.09/48.57
TOP(mark(z0)) → c9(TOP(proper(z0)), PROPER(z0)) 148.09/48.57
TOP(ok(z0)) → c10(TOP(active(z0)), ACTIVE(z0)) 148.09/48.57
ACTIVE(f(g(z0), z1)) → c(G(z0))
K tuples:none
ACTIVE(f(z0, z1)) → c1(F(active(z0), z1), ACTIVE(z0)) 148.09/48.57
ACTIVE(g(z0)) → c2(G(active(z0)), ACTIVE(z0)) 148.09/48.57
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.57
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.57
G(mark(z0)) → c5(G(z0)) 148.09/48.57
G(ok(z0)) → c6(G(z0)) 148.09/48.57
PROPER(f(z0, z1)) → c7(F(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 148.09/48.57
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0)) 148.09/48.57
TOP(mark(z0)) → c9(TOP(proper(z0)), PROPER(z0)) 148.09/48.57
TOP(ok(z0)) → c10(TOP(active(z0)), ACTIVE(z0)) 148.09/48.57
ACTIVE(f(g(z0), z1)) → c(G(z0))
active, f, g, proper, top
ACTIVE, F, G, PROPER, TOP
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c
We considered the (Usable) Rules:
ACTIVE(f(g(z0), z1)) → c(G(z0))
And the Tuples:
active(f(g(z0), z1)) → mark(f(z0, f(g(z0), z1))) 148.09/48.57
active(f(z0, z1)) → f(active(z0), z1) 148.09/48.57
active(g(z0)) → g(active(z0)) 148.09/48.57
g(mark(z0)) → mark(g(z0)) 148.09/48.57
g(ok(z0)) → ok(g(z0)) 148.09/48.57
f(mark(z0), z1) → mark(f(z0, z1)) 148.09/48.57
f(ok(z0), ok(z1)) → ok(f(z0, z1)) 148.09/48.57
proper(f(z0, z1)) → f(proper(z0), proper(z1)) 148.09/48.57
proper(g(z0)) → g(proper(z0))
The order we found is given by the following interpretation:
ACTIVE(f(z0, z1)) → c1(F(active(z0), z1), ACTIVE(z0)) 148.09/48.57
ACTIVE(g(z0)) → c2(G(active(z0)), ACTIVE(z0)) 148.09/48.57
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.57
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.57
G(mark(z0)) → c5(G(z0)) 148.09/48.57
G(ok(z0)) → c6(G(z0)) 148.09/48.57
PROPER(f(z0, z1)) → c7(F(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 148.09/48.57
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0)) 148.09/48.57
TOP(mark(z0)) → c9(TOP(proper(z0)), PROPER(z0)) 148.09/48.57
TOP(ok(z0)) → c10(TOP(active(z0)), ACTIVE(z0)) 148.09/48.57
ACTIVE(f(g(z0), z1)) → c(G(z0))
POL(ACTIVE(x1)) = [2] 148.09/48.57
POL(F(x1, x2)) = 0 148.09/48.57
POL(G(x1)) = 0 148.09/48.57
POL(PROPER(x1)) = 0 148.09/48.57
POL(TOP(x1)) = x1 148.09/48.57
POL(active(x1)) = 0 148.09/48.57
POL(c(x1)) = x1 148.09/48.57
POL(c1(x1, x2)) = x1 + x2 148.09/48.57
POL(c10(x1, x2)) = x1 + x2 148.09/48.57
POL(c2(x1, x2)) = x1 + x2 148.09/48.57
POL(c3(x1)) = x1 148.09/48.57
POL(c4(x1)) = x1 148.09/48.57
POL(c5(x1)) = x1 148.09/48.57
POL(c6(x1)) = x1 148.09/48.57
POL(c7(x1, x2, x3)) = x1 + x2 + x3 148.09/48.57
POL(c8(x1, x2)) = x1 + x2 148.09/48.57
POL(c9(x1, x2)) = x1 + x2 148.09/48.57
POL(f(x1, x2)) = x1 148.09/48.57
POL(g(x1)) = x1 148.09/48.57
POL(mark(x1)) = 0 148.09/48.57
POL(ok(x1)) = [2] 148.09/48.57
POL(proper(x1)) = 0
Tuples:
active(f(g(z0), z1)) → mark(f(z0, f(g(z0), z1))) 148.09/48.57
active(f(z0, z1)) → f(active(z0), z1) 148.09/48.57
active(g(z0)) → g(active(z0)) 148.09/48.57
f(mark(z0), z1) → mark(f(z0, z1)) 148.09/48.58
f(ok(z0), ok(z1)) → ok(f(z0, z1)) 148.09/48.58
g(mark(z0)) → mark(g(z0)) 148.09/48.58
g(ok(z0)) → ok(g(z0)) 148.09/48.58
proper(f(z0, z1)) → f(proper(z0), proper(z1)) 148.09/48.58
proper(g(z0)) → g(proper(z0)) 148.09/48.58
top(mark(z0)) → top(proper(z0)) 148.09/48.58
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(f(z0, z1)) → c1(F(active(z0), z1), ACTIVE(z0)) 148.09/48.58
ACTIVE(g(z0)) → c2(G(active(z0)), ACTIVE(z0)) 148.09/48.58
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.58
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.58
G(mark(z0)) → c5(G(z0)) 148.09/48.58
G(ok(z0)) → c6(G(z0)) 148.09/48.58
PROPER(f(z0, z1)) → c7(F(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 148.09/48.58
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(mark(z0)) → c9(TOP(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(ok(z0)) → c10(TOP(active(z0)), ACTIVE(z0)) 148.09/48.58
ACTIVE(f(g(z0), z1)) → c(G(z0))
K tuples:
ACTIVE(f(z0, z1)) → c1(F(active(z0), z1), ACTIVE(z0)) 148.09/48.58
ACTIVE(g(z0)) → c2(G(active(z0)), ACTIVE(z0)) 148.09/48.58
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.58
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.58
G(mark(z0)) → c5(G(z0)) 148.09/48.58
G(ok(z0)) → c6(G(z0)) 148.09/48.58
PROPER(f(z0, z1)) → c7(F(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 148.09/48.58
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(mark(z0)) → c9(TOP(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(ok(z0)) → c10(TOP(active(z0)), ACTIVE(z0))
Defined Rule Symbols:
ACTIVE(f(g(z0), z1)) → c(G(z0))
active, f, g, proper, top
ACTIVE, F, G, PROPER, TOP
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c
We considered the (Usable) Rules:
TOP(mark(z0)) → c9(TOP(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(ok(z0)) → c10(TOP(active(z0)), ACTIVE(z0))
And the Tuples:
active(f(g(z0), z1)) → mark(f(z0, f(g(z0), z1))) 148.09/48.58
active(f(z0, z1)) → f(active(z0), z1) 148.09/48.58
active(g(z0)) → g(active(z0)) 148.09/48.58
g(mark(z0)) → mark(g(z0)) 148.09/48.58
g(ok(z0)) → ok(g(z0)) 148.09/48.58
f(mark(z0), z1) → mark(f(z0, z1)) 148.09/48.58
f(ok(z0), ok(z1)) → ok(f(z0, z1)) 148.09/48.58
proper(f(z0, z1)) → f(proper(z0), proper(z1)) 148.09/48.58
proper(g(z0)) → g(proper(z0))
The order we found is given by the following interpretation:
ACTIVE(f(z0, z1)) → c1(F(active(z0), z1), ACTIVE(z0)) 148.09/48.58
ACTIVE(g(z0)) → c2(G(active(z0)), ACTIVE(z0)) 148.09/48.58
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.58
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.58
G(mark(z0)) → c5(G(z0)) 148.09/48.58
G(ok(z0)) → c6(G(z0)) 148.09/48.58
PROPER(f(z0, z1)) → c7(F(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 148.09/48.58
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(mark(z0)) → c9(TOP(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(ok(z0)) → c10(TOP(active(z0)), ACTIVE(z0)) 148.09/48.58
ACTIVE(f(g(z0), z1)) → c(G(z0))
POL(ACTIVE(x1)) = [1] 148.09/48.58
POL(F(x1, x2)) = 0 148.09/48.58
POL(G(x1)) = 0 148.09/48.58
POL(PROPER(x1)) = 0 148.09/48.58
POL(TOP(x1)) = x1 148.09/48.58
POL(active(x1)) = [1] 148.09/48.58
POL(c(x1)) = x1 148.09/48.58
POL(c1(x1, x2)) = x1 + x2 148.09/48.58
POL(c10(x1, x2)) = x1 + x2 148.09/48.58
POL(c2(x1, x2)) = x1 + x2 148.09/48.58
POL(c3(x1)) = x1 148.09/48.58
POL(c4(x1)) = x1 148.09/48.58
POL(c5(x1)) = x1 148.09/48.58
POL(c6(x1)) = x1 148.09/48.58
POL(c7(x1, x2, x3)) = x1 + x2 + x3 148.09/48.58
POL(c8(x1, x2)) = x1 + x2 148.09/48.58
POL(c9(x1, x2)) = x1 + x2 148.09/48.58
POL(f(x1, x2)) = x1 148.09/48.58
POL(g(x1)) = x1 148.09/48.58
POL(mark(x1)) = [1] 148.09/48.58
POL(ok(x1)) = [4] 148.09/48.58
POL(proper(x1)) = 0
Tuples:
active(f(g(z0), z1)) → mark(f(z0, f(g(z0), z1))) 148.09/48.58
active(f(z0, z1)) → f(active(z0), z1) 148.09/48.58
active(g(z0)) → g(active(z0)) 148.09/48.58
f(mark(z0), z1) → mark(f(z0, z1)) 148.09/48.58
f(ok(z0), ok(z1)) → ok(f(z0, z1)) 148.09/48.58
g(mark(z0)) → mark(g(z0)) 148.09/48.58
g(ok(z0)) → ok(g(z0)) 148.09/48.58
proper(f(z0, z1)) → f(proper(z0), proper(z1)) 148.09/48.58
proper(g(z0)) → g(proper(z0)) 148.09/48.58
top(mark(z0)) → top(proper(z0)) 148.09/48.58
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(f(z0, z1)) → c1(F(active(z0), z1), ACTIVE(z0)) 148.09/48.58
ACTIVE(g(z0)) → c2(G(active(z0)), ACTIVE(z0)) 148.09/48.58
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.58
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.58
G(mark(z0)) → c5(G(z0)) 148.09/48.58
G(ok(z0)) → c6(G(z0)) 148.09/48.58
PROPER(f(z0, z1)) → c7(F(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 148.09/48.58
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(mark(z0)) → c9(TOP(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(ok(z0)) → c10(TOP(active(z0)), ACTIVE(z0)) 148.09/48.58
ACTIVE(f(g(z0), z1)) → c(G(z0))
K tuples:
ACTIVE(f(z0, z1)) → c1(F(active(z0), z1), ACTIVE(z0)) 148.09/48.58
ACTIVE(g(z0)) → c2(G(active(z0)), ACTIVE(z0)) 148.09/48.58
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.58
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.58
G(mark(z0)) → c5(G(z0)) 148.09/48.58
G(ok(z0)) → c6(G(z0)) 148.09/48.58
PROPER(f(z0, z1)) → c7(F(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 148.09/48.58
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0))
Defined Rule Symbols:
ACTIVE(f(g(z0), z1)) → c(G(z0)) 148.09/48.58
TOP(mark(z0)) → c9(TOP(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(ok(z0)) → c10(TOP(active(z0)), ACTIVE(z0))
active, f, g, proper, top
ACTIVE, F, G, PROPER, TOP
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c
We considered the (Usable) Rules:
F(ok(z0), ok(z1)) → c4(F(z0, z1))
And the Tuples:
active(f(g(z0), z1)) → mark(f(z0, f(g(z0), z1))) 148.09/48.58
active(f(z0, z1)) → f(active(z0), z1) 148.09/48.58
active(g(z0)) → g(active(z0)) 148.09/48.58
g(mark(z0)) → mark(g(z0)) 148.09/48.58
g(ok(z0)) → ok(g(z0)) 148.09/48.58
f(mark(z0), z1) → mark(f(z0, z1)) 148.09/48.58
f(ok(z0), ok(z1)) → ok(f(z0, z1)) 148.09/48.58
proper(f(z0, z1)) → f(proper(z0), proper(z1)) 148.09/48.58
proper(g(z0)) → g(proper(z0))
The order we found is given by the following interpretation:
ACTIVE(f(z0, z1)) → c1(F(active(z0), z1), ACTIVE(z0)) 148.09/48.58
ACTIVE(g(z0)) → c2(G(active(z0)), ACTIVE(z0)) 148.09/48.58
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.58
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.58
G(mark(z0)) → c5(G(z0)) 148.09/48.58
G(ok(z0)) → c6(G(z0)) 148.09/48.58
PROPER(f(z0, z1)) → c7(F(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 148.09/48.58
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(mark(z0)) → c9(TOP(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(ok(z0)) → c10(TOP(active(z0)), ACTIVE(z0)) 148.09/48.58
ACTIVE(f(g(z0), z1)) → c(G(z0))
POL(ACTIVE(x1)) = x1 148.09/48.58
POL(F(x1, x2)) = x22 148.09/48.58
POL(G(x1)) = 0 148.09/48.58
POL(PROPER(x1)) = 0 148.09/48.58
POL(TOP(x1)) = x12 148.09/48.58
POL(active(x1)) = x1 148.09/48.58
POL(c(x1)) = x1 148.09/48.58
POL(c1(x1, x2)) = x1 + x2 148.09/48.58
POL(c10(x1, x2)) = x1 + x2 148.09/48.58
POL(c2(x1, x2)) = x1 + x2 148.09/48.58
POL(c3(x1)) = x1 148.09/48.58
POL(c4(x1)) = x1 148.09/48.58
POL(c5(x1)) = x1 148.09/48.58
POL(c6(x1)) = x1 148.09/48.58
POL(c7(x1, x2, x3)) = x1 + x2 + x3 148.09/48.58
POL(c8(x1, x2)) = x1 + x2 148.09/48.58
POL(c9(x1, x2)) = x1 + x2 148.09/48.58
POL(f(x1, x2)) = [2]x1 + x22 148.09/48.58
POL(g(x1)) = x1 148.09/48.58
POL(mark(x1)) = 0 148.09/48.58
POL(ok(x1)) = [1] + x1 148.09/48.58
POL(proper(x1)) = 0
Tuples:
active(f(g(z0), z1)) → mark(f(z0, f(g(z0), z1))) 148.09/48.58
active(f(z0, z1)) → f(active(z0), z1) 148.09/48.58
active(g(z0)) → g(active(z0)) 148.09/48.58
f(mark(z0), z1) → mark(f(z0, z1)) 148.09/48.58
f(ok(z0), ok(z1)) → ok(f(z0, z1)) 148.09/48.58
g(mark(z0)) → mark(g(z0)) 148.09/48.58
g(ok(z0)) → ok(g(z0)) 148.09/48.58
proper(f(z0, z1)) → f(proper(z0), proper(z1)) 148.09/48.58
proper(g(z0)) → g(proper(z0)) 148.09/48.58
top(mark(z0)) → top(proper(z0)) 148.09/48.58
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(f(z0, z1)) → c1(F(active(z0), z1), ACTIVE(z0)) 148.09/48.58
ACTIVE(g(z0)) → c2(G(active(z0)), ACTIVE(z0)) 148.09/48.58
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.58
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.58
G(mark(z0)) → c5(G(z0)) 148.09/48.58
G(ok(z0)) → c6(G(z0)) 148.09/48.58
PROPER(f(z0, z1)) → c7(F(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 148.09/48.58
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(mark(z0)) → c9(TOP(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(ok(z0)) → c10(TOP(active(z0)), ACTIVE(z0)) 148.09/48.58
ACTIVE(f(g(z0), z1)) → c(G(z0))
K tuples:
ACTIVE(f(z0, z1)) → c1(F(active(z0), z1), ACTIVE(z0)) 148.09/48.58
ACTIVE(g(z0)) → c2(G(active(z0)), ACTIVE(z0)) 148.09/48.58
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.58
G(mark(z0)) → c5(G(z0)) 148.09/48.58
G(ok(z0)) → c6(G(z0)) 148.09/48.58
PROPER(f(z0, z1)) → c7(F(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 148.09/48.58
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0))
Defined Rule Symbols:
ACTIVE(f(g(z0), z1)) → c(G(z0)) 148.09/48.58
TOP(mark(z0)) → c9(TOP(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(ok(z0)) → c10(TOP(active(z0)), ACTIVE(z0)) 148.09/48.58
F(ok(z0), ok(z1)) → c4(F(z0, z1))
active, f, g, proper, top
ACTIVE, F, G, PROPER, TOP
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c
We considered the (Usable) Rules:
G(ok(z0)) → c6(G(z0))
And the Tuples:
active(f(g(z0), z1)) → mark(f(z0, f(g(z0), z1))) 148.09/48.58
active(f(z0, z1)) → f(active(z0), z1) 148.09/48.58
active(g(z0)) → g(active(z0)) 148.09/48.58
g(mark(z0)) → mark(g(z0)) 148.09/48.58
g(ok(z0)) → ok(g(z0)) 148.09/48.58
f(mark(z0), z1) → mark(f(z0, z1)) 148.09/48.58
f(ok(z0), ok(z1)) → ok(f(z0, z1)) 148.09/48.58
proper(f(z0, z1)) → f(proper(z0), proper(z1)) 148.09/48.58
proper(g(z0)) → g(proper(z0))
The order we found is given by the following interpretation:
ACTIVE(f(z0, z1)) → c1(F(active(z0), z1), ACTIVE(z0)) 148.09/48.58
ACTIVE(g(z0)) → c2(G(active(z0)), ACTIVE(z0)) 148.09/48.58
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.58
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.58
G(mark(z0)) → c5(G(z0)) 148.09/48.58
G(ok(z0)) → c6(G(z0)) 148.09/48.58
PROPER(f(z0, z1)) → c7(F(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 148.09/48.58
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(mark(z0)) → c9(TOP(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(ok(z0)) → c10(TOP(active(z0)), ACTIVE(z0)) 148.09/48.58
ACTIVE(f(g(z0), z1)) → c(G(z0))
POL(ACTIVE(x1)) = x1 148.09/48.58
POL(F(x1, x2)) = 0 148.09/48.58
POL(G(x1)) = x12 148.09/48.58
POL(PROPER(x1)) = 0 148.09/48.58
POL(TOP(x1)) = x12 148.09/48.58
POL(active(x1)) = x1 148.09/48.58
POL(c(x1)) = x1 148.09/48.58
POL(c1(x1, x2)) = x1 + x2 148.09/48.58
POL(c10(x1, x2)) = x1 + x2 148.09/48.58
POL(c2(x1, x2)) = x1 + x2 148.09/48.58
POL(c3(x1)) = x1 148.09/48.58
POL(c4(x1)) = x1 148.09/48.58
POL(c5(x1)) = x1 148.09/48.58
POL(c6(x1)) = x1 148.09/48.58
POL(c7(x1, x2, x3)) = x1 + x2 + x3 148.09/48.58
POL(c8(x1, x2)) = x1 + x2 148.09/48.58
POL(c9(x1, x2)) = x1 + x2 148.09/48.58
POL(f(x1, x2)) = [2]x1 + [3]x12 148.09/48.58
POL(g(x1)) = [2]x1 + [2]x12 148.09/48.58
POL(mark(x1)) = x1 148.09/48.58
POL(ok(x1)) = [2] + x1 148.09/48.58
POL(proper(x1)) = 0
Tuples:
active(f(g(z0), z1)) → mark(f(z0, f(g(z0), z1))) 148.09/48.58
active(f(z0, z1)) → f(active(z0), z1) 148.09/48.58
active(g(z0)) → g(active(z0)) 148.09/48.58
f(mark(z0), z1) → mark(f(z0, z1)) 148.09/48.58
f(ok(z0), ok(z1)) → ok(f(z0, z1)) 148.09/48.58
g(mark(z0)) → mark(g(z0)) 148.09/48.58
g(ok(z0)) → ok(g(z0)) 148.09/48.58
proper(f(z0, z1)) → f(proper(z0), proper(z1)) 148.09/48.58
proper(g(z0)) → g(proper(z0)) 148.09/48.58
top(mark(z0)) → top(proper(z0)) 148.09/48.58
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(f(z0, z1)) → c1(F(active(z0), z1), ACTIVE(z0)) 148.09/48.58
ACTIVE(g(z0)) → c2(G(active(z0)), ACTIVE(z0)) 148.09/48.58
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.58
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.58
G(mark(z0)) → c5(G(z0)) 148.09/48.58
G(ok(z0)) → c6(G(z0)) 148.09/48.58
PROPER(f(z0, z1)) → c7(F(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 148.09/48.58
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(mark(z0)) → c9(TOP(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(ok(z0)) → c10(TOP(active(z0)), ACTIVE(z0)) 148.09/48.58
ACTIVE(f(g(z0), z1)) → c(G(z0))
K tuples:
ACTIVE(f(z0, z1)) → c1(F(active(z0), z1), ACTIVE(z0)) 148.09/48.58
ACTIVE(g(z0)) → c2(G(active(z0)), ACTIVE(z0)) 148.09/48.58
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.58
G(mark(z0)) → c5(G(z0)) 148.09/48.58
PROPER(f(z0, z1)) → c7(F(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 148.09/48.58
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0))
Defined Rule Symbols:
ACTIVE(f(g(z0), z1)) → c(G(z0)) 148.09/48.58
TOP(mark(z0)) → c9(TOP(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(ok(z0)) → c10(TOP(active(z0)), ACTIVE(z0)) 148.09/48.58
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.58
G(ok(z0)) → c6(G(z0))
active, f, g, proper, top
ACTIVE, F, G, PROPER, TOP
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c
We considered the (Usable) Rules:
ACTIVE(g(z0)) → c2(G(active(z0)), ACTIVE(z0))
And the Tuples:
active(f(g(z0), z1)) → mark(f(z0, f(g(z0), z1))) 148.09/48.58
active(f(z0, z1)) → f(active(z0), z1) 148.09/48.58
active(g(z0)) → g(active(z0)) 148.09/48.58
g(mark(z0)) → mark(g(z0)) 148.09/48.58
g(ok(z0)) → ok(g(z0)) 148.09/48.58
f(mark(z0), z1) → mark(f(z0, z1)) 148.09/48.58
f(ok(z0), ok(z1)) → ok(f(z0, z1)) 148.09/48.58
proper(f(z0, z1)) → f(proper(z0), proper(z1)) 148.09/48.58
proper(g(z0)) → g(proper(z0))
The order we found is given by the following interpretation:
ACTIVE(f(z0, z1)) → c1(F(active(z0), z1), ACTIVE(z0)) 148.09/48.58
ACTIVE(g(z0)) → c2(G(active(z0)), ACTIVE(z0)) 148.09/48.58
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.58
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.58
G(mark(z0)) → c5(G(z0)) 148.09/48.58
G(ok(z0)) → c6(G(z0)) 148.09/48.58
PROPER(f(z0, z1)) → c7(F(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 148.09/48.58
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(mark(z0)) → c9(TOP(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(ok(z0)) → c10(TOP(active(z0)), ACTIVE(z0)) 148.09/48.58
ACTIVE(f(g(z0), z1)) → c(G(z0))
POL(ACTIVE(x1)) = x1 148.09/48.58
POL(F(x1, x2)) = 0 148.09/48.58
POL(G(x1)) = 0 148.09/48.58
POL(PROPER(x1)) = 0 148.09/48.58
POL(TOP(x1)) = [3]x1 + x12 148.09/48.58
POL(active(x1)) = x1 148.09/48.58
POL(c(x1)) = x1 148.09/48.58
POL(c1(x1, x2)) = x1 + x2 148.09/48.58
POL(c10(x1, x2)) = x1 + x2 148.09/48.58
POL(c2(x1, x2)) = x1 + x2 148.09/48.58
POL(c3(x1)) = x1 148.09/48.58
POL(c4(x1)) = x1 148.09/48.58
POL(c5(x1)) = x1 148.09/48.58
POL(c6(x1)) = x1 148.09/48.58
POL(c7(x1, x2, x3)) = x1 + x2 + x3 148.09/48.58
POL(c8(x1, x2)) = x1 + x2 148.09/48.58
POL(c9(x1, x2)) = x1 + x2 148.09/48.58
POL(f(x1, x2)) = [2]x1 148.09/48.58
POL(g(x1)) = [1] + [2]x1 148.09/48.58
POL(mark(x1)) = x1 148.09/48.58
POL(ok(x1)) = [2] + x1 148.09/48.58
POL(proper(x1)) = x1
Tuples:
active(f(g(z0), z1)) → mark(f(z0, f(g(z0), z1))) 148.09/48.58
active(f(z0, z1)) → f(active(z0), z1) 148.09/48.58
active(g(z0)) → g(active(z0)) 148.09/48.58
f(mark(z0), z1) → mark(f(z0, z1)) 148.09/48.58
f(ok(z0), ok(z1)) → ok(f(z0, z1)) 148.09/48.58
g(mark(z0)) → mark(g(z0)) 148.09/48.58
g(ok(z0)) → ok(g(z0)) 148.09/48.58
proper(f(z0, z1)) → f(proper(z0), proper(z1)) 148.09/48.58
proper(g(z0)) → g(proper(z0)) 148.09/48.58
top(mark(z0)) → top(proper(z0)) 148.09/48.58
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(f(z0, z1)) → c1(F(active(z0), z1), ACTIVE(z0)) 148.09/48.58
ACTIVE(g(z0)) → c2(G(active(z0)), ACTIVE(z0)) 148.09/48.58
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.58
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.58
G(mark(z0)) → c5(G(z0)) 148.09/48.58
G(ok(z0)) → c6(G(z0)) 148.09/48.58
PROPER(f(z0, z1)) → c7(F(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 148.09/48.58
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(mark(z0)) → c9(TOP(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(ok(z0)) → c10(TOP(active(z0)), ACTIVE(z0)) 148.09/48.58
ACTIVE(f(g(z0), z1)) → c(G(z0))
K tuples:
ACTIVE(f(z0, z1)) → c1(F(active(z0), z1), ACTIVE(z0)) 148.09/48.58
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.58
G(mark(z0)) → c5(G(z0)) 148.09/48.58
PROPER(f(z0, z1)) → c7(F(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 148.09/48.58
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0))
Defined Rule Symbols:
ACTIVE(f(g(z0), z1)) → c(G(z0)) 148.09/48.58
TOP(mark(z0)) → c9(TOP(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(ok(z0)) → c10(TOP(active(z0)), ACTIVE(z0)) 148.09/48.58
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.58
G(ok(z0)) → c6(G(z0)) 148.09/48.58
ACTIVE(g(z0)) → c2(G(active(z0)), ACTIVE(z0))
active, f, g, proper, top
ACTIVE, F, G, PROPER, TOP
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c
We considered the (Usable) Rules:
ACTIVE(f(z0, z1)) → c1(F(active(z0), z1), ACTIVE(z0))
And the Tuples:
active(f(g(z0), z1)) → mark(f(z0, f(g(z0), z1))) 148.09/48.58
active(f(z0, z1)) → f(active(z0), z1) 148.09/48.58
active(g(z0)) → g(active(z0)) 148.09/48.58
g(mark(z0)) → mark(g(z0)) 148.09/48.58
g(ok(z0)) → ok(g(z0)) 148.09/48.58
f(mark(z0), z1) → mark(f(z0, z1)) 148.09/48.58
f(ok(z0), ok(z1)) → ok(f(z0, z1)) 148.09/48.58
proper(f(z0, z1)) → f(proper(z0), proper(z1)) 148.09/48.58
proper(g(z0)) → g(proper(z0))
The order we found is given by the following interpretation:
ACTIVE(f(z0, z1)) → c1(F(active(z0), z1), ACTIVE(z0)) 148.09/48.58
ACTIVE(g(z0)) → c2(G(active(z0)), ACTIVE(z0)) 148.09/48.58
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.58
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.58
G(mark(z0)) → c5(G(z0)) 148.09/48.58
G(ok(z0)) → c6(G(z0)) 148.09/48.58
PROPER(f(z0, z1)) → c7(F(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 148.09/48.58
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(mark(z0)) → c9(TOP(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(ok(z0)) → c10(TOP(active(z0)), ACTIVE(z0)) 148.09/48.58
ACTIVE(f(g(z0), z1)) → c(G(z0))
POL(ACTIVE(x1)) = x1 148.09/48.58
POL(F(x1, x2)) = 0 148.09/48.58
POL(G(x1)) = 0 148.09/48.58
POL(PROPER(x1)) = 0 148.09/48.58
POL(TOP(x1)) = x12 148.09/48.58
POL(active(x1)) = x1 148.09/48.58
POL(c(x1)) = x1 148.09/48.58
POL(c1(x1, x2)) = x1 + x2 148.09/48.58
POL(c10(x1, x2)) = x1 + x2 148.09/48.58
POL(c2(x1, x2)) = x1 + x2 148.09/48.58
POL(c3(x1)) = x1 148.09/48.58
POL(c4(x1)) = x1 148.09/48.58
POL(c5(x1)) = x1 148.09/48.58
POL(c6(x1)) = x1 148.09/48.58
POL(c7(x1, x2, x3)) = x1 + x2 + x3 148.09/48.58
POL(c8(x1, x2)) = x1 + x2 148.09/48.58
POL(c9(x1, x2)) = x1 + x2 148.09/48.58
POL(f(x1, x2)) = [2] + x1 148.09/48.58
POL(g(x1)) = [2]x1 148.09/48.58
POL(mark(x1)) = x1 148.09/48.58
POL(ok(x1)) = [1] + x1 148.09/48.58
POL(proper(x1)) = x1
Tuples:
active(f(g(z0), z1)) → mark(f(z0, f(g(z0), z1))) 148.09/48.58
active(f(z0, z1)) → f(active(z0), z1) 148.09/48.58
active(g(z0)) → g(active(z0)) 148.09/48.58
f(mark(z0), z1) → mark(f(z0, z1)) 148.09/48.58
f(ok(z0), ok(z1)) → ok(f(z0, z1)) 148.09/48.58
g(mark(z0)) → mark(g(z0)) 148.09/48.58
g(ok(z0)) → ok(g(z0)) 148.09/48.58
proper(f(z0, z1)) → f(proper(z0), proper(z1)) 148.09/48.58
proper(g(z0)) → g(proper(z0)) 148.09/48.58
top(mark(z0)) → top(proper(z0)) 148.09/48.58
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(f(z0, z1)) → c1(F(active(z0), z1), ACTIVE(z0)) 148.09/48.58
ACTIVE(g(z0)) → c2(G(active(z0)), ACTIVE(z0)) 148.09/48.58
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.58
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.58
G(mark(z0)) → c5(G(z0)) 148.09/48.58
G(ok(z0)) → c6(G(z0)) 148.09/48.58
PROPER(f(z0, z1)) → c7(F(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 148.09/48.58
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(mark(z0)) → c9(TOP(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(ok(z0)) → c10(TOP(active(z0)), ACTIVE(z0)) 148.09/48.58
ACTIVE(f(g(z0), z1)) → c(G(z0))
K tuples:
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.58
G(mark(z0)) → c5(G(z0)) 148.09/48.58
PROPER(f(z0, z1)) → c7(F(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 148.09/48.58
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0))
Defined Rule Symbols:
ACTIVE(f(g(z0), z1)) → c(G(z0)) 148.09/48.58
TOP(mark(z0)) → c9(TOP(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(ok(z0)) → c10(TOP(active(z0)), ACTIVE(z0)) 148.09/48.58
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.58
G(ok(z0)) → c6(G(z0)) 148.09/48.58
ACTIVE(g(z0)) → c2(G(active(z0)), ACTIVE(z0)) 148.09/48.58
ACTIVE(f(z0, z1)) → c1(F(active(z0), z1), ACTIVE(z0))
active, f, g, proper, top
ACTIVE, F, G, PROPER, TOP
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c
ACTIVE(f(f(g(z0), z1), x1)) → c1(F(mark(f(z0, f(g(z0), z1))), x1), ACTIVE(f(g(z0), z1))) 148.09/48.58
ACTIVE(f(f(z0, z1), x1)) → c1(F(f(active(z0), z1), x1), ACTIVE(f(z0, z1))) 148.09/48.58
ACTIVE(f(g(z0), x1)) → c1(F(g(active(z0)), x1), ACTIVE(g(z0)))
Tuples:
active(f(g(z0), z1)) → mark(f(z0, f(g(z0), z1))) 148.09/48.58
active(f(z0, z1)) → f(active(z0), z1) 148.09/48.58
active(g(z0)) → g(active(z0)) 148.09/48.58
f(mark(z0), z1) → mark(f(z0, z1)) 148.09/48.58
f(ok(z0), ok(z1)) → ok(f(z0, z1)) 148.09/48.58
g(mark(z0)) → mark(g(z0)) 148.09/48.58
g(ok(z0)) → ok(g(z0)) 148.09/48.58
proper(f(z0, z1)) → f(proper(z0), proper(z1)) 148.09/48.58
proper(g(z0)) → g(proper(z0)) 148.09/48.58
top(mark(z0)) → top(proper(z0)) 148.09/48.58
top(ok(z0)) → top(active(z0))
S tuples:
ACTIVE(g(z0)) → c2(G(active(z0)), ACTIVE(z0)) 148.09/48.58
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.58
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.58
G(mark(z0)) → c5(G(z0)) 148.09/48.58
G(ok(z0)) → c6(G(z0)) 148.09/48.58
PROPER(f(z0, z1)) → c7(F(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 148.09/48.58
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(mark(z0)) → c9(TOP(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(ok(z0)) → c10(TOP(active(z0)), ACTIVE(z0)) 148.09/48.58
ACTIVE(f(g(z0), z1)) → c(G(z0)) 148.09/48.58
ACTIVE(f(f(g(z0), z1), x1)) → c1(F(mark(f(z0, f(g(z0), z1))), x1), ACTIVE(f(g(z0), z1))) 148.09/48.58
ACTIVE(f(f(z0, z1), x1)) → c1(F(f(active(z0), z1), x1), ACTIVE(f(z0, z1))) 148.09/48.58
ACTIVE(f(g(z0), x1)) → c1(F(g(active(z0)), x1), ACTIVE(g(z0)))
K tuples:
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.58
G(mark(z0)) → c5(G(z0)) 148.09/48.58
PROPER(f(z0, z1)) → c7(F(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 148.09/48.58
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0))
Defined Rule Symbols:
ACTIVE(f(g(z0), z1)) → c(G(z0)) 148.09/48.58
TOP(mark(z0)) → c9(TOP(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(ok(z0)) → c10(TOP(active(z0)), ACTIVE(z0)) 148.09/48.58
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.58
G(ok(z0)) → c6(G(z0)) 148.09/48.58
ACTIVE(g(z0)) → c2(G(active(z0)), ACTIVE(z0)) 148.09/48.58
ACTIVE(f(z0, z1)) → c1(F(active(z0), z1), ACTIVE(z0))
active, f, g, proper, top
ACTIVE, F, G, PROPER, TOP
c2, c3, c4, c5, c6, c7, c8, c9, c10, c, c1
ACTIVE(g(f(g(z0), z1))) → c2(G(mark(f(z0, f(g(z0), z1)))), ACTIVE(f(g(z0), z1))) 148.09/48.58
ACTIVE(g(f(z0, z1))) → c2(G(f(active(z0), z1)), ACTIVE(f(z0, z1))) 148.09/48.58
ACTIVE(g(g(z0))) → c2(G(g(active(z0))), ACTIVE(g(z0)))
Tuples:
active(f(g(z0), z1)) → mark(f(z0, f(g(z0), z1))) 148.09/48.58
active(f(z0, z1)) → f(active(z0), z1) 148.09/48.58
active(g(z0)) → g(active(z0)) 148.09/48.58
f(mark(z0), z1) → mark(f(z0, z1)) 148.09/48.58
f(ok(z0), ok(z1)) → ok(f(z0, z1)) 148.09/48.58
g(mark(z0)) → mark(g(z0)) 148.09/48.58
g(ok(z0)) → ok(g(z0)) 148.09/48.58
proper(f(z0, z1)) → f(proper(z0), proper(z1)) 148.09/48.58
proper(g(z0)) → g(proper(z0)) 148.09/48.58
top(mark(z0)) → top(proper(z0)) 148.09/48.58
top(ok(z0)) → top(active(z0))
S tuples:
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.58
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.58
G(mark(z0)) → c5(G(z0)) 148.09/48.58
G(ok(z0)) → c6(G(z0)) 148.09/48.58
PROPER(f(z0, z1)) → c7(F(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 148.09/48.58
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(mark(z0)) → c9(TOP(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(ok(z0)) → c10(TOP(active(z0)), ACTIVE(z0)) 148.09/48.58
ACTIVE(f(g(z0), z1)) → c(G(z0)) 148.09/48.58
ACTIVE(f(f(g(z0), z1), x1)) → c1(F(mark(f(z0, f(g(z0), z1))), x1), ACTIVE(f(g(z0), z1))) 148.09/48.58
ACTIVE(f(f(z0, z1), x1)) → c1(F(f(active(z0), z1), x1), ACTIVE(f(z0, z1))) 148.09/48.58
ACTIVE(f(g(z0), x1)) → c1(F(g(active(z0)), x1), ACTIVE(g(z0))) 148.09/48.58
ACTIVE(g(f(g(z0), z1))) → c2(G(mark(f(z0, f(g(z0), z1)))), ACTIVE(f(g(z0), z1))) 148.09/48.58
ACTIVE(g(f(z0, z1))) → c2(G(f(active(z0), z1)), ACTIVE(f(z0, z1))) 148.09/48.58
ACTIVE(g(g(z0))) → c2(G(g(active(z0))), ACTIVE(g(z0)))
K tuples:
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.58
G(mark(z0)) → c5(G(z0)) 148.09/48.58
PROPER(f(z0, z1)) → c7(F(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 148.09/48.58
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0))
Defined Rule Symbols:
ACTIVE(f(g(z0), z1)) → c(G(z0)) 148.09/48.58
TOP(mark(z0)) → c9(TOP(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(ok(z0)) → c10(TOP(active(z0)), ACTIVE(z0)) 148.09/48.58
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.58
G(ok(z0)) → c6(G(z0)) 148.09/48.58
ACTIVE(g(z0)) → c2(G(active(z0)), ACTIVE(z0)) 148.09/48.58
ACTIVE(f(z0, z1)) → c1(F(active(z0), z1), ACTIVE(z0))
active, f, g, proper, top
F, G, PROPER, TOP, ACTIVE
c3, c4, c5, c6, c7, c8, c9, c10, c, c1, c2
PROPER(f(x0, f(z0, z1))) → c7(F(proper(x0), f(proper(z0), proper(z1))), PROPER(x0), PROPER(f(z0, z1))) 148.09/48.58
PROPER(f(x0, g(z0))) → c7(F(proper(x0), g(proper(z0))), PROPER(x0), PROPER(g(z0))) 148.09/48.58
PROPER(f(f(z0, z1), x1)) → c7(F(f(proper(z0), proper(z1)), proper(x1)), PROPER(f(z0, z1)), PROPER(x1)) 148.09/48.58
PROPER(f(g(z0), x1)) → c7(F(g(proper(z0)), proper(x1)), PROPER(g(z0)), PROPER(x1))
Tuples:
active(f(g(z0), z1)) → mark(f(z0, f(g(z0), z1))) 148.09/48.58
active(f(z0, z1)) → f(active(z0), z1) 148.09/48.58
active(g(z0)) → g(active(z0)) 148.09/48.58
f(mark(z0), z1) → mark(f(z0, z1)) 148.09/48.58
f(ok(z0), ok(z1)) → ok(f(z0, z1)) 148.09/48.58
g(mark(z0)) → mark(g(z0)) 148.09/48.58
g(ok(z0)) → ok(g(z0)) 148.09/48.58
proper(f(z0, z1)) → f(proper(z0), proper(z1)) 148.09/48.58
proper(g(z0)) → g(proper(z0)) 148.09/48.58
top(mark(z0)) → top(proper(z0)) 148.09/48.58
top(ok(z0)) → top(active(z0))
S tuples:
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.58
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.58
G(mark(z0)) → c5(G(z0)) 148.09/48.58
G(ok(z0)) → c6(G(z0)) 148.09/48.58
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(mark(z0)) → c9(TOP(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(ok(z0)) → c10(TOP(active(z0)), ACTIVE(z0)) 148.09/48.58
ACTIVE(f(g(z0), z1)) → c(G(z0)) 148.09/48.58
ACTIVE(f(f(g(z0), z1), x1)) → c1(F(mark(f(z0, f(g(z0), z1))), x1), ACTIVE(f(g(z0), z1))) 148.09/48.58
ACTIVE(f(f(z0, z1), x1)) → c1(F(f(active(z0), z1), x1), ACTIVE(f(z0, z1))) 148.09/48.58
ACTIVE(f(g(z0), x1)) → c1(F(g(active(z0)), x1), ACTIVE(g(z0))) 148.09/48.58
ACTIVE(g(f(g(z0), z1))) → c2(G(mark(f(z0, f(g(z0), z1)))), ACTIVE(f(g(z0), z1))) 148.09/48.58
ACTIVE(g(f(z0, z1))) → c2(G(f(active(z0), z1)), ACTIVE(f(z0, z1))) 148.09/48.58
ACTIVE(g(g(z0))) → c2(G(g(active(z0))), ACTIVE(g(z0))) 148.09/48.58
PROPER(f(x0, f(z0, z1))) → c7(F(proper(x0), f(proper(z0), proper(z1))), PROPER(x0), PROPER(f(z0, z1))) 148.09/48.58
PROPER(f(x0, g(z0))) → c7(F(proper(x0), g(proper(z0))), PROPER(x0), PROPER(g(z0))) 148.09/48.58
PROPER(f(f(z0, z1), x1)) → c7(F(f(proper(z0), proper(z1)), proper(x1)), PROPER(f(z0, z1)), PROPER(x1)) 148.09/48.58
PROPER(f(g(z0), x1)) → c7(F(g(proper(z0)), proper(x1)), PROPER(g(z0)), PROPER(x1))
K tuples:
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.58
G(mark(z0)) → c5(G(z0)) 148.09/48.58
PROPER(g(z0)) → c8(G(proper(z0)), PROPER(z0)) 148.09/48.58
PROPER(f(x0, f(z0, z1))) → c7(F(proper(x0), f(proper(z0), proper(z1))), PROPER(x0), PROPER(f(z0, z1))) 148.09/48.58
PROPER(f(x0, g(z0))) → c7(F(proper(x0), g(proper(z0))), PROPER(x0), PROPER(g(z0))) 148.09/48.58
PROPER(f(f(z0, z1), x1)) → c7(F(f(proper(z0), proper(z1)), proper(x1)), PROPER(f(z0, z1)), PROPER(x1)) 148.09/48.58
PROPER(f(g(z0), x1)) → c7(F(g(proper(z0)), proper(x1)), PROPER(g(z0)), PROPER(x1))
Defined Rule Symbols:
ACTIVE(f(g(z0), z1)) → c(G(z0)) 148.09/48.58
TOP(mark(z0)) → c9(TOP(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(ok(z0)) → c10(TOP(active(z0)), ACTIVE(z0)) 148.09/48.58
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.58
G(ok(z0)) → c6(G(z0)) 148.09/48.58
ACTIVE(g(z0)) → c2(G(active(z0)), ACTIVE(z0)) 148.09/48.58
ACTIVE(f(z0, z1)) → c1(F(active(z0), z1), ACTIVE(z0))
active, f, g, proper, top
F, G, PROPER, TOP, ACTIVE
c3, c4, c5, c6, c8, c9, c10, c, c1, c2, c7
PROPER(g(f(z0, z1))) → c8(G(f(proper(z0), proper(z1))), PROPER(f(z0, z1))) 148.09/48.58
PROPER(g(g(z0))) → c8(G(g(proper(z0))), PROPER(g(z0)))
Tuples:
active(f(g(z0), z1)) → mark(f(z0, f(g(z0), z1))) 148.09/48.58
active(f(z0, z1)) → f(active(z0), z1) 148.09/48.58
active(g(z0)) → g(active(z0)) 148.09/48.58
f(mark(z0), z1) → mark(f(z0, z1)) 148.09/48.58
f(ok(z0), ok(z1)) → ok(f(z0, z1)) 148.09/48.58
g(mark(z0)) → mark(g(z0)) 148.09/48.58
g(ok(z0)) → ok(g(z0)) 148.09/48.58
proper(f(z0, z1)) → f(proper(z0), proper(z1)) 148.09/48.58
proper(g(z0)) → g(proper(z0)) 148.09/48.58
top(mark(z0)) → top(proper(z0)) 148.09/48.58
top(ok(z0)) → top(active(z0))
S tuples:
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.58
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.58
G(mark(z0)) → c5(G(z0)) 148.09/48.58
G(ok(z0)) → c6(G(z0)) 148.09/48.58
TOP(mark(z0)) → c9(TOP(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(ok(z0)) → c10(TOP(active(z0)), ACTIVE(z0)) 148.09/48.58
ACTIVE(f(g(z0), z1)) → c(G(z0)) 148.09/48.58
ACTIVE(f(f(g(z0), z1), x1)) → c1(F(mark(f(z0, f(g(z0), z1))), x1), ACTIVE(f(g(z0), z1))) 148.09/48.58
ACTIVE(f(f(z0, z1), x1)) → c1(F(f(active(z0), z1), x1), ACTIVE(f(z0, z1))) 148.09/48.58
ACTIVE(f(g(z0), x1)) → c1(F(g(active(z0)), x1), ACTIVE(g(z0))) 148.09/48.58
ACTIVE(g(f(g(z0), z1))) → c2(G(mark(f(z0, f(g(z0), z1)))), ACTIVE(f(g(z0), z1))) 148.09/48.58
ACTIVE(g(f(z0, z1))) → c2(G(f(active(z0), z1)), ACTIVE(f(z0, z1))) 148.09/48.58
ACTIVE(g(g(z0))) → c2(G(g(active(z0))), ACTIVE(g(z0))) 148.09/48.58
PROPER(f(x0, f(z0, z1))) → c7(F(proper(x0), f(proper(z0), proper(z1))), PROPER(x0), PROPER(f(z0, z1))) 148.09/48.58
PROPER(f(x0, g(z0))) → c7(F(proper(x0), g(proper(z0))), PROPER(x0), PROPER(g(z0))) 148.09/48.58
PROPER(f(f(z0, z1), x1)) → c7(F(f(proper(z0), proper(z1)), proper(x1)), PROPER(f(z0, z1)), PROPER(x1)) 148.09/48.58
PROPER(f(g(z0), x1)) → c7(F(g(proper(z0)), proper(x1)), PROPER(g(z0)), PROPER(x1)) 148.09/48.58
PROPER(g(f(z0, z1))) → c8(G(f(proper(z0), proper(z1))), PROPER(f(z0, z1))) 148.09/48.58
PROPER(g(g(z0))) → c8(G(g(proper(z0))), PROPER(g(z0)))
K tuples:
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.58
G(mark(z0)) → c5(G(z0)) 148.09/48.58
PROPER(f(x0, f(z0, z1))) → c7(F(proper(x0), f(proper(z0), proper(z1))), PROPER(x0), PROPER(f(z0, z1))) 148.09/48.58
PROPER(f(x0, g(z0))) → c7(F(proper(x0), g(proper(z0))), PROPER(x0), PROPER(g(z0))) 148.09/48.58
PROPER(f(f(z0, z1), x1)) → c7(F(f(proper(z0), proper(z1)), proper(x1)), PROPER(f(z0, z1)), PROPER(x1)) 148.09/48.58
PROPER(f(g(z0), x1)) → c7(F(g(proper(z0)), proper(x1)), PROPER(g(z0)), PROPER(x1)) 148.09/48.58
PROPER(g(f(z0, z1))) → c8(G(f(proper(z0), proper(z1))), PROPER(f(z0, z1))) 148.09/48.58
PROPER(g(g(z0))) → c8(G(g(proper(z0))), PROPER(g(z0)))
Defined Rule Symbols:
ACTIVE(f(g(z0), z1)) → c(G(z0)) 148.09/48.58
TOP(mark(z0)) → c9(TOP(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(ok(z0)) → c10(TOP(active(z0)), ACTIVE(z0)) 148.09/48.58
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.58
G(ok(z0)) → c6(G(z0)) 148.09/48.58
ACTIVE(g(z0)) → c2(G(active(z0)), ACTIVE(z0)) 148.09/48.58
ACTIVE(f(z0, z1)) → c1(F(active(z0), z1), ACTIVE(z0))
active, f, g, proper, top
F, G, TOP, ACTIVE, PROPER
c3, c4, c5, c6, c9, c10, c, c1, c2, c7, c8
TOP(mark(f(z0, z1))) → c9(TOP(f(proper(z0), proper(z1))), PROPER(f(z0, z1))) 148.09/48.58
TOP(mark(g(z0))) → c9(TOP(g(proper(z0))), PROPER(g(z0)))
Tuples:
active(f(g(z0), z1)) → mark(f(z0, f(g(z0), z1))) 148.09/48.58
active(f(z0, z1)) → f(active(z0), z1) 148.09/48.58
active(g(z0)) → g(active(z0)) 148.09/48.58
f(mark(z0), z1) → mark(f(z0, z1)) 148.09/48.58
f(ok(z0), ok(z1)) → ok(f(z0, z1)) 148.09/48.58
g(mark(z0)) → mark(g(z0)) 148.09/48.58
g(ok(z0)) → ok(g(z0)) 148.09/48.58
proper(f(z0, z1)) → f(proper(z0), proper(z1)) 148.09/48.58
proper(g(z0)) → g(proper(z0)) 148.09/48.58
top(mark(z0)) → top(proper(z0)) 148.09/48.58
top(ok(z0)) → top(active(z0))
S tuples:
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.58
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.58
G(mark(z0)) → c5(G(z0)) 148.09/48.58
G(ok(z0)) → c6(G(z0)) 148.09/48.58
TOP(ok(z0)) → c10(TOP(active(z0)), ACTIVE(z0)) 148.09/48.58
ACTIVE(f(g(z0), z1)) → c(G(z0)) 148.09/48.58
ACTIVE(f(f(g(z0), z1), x1)) → c1(F(mark(f(z0, f(g(z0), z1))), x1), ACTIVE(f(g(z0), z1))) 148.09/48.58
ACTIVE(f(f(z0, z1), x1)) → c1(F(f(active(z0), z1), x1), ACTIVE(f(z0, z1))) 148.09/48.58
ACTIVE(f(g(z0), x1)) → c1(F(g(active(z0)), x1), ACTIVE(g(z0))) 148.09/48.58
ACTIVE(g(f(g(z0), z1))) → c2(G(mark(f(z0, f(g(z0), z1)))), ACTIVE(f(g(z0), z1))) 148.09/48.58
ACTIVE(g(f(z0, z1))) → c2(G(f(active(z0), z1)), ACTIVE(f(z0, z1))) 148.09/48.58
ACTIVE(g(g(z0))) → c2(G(g(active(z0))), ACTIVE(g(z0))) 148.09/48.58
PROPER(f(x0, f(z0, z1))) → c7(F(proper(x0), f(proper(z0), proper(z1))), PROPER(x0), PROPER(f(z0, z1))) 148.09/48.58
PROPER(f(x0, g(z0))) → c7(F(proper(x0), g(proper(z0))), PROPER(x0), PROPER(g(z0))) 148.09/48.58
PROPER(f(f(z0, z1), x1)) → c7(F(f(proper(z0), proper(z1)), proper(x1)), PROPER(f(z0, z1)), PROPER(x1)) 148.09/48.58
PROPER(f(g(z0), x1)) → c7(F(g(proper(z0)), proper(x1)), PROPER(g(z0)), PROPER(x1)) 148.09/48.58
PROPER(g(f(z0, z1))) → c8(G(f(proper(z0), proper(z1))), PROPER(f(z0, z1))) 148.09/48.58
PROPER(g(g(z0))) → c8(G(g(proper(z0))), PROPER(g(z0))) 148.09/48.58
TOP(mark(f(z0, z1))) → c9(TOP(f(proper(z0), proper(z1))), PROPER(f(z0, z1))) 148.09/48.58
TOP(mark(g(z0))) → c9(TOP(g(proper(z0))), PROPER(g(z0)))
K tuples:
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.58
G(mark(z0)) → c5(G(z0)) 148.09/48.58
PROPER(f(x0, f(z0, z1))) → c7(F(proper(x0), f(proper(z0), proper(z1))), PROPER(x0), PROPER(f(z0, z1))) 148.09/48.58
PROPER(f(x0, g(z0))) → c7(F(proper(x0), g(proper(z0))), PROPER(x0), PROPER(g(z0))) 148.09/48.58
PROPER(f(f(z0, z1), x1)) → c7(F(f(proper(z0), proper(z1)), proper(x1)), PROPER(f(z0, z1)), PROPER(x1)) 148.09/48.58
PROPER(f(g(z0), x1)) → c7(F(g(proper(z0)), proper(x1)), PROPER(g(z0)), PROPER(x1)) 148.09/48.58
PROPER(g(f(z0, z1))) → c8(G(f(proper(z0), proper(z1))), PROPER(f(z0, z1))) 148.09/48.58
PROPER(g(g(z0))) → c8(G(g(proper(z0))), PROPER(g(z0)))
Defined Rule Symbols:
ACTIVE(f(g(z0), z1)) → c(G(z0)) 148.09/48.58
TOP(mark(z0)) → c9(TOP(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(ok(z0)) → c10(TOP(active(z0)), ACTIVE(z0)) 148.09/48.58
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.58
G(ok(z0)) → c6(G(z0)) 148.09/48.58
ACTIVE(g(z0)) → c2(G(active(z0)), ACTIVE(z0)) 148.09/48.58
ACTIVE(f(z0, z1)) → c1(F(active(z0), z1), ACTIVE(z0))
active, f, g, proper, top
F, G, TOP, ACTIVE, PROPER
c3, c4, c5, c6, c10, c, c1, c2, c7, c8, c9
TOP(ok(f(g(z0), z1))) → c10(TOP(mark(f(z0, f(g(z0), z1)))), ACTIVE(f(g(z0), z1))) 148.09/48.58
TOP(ok(f(z0, z1))) → c10(TOP(f(active(z0), z1)), ACTIVE(f(z0, z1))) 148.09/48.58
TOP(ok(g(z0))) → c10(TOP(g(active(z0))), ACTIVE(g(z0)))
Tuples:
active(f(g(z0), z1)) → mark(f(z0, f(g(z0), z1))) 148.09/48.58
active(f(z0, z1)) → f(active(z0), z1) 148.09/48.58
active(g(z0)) → g(active(z0)) 148.09/48.58
f(mark(z0), z1) → mark(f(z0, z1)) 148.09/48.58
f(ok(z0), ok(z1)) → ok(f(z0, z1)) 148.09/48.58
g(mark(z0)) → mark(g(z0)) 148.09/48.58
g(ok(z0)) → ok(g(z0)) 148.09/48.58
proper(f(z0, z1)) → f(proper(z0), proper(z1)) 148.09/48.58
proper(g(z0)) → g(proper(z0)) 148.09/48.58
top(mark(z0)) → top(proper(z0)) 148.09/48.58
top(ok(z0)) → top(active(z0))
S tuples:
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.58
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.58
G(mark(z0)) → c5(G(z0)) 148.09/48.58
G(ok(z0)) → c6(G(z0)) 148.09/48.58
ACTIVE(f(g(z0), z1)) → c(G(z0)) 148.09/48.58
ACTIVE(f(f(g(z0), z1), x1)) → c1(F(mark(f(z0, f(g(z0), z1))), x1), ACTIVE(f(g(z0), z1))) 148.09/48.58
ACTIVE(f(f(z0, z1), x1)) → c1(F(f(active(z0), z1), x1), ACTIVE(f(z0, z1))) 148.09/48.58
ACTIVE(f(g(z0), x1)) → c1(F(g(active(z0)), x1), ACTIVE(g(z0))) 148.09/48.58
ACTIVE(g(f(g(z0), z1))) → c2(G(mark(f(z0, f(g(z0), z1)))), ACTIVE(f(g(z0), z1))) 148.09/48.58
ACTIVE(g(f(z0, z1))) → c2(G(f(active(z0), z1)), ACTIVE(f(z0, z1))) 148.09/48.58
ACTIVE(g(g(z0))) → c2(G(g(active(z0))), ACTIVE(g(z0))) 148.09/48.58
PROPER(f(x0, f(z0, z1))) → c7(F(proper(x0), f(proper(z0), proper(z1))), PROPER(x0), PROPER(f(z0, z1))) 148.09/48.58
PROPER(f(x0, g(z0))) → c7(F(proper(x0), g(proper(z0))), PROPER(x0), PROPER(g(z0))) 148.09/48.58
PROPER(f(f(z0, z1), x1)) → c7(F(f(proper(z0), proper(z1)), proper(x1)), PROPER(f(z0, z1)), PROPER(x1)) 148.09/48.58
PROPER(f(g(z0), x1)) → c7(F(g(proper(z0)), proper(x1)), PROPER(g(z0)), PROPER(x1)) 148.09/48.58
PROPER(g(f(z0, z1))) → c8(G(f(proper(z0), proper(z1))), PROPER(f(z0, z1))) 148.09/48.58
PROPER(g(g(z0))) → c8(G(g(proper(z0))), PROPER(g(z0))) 148.09/48.58
TOP(mark(f(z0, z1))) → c9(TOP(f(proper(z0), proper(z1))), PROPER(f(z0, z1))) 148.09/48.58
TOP(mark(g(z0))) → c9(TOP(g(proper(z0))), PROPER(g(z0))) 148.09/48.58
TOP(ok(f(g(z0), z1))) → c10(TOP(mark(f(z0, f(g(z0), z1)))), ACTIVE(f(g(z0), z1))) 148.09/48.58
TOP(ok(f(z0, z1))) → c10(TOP(f(active(z0), z1)), ACTIVE(f(z0, z1))) 148.09/48.58
TOP(ok(g(z0))) → c10(TOP(g(active(z0))), ACTIVE(g(z0)))
K tuples:
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.58
G(mark(z0)) → c5(G(z0)) 148.09/48.58
PROPER(f(x0, f(z0, z1))) → c7(F(proper(x0), f(proper(z0), proper(z1))), PROPER(x0), PROPER(f(z0, z1))) 148.09/48.58
PROPER(f(x0, g(z0))) → c7(F(proper(x0), g(proper(z0))), PROPER(x0), PROPER(g(z0))) 148.09/48.58
PROPER(f(f(z0, z1), x1)) → c7(F(f(proper(z0), proper(z1)), proper(x1)), PROPER(f(z0, z1)), PROPER(x1)) 148.09/48.58
PROPER(f(g(z0), x1)) → c7(F(g(proper(z0)), proper(x1)), PROPER(g(z0)), PROPER(x1)) 148.09/48.58
PROPER(g(f(z0, z1))) → c8(G(f(proper(z0), proper(z1))), PROPER(f(z0, z1))) 148.09/48.58
PROPER(g(g(z0))) → c8(G(g(proper(z0))), PROPER(g(z0)))
Defined Rule Symbols:
ACTIVE(f(g(z0), z1)) → c(G(z0)) 148.09/48.58
TOP(mark(z0)) → c9(TOP(proper(z0)), PROPER(z0)) 148.09/48.58
TOP(ok(z0)) → c10(TOP(active(z0)), ACTIVE(z0)) 148.09/48.58
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.58
G(ok(z0)) → c6(G(z0)) 148.09/48.58
ACTIVE(g(z0)) → c2(G(active(z0)), ACTIVE(z0)) 148.09/48.58
ACTIVE(f(z0, z1)) → c1(F(active(z0), z1), ACTIVE(z0))
active, f, g, proper, top
F, G, ACTIVE, PROPER, TOP
c3, c4, c5, c6, c, c1, c2, c7, c8, c9, c10
ACTIVE(f(g(z0), z1)) → c(G(z0)) 148.09/48.58
ACTIVE(f(f(g(z0), z1), x1)) → c1(F(mark(f(z0, f(g(z0), z1))), x1), ACTIVE(f(g(z0), z1))) 148.09/48.58
ACTIVE(f(f(z0, z1), x1)) → c1(F(f(active(z0), z1), x1), ACTIVE(f(z0, z1))) 148.09/48.58
ACTIVE(f(g(z0), x1)) → c1(F(g(active(z0)), x1), ACTIVE(g(z0))) 148.09/48.58
ACTIVE(g(f(g(z0), z1))) → c2(G(mark(f(z0, f(g(z0), z1)))), ACTIVE(f(g(z0), z1))) 148.09/48.58
ACTIVE(g(f(z0, z1))) → c2(G(f(active(z0), z1)), ACTIVE(f(z0, z1))) 148.09/48.58
ACTIVE(g(g(z0))) → c2(G(g(active(z0))), ACTIVE(g(z0))) 148.09/48.58
PROPER(f(x0, f(z0, z1))) → c7(F(proper(x0), f(proper(z0), proper(z1))), PROPER(x0), PROPER(f(z0, z1))) 148.09/48.58
PROPER(f(x0, g(z0))) → c7(F(proper(x0), g(proper(z0))), PROPER(x0), PROPER(g(z0))) 148.09/48.58
PROPER(f(f(z0, z1), x1)) → c7(F(f(proper(z0), proper(z1)), proper(x1)), PROPER(f(z0, z1)), PROPER(x1)) 148.09/48.58
PROPER(f(g(z0), x1)) → c7(F(g(proper(z0)), proper(x1)), PROPER(g(z0)), PROPER(x1)) 148.09/48.58
PROPER(g(f(z0, z1))) → c8(G(f(proper(z0), proper(z1))), PROPER(f(z0, z1))) 148.09/48.58
PROPER(g(g(z0))) → c8(G(g(proper(z0))), PROPER(g(z0))) 148.09/48.58
TOP(mark(f(z0, z1))) → c9(TOP(f(proper(z0), proper(z1))), PROPER(f(z0, z1))) 148.09/48.58
TOP(mark(g(z0))) → c9(TOP(g(proper(z0))), PROPER(g(z0))) 148.09/48.58
TOP(ok(f(g(z0), z1))) → c10(TOP(mark(f(z0, f(g(z0), z1)))), ACTIVE(f(g(z0), z1))) 148.09/48.58
TOP(ok(f(z0, z1))) → c10(TOP(f(active(z0), z1)), ACTIVE(f(z0, z1))) 148.09/48.58
TOP(ok(g(z0))) → c10(TOP(g(active(z0))), ACTIVE(g(z0)))
Tuples:
active(f(g(z0), z1)) → mark(f(z0, f(g(z0), z1))) 148.09/48.58
active(f(z0, z1)) → f(active(z0), z1) 148.09/48.58
active(g(z0)) → g(active(z0)) 148.09/48.58
f(mark(z0), z1) → mark(f(z0, z1)) 148.09/48.58
f(ok(z0), ok(z1)) → ok(f(z0, z1)) 148.09/48.58
g(mark(z0)) → mark(g(z0)) 148.09/48.58
g(ok(z0)) → ok(g(z0)) 148.09/48.58
proper(f(z0, z1)) → f(proper(z0), proper(z1)) 148.09/48.58
proper(g(z0)) → g(proper(z0)) 148.09/48.58
top(mark(z0)) → top(proper(z0)) 148.09/48.58
top(ok(z0)) → top(active(z0))
S tuples:
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.58
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.58
G(mark(z0)) → c5(G(z0)) 148.09/48.58
G(ok(z0)) → c6(G(z0))
K tuples:
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.58
G(mark(z0)) → c5(G(z0))
Defined Rule Symbols:
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.58
G(ok(z0)) → c6(G(z0))
active, f, g, proper, top
F, G
c3, c4, c5, c6
We considered the (Usable) Rules:none
F(mark(z0), z1) → c3(F(z0, z1))
The order we found is given by the following interpretation:
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.58
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.58
G(mark(z0)) → c5(G(z0)) 148.09/48.58
G(ok(z0)) → c6(G(z0))
POL(F(x1, x2)) = x1 + [3]x2 148.09/48.58
POL(G(x1)) = 0 148.09/48.58
POL(c3(x1)) = x1 148.09/48.58
POL(c4(x1)) = x1 148.09/48.58
POL(c5(x1)) = x1 148.09/48.58
POL(c6(x1)) = x1 148.09/48.58
POL(mark(x1)) = [1] + x1 148.09/48.58
POL(ok(x1)) = x1
Tuples:
active(f(g(z0), z1)) → mark(f(z0, f(g(z0), z1))) 148.09/48.58
active(f(z0, z1)) → f(active(z0), z1) 148.09/48.58
active(g(z0)) → g(active(z0)) 148.09/48.58
f(mark(z0), z1) → mark(f(z0, z1)) 148.09/48.58
f(ok(z0), ok(z1)) → ok(f(z0, z1)) 148.09/48.58
g(mark(z0)) → mark(g(z0)) 148.09/48.58
g(ok(z0)) → ok(g(z0)) 148.09/48.58
proper(f(z0, z1)) → f(proper(z0), proper(z1)) 148.09/48.58
proper(g(z0)) → g(proper(z0)) 148.09/48.58
top(mark(z0)) → top(proper(z0)) 148.09/48.58
top(ok(z0)) → top(active(z0))
S tuples:
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.58
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.58
G(mark(z0)) → c5(G(z0)) 148.09/48.58
G(ok(z0)) → c6(G(z0))
K tuples:
G(mark(z0)) → c5(G(z0))
Defined Rule Symbols:
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.58
G(ok(z0)) → c6(G(z0)) 148.09/48.58
F(mark(z0), z1) → c3(F(z0, z1))
active, f, g, proper, top
F, G
c3, c4, c5, c6
We considered the (Usable) Rules:none
G(mark(z0)) → c5(G(z0))
The order we found is given by the following interpretation:
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.58
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.58
G(mark(z0)) → c5(G(z0)) 148.09/48.58
G(ok(z0)) → c6(G(z0))
POL(F(x1, x2)) = [5]x1 + [5]x2 148.09/48.58
POL(G(x1)) = [5]x1 148.09/48.58
POL(c3(x1)) = x1 148.09/48.58
POL(c4(x1)) = x1 148.09/48.58
POL(c5(x1)) = x1 148.09/48.58
POL(c6(x1)) = x1 148.09/48.58
POL(mark(x1)) = [1] + x1 148.09/48.58
POL(ok(x1)) = x1
Tuples:
active(f(g(z0), z1)) → mark(f(z0, f(g(z0), z1))) 148.09/48.58
active(f(z0, z1)) → f(active(z0), z1) 148.09/48.58
active(g(z0)) → g(active(z0)) 148.09/48.58
f(mark(z0), z1) → mark(f(z0, z1)) 148.09/48.58
f(ok(z0), ok(z1)) → ok(f(z0, z1)) 148.09/48.58
g(mark(z0)) → mark(g(z0)) 148.09/48.58
g(ok(z0)) → ok(g(z0)) 148.09/48.58
proper(f(z0, z1)) → f(proper(z0), proper(z1)) 148.09/48.58
proper(g(z0)) → g(proper(z0)) 148.09/48.58
top(mark(z0)) → top(proper(z0)) 148.09/48.58
top(ok(z0)) → top(active(z0))
S tuples:none
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.58
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.58
G(mark(z0)) → c5(G(z0)) 148.09/48.58
G(ok(z0)) → c6(G(z0))
Defined Rule Symbols:
F(ok(z0), ok(z1)) → c4(F(z0, z1)) 148.09/48.58
G(ok(z0)) → c6(G(z0)) 148.09/48.58
F(mark(z0), z1) → c3(F(z0, z1)) 148.09/48.58
G(mark(z0)) → c5(G(z0))
active, f, g, proper, top
F, G
c3, c4, c5, c6