YES(O(1), O(n^1)) 0.00/0.70 YES(O(1), O(n^1)) 0.00/0.72 0.00/0.72 0.00/0.72
0.00/0.72 0.00/0.720 CpxTRS0.00/0.72
↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))0.00/0.72
↳2 CdtProblem0.00/0.72
↳3 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))0.00/0.72
↳4 CdtProblem0.00/0.72
↳5 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))0.00/0.72
↳6 CdtProblem0.00/0.72
↳7 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))0.00/0.72
↳8 CdtProblem0.00/0.72
↳9 SIsEmptyProof (BOTH BOUNDS(ID, ID))0.00/0.72
↳10 BOUNDS(O(1), O(1))0.00/0.72
and(tt, X) → activate(X) 0.00/0.72
plus(N, 0) → N 0.00/0.72
plus(N, s(M)) → s(plus(N, M)) 0.00/0.72
activate(X) → X
Tuples:
and(tt, z0) → activate(z0) 0.00/0.72
plus(z0, 0) → z0 0.00/0.72
plus(z0, s(z1)) → s(plus(z0, z1)) 0.00/0.72
activate(z0) → z0
S tuples:
AND(tt, z0) → c(ACTIVATE(z0)) 0.00/0.72
PLUS(z0, s(z1)) → c2(PLUS(z0, z1))
K tuples:none
AND(tt, z0) → c(ACTIVATE(z0)) 0.00/0.72
PLUS(z0, s(z1)) → c2(PLUS(z0, z1))
and, plus, activate
AND, PLUS
c, c2
Tuples:
and(tt, z0) → activate(z0) 0.00/0.72
plus(z0, 0) → z0 0.00/0.72
plus(z0, s(z1)) → s(plus(z0, z1)) 0.00/0.72
activate(z0) → z0
S tuples:
PLUS(z0, s(z1)) → c2(PLUS(z0, z1)) 0.00/0.72
AND(tt, z0) → c
K tuples:none
PLUS(z0, s(z1)) → c2(PLUS(z0, z1)) 0.00/0.72
AND(tt, z0) → c
and, plus, activate
PLUS, AND
c2, c
AND(tt, z0) → c
Tuples:
and(tt, z0) → activate(z0) 0.00/0.72
plus(z0, 0) → z0 0.00/0.72
plus(z0, s(z1)) → s(plus(z0, z1)) 0.00/0.72
activate(z0) → z0
S tuples:
PLUS(z0, s(z1)) → c2(PLUS(z0, z1))
K tuples:none
PLUS(z0, s(z1)) → c2(PLUS(z0, z1))
and, plus, activate
PLUS
c2
We considered the (Usable) Rules:none
PLUS(z0, s(z1)) → c2(PLUS(z0, z1))
The order we found is given by the following interpretation:
PLUS(z0, s(z1)) → c2(PLUS(z0, z1))
POL(PLUS(x1, x2)) = [3]x2 0.00/0.72
POL(c2(x1)) = x1 0.00/0.72
POL(s(x1)) = [1] + x1
Tuples:
and(tt, z0) → activate(z0) 0.00/0.72
plus(z0, 0) → z0 0.00/0.72
plus(z0, s(z1)) → s(plus(z0, z1)) 0.00/0.72
activate(z0) → z0
S tuples:none
PLUS(z0, s(z1)) → c2(PLUS(z0, z1))
Defined Rule Symbols:
PLUS(z0, s(z1)) → c2(PLUS(z0, z1))
and, plus, activate
PLUS
c2