YES(O(1), O(n^1)) 0.00/0.71 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 CdtUnreachableProof (⇔)0.00/0.72
↳4 CdtProblem0.00/0.72
↳5 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))0.00/0.72
↳6 CdtProblem0.00/0.72
↳7 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))0.00/0.72
↳8 CdtProblem0.00/0.72
↳9 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))0.00/0.72
↳10 CdtProblem0.00/0.72
↳11 SIsEmptyProof (BOTH BOUNDS(ID, ID))0.00/0.72
↳12 BOUNDS(O(1), O(1))0.00/0.72
f(f(a)) → f(g(n__f(n__a))) 0.00/0.72
f(X) → n__f(X) 0.00/0.72
a → n__a 0.00/0.72
activate(n__f(X)) → f(activate(X)) 0.00/0.72
activate(n__a) → a 0.00/0.72
activate(X) → X
Tuples:
f(f(a)) → f(g(n__f(n__a))) 0.00/0.72
f(z0) → n__f(z0) 0.00/0.72
a → n__a 0.00/0.72
activate(n__f(z0)) → f(activate(z0)) 0.00/0.72
activate(n__a) → a 0.00/0.72
activate(z0) → z0
S tuples:
F(f(a)) → c(F(g(n__f(n__a)))) 0.00/0.72
ACTIVATE(n__f(z0)) → c3(F(activate(z0)), ACTIVATE(z0)) 0.00/0.72
ACTIVATE(n__a) → c4(A)
K tuples:none
F(f(a)) → c(F(g(n__f(n__a)))) 0.00/0.72
ACTIVATE(n__f(z0)) → c3(F(activate(z0)), ACTIVATE(z0)) 0.00/0.72
ACTIVATE(n__a) → c4(A)
f, a, activate
F, ACTIVATE
c, c3, c4
F(f(a)) → c(F(g(n__f(n__a))))
Tuples:
f(f(a)) → f(g(n__f(n__a))) 0.00/0.72
f(z0) → n__f(z0) 0.00/0.72
a → n__a 0.00/0.72
activate(n__f(z0)) → f(activate(z0)) 0.00/0.72
activate(n__a) → a 0.00/0.72
activate(z0) → z0
S tuples:
ACTIVATE(n__f(z0)) → c3(F(activate(z0)), ACTIVATE(z0)) 0.00/0.72
ACTIVATE(n__a) → c4(A)
K tuples:none
ACTIVATE(n__f(z0)) → c3(F(activate(z0)), ACTIVATE(z0)) 0.00/0.72
ACTIVATE(n__a) → c4(A)
f, a, activate
ACTIVATE
c3, c4
Tuples:
f(f(a)) → f(g(n__f(n__a))) 0.00/0.72
f(z0) → n__f(z0) 0.00/0.72
a → n__a 0.00/0.72
activate(n__f(z0)) → f(activate(z0)) 0.00/0.72
activate(n__a) → a 0.00/0.72
activate(z0) → z0
S tuples:
ACTIVATE(n__f(z0)) → c3(ACTIVATE(z0)) 0.00/0.72
ACTIVATE(n__a) → c4
K tuples:none
ACTIVATE(n__f(z0)) → c3(ACTIVATE(z0)) 0.00/0.72
ACTIVATE(n__a) → c4
f, a, activate
ACTIVATE
c3, c4
ACTIVATE(n__a) → c4
Tuples:
f(f(a)) → f(g(n__f(n__a))) 0.00/0.72
f(z0) → n__f(z0) 0.00/0.72
a → n__a 0.00/0.72
activate(n__f(z0)) → f(activate(z0)) 0.00/0.72
activate(n__a) → a 0.00/0.72
activate(z0) → z0
S tuples:
ACTIVATE(n__f(z0)) → c3(ACTIVATE(z0)) 0.00/0.72
ACTIVATE(n__a) → c4
K tuples:none
ACTIVATE(n__f(z0)) → c3(ACTIVATE(z0)) 0.00/0.72
ACTIVATE(n__a) → c4
f, a, activate
ACTIVATE
c3, c4
We considered the (Usable) Rules:none
ACTIVATE(n__f(z0)) → c3(ACTIVATE(z0)) 0.00/0.72
ACTIVATE(n__a) → c4
The order we found is given by the following interpretation:
ACTIVATE(n__f(z0)) → c3(ACTIVATE(z0)) 0.00/0.72
ACTIVATE(n__a) → c4
POL(ACTIVATE(x1)) = [3] + [3]x1 0.00/0.72
POL(c3(x1)) = x1 0.00/0.72
POL(c4) = 0 0.00/0.72
POL(n__a) = [5] 0.00/0.72
POL(n__f(x1)) = [3] + x1
Tuples:
f(f(a)) → f(g(n__f(n__a))) 0.00/0.72
f(z0) → n__f(z0) 0.00/0.72
a → n__a 0.00/0.72
activate(n__f(z0)) → f(activate(z0)) 0.00/0.72
activate(n__a) → a 0.00/0.72
activate(z0) → z0
S tuples:none
ACTIVATE(n__f(z0)) → c3(ACTIVATE(z0)) 0.00/0.72
ACTIVATE(n__a) → c4
Defined Rule Symbols:
ACTIVATE(n__f(z0)) → c3(ACTIVATE(z0)) 0.00/0.72
ACTIVATE(n__a) → c4
f, a, activate
ACTIVATE
c3, c4