YES(O(1), O(n^1)) 0.00/0.73 YES(O(1), O(n^1)) 0.00/0.74 0.00/0.74 0.00/0.74
0.00/0.74 0.00/0.740 CpxTRS0.00/0.74
↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))0.00/0.74
↳2 CdtProblem0.00/0.74
↳3 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))0.00/0.74
↳4 CdtProblem0.00/0.74
↳5 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))0.00/0.74
↳6 CdtProblem0.00/0.74
↳7 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))0.00/0.74
↳8 CdtProblem0.00/0.74
↳9 SIsEmptyProof (BOTH BOUNDS(ID, ID))0.00/0.74
↳10 BOUNDS(O(1), O(1))0.00/0.74
f(f(a)) → c(n__f(n__g(n__f(n__a)))) 0.00/0.74
f(X) → n__f(X) 0.00/0.74
g(X) → n__g(X) 0.00/0.74
a → n__a 0.00/0.74
activate(n__f(X)) → f(activate(X)) 0.00/0.74
activate(n__g(X)) → g(activate(X)) 0.00/0.74
activate(n__a) → a 0.00/0.74
activate(X) → X
Tuples:
f(f(a)) → c(n__f(n__g(n__f(n__a)))) 0.00/0.74
f(z0) → n__f(z0) 0.00/0.74
g(z0) → n__g(z0) 0.00/0.74
a → n__a 0.00/0.74
activate(n__f(z0)) → f(activate(z0)) 0.00/0.74
activate(n__g(z0)) → g(activate(z0)) 0.00/0.74
activate(n__a) → a 0.00/0.74
activate(z0) → z0
S tuples:
ACTIVATE(n__f(z0)) → c5(F(activate(z0)), ACTIVATE(z0)) 0.00/0.74
ACTIVATE(n__g(z0)) → c6(G(activate(z0)), ACTIVATE(z0)) 0.00/0.74
ACTIVATE(n__a) → c7(A)
K tuples:none
ACTIVATE(n__f(z0)) → c5(F(activate(z0)), ACTIVATE(z0)) 0.00/0.74
ACTIVATE(n__g(z0)) → c6(G(activate(z0)), ACTIVATE(z0)) 0.00/0.74
ACTIVATE(n__a) → c7(A)
f, g, a, activate
ACTIVATE
c5, c6, c7
Tuples:
f(f(a)) → c(n__f(n__g(n__f(n__a)))) 0.00/0.74
f(z0) → n__f(z0) 0.00/0.74
g(z0) → n__g(z0) 0.00/0.74
a → n__a 0.00/0.74
activate(n__f(z0)) → f(activate(z0)) 0.00/0.74
activate(n__g(z0)) → g(activate(z0)) 0.00/0.74
activate(n__a) → a 0.00/0.74
activate(z0) → z0
S tuples:
ACTIVATE(n__f(z0)) → c5(ACTIVATE(z0)) 0.00/0.74
ACTIVATE(n__g(z0)) → c6(ACTIVATE(z0)) 0.00/0.74
ACTIVATE(n__a) → c7
K tuples:none
ACTIVATE(n__f(z0)) → c5(ACTIVATE(z0)) 0.00/0.74
ACTIVATE(n__g(z0)) → c6(ACTIVATE(z0)) 0.00/0.74
ACTIVATE(n__a) → c7
f, g, a, activate
ACTIVATE
c5, c6, c7
ACTIVATE(n__a) → c7
Tuples:
f(f(a)) → c(n__f(n__g(n__f(n__a)))) 0.00/0.74
f(z0) → n__f(z0) 0.00/0.74
g(z0) → n__g(z0) 0.00/0.74
a → n__a 0.00/0.74
activate(n__f(z0)) → f(activate(z0)) 0.00/0.74
activate(n__g(z0)) → g(activate(z0)) 0.00/0.74
activate(n__a) → a 0.00/0.74
activate(z0) → z0
S tuples:
ACTIVATE(n__f(z0)) → c5(ACTIVATE(z0)) 0.00/0.74
ACTIVATE(n__g(z0)) → c6(ACTIVATE(z0)) 0.00/0.74
ACTIVATE(n__a) → c7
K tuples:none
ACTIVATE(n__f(z0)) → c5(ACTIVATE(z0)) 0.00/0.74
ACTIVATE(n__g(z0)) → c6(ACTIVATE(z0)) 0.00/0.74
ACTIVATE(n__a) → c7
f, g, a, activate
ACTIVATE
c5, c6, c7
We considered the (Usable) Rules:none
ACTIVATE(n__f(z0)) → c5(ACTIVATE(z0)) 0.00/0.74
ACTIVATE(n__g(z0)) → c6(ACTIVATE(z0)) 0.00/0.74
ACTIVATE(n__a) → c7
The order we found is given by the following interpretation:
ACTIVATE(n__f(z0)) → c5(ACTIVATE(z0)) 0.00/0.74
ACTIVATE(n__g(z0)) → c6(ACTIVATE(z0)) 0.00/0.74
ACTIVATE(n__a) → c7
POL(ACTIVATE(x1)) = [5] + [3]x1 0.00/0.74
POL(c5(x1)) = x1 0.00/0.74
POL(c6(x1)) = x1 0.00/0.74
POL(c7) = 0 0.00/0.74
POL(n__a) = [5] 0.00/0.74
POL(n__f(x1)) = [5] + x1 0.00/0.74
POL(n__g(x1)) = [5] + x1
Tuples:
f(f(a)) → c(n__f(n__g(n__f(n__a)))) 0.00/0.74
f(z0) → n__f(z0) 0.00/0.74
g(z0) → n__g(z0) 0.00/0.74
a → n__a 0.00/0.74
activate(n__f(z0)) → f(activate(z0)) 0.00/0.74
activate(n__g(z0)) → g(activate(z0)) 0.00/0.74
activate(n__a) → a 0.00/0.74
activate(z0) → z0
S tuples:none
ACTIVATE(n__f(z0)) → c5(ACTIVATE(z0)) 0.00/0.74
ACTIVATE(n__g(z0)) → c6(ACTIVATE(z0)) 0.00/0.74
ACTIVATE(n__a) → c7
Defined Rule Symbols:
ACTIVATE(n__f(z0)) → c5(ACTIVATE(z0)) 0.00/0.74
ACTIVATE(n__g(z0)) → c6(ACTIVATE(z0)) 0.00/0.74
ACTIVATE(n__a) → c7
f, g, a, activate
ACTIVATE
c5, c6, c7