YES(O(1), O(n^1)) 0.00/0.74 YES(O(1), O(n^1)) 0.00/0.76 0.00/0.76 0.00/0.76
0.00/0.76 0.00/0.760 CpxTRS0.00/0.76
↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))0.00/0.76
↳2 CdtProblem0.00/0.76
↳3 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))0.00/0.76
↳4 CdtProblem0.00/0.76
↳5 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))0.00/0.76
↳6 CdtProblem0.00/0.76
↳7 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))0.00/0.76
↳8 CdtProblem0.00/0.76
↳9 CdtKnowledgeProof (⇔)0.00/0.76
↳10 BOUNDS(O(1), O(1))0.00/0.76
f(n__f(n__a)) → f(n__g(n__f(n__a))) 0.00/0.76
f(X) → n__f(X) 0.00/0.76
a → n__a 0.00/0.76
g(X) → n__g(X) 0.00/0.76
activate(n__f(X)) → f(X) 0.00/0.76
activate(n__a) → a 0.00/0.76
activate(n__g(X)) → g(activate(X)) 0.00/0.76
activate(X) → X
Tuples:
f(n__f(n__a)) → f(n__g(n__f(n__a))) 0.00/0.76
f(z0) → n__f(z0) 0.00/0.76
a → n__a 0.00/0.76
g(z0) → n__g(z0) 0.00/0.76
activate(n__f(z0)) → f(z0) 0.00/0.76
activate(n__a) → a 0.00/0.76
activate(n__g(z0)) → g(activate(z0)) 0.00/0.76
activate(z0) → z0
S tuples:
F(n__f(n__a)) → c(F(n__g(n__f(n__a)))) 0.00/0.76
ACTIVATE(n__f(z0)) → c4(F(z0)) 0.00/0.76
ACTIVATE(n__a) → c5(A) 0.00/0.76
ACTIVATE(n__g(z0)) → c6(G(activate(z0)), ACTIVATE(z0))
K tuples:none
F(n__f(n__a)) → c(F(n__g(n__f(n__a)))) 0.00/0.76
ACTIVATE(n__f(z0)) → c4(F(z0)) 0.00/0.76
ACTIVATE(n__a) → c5(A) 0.00/0.76
ACTIVATE(n__g(z0)) → c6(G(activate(z0)), ACTIVATE(z0))
f, a, g, activate
F, ACTIVATE
c, c4, c5, c6
Tuples:
f(n__f(n__a)) → f(n__g(n__f(n__a))) 0.00/0.76
f(z0) → n__f(z0) 0.00/0.76
a → n__a 0.00/0.76
g(z0) → n__g(z0) 0.00/0.76
activate(n__f(z0)) → f(z0) 0.00/0.76
activate(n__a) → a 0.00/0.76
activate(n__g(z0)) → g(activate(z0)) 0.00/0.76
activate(z0) → z0
S tuples:
ACTIVATE(n__f(z0)) → c4(F(z0)) 0.00/0.76
F(n__f(n__a)) → c 0.00/0.76
ACTIVATE(n__a) → c5 0.00/0.76
ACTIVATE(n__g(z0)) → c6(ACTIVATE(z0))
K tuples:none
ACTIVATE(n__f(z0)) → c4(F(z0)) 0.00/0.76
F(n__f(n__a)) → c 0.00/0.76
ACTIVATE(n__a) → c5 0.00/0.76
ACTIVATE(n__g(z0)) → c6(ACTIVATE(z0))
f, a, g, activate
ACTIVATE, F
c4, c, c5, c6
ACTIVATE(n__a) → c5 0.00/0.76
ACTIVATE(n__f(z0)) → c4(F(z0)) 0.00/0.76
F(n__f(n__a)) → c
Tuples:
f(n__f(n__a)) → f(n__g(n__f(n__a))) 0.00/0.76
f(z0) → n__f(z0) 0.00/0.76
a → n__a 0.00/0.76
g(z0) → n__g(z0) 0.00/0.76
activate(n__f(z0)) → f(z0) 0.00/0.76
activate(n__a) → a 0.00/0.76
activate(n__g(z0)) → g(activate(z0)) 0.00/0.76
activate(z0) → z0
S tuples:
ACTIVATE(n__f(z0)) → c4(F(z0)) 0.00/0.76
F(n__f(n__a)) → c 0.00/0.76
ACTIVATE(n__a) → c5 0.00/0.76
ACTIVATE(n__g(z0)) → c6(ACTIVATE(z0))
K tuples:none
ACTIVATE(n__f(z0)) → c4(F(z0)) 0.00/0.76
F(n__f(n__a)) → c 0.00/0.76
ACTIVATE(n__a) → c5 0.00/0.76
ACTIVATE(n__g(z0)) → c6(ACTIVATE(z0))
f, a, g, activate
ACTIVATE, F
c4, c, c5, c6
We considered the (Usable) Rules:none
ACTIVATE(n__a) → c5 0.00/0.76
ACTIVATE(n__g(z0)) → c6(ACTIVATE(z0))
The order we found is given by the following interpretation:
ACTIVATE(n__f(z0)) → c4(F(z0)) 0.00/0.76
F(n__f(n__a)) → c 0.00/0.76
ACTIVATE(n__a) → c5 0.00/0.76
ACTIVATE(n__g(z0)) → c6(ACTIVATE(z0))
POL(ACTIVATE(x1)) = x1 0.00/0.76
POL(F(x1)) = 0 0.00/0.76
POL(c) = 0 0.00/0.76
POL(c4(x1)) = x1 0.00/0.76
POL(c5) = 0 0.00/0.76
POL(c6(x1)) = x1 0.00/0.76
POL(n__a) = [1] 0.00/0.76
POL(n__f(x1)) = 0 0.00/0.76
POL(n__g(x1)) = [1] + x1
Tuples:
f(n__f(n__a)) → f(n__g(n__f(n__a))) 0.00/0.76
f(z0) → n__f(z0) 0.00/0.76
a → n__a 0.00/0.76
g(z0) → n__g(z0) 0.00/0.76
activate(n__f(z0)) → f(z0) 0.00/0.76
activate(n__a) → a 0.00/0.76
activate(n__g(z0)) → g(activate(z0)) 0.00/0.76
activate(z0) → z0
S tuples:
ACTIVATE(n__f(z0)) → c4(F(z0)) 0.00/0.76
F(n__f(n__a)) → c 0.00/0.76
ACTIVATE(n__a) → c5 0.00/0.76
ACTIVATE(n__g(z0)) → c6(ACTIVATE(z0))
K tuples:
ACTIVATE(n__f(z0)) → c4(F(z0)) 0.00/0.76
F(n__f(n__a)) → c
Defined Rule Symbols:
ACTIVATE(n__a) → c5 0.00/0.76
ACTIVATE(n__g(z0)) → c6(ACTIVATE(z0))
f, a, g, activate
ACTIVATE, F
c4, c, c5, c6
Now S is empty
ACTIVATE(n__f(z0)) → c4(F(z0)) 0.00/0.76
F(n__f(n__a)) → c 0.00/0.76
F(n__f(n__a)) → c