YES(O(1), O(n^1)) 0.00/0.79 YES(O(1), O(n^1)) 0.00/0.81 0.00/0.81 0.00/0.81
0.00/0.81 0.00/0.810 CpxTRS0.00/0.81
↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))0.00/0.81
↳2 CdtProblem0.00/0.81
↳3 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))0.00/0.81
↳4 CdtProblem0.00/0.81
↳5 CdtLeafRemovalProof (ComplexityIfPolyImplication)0.00/0.81
↳6 CdtProblem0.00/0.81
↳7 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))0.00/0.81
↳8 CdtProblem0.00/0.81
↳9 SIsEmptyProof (BOTH BOUNDS(ID, ID))0.00/0.81
↳10 BOUNDS(O(1), O(1))0.00/0.81
f(0) → cons(0, n__f(s(0))) 0.00/0.81
f(s(0)) → f(p(s(0))) 0.00/0.81
p(s(0)) → 0 0.00/0.81
f(X) → n__f(X) 0.00/0.81
activate(n__f(X)) → f(X) 0.00/0.81
activate(X) → X
Tuples:
f(0) → cons(0, n__f(s(0))) 0.00/0.81
f(s(0)) → f(p(s(0))) 0.00/0.81
f(z0) → n__f(z0) 0.00/0.81
p(s(0)) → 0 0.00/0.81
activate(n__f(z0)) → f(z0) 0.00/0.81
activate(z0) → z0
S tuples:
F(s(0)) → c1(F(p(s(0))), P(s(0))) 0.00/0.81
ACTIVATE(n__f(z0)) → c4(F(z0))
K tuples:none
F(s(0)) → c1(F(p(s(0))), P(s(0))) 0.00/0.81
ACTIVATE(n__f(z0)) → c4(F(z0))
f, p, activate
F, ACTIVATE
c1, c4
Tuples:
f(0) → cons(0, n__f(s(0))) 0.00/0.81
f(s(0)) → f(p(s(0))) 0.00/0.81
f(z0) → n__f(z0) 0.00/0.81
p(s(0)) → 0 0.00/0.81
activate(n__f(z0)) → f(z0) 0.00/0.81
activate(z0) → z0
S tuples:
ACTIVATE(n__f(z0)) → c4(F(z0)) 0.00/0.81
F(s(0)) → c1(F(p(s(0))))
K tuples:none
ACTIVATE(n__f(z0)) → c4(F(z0)) 0.00/0.81
F(s(0)) → c1(F(p(s(0))))
f, p, activate
ACTIVATE, F
c4, c1
ACTIVATE(n__f(z0)) → c4(F(z0))
Tuples:
f(0) → cons(0, n__f(s(0))) 0.00/0.81
f(s(0)) → f(p(s(0))) 0.00/0.81
f(z0) → n__f(z0) 0.00/0.81
p(s(0)) → 0 0.00/0.81
activate(n__f(z0)) → f(z0) 0.00/0.81
activate(z0) → z0
S tuples:
F(s(0)) → c1(F(p(s(0))))
K tuples:none
F(s(0)) → c1(F(p(s(0))))
f, p, activate
F
c1
We considered the (Usable) Rules:
F(s(0)) → c1(F(p(s(0))))
And the Tuples:
p(s(0)) → 0
The order we found is given by the following interpretation:
F(s(0)) → c1(F(p(s(0))))
POL(0) = [3] 0.00/0.81
POL(F(x1)) = [4]x1 0.00/0.81
POL(c1(x1)) = x1 0.00/0.81
POL(p(x1)) = [4] 0.00/0.81
POL(s(x1)) = [5] + x1
Tuples:
f(0) → cons(0, n__f(s(0))) 0.00/0.81
f(s(0)) → f(p(s(0))) 0.00/0.81
f(z0) → n__f(z0) 0.00/0.81
p(s(0)) → 0 0.00/0.81
activate(n__f(z0)) → f(z0) 0.00/0.81
activate(z0) → z0
S tuples:none
F(s(0)) → c1(F(p(s(0))))
Defined Rule Symbols:
F(s(0)) → c1(F(p(s(0))))
f, p, activate
F
c1