YES(O(1), O(n^1)) 0.00/0.69 YES(O(1), O(n^1)) 0.00/0.70 0.00/0.70 0.00/0.70
0.00/0.70 0.00/0.700 CpxTRS0.00/0.70
↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))0.00/0.70
↳2 CdtProblem0.00/0.70
↳3 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))0.00/0.70
↳4 CdtProblem0.00/0.70
↳5 SIsEmptyProof (BOTH BOUNDS(ID, ID))0.00/0.70
↳6 BOUNDS(O(1), O(1))0.00/0.70
f(S(x), x2) → f(x2, x) 0.00/0.70
f(0, x2) → 0
Tuples:
f(S(z0), z1) → f(z1, z0) 0.00/0.70
f(0, z0) → 0
S tuples:
F(S(z0), z1) → c(F(z1, z0))
K tuples:none
F(S(z0), z1) → c(F(z1, z0))
f
F
c
We considered the (Usable) Rules:none
F(S(z0), z1) → c(F(z1, z0))
The order we found is given by the following interpretation:
F(S(z0), z1) → c(F(z1, z0))
POL(F(x1, x2)) = [5]x1 + [5]x2 0.00/0.70
POL(S(x1)) = [1] + x1 0.00/0.70
POL(c(x1)) = x1
Tuples:
f(S(z0), z1) → f(z1, z0) 0.00/0.70
f(0, z0) → 0
S tuples:none
F(S(z0), z1) → c(F(z1, z0))
Defined Rule Symbols:
F(S(z0), z1) → c(F(z1, z0))
f
F
c