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(g(x)) → g(g(f(x))) 0.00/0.70
f(g(x)) → g(g(g(x)))
Tuples:
f(g(z0)) → g(g(f(z0))) 0.00/0.70
f(g(z0)) → g(g(g(z0)))
S tuples:
F(g(z0)) → c(F(z0))
K tuples:none
F(g(z0)) → c(F(z0))
f
F
c
We considered the (Usable) Rules:none
F(g(z0)) → c(F(z0))
The order we found is given by the following interpretation:
F(g(z0)) → c(F(z0))
POL(F(x1)) = [3]x1 0.00/0.70
POL(c(x1)) = x1 0.00/0.70
POL(g(x1)) = [1] + x1
Tuples:
f(g(z0)) → g(g(f(z0))) 0.00/0.70
f(g(z0)) → g(g(g(z0)))
S tuples:none
F(g(z0)) → c(F(z0))
Defined Rule Symbols:
F(g(z0)) → c(F(z0))
f
F
c