(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
f(s(s(s(s(s(s(s(s(x)))))))), y, y) → f(id(s(s(s(s(s(s(s(s(x))))))))), y, y)
id(s(x)) → s(id(x))
id(0) → 0
Rewrite Strategy: FULL
(1) CpxTrsToCpxRelTrsProof (BOTH BOUNDS(ID, ID) transformation)
Transformed TRS to relative TRS where S is empty.
(2) Obligation:
Runtime Complexity Relative TRS:
The TRS R consists of the following rules:
f(s(s(s(s(s(s(s(s(x)))))))), y, y) → f(id(s(s(s(s(s(s(s(s(x))))))))), y, y)
id(s(x)) → s(id(x))
id(0) → 0
S is empty.
Rewrite Strategy: FULL
(3) InfiniteLowerBoundProof (EQUIVALENT transformation)
The loop following loop proves infinite runtime complexity:
The rewrite sequence
f(s(s(s(s(s(s(s(s(x)))))))), y7482_1, y7482_1) →+ f(s(s(s(s(s(s(s(s(id(x))))))))), y7482_1, y7482_1)
gives rise to a decreasing loop by considering the right hand sides subterm at position [].
The pumping substitution is [ ].
The result substitution is [x / id(x)].
(4) BOUNDS(INF, INF)