(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
f(h(x)) → f(i(x))
f(i(x)) → a
i(x) → h(x)
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(h(x)) → f(i(x))
f(i(x)) → a
i(x) → h(x)
S is empty.
Rewrite Strategy: FULL
(3) SlicingProof (LOWER BOUND(ID) transformation)
Sliced the following arguments:
h/0
i/0
(4) Obligation:
Runtime Complexity Relative TRS:
The TRS R consists of the following rules:
f(h) → f(i)
f(i) → a
i → h
S is empty.
Rewrite Strategy: FULL
(5) InfiniteLowerBoundProof (EQUIVALENT transformation)
The loop following loop proves infinite runtime complexity:
The rewrite sequence
f(h) →+ f(h)
gives rise to a decreasing loop by considering the right hand sides subterm at position [].
The pumping substitution is [ ].
The result substitution is [ ].
(6) BOUNDS(INF, INF)