(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
f(x, g(x)) → x
f(x, h(y)) → f(h(x), y)
Rewrite Strategy: INNERMOST
(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(x, g(x)) → x
f(x, h(y)) → f(h(x), y)
S is empty.
Rewrite Strategy: INNERMOST
(3) DecreasingLoopProof (EQUIVALENT transformation)
The following loop(s) give(s) rise to the lower bound Ω(n1):
The rewrite sequence
f(x, h(y)) →+ f(h(x), y)
gives rise to a decreasing loop by considering the right hand sides subterm at position [].
The pumping substitution is [y / h(y)].
The result substitution is [x / h(x)].
(4) BOUNDS(n^1, INF)