(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
f(h(x), y) → h(f(y, f(x, h(a))))
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), y) → h(f(y, f(x, h(a))))
S is empty.
Rewrite Strategy: FULL
(3) InfiniteLowerBoundProof (EQUIVALENT transformation)
The loop following loop proves infinite runtime complexity:
The rewrite sequence
f(h(h(x5_0)), h(h(x363_0))) →+ h(h(f(h(h(f(f(x5_0, h(a)), f(a, h(a))))), h(h(f(f(x363_0, h(a)), f(a, h(a))))))))
gives rise to a decreasing loop by considering the right hand sides subterm at position [0,0].
The pumping substitution is [ ].
The result substitution is [x5_0 / f(f(x5_0, h(a)), f(a, h(a))), x363_0 / f(f(x363_0, h(a)), f(a, h(a)))].
(4) BOUNDS(INF, INF)