(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
a(b(x)) → b(b(a(a(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:
a(b(x)) → b(b(a(a(x))))
S is empty.
Rewrite Strategy: FULL
(3) InfiniteLowerBoundProof (EQUIVALENT transformation)
The loop following loop proves infinite runtime complexity:
The rewrite sequence
a(b(b(x1_0))) →+ b(b(a(b(b(a(a(x1_0)))))))
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 [x1_0 / a(a(x1_0))].
(4) BOUNDS(INF, INF)