The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).

(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) 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))].

(2) BOUNDS(INF, INF)