The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(O(1), O(n^1)).

(0) Obligation:

Runtime Complexity TRS:
The TRS R consists of the following rules:

a(a(b(x1))) → c(b(a(a(a(x1)))))
a(c(x1)) → b(a(x1))

Rewrite Strategy: INNERMOST

(1) CpxTrsMatchBoundsProof (EQUIVALENT transformation)

A linear upper bound on the runtime complexity of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1.
The certificate found is represented by the following graph.

Start state: 928
Accept states: [929]
Transitions:
928→929[a_1|0]
928→928[b_1|0, c_1|0]
928→930[a_1|1]
930→929[b_1|1]
930→930[b_1|1]

(2) BOUNDS(O(1), O(n^1))