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(a(c(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: 1172
Accept states: [1173]
Transitions:
1172→1173[a_1|0]
1172→1172[b_1|0, c_1|0]
1172→1174[a_1|1]
1174→1173[b_1|1]
1174→1174[b_1|1]

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