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(x1) → x1
a(b(x1)) → b(b(a(a(c(a(x1))))))
c(c(b(x1))) → 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 2.
The certificate found is represented by the following graph.

Start state: 620
Accept states: [621, 622]
Transitions:
620→621[a_1|0]
620→622[c_1|0]
620→620[b_1|0]
620→623[a_1|1]
620→624[c_1|2]
623→624[c_1|1]
624→625[a_1|1]
624→626[a_1|2]
624→627[b_1|2]
625→626[a_1|1]
625→627[b_1|2]
626→627[b_1|1]
627→621[b_1|1]
627→623[b_1|1]

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