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(c(a(c(x1)))))
c(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 3.
The certificate found is represented by the following graph.

Start state: 437
Accept states: [438, 439]
Transitions:
437→438[a_1|0]
437→439[c_1|0]
437→437[b_1|0]
437→440[c_1|1]
437→444[a_1|2]
437→442[b_1|3]
440→441[a_1|1]
440→442[c_1|2]
441→442[c_1|1]
442→443[b_1|1]
443→438[b_1|1]
443→444[b_1|1]
444→442[b_1|2]

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