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)) → c(a(c(x1)))
c(c(x1)) → b(b(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: 452
Accept states: [453, 454]
Transitions:
452→453[a_1|0]
452→454[c_1|0]
452→452[b_1|0]
452→455[c_1|1]
452→457[a_1|2]
452→458[b_1|3]
455→456[a_1|1]
455→453[c_1|2]
455→457[c_1|2]
456→453[c_1|1]
456→457[c_1|1]
457→458[b_1|2]
458→459[b_1|2]
459→453[b_1|2]
459→457[b_1|2]

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