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

Start state: 450
Accept states: [451, 452]
Transitions:
450→451[a_1|0]
450→452[c_1|0]
450→450[b_1|0]
450→453[a_1|1]
450→454[c_1|2]
453→454[c_1|1]
454→455[a_1|1]
454→456[b_1|2]
455→456[b_1|1]
456→451[b_1|1]
456→453[b_1|1]

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