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

Start state: 1107
Accept states: [1108, 1109]
Transitions:
1107→1108[a_1|0]
1107→1109[b_1|0]
1107→1107[c_1|0]
1107→1110[a_1|1]
1107→1111[b_1|2]
1110→1111[b_1|1]
1111→1109[c_1|1]
1111→1111[c_1|1]

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