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:

b(a(b(x1))) → a(b(a(x1)))
b(b(a(x1))) → b(b(b(x1)))
c(a(x1)) → a(b(c(x1)))
c(b(x1)) → b(a(c(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: 1206
Accept states: [1207, 1208]
Transitions:
1206→1207[b_1|0]
1206→1208[c_1|0]
1206→1206[a_1|0]
1206→1209[c_1|1]
1209→1210[b_1|1]
1209→1211[a_1|2]
1210→1208[a_1|1]
1210→1209[a_1|1]
1211→1212[b_1|2]
1212→1210[a_1|2]

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