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)) → x1
a(c(x1)) → c(c(a(a(b(x1)))))
b(b(x1)) → 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: 1017
Accept states: [1018, 1019]
Transitions:
1017→1018[a_1|0]
1017→1019[b_1|0]
1017→1017[c_1|0]
1017→1020[b_1|1]
1017→1022[a_1|2]
1017→1023[c_1|2]
1020→1021[a_1|1]
1020→1022[a_1|2]
1020→1023[c_1|2]
1021→1022[a_1|1]
1021→1023[c_1|2]
1022→1023[c_1|1]
1023→1018[c_1|1]
1023→1022[c_1|1]

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