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) → b(x1)
b(b(b(c(x1)))) → c(c(a(a(a(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 1.
The certificate found is represented by the following graph.

Start state: 719
Accept states: [720, 721]
Transitions:
719→720[a_1|0, b_1|1]
719→721[b_1|0]
719→719[c_1|0]

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