The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1).

(0) Obligation:

Runtime Complexity TRS:
The TRS R consists of the following rules:

a__g(X) → a__h(X)
a__c → d
a__h(d) → a__g(c)
mark(g(X)) → a__g(X)
mark(h(X)) → a__h(X)
mark(c) → a__c
mark(d) → d
a__g(X) → g(X)
a__h(X) → h(X)
a__c → c

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 3.
The certificate found is represented by the following graph.

Start state: 1
Accept states: [2]
Transitions:
1→2[a__g_1|0, a__c|0, a__h_1|0, mark_1|0, a__h_1|1, g_1|1, d|1, c|1, h_1|1, a__g_1|1, a__c|1, a__h_1|2, g_1|2, d|2, c|2, h_1|2, h_1|3]
1→3[a__g_1|1, a__h_1|2, g_1|2, h_1|3]
2→2[d|0, c|0, g_1|0, h_1|0]
3→2[c|1]

(2) BOUNDS(1, n^1)