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:

active(g(X)) → mark(h(X))
active(c) → mark(d)
active(h(d)) → mark(g(c))
proper(g(X)) → g(proper(X))
proper(h(X)) → h(proper(X))
proper(c) → ok(c)
proper(d) → ok(d)
g(ok(X)) → ok(g(X))
h(ok(X)) → ok(h(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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 4.
The certificate found is represented by the following graph.

Start state: 1
Accept states: [2]
Transitions:
1→2[active_1|0, proper_1|0, g_1|0, h_1|0, top_1|0]
1→3[mark_1|1]
1→4[ok_1|1]
1→5[ok_1|1]
1→6[ok_1|1]
1→7[ok_1|1]
1→8[top_1|1]
1→9[top_1|1]
1→10[top_1|2]
1→11[top_1|2]
1→14[top_1|3]
1→15[top_1|3]
1→17[top_1|4]
2→2[mark_1|0, c|0, d|0, ok_1|0]
3→2[d|1]
4→2[c|1]
5→2[d|1]
6→2[g_1|1]
6→6[ok_1|1]
7→2[h_1|1]
7→7[ok_1|1]
8→2[proper_1|1]
8→4[ok_1|1]
8→5[ok_1|1]
9→2[active_1|1]
9→3[mark_1|1]
10→4[active_1|2]
10→5[active_1|2]
10→12[mark_1|2]
11→3[proper_1|2]
11→13[ok_1|2]
12→2[d|2]
13→2[d|2]
14→12[proper_1|3]
14→16[ok_1|3]
15→13[active_1|3]
16→2[d|3]
17→16[active_1|4]

(2) BOUNDS(1, n^1)