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:

active(f(X)) → mark(g(h(f(X))))
active(f(X)) → f(active(X))
active(h(X)) → h(active(X))
f(mark(X)) → mark(f(X))
h(mark(X)) → mark(h(X))
proper(f(X)) → f(proper(X))
proper(g(X)) → g(proper(X))
proper(h(X)) → h(proper(X))
f(ok(X)) → ok(f(X))
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 1.
The certificate found is represented by the following graph.

Start state: 3506
Accept states: [3507, 3508, 3509, 3510, 3511, 3512]
Transitions:
3506→3507[active_1|0]
3506→3508[f_1|0]
3506→3509[h_1|0]
3506→3510[proper_1|0]
3506→3511[g_1|0]
3506→3512[top_1|0]
3506→3506[mark_1|0, ok_1|0]
3506→3513[f_1|1]
3506→3514[h_1|1]
3506→3515[proper_1|1]
3506→3516[f_1|1]
3506→3517[h_1|1]
3506→3518[g_1|1]
3506→3519[active_1|1]
3513→3508[mark_1|1]
3513→3513[mark_1|1]
3513→3516[mark_1|1]
3514→3509[mark_1|1]
3514→3514[mark_1|1]
3514→3517[mark_1|1]
3515→3512[top_1|1]
3516→3508[ok_1|1]
3516→3513[ok_1|1]
3516→3516[ok_1|1]
3517→3509[ok_1|1]
3517→3514[ok_1|1]
3517→3517[ok_1|1]
3518→3511[ok_1|1]
3518→3518[ok_1|1]
3519→3512[top_1|1]

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