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:

0(q0(0(x1))) → 0(0(q0(x1)))
0(q0(1(x1))) → 0(1(q0(x1)))
1(q0(0(x1))) → 0(0(q1(x1)))
1(q0(1(x1))) → 0(1(q1(x1)))
1(q1(0(x1))) → 1(0(q1(x1)))
1(q1(1(x1))) → 1(1(q1(x1)))
0(q1(0(x1))) → 0(0(q2(x1)))
0(q1(1(x1))) → 0(1(q2(x1)))
1(q2(0(x1))) → 1(0(q2(x1)))
1(q2(1(x1))) → 1(1(q2(x1)))
0(q2(x1)) → q3(1(x1))
1(q3(x1)) → q3(1(x1))
0(q3(x1)) → q4(0(x1))
1(q4(x1)) → q4(1(x1))
0(q4(0(x1))) → 1(0(q5(x1)))
0(q4(1(x1))) → 1(1(q5(x1)))
1(q5(0(x1))) → 0(0(q1(x1)))
1(q5(1(x1))) → 0(1(q1(x1)))
0(q5(x1)) → q6(0(x1))
1(q6(x1)) → q6(1(x1))
1(q7(0(x1))) → 0(0(q8(x1)))
1(q7(1(x1))) → 0(1(q8(x1)))
0(q8(x1)) → 0(q0(x1))
1(q8(0(x1))) → 1(0(q8(x1)))
1(q8(1(x1))) → 1(1(q8(x1)))
0(q6(x1)) → q9(0(x1))
0(q9(0(x1))) → 1(0(q7(x1)))
0(q9(1(x1))) → 1(1(q7(x1)))
1(q9(x1)) → q9(1(x1))
h(q0(x1)) → h(0(q0(x1)))
q0(h(x1)) → q0(0(h(x1)))
h(q1(x1)) → h(0(q1(x1)))
q1(h(x1)) → q1(0(h(x1)))
h(q2(x1)) → h(0(q2(x1)))
q2(h(x1)) → q2(0(h(x1)))
h(q3(x1)) → h(0(q3(x1)))
q3(h(x1)) → q3(0(h(x1)))
h(q4(x1)) → h(0(q4(x1)))
q4(h(x1)) → q4(0(h(x1)))
h(q5(x1)) → h(0(q5(x1)))
q5(h(x1)) → q5(0(h(x1)))
h(q6(x1)) → h(0(q6(x1)))
q6(h(x1)) → q6(0(h(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: 6521
Accept states: [6522, 6523, 6524, 6525, 6526, 6527, 6528, 6529, 6530, 6531]
Transitions:
6521→6522[0_1|0]
6521→6523[1_1|0]
6521→6524[h_1|0]
6521→6525[q0_1|0]
6521→6526[q1_1|0]
6521→6527[q2_1|0]
6521→6528[q3_1|0]
6521→6529[q4_1|0]
6521→6530[q5_1|0]
6521→6531[q6_1|0]
6521→6521[q7_1|0, q8_1|0, q9_1|0]
6521→6532[q0_1|1]
6521→6533[1_1|1]
6532→6522[0_1|1]
6533→6523[q9_1|1]
6533→6533[q9_1|1]

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