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:

s(b(x1)) → b(s(s(s(x1))))
s(b(s(x1))) → b(t(x1))
t(b(x1)) → b(s(x1))
t(b(s(x1))) → u(t(b(x1)))
b(u(x1)) → b(s(x1))
t(s(x1)) → t(t(x1))
t(u(x1)) → u(t(x1))
s(u(x1)) → s(s(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: 1553
Accept states: [1554, 1555, 1556]
Transitions:
1553→1554[s_1|0]
1553→1555[t_1|0]
1553→1556[b_1|0]
1553→1553[u_1|0]
1553→1557[s_1|1]
1553→1558[t_1|1]
1553→1559[s_1|1]
1557→1554[s_1|1]
1557→1557[s_1|1]
1557→1559[s_1|1]
1558→1555[u_1|1]
1558→1558[u_1|1]
1559→1556[b_1|1]

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