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

(0) Obligation:

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

start(i) → busy(F, closed, stop, false, false, false, i)
busy(BF, d, stop, b1, b2, b3, i) → incorrect
busy(FS, d, stop, b1, b2, b3, i) → incorrect
busy(fl, open, up, b1, b2, b3, i) → incorrect
busy(fl, open, down, b1, b2, b3, i) → incorrect
busy(B, closed, stop, false, false, false, empty) → correct
busy(F, closed, stop, false, false, false, empty) → correct
busy(S, closed, stop, false, false, false, empty) → correct
busy(B, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) → idle(B, closed, stop, false, false, false, newbuttons(i1, i2, i3, i))
busy(F, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) → idle(F, closed, stop, false, false, false, newbuttons(i1, i2, i3, i))
busy(S, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) → idle(S, closed, stop, false, false, false, newbuttons(i1, i2, i3, i))
busy(B, open, stop, false, b2, b3, i) → idle(B, closed, stop, false, b2, b3, i)
busy(F, open, stop, b1, false, b3, i) → idle(F, closed, stop, b1, false, b3, i)
busy(S, open, stop, b1, b2, false, i) → idle(S, closed, stop, b1, b2, false, i)
busy(B, d, stop, true, b2, b3, i) → idle(B, open, stop, false, b2, b3, i)
busy(F, d, stop, b1, true, b3, i) → idle(F, open, stop, b1, false, b3, i)
busy(S, d, stop, b1, b2, true, i) → idle(S, open, stop, b1, b2, false, i)
busy(B, closed, down, b1, b2, b3, i) → idle(B, closed, stop, b1, b2, b3, i)
busy(S, closed, up, b1, b2, b3, i) → idle(S, closed, stop, b1, b2, b3, i)
busy(B, closed, up, true, b2, b3, i) → idle(B, closed, stop, true, b2, b3, i)
busy(F, closed, up, b1, true, b3, i) → idle(F, closed, stop, b1, true, b3, i)
busy(F, closed, down, b1, true, b3, i) → idle(F, closed, stop, b1, true, b3, i)
busy(S, closed, down, b1, b2, true, i) → idle(S, closed, stop, b1, b2, true, i)
busy(B, closed, up, false, b2, b3, i) → idle(BF, closed, up, false, b2, b3, i)
busy(F, closed, up, b1, false, b3, i) → idle(FS, closed, up, b1, false, b3, i)
busy(F, closed, down, b1, false, b3, i) → idle(BF, closed, down, b1, false, b3, i)
busy(S, closed, down, b1, b2, false, i) → idle(FS, closed, down, b1, b2, false, i)
busy(BF, closed, up, b1, b2, b3, i) → idle(F, closed, up, b1, b2, b3, i)
busy(BF, closed, down, b1, b2, b3, i) → idle(B, closed, down, b1, b2, b3, i)
busy(FS, closed, up, b1, b2, b3, i) → idle(S, closed, up, b1, b2, b3, i)
busy(FS, closed, down, b1, b2, b3, i) → idle(F, closed, down, b1, b2, b3, i)
busy(B, closed, stop, false, true, b3, i) → idle(B, closed, up, false, true, b3, i)
busy(B, closed, stop, false, false, true, i) → idle(B, closed, up, false, false, true, i)
busy(F, closed, stop, true, false, b3, i) → idle(F, closed, down, true, false, b3, i)
busy(F, closed, stop, false, false, true, i) → idle(F, closed, up, false, false, true, i)
busy(S, closed, stop, b1, true, false, i) → idle(S, closed, down, b1, true, false, i)
busy(S, closed, stop, true, false, false, i) → idle(S, closed, down, true, false, false, i)
idle(fl, d, m, b1, b2, b3, empty) → busy(fl, d, m, b1, b2, b3, empty)
idle(fl, d, m, b1, b2, b3, newbuttons(i1, i2, i3, i)) → busy(fl, d, m, or(b1, i1), or(b2, i2), or(b3, i3), i)
or(true, b) → true
or(false, b) → b

Rewrite Strategy: FULL

(1) DecreasingLoopProof (EQUIVALENT transformation)

The following loop(s) give(s) rise to the lower bound Ω(n¹):
The rewrite sequence
idle(B, d, stop, false, b2, b3, newbuttons(true, i2, i3, i)) →⁺ idle(B, open, stop, false, or(b2, i2), or(b3, i3), i)
gives rise to a decreasing loop by considering the right hand sides subterm at position [].
The pumping substitution is [i / newbuttons(true, i2, i3, i)].
The result substitution is [d / open, b2 / or(b2, i2), b3 / or(b3, i3)].

(2) BOUNDS(n^1, INF)