Termination w.r.t. Q proof of TRS/HMt009.trs

Termination w.r.t. Q of the following Term Rewriting System could not be shown:

Q restricted rewrite system:
The TRS R consists of the following rules:

start₁(i) -> busy₇(F, closed, stop, false, false, false, i)
busy₇(BF, d, stop, b1, b2, b3, i) -> incorrect
busy₇(FS, d, stop, b1, b2, b3, i) -> incorrect
busy₇(fl, open, up, b1, b2, b3, i) -> incorrect
busy₇(fl, open, down, b1, b2, b3, i) -> incorrect
busy₇(B, closed, stop, false, false, false, empty) -> correct
busy₇(F, closed, stop, false, false, false, empty) -> correct
busy₇(S, closed, stop, false, false, false, empty) -> correct
busy₇(B, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i)) -> idle₇(B, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i))
busy₇(F, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i)) -> idle₇(F, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i))
busy₇(S, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i)) -> idle₇(S, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i))
busy₇(B, open, stop, false, b2, b3, i) -> idle₇(B, closed, stop, false, b2, b3, i)
busy₇(F, open, stop, b1, false, b3, i) -> idle₇(F, closed, stop, b1, false, b3, i)
busy₇(S, open, stop, b1, b2, false, i) -> idle₇(S, closed, stop, b1, b2, false, i)
busy₇(B, d, stop, true, b2, b3, i) -> idle₇(B, open, stop, false, b2, b3, i)
busy₇(F, d, stop, b1, true, b3, i) -> idle₇(F, open, stop, b1, false, b3, i)
busy₇(S, d, stop, b1, b2, true, i) -> idle₇(S, open, stop, b1, b2, false, i)
busy₇(B, closed, down, b1, b2, b3, i) -> idle₇(B, closed, stop, b1, b2, b3, i)
busy₇(S, closed, up, b1, b2, b3, i) -> idle₇(S, closed, stop, b1, b2, b3, i)
busy₇(B, closed, up, true, b2, b3, i) -> idle₇(B, closed, stop, true, b2, b3, i)
busy₇(F, closed, up, b1, true, b3, i) -> idle₇(F, closed, stop, b1, true, b3, i)
busy₇(F, closed, down, b1, true, b3, i) -> idle₇(F, closed, stop, b1, true, b3, i)
busy₇(S, closed, down, b1, b2, true, i) -> idle₇(S, closed, stop, b1, b2, true, i)
busy₇(B, closed, up, false, b2, b3, i) -> idle₇(BF, closed, up, false, b2, b3, i)
busy₇(F, closed, up, b1, false, b3, i) -> idle₇(FS, closed, up, b1, false, b3, i)
busy₇(F, closed, down, b1, false, b3, i) -> idle₇(BF, closed, down, b1, false, b3, i)
busy₇(S, closed, down, b1, b2, false, i) -> idle₇(FS, closed, down, b1, b2, false, i)
busy₇(BF, closed, up, b1, b2, b3, i) -> idle₇(F, closed, up, b1, b2, b3, i)
busy₇(BF, closed, down, b1, b2, b3, i) -> idle₇(B, closed, down, b1, b2, b3, i)
busy₇(FS, closed, up, b1, b2, b3, i) -> idle₇(S, closed, up, b1, b2, b3, i)
busy₇(FS, closed, down, b1, b2, b3, i) -> idle₇(F, closed, down, b1, b2, b3, i)
busy₇(B, closed, stop, false, true, b3, i) -> idle₇(B, closed, up, false, true, b3, i)
busy₇(B, closed, stop, false, false, true, i) -> idle₇(B, closed, up, false, false, true, i)
busy₇(F, closed, stop, true, false, b3, i) -> idle₇(F, closed, down, true, false, b3, i)
busy₇(F, closed, stop, false, false, true, i) -> idle₇(F, closed, up, false, false, true, i)
busy₇(S, closed, stop, b1, true, false, i) -> idle₇(S, closed, down, b1, true, false, i)
busy₇(S, closed, stop, true, false, false, i) -> idle₇(S, closed, down, true, false, false, i)
idle₇(fl, d, m, b1, b2, b3, empty) -> busy₇(fl, d, m, b1, b2, b3, empty)
idle₇(fl, d, m, b1, b2, b3, newbuttons₄(i1, i2, i3, i)) -> busy₇(fl, d, m, or₂(b1, i1), or₂(b2, i2), or₂(b3, i3), i)
or₂(true, b) -> true
or₂(false, b) -> b

Q is empty.

↳ QTRS

  ↳ DependencyPairsProof

Q restricted rewrite system:
The TRS R consists of the following rules:

start₁(i) -> busy₇(F, closed, stop, false, false, false, i)
busy₇(BF, d, stop, b1, b2, b3, i) -> incorrect
busy₇(FS, d, stop, b1, b2, b3, i) -> incorrect
busy₇(fl, open, up, b1, b2, b3, i) -> incorrect
busy₇(fl, open, down, b1, b2, b3, i) -> incorrect
busy₇(B, closed, stop, false, false, false, empty) -> correct
busy₇(F, closed, stop, false, false, false, empty) -> correct
busy₇(S, closed, stop, false, false, false, empty) -> correct
busy₇(B, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i)) -> idle₇(B, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i))
busy₇(F, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i)) -> idle₇(F, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i))
busy₇(S, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i)) -> idle₇(S, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i))
busy₇(B, open, stop, false, b2, b3, i) -> idle₇(B, closed, stop, false, b2, b3, i)
busy₇(F, open, stop, b1, false, b3, i) -> idle₇(F, closed, stop, b1, false, b3, i)
busy₇(S, open, stop, b1, b2, false, i) -> idle₇(S, closed, stop, b1, b2, false, i)
busy₇(B, d, stop, true, b2, b3, i) -> idle₇(B, open, stop, false, b2, b3, i)
busy₇(F, d, stop, b1, true, b3, i) -> idle₇(F, open, stop, b1, false, b3, i)
busy₇(S, d, stop, b1, b2, true, i) -> idle₇(S, open, stop, b1, b2, false, i)
busy₇(B, closed, down, b1, b2, b3, i) -> idle₇(B, closed, stop, b1, b2, b3, i)
busy₇(S, closed, up, b1, b2, b3, i) -> idle₇(S, closed, stop, b1, b2, b3, i)
busy₇(B, closed, up, true, b2, b3, i) -> idle₇(B, closed, stop, true, b2, b3, i)
busy₇(F, closed, up, b1, true, b3, i) -> idle₇(F, closed, stop, b1, true, b3, i)
busy₇(F, closed, down, b1, true, b3, i) -> idle₇(F, closed, stop, b1, true, b3, i)
busy₇(S, closed, down, b1, b2, true, i) -> idle₇(S, closed, stop, b1, b2, true, i)
busy₇(B, closed, up, false, b2, b3, i) -> idle₇(BF, closed, up, false, b2, b3, i)
busy₇(F, closed, up, b1, false, b3, i) -> idle₇(FS, closed, up, b1, false, b3, i)
busy₇(F, closed, down, b1, false, b3, i) -> idle₇(BF, closed, down, b1, false, b3, i)
busy₇(S, closed, down, b1, b2, false, i) -> idle₇(FS, closed, down, b1, b2, false, i)
busy₇(BF, closed, up, b1, b2, b3, i) -> idle₇(F, closed, up, b1, b2, b3, i)
busy₇(BF, closed, down, b1, b2, b3, i) -> idle₇(B, closed, down, b1, b2, b3, i)
busy₇(FS, closed, up, b1, b2, b3, i) -> idle₇(S, closed, up, b1, b2, b3, i)
busy₇(FS, closed, down, b1, b2, b3, i) -> idle₇(F, closed, down, b1, b2, b3, i)
busy₇(B, closed, stop, false, true, b3, i) -> idle₇(B, closed, up, false, true, b3, i)
busy₇(B, closed, stop, false, false, true, i) -> idle₇(B, closed, up, false, false, true, i)
busy₇(F, closed, stop, true, false, b3, i) -> idle₇(F, closed, down, true, false, b3, i)
busy₇(F, closed, stop, false, false, true, i) -> idle₇(F, closed, up, false, false, true, i)
busy₇(S, closed, stop, b1, true, false, i) -> idle₇(S, closed, down, b1, true, false, i)
busy₇(S, closed, stop, true, false, false, i) -> idle₇(S, closed, down, true, false, false, i)
idle₇(fl, d, m, b1, b2, b3, empty) -> busy₇(fl, d, m, b1, b2, b3, empty)
idle₇(fl, d, m, b1, b2, b3, newbuttons₄(i1, i2, i3, i)) -> busy₇(fl, d, m, or₂(b1, i1), or₂(b2, i2), or₂(b3, i3), i)
or₂(true, b) -> true
or₂(false, b) -> b

Q is empty.

Using Dependency Pairs [1,13] we result in the following initial DP problem:
Q DP problem:
The TRS P consists of the following rules:

BUSY₇(S, closed, stop, true, false, false, i) -> IDLE₇(S, closed, down, true, false, false, i)
IDLE₇(fl, d, m, b1, b2, b3, newbuttons₄(i1, i2, i3, i)) -> BUSY₇(fl, d, m, or₂(b1, i1), or₂(b2, i2), or₂(b3, i3), i)
BUSY₇(B, open, stop, false, b2, b3, i) -> IDLE₇(B, closed, stop, false, b2, b3, i)
BUSY₇(S, d, stop, b1, b2, true, i) -> IDLE₇(S, open, stop, b1, b2, false, i)
BUSY₇(F, open, stop, b1, false, b3, i) -> IDLE₇(F, closed, stop, b1, false, b3, i)
BUSY₇(S, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i)) -> IDLE₇(S, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i))
BUSY₇(F, closed, stop, true, false, b3, i) -> IDLE₇(F, closed, down, true, false, b3, i)
BUSY₇(B, closed, stop, false, true, b3, i) -> IDLE₇(B, closed, up, false, true, b3, i)
BUSY₇(F, closed, stop, false, false, true, i) -> IDLE₇(F, closed, up, false, false, true, i)
BUSY₇(S, open, stop, b1, b2, false, i) -> IDLE₇(S, closed, stop, b1, b2, false, i)
BUSY₇(BF, closed, down, b1, b2, b3, i) -> IDLE₇(B, closed, down, b1, b2, b3, i)
IDLE₇(fl, d, m, b1, b2, b3, newbuttons₄(i1, i2, i3, i)) -> OR₂(b3, i3)
START₁(i) -> BUSY₇(F, closed, stop, false, false, false, i)
IDLE₇(fl, d, m, b1, b2, b3, newbuttons₄(i1, i2, i3, i)) -> OR₂(b2, i2)
BUSY₇(BF, closed, up, b1, b2, b3, i) -> IDLE₇(F, closed, up, b1, b2, b3, i)
BUSY₇(F, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i)) -> IDLE₇(F, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i))
BUSY₇(F, d, stop, b1, true, b3, i) -> IDLE₇(F, open, stop, b1, false, b3, i)
BUSY₇(B, closed, stop, false, false, true, i) -> IDLE₇(B, closed, up, false, false, true, i)
BUSY₇(F, closed, down, b1, false, b3, i) -> IDLE₇(BF, closed, down, b1, false, b3, i)
BUSY₇(FS, closed, down, b1, b2, b3, i) -> IDLE₇(F, closed, down, b1, b2, b3, i)
BUSY₇(S, closed, stop, b1, true, false, i) -> IDLE₇(S, closed, down, b1, true, false, i)
BUSY₇(F, closed, up, b1, true, b3, i) -> IDLE₇(F, closed, stop, b1, true, b3, i)
BUSY₇(S, closed, down, b1, b2, true, i) -> IDLE₇(S, closed, stop, b1, b2, true, i)
BUSY₇(F, closed, up, b1, false, b3, i) -> IDLE₇(FS, closed, up, b1, false, b3, i)
BUSY₇(F, closed, down, b1, true, b3, i) -> IDLE₇(F, closed, stop, b1, true, b3, i)
BUSY₇(B, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i)) -> IDLE₇(B, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i))
IDLE₇(fl, d, m, b1, b2, b3, newbuttons₄(i1, i2, i3, i)) -> OR₂(b1, i1)
IDLE₇(fl, d, m, b1, b2, b3, empty) -> BUSY₇(fl, d, m, b1, b2, b3, empty)
BUSY₇(S, closed, up, b1, b2, b3, i) -> IDLE₇(S, closed, stop, b1, b2, b3, i)
BUSY₇(B, closed, up, false, b2, b3, i) -> IDLE₇(BF, closed, up, false, b2, b3, i)
BUSY₇(B, d, stop, true, b2, b3, i) -> IDLE₇(B, open, stop, false, b2, b3, i)
BUSY₇(S, closed, down, b1, b2, false, i) -> IDLE₇(FS, closed, down, b1, b2, false, i)
BUSY₇(B, closed, up, true, b2, b3, i) -> IDLE₇(B, closed, stop, true, b2, b3, i)
BUSY₇(B, closed, down, b1, b2, b3, i) -> IDLE₇(B, closed, stop, b1, b2, b3, i)
BUSY₇(FS, closed, up, b1, b2, b3, i) -> IDLE₇(S, closed, up, b1, b2, b3, i)

The TRS R consists of the following rules:

start₁(i) -> busy₇(F, closed, stop, false, false, false, i)
busy₇(BF, d, stop, b1, b2, b3, i) -> incorrect
busy₇(FS, d, stop, b1, b2, b3, i) -> incorrect
busy₇(fl, open, up, b1, b2, b3, i) -> incorrect
busy₇(fl, open, down, b1, b2, b3, i) -> incorrect
busy₇(B, closed, stop, false, false, false, empty) -> correct
busy₇(F, closed, stop, false, false, false, empty) -> correct
busy₇(S, closed, stop, false, false, false, empty) -> correct
busy₇(B, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i)) -> idle₇(B, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i))
busy₇(F, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i)) -> idle₇(F, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i))
busy₇(S, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i)) -> idle₇(S, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i))
busy₇(B, open, stop, false, b2, b3, i) -> idle₇(B, closed, stop, false, b2, b3, i)
busy₇(F, open, stop, b1, false, b3, i) -> idle₇(F, closed, stop, b1, false, b3, i)
busy₇(S, open, stop, b1, b2, false, i) -> idle₇(S, closed, stop, b1, b2, false, i)
busy₇(B, d, stop, true, b2, b3, i) -> idle₇(B, open, stop, false, b2, b3, i)
busy₇(F, d, stop, b1, true, b3, i) -> idle₇(F, open, stop, b1, false, b3, i)
busy₇(S, d, stop, b1, b2, true, i) -> idle₇(S, open, stop, b1, b2, false, i)
busy₇(B, closed, down, b1, b2, b3, i) -> idle₇(B, closed, stop, b1, b2, b3, i)
busy₇(S, closed, up, b1, b2, b3, i) -> idle₇(S, closed, stop, b1, b2, b3, i)
busy₇(B, closed, up, true, b2, b3, i) -> idle₇(B, closed, stop, true, b2, b3, i)
busy₇(F, closed, up, b1, true, b3, i) -> idle₇(F, closed, stop, b1, true, b3, i)
busy₇(F, closed, down, b1, true, b3, i) -> idle₇(F, closed, stop, b1, true, b3, i)
busy₇(S, closed, down, b1, b2, true, i) -> idle₇(S, closed, stop, b1, b2, true, i)
busy₇(B, closed, up, false, b2, b3, i) -> idle₇(BF, closed, up, false, b2, b3, i)
busy₇(F, closed, up, b1, false, b3, i) -> idle₇(FS, closed, up, b1, false, b3, i)
busy₇(F, closed, down, b1, false, b3, i) -> idle₇(BF, closed, down, b1, false, b3, i)
busy₇(S, closed, down, b1, b2, false, i) -> idle₇(FS, closed, down, b1, b2, false, i)
busy₇(BF, closed, up, b1, b2, b3, i) -> idle₇(F, closed, up, b1, b2, b3, i)
busy₇(BF, closed, down, b1, b2, b3, i) -> idle₇(B, closed, down, b1, b2, b3, i)
busy₇(FS, closed, up, b1, b2, b3, i) -> idle₇(S, closed, up, b1, b2, b3, i)
busy₇(FS, closed, down, b1, b2, b3, i) -> idle₇(F, closed, down, b1, b2, b3, i)
busy₇(B, closed, stop, false, true, b3, i) -> idle₇(B, closed, up, false, true, b3, i)
busy₇(B, closed, stop, false, false, true, i) -> idle₇(B, closed, up, false, false, true, i)
busy₇(F, closed, stop, true, false, b3, i) -> idle₇(F, closed, down, true, false, b3, i)
busy₇(F, closed, stop, false, false, true, i) -> idle₇(F, closed, up, false, false, true, i)
busy₇(S, closed, stop, b1, true, false, i) -> idle₇(S, closed, down, b1, true, false, i)
busy₇(S, closed, stop, true, false, false, i) -> idle₇(S, closed, down, true, false, false, i)
idle₇(fl, d, m, b1, b2, b3, empty) -> busy₇(fl, d, m, b1, b2, b3, empty)
idle₇(fl, d, m, b1, b2, b3, newbuttons₄(i1, i2, i3, i)) -> busy₇(fl, d, m, or₂(b1, i1), or₂(b2, i2), or₂(b3, i3), i)
or₂(true, b) -> true
or₂(false, b) -> b

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

Q DP problem:
The TRS P consists of the following rules:

BUSY₇(S, closed, stop, true, false, false, i) -> IDLE₇(S, closed, down, true, false, false, i)
IDLE₇(fl, d, m, b1, b2, b3, newbuttons₄(i1, i2, i3, i)) -> BUSY₇(fl, d, m, or₂(b1, i1), or₂(b2, i2), or₂(b3, i3), i)
BUSY₇(B, open, stop, false, b2, b3, i) -> IDLE₇(B, closed, stop, false, b2, b3, i)
BUSY₇(S, d, stop, b1, b2, true, i) -> IDLE₇(S, open, stop, b1, b2, false, i)
BUSY₇(F, open, stop, b1, false, b3, i) -> IDLE₇(F, closed, stop, b1, false, b3, i)
BUSY₇(S, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i)) -> IDLE₇(S, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i))
BUSY₇(F, closed, stop, true, false, b3, i) -> IDLE₇(F, closed, down, true, false, b3, i)
BUSY₇(B, closed, stop, false, true, b3, i) -> IDLE₇(B, closed, up, false, true, b3, i)
BUSY₇(F, closed, stop, false, false, true, i) -> IDLE₇(F, closed, up, false, false, true, i)
BUSY₇(S, open, stop, b1, b2, false, i) -> IDLE₇(S, closed, stop, b1, b2, false, i)
BUSY₇(BF, closed, down, b1, b2, b3, i) -> IDLE₇(B, closed, down, b1, b2, b3, i)
IDLE₇(fl, d, m, b1, b2, b3, newbuttons₄(i1, i2, i3, i)) -> OR₂(b3, i3)
START₁(i) -> BUSY₇(F, closed, stop, false, false, false, i)
IDLE₇(fl, d, m, b1, b2, b3, newbuttons₄(i1, i2, i3, i)) -> OR₂(b2, i2)
BUSY₇(BF, closed, up, b1, b2, b3, i) -> IDLE₇(F, closed, up, b1, b2, b3, i)
BUSY₇(F, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i)) -> IDLE₇(F, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i))
BUSY₇(F, d, stop, b1, true, b3, i) -> IDLE₇(F, open, stop, b1, false, b3, i)
BUSY₇(B, closed, stop, false, false, true, i) -> IDLE₇(B, closed, up, false, false, true, i)
BUSY₇(F, closed, down, b1, false, b3, i) -> IDLE₇(BF, closed, down, b1, false, b3, i)
BUSY₇(FS, closed, down, b1, b2, b3, i) -> IDLE₇(F, closed, down, b1, b2, b3, i)
BUSY₇(S, closed, stop, b1, true, false, i) -> IDLE₇(S, closed, down, b1, true, false, i)
BUSY₇(F, closed, up, b1, true, b3, i) -> IDLE₇(F, closed, stop, b1, true, b3, i)
BUSY₇(S, closed, down, b1, b2, true, i) -> IDLE₇(S, closed, stop, b1, b2, true, i)
BUSY₇(F, closed, up, b1, false, b3, i) -> IDLE₇(FS, closed, up, b1, false, b3, i)
BUSY₇(F, closed, down, b1, true, b3, i) -> IDLE₇(F, closed, stop, b1, true, b3, i)
BUSY₇(B, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i)) -> IDLE₇(B, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i))
IDLE₇(fl, d, m, b1, b2, b3, newbuttons₄(i1, i2, i3, i)) -> OR₂(b1, i1)
IDLE₇(fl, d, m, b1, b2, b3, empty) -> BUSY₇(fl, d, m, b1, b2, b3, empty)
BUSY₇(S, closed, up, b1, b2, b3, i) -> IDLE₇(S, closed, stop, b1, b2, b3, i)
BUSY₇(B, closed, up, false, b2, b3, i) -> IDLE₇(BF, closed, up, false, b2, b3, i)
BUSY₇(B, d, stop, true, b2, b3, i) -> IDLE₇(B, open, stop, false, b2, b3, i)
BUSY₇(S, closed, down, b1, b2, false, i) -> IDLE₇(FS, closed, down, b1, b2, false, i)
BUSY₇(B, closed, up, true, b2, b3, i) -> IDLE₇(B, closed, stop, true, b2, b3, i)
BUSY₇(B, closed, down, b1, b2, b3, i) -> IDLE₇(B, closed, stop, b1, b2, b3, i)
BUSY₇(FS, closed, up, b1, b2, b3, i) -> IDLE₇(S, closed, up, b1, b2, b3, i)

The TRS R consists of the following rules:

start₁(i) -> busy₇(F, closed, stop, false, false, false, i)
busy₇(BF, d, stop, b1, b2, b3, i) -> incorrect
busy₇(FS, d, stop, b1, b2, b3, i) -> incorrect
busy₇(fl, open, up, b1, b2, b3, i) -> incorrect
busy₇(fl, open, down, b1, b2, b3, i) -> incorrect
busy₇(B, closed, stop, false, false, false, empty) -> correct
busy₇(F, closed, stop, false, false, false, empty) -> correct
busy₇(S, closed, stop, false, false, false, empty) -> correct
busy₇(B, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i)) -> idle₇(B, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i))
busy₇(F, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i)) -> idle₇(F, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i))
busy₇(S, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i)) -> idle₇(S, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i))
busy₇(B, open, stop, false, b2, b3, i) -> idle₇(B, closed, stop, false, b2, b3, i)
busy₇(F, open, stop, b1, false, b3, i) -> idle₇(F, closed, stop, b1, false, b3, i)
busy₇(S, open, stop, b1, b2, false, i) -> idle₇(S, closed, stop, b1, b2, false, i)
busy₇(B, d, stop, true, b2, b3, i) -> idle₇(B, open, stop, false, b2, b3, i)
busy₇(F, d, stop, b1, true, b3, i) -> idle₇(F, open, stop, b1, false, b3, i)
busy₇(S, d, stop, b1, b2, true, i) -> idle₇(S, open, stop, b1, b2, false, i)
busy₇(B, closed, down, b1, b2, b3, i) -> idle₇(B, closed, stop, b1, b2, b3, i)
busy₇(S, closed, up, b1, b2, b3, i) -> idle₇(S, closed, stop, b1, b2, b3, i)
busy₇(B, closed, up, true, b2, b3, i) -> idle₇(B, closed, stop, true, b2, b3, i)
busy₇(F, closed, up, b1, true, b3, i) -> idle₇(F, closed, stop, b1, true, b3, i)
busy₇(F, closed, down, b1, true, b3, i) -> idle₇(F, closed, stop, b1, true, b3, i)
busy₇(S, closed, down, b1, b2, true, i) -> idle₇(S, closed, stop, b1, b2, true, i)
busy₇(B, closed, up, false, b2, b3, i) -> idle₇(BF, closed, up, false, b2, b3, i)
busy₇(F, closed, up, b1, false, b3, i) -> idle₇(FS, closed, up, b1, false, b3, i)
busy₇(F, closed, down, b1, false, b3, i) -> idle₇(BF, closed, down, b1, false, b3, i)
busy₇(S, closed, down, b1, b2, false, i) -> idle₇(FS, closed, down, b1, b2, false, i)
busy₇(BF, closed, up, b1, b2, b3, i) -> idle₇(F, closed, up, b1, b2, b3, i)
busy₇(BF, closed, down, b1, b2, b3, i) -> idle₇(B, closed, down, b1, b2, b3, i)
busy₇(FS, closed, up, b1, b2, b3, i) -> idle₇(S, closed, up, b1, b2, b3, i)
busy₇(FS, closed, down, b1, b2, b3, i) -> idle₇(F, closed, down, b1, b2, b3, i)
busy₇(B, closed, stop, false, true, b3, i) -> idle₇(B, closed, up, false, true, b3, i)
busy₇(B, closed, stop, false, false, true, i) -> idle₇(B, closed, up, false, false, true, i)
busy₇(F, closed, stop, true, false, b3, i) -> idle₇(F, closed, down, true, false, b3, i)
busy₇(F, closed, stop, false, false, true, i) -> idle₇(F, closed, up, false, false, true, i)
busy₇(S, closed, stop, b1, true, false, i) -> idle₇(S, closed, down, b1, true, false, i)
busy₇(S, closed, stop, true, false, false, i) -> idle₇(S, closed, down, true, false, false, i)
idle₇(fl, d, m, b1, b2, b3, empty) -> busy₇(fl, d, m, b1, b2, b3, empty)
idle₇(fl, d, m, b1, b2, b3, newbuttons₄(i1, i2, i3, i)) -> busy₇(fl, d, m, or₂(b1, i1), or₂(b2, i2), or₂(b3, i3), i)
or₂(true, b) -> true
or₂(false, b) -> b

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [13,14,18] contains 1 SCC with 4 less nodes.

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

BUSY₇(S, closed, stop, true, false, false, i) -> IDLE₇(S, closed, down, true, false, false, i)
IDLE₇(fl, d, m, b1, b2, b3, newbuttons₄(i1, i2, i3, i)) -> BUSY₇(fl, d, m, or₂(b1, i1), or₂(b2, i2), or₂(b3, i3), i)
BUSY₇(B, open, stop, false, b2, b3, i) -> IDLE₇(B, closed, stop, false, b2, b3, i)
BUSY₇(S, d, stop, b1, b2, true, i) -> IDLE₇(S, open, stop, b1, b2, false, i)
BUSY₇(F, open, stop, b1, false, b3, i) -> IDLE₇(F, closed, stop, b1, false, b3, i)
BUSY₇(S, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i)) -> IDLE₇(S, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i))
BUSY₇(F, closed, stop, true, false, b3, i) -> IDLE₇(F, closed, down, true, false, b3, i)
BUSY₇(B, closed, stop, false, true, b3, i) -> IDLE₇(B, closed, up, false, true, b3, i)
BUSY₇(F, closed, stop, false, false, true, i) -> IDLE₇(F, closed, up, false, false, true, i)
BUSY₇(S, open, stop, b1, b2, false, i) -> IDLE₇(S, closed, stop, b1, b2, false, i)
BUSY₇(BF, closed, down, b1, b2, b3, i) -> IDLE₇(B, closed, down, b1, b2, b3, i)
BUSY₇(BF, closed, up, b1, b2, b3, i) -> IDLE₇(F, closed, up, b1, b2, b3, i)
BUSY₇(F, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i)) -> IDLE₇(F, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i))
BUSY₇(F, d, stop, b1, true, b3, i) -> IDLE₇(F, open, stop, b1, false, b3, i)
BUSY₇(B, closed, stop, false, false, true, i) -> IDLE₇(B, closed, up, false, false, true, i)
BUSY₇(F, closed, down, b1, false, b3, i) -> IDLE₇(BF, closed, down, b1, false, b3, i)
BUSY₇(FS, closed, down, b1, b2, b3, i) -> IDLE₇(F, closed, down, b1, b2, b3, i)
BUSY₇(S, closed, stop, b1, true, false, i) -> IDLE₇(S, closed, down, b1, true, false, i)
BUSY₇(F, closed, up, b1, true, b3, i) -> IDLE₇(F, closed, stop, b1, true, b3, i)
BUSY₇(S, closed, down, b1, b2, true, i) -> IDLE₇(S, closed, stop, b1, b2, true, i)
BUSY₇(F, closed, up, b1, false, b3, i) -> IDLE₇(FS, closed, up, b1, false, b3, i)
BUSY₇(F, closed, down, b1, true, b3, i) -> IDLE₇(F, closed, stop, b1, true, b3, i)
BUSY₇(B, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i)) -> IDLE₇(B, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i))
IDLE₇(fl, d, m, b1, b2, b3, empty) -> BUSY₇(fl, d, m, b1, b2, b3, empty)
BUSY₇(S, closed, up, b1, b2, b3, i) -> IDLE₇(S, closed, stop, b1, b2, b3, i)
BUSY₇(B, closed, up, false, b2, b3, i) -> IDLE₇(BF, closed, up, false, b2, b3, i)
BUSY₇(B, d, stop, true, b2, b3, i) -> IDLE₇(B, open, stop, false, b2, b3, i)
BUSY₇(S, closed, down, b1, b2, false, i) -> IDLE₇(FS, closed, down, b1, b2, false, i)
BUSY₇(B, closed, up, true, b2, b3, i) -> IDLE₇(B, closed, stop, true, b2, b3, i)
BUSY₇(B, closed, down, b1, b2, b3, i) -> IDLE₇(B, closed, stop, b1, b2, b3, i)
BUSY₇(FS, closed, up, b1, b2, b3, i) -> IDLE₇(S, closed, up, b1, b2, b3, i)

The TRS R consists of the following rules:

start₁(i) -> busy₇(F, closed, stop, false, false, false, i)
busy₇(BF, d, stop, b1, b2, b3, i) -> incorrect
busy₇(FS, d, stop, b1, b2, b3, i) -> incorrect
busy₇(fl, open, up, b1, b2, b3, i) -> incorrect
busy₇(fl, open, down, b1, b2, b3, i) -> incorrect
busy₇(B, closed, stop, false, false, false, empty) -> correct
busy₇(F, closed, stop, false, false, false, empty) -> correct
busy₇(S, closed, stop, false, false, false, empty) -> correct
busy₇(B, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i)) -> idle₇(B, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i))
busy₇(F, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i)) -> idle₇(F, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i))
busy₇(S, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i)) -> idle₇(S, closed, stop, false, false, false, newbuttons₄(i1, i2, i3, i))
busy₇(B, open, stop, false, b2, b3, i) -> idle₇(B, closed, stop, false, b2, b3, i)
busy₇(F, open, stop, b1, false, b3, i) -> idle₇(F, closed, stop, b1, false, b3, i)
busy₇(S, open, stop, b1, b2, false, i) -> idle₇(S, closed, stop, b1, b2, false, i)
busy₇(B, d, stop, true, b2, b3, i) -> idle₇(B, open, stop, false, b2, b3, i)
busy₇(F, d, stop, b1, true, b3, i) -> idle₇(F, open, stop, b1, false, b3, i)
busy₇(S, d, stop, b1, b2, true, i) -> idle₇(S, open, stop, b1, b2, false, i)
busy₇(B, closed, down, b1, b2, b3, i) -> idle₇(B, closed, stop, b1, b2, b3, i)
busy₇(S, closed, up, b1, b2, b3, i) -> idle₇(S, closed, stop, b1, b2, b3, i)
busy₇(B, closed, up, true, b2, b3, i) -> idle₇(B, closed, stop, true, b2, b3, i)
busy₇(F, closed, up, b1, true, b3, i) -> idle₇(F, closed, stop, b1, true, b3, i)
busy₇(F, closed, down, b1, true, b3, i) -> idle₇(F, closed, stop, b1, true, b3, i)
busy₇(S, closed, down, b1, b2, true, i) -> idle₇(S, closed, stop, b1, b2, true, i)
busy₇(B, closed, up, false, b2, b3, i) -> idle₇(BF, closed, up, false, b2, b3, i)
busy₇(F, closed, up, b1, false, b3, i) -> idle₇(FS, closed, up, b1, false, b3, i)
busy₇(F, closed, down, b1, false, b3, i) -> idle₇(BF, closed, down, b1, false, b3, i)
busy₇(S, closed, down, b1, b2, false, i) -> idle₇(FS, closed, down, b1, b2, false, i)
busy₇(BF, closed, up, b1, b2, b3, i) -> idle₇(F, closed, up, b1, b2, b3, i)
busy₇(BF, closed, down, b1, b2, b3, i) -> idle₇(B, closed, down, b1, b2, b3, i)
busy₇(FS, closed, up, b1, b2, b3, i) -> idle₇(S, closed, up, b1, b2, b3, i)
busy₇(FS, closed, down, b1, b2, b3, i) -> idle₇(F, closed, down, b1, b2, b3, i)
busy₇(B, closed, stop, false, true, b3, i) -> idle₇(B, closed, up, false, true, b3, i)
busy₇(B, closed, stop, false, false, true, i) -> idle₇(B, closed, up, false, false, true, i)
busy₇(F, closed, stop, true, false, b3, i) -> idle₇(F, closed, down, true, false, b3, i)
busy₇(F, closed, stop, false, false, true, i) -> idle₇(F, closed, up, false, false, true, i)
busy₇(S, closed, stop, b1, true, false, i) -> idle₇(S, closed, down, b1, true, false, i)
busy₇(S, closed, stop, true, false, false, i) -> idle₇(S, closed, down, true, false, false, i)
idle₇(fl, d, m, b1, b2, b3, empty) -> busy₇(fl, d, m, b1, b2, b3, empty)
idle₇(fl, d, m, b1, b2, b3, newbuttons₄(i1, i2, i3, i)) -> busy₇(fl, d, m, or₂(b1, i1), or₂(b2, i2), or₂(b3, i3), i)
or₂(true, b) -> true
or₂(false, b) -> b

Q is empty.
We have to consider all minimal (P,Q,R)-chains.