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
↳ QTRS
↳ DependencyPairsProof
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
BUSY(B, closed, stop, false, false, true, i) → IDLE(B, closed, up, false, false, true, i)
BUSY(B, d, stop, true, b2, b3, i) → IDLE(B, open, stop, false, b2, b3, i)
BUSY(F, closed, up, b1, true, b3, i) → IDLE(F, closed, stop, b1, true, b3, i)
IDLE(fl, d, m, b1, b2, b3, newbuttons(i1, i2, i3, i)) → OR(b3, i3)
BUSY(F, closed, down, b1, true, b3, i) → IDLE(F, closed, stop, b1, true, b3, i)
BUSY(B, closed, down, b1, b2, b3, i) → IDLE(B, closed, stop, b1, b2, b3, i)
BUSY(S, closed, stop, true, false, false, i) → IDLE(S, closed, down, true, false, false, i)
BUSY(F, closed, stop, true, false, b3, i) → IDLE(F, closed, down, true, false, b3, i)
BUSY(S, open, stop, b1, b2, false, i) → IDLE(S, closed, stop, b1, b2, false, i)
BUSY(S, closed, up, b1, b2, b3, i) → IDLE(S, closed, stop, b1, b2, b3, i)
BUSY(F, open, stop, b1, false, b3, i) → IDLE(F, closed, stop, b1, false, b3, i)
BUSY(BF, closed, down, b1, b2, b3, i) → IDLE(B, closed, down, b1, b2, b3, 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))
IDLE(fl, d, m, b1, b2, b3, newbuttons(i1, i2, i3, i)) → OR(b1, i1)
START(i) → BUSY(F, closed, stop, false, false, false, i)
BUSY(B, closed, up, false, b2, b3, i) → IDLE(BF, closed, up, false, b2, b3, i)
BUSY(FS, closed, up, b1, b2, b3, i) → IDLE(S, closed, up, b1, b2, b3, i)
BUSY(B, open, stop, false, b2, b3, i) → IDLE(B, closed, stop, false, b2, b3, i)
BUSY(FS, closed, down, b1, b2, b3, i) → IDLE(F, closed, down, b1, b2, 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(F, d, stop, b1, true, b3, i) → IDLE(F, open, stop, b1, false, b3, i)
BUSY(S, closed, stop, b1, true, false, i) → IDLE(S, closed, down, b1, true, false, i)
BUSY(S, closed, down, b1, b2, true, i) → IDLE(S, closed, stop, b1, b2, true, i)
BUSY(B, closed, up, true, b2, b3, i) → IDLE(B, closed, stop, true, b2, b3, i)
BUSY(S, d, stop, b1, b2, true, i) → IDLE(S, open, stop, b1, b2, false, i)
IDLE(fl, d, m, b1, b2, b3, empty) → BUSY(fl, d, m, b1, b2, b3, empty)
BUSY(B, closed, stop, false, true, b3, i) → IDLE(B, closed, up, false, true, b3, i)
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)
BUSY(F, closed, stop, false, false, true, i) → IDLE(F, closed, up, false, false, true, 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(F, closed, down, b1, false, b3, i) → IDLE(BF, closed, down, b1, false, b3, i)
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, up, b1, false, b3, i) → IDLE(FS, closed, up, b1, false, b3, i)
IDLE(fl, d, m, b1, b2, b3, newbuttons(i1, i2, i3, i)) → OR(b2, i2)
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
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
BUSY(B, closed, stop, false, false, true, i) → IDLE(B, closed, up, false, false, true, i)
BUSY(B, d, stop, true, b2, b3, i) → IDLE(B, open, stop, false, b2, b3, i)
BUSY(F, closed, up, b1, true, b3, i) → IDLE(F, closed, stop, b1, true, b3, i)
IDLE(fl, d, m, b1, b2, b3, newbuttons(i1, i2, i3, i)) → OR(b3, i3)
BUSY(F, closed, down, b1, true, b3, i) → IDLE(F, closed, stop, b1, true, b3, i)
BUSY(B, closed, down, b1, b2, b3, i) → IDLE(B, closed, stop, b1, b2, b3, i)
BUSY(S, closed, stop, true, false, false, i) → IDLE(S, closed, down, true, false, false, i)
BUSY(F, closed, stop, true, false, b3, i) → IDLE(F, closed, down, true, false, b3, i)
BUSY(S, open, stop, b1, b2, false, i) → IDLE(S, closed, stop, b1, b2, false, i)
BUSY(S, closed, up, b1, b2, b3, i) → IDLE(S, closed, stop, b1, b2, b3, i)
BUSY(F, open, stop, b1, false, b3, i) → IDLE(F, closed, stop, b1, false, b3, i)
BUSY(BF, closed, down, b1, b2, b3, i) → IDLE(B, closed, down, b1, b2, b3, 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))
IDLE(fl, d, m, b1, b2, b3, newbuttons(i1, i2, i3, i)) → OR(b1, i1)
START(i) → BUSY(F, closed, stop, false, false, false, i)
BUSY(B, closed, up, false, b2, b3, i) → IDLE(BF, closed, up, false, b2, b3, i)
BUSY(FS, closed, up, b1, b2, b3, i) → IDLE(S, closed, up, b1, b2, b3, i)
BUSY(B, open, stop, false, b2, b3, i) → IDLE(B, closed, stop, false, b2, b3, i)
BUSY(FS, closed, down, b1, b2, b3, i) → IDLE(F, closed, down, b1, b2, 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(F, d, stop, b1, true, b3, i) → IDLE(F, open, stop, b1, false, b3, i)
BUSY(S, closed, stop, b1, true, false, i) → IDLE(S, closed, down, b1, true, false, i)
BUSY(S, closed, down, b1, b2, true, i) → IDLE(S, closed, stop, b1, b2, true, i)
BUSY(B, closed, up, true, b2, b3, i) → IDLE(B, closed, stop, true, b2, b3, i)
BUSY(S, d, stop, b1, b2, true, i) → IDLE(S, open, stop, b1, b2, false, i)
IDLE(fl, d, m, b1, b2, b3, empty) → BUSY(fl, d, m, b1, b2, b3, empty)
BUSY(B, closed, stop, false, true, b3, i) → IDLE(B, closed, up, false, true, b3, i)
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)
BUSY(F, closed, stop, false, false, true, i) → IDLE(F, closed, up, false, false, true, 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(F, closed, down, b1, false, b3, i) → IDLE(BF, closed, down, b1, false, b3, i)
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, up, b1, false, b3, i) → IDLE(FS, closed, up, b1, false, b3, i)
IDLE(fl, d, m, b1, b2, b3, newbuttons(i1, i2, i3, i)) → OR(b2, i2)
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
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
BUSY(B, closed, stop, false, false, true, i) → IDLE(B, closed, up, false, false, true, i)
BUSY(B, d, stop, true, b2, b3, i) → IDLE(B, open, stop, false, 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(B, closed, down, b1, b2, b3, i) → IDLE(B, closed, stop, b1, b2, b3, i)
BUSY(S, closed, stop, true, false, false, i) → IDLE(S, closed, down, true, false, false, i)
BUSY(F, closed, stop, true, false, b3, i) → IDLE(F, closed, down, true, false, b3, i)
BUSY(S, open, stop, b1, b2, false, i) → IDLE(S, closed, stop, b1, b2, false, i)
BUSY(S, closed, up, b1, b2, b3, i) → IDLE(S, closed, stop, b1, b2, b3, i)
BUSY(F, open, stop, b1, false, b3, i) → IDLE(F, closed, stop, b1, false, b3, i)
BUSY(BF, closed, down, b1, b2, b3, i) → IDLE(B, closed, down, b1, b2, b3, 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(B, closed, up, false, b2, b3, i) → IDLE(BF, closed, up, false, b2, b3, i)
BUSY(FS, closed, up, b1, b2, b3, i) → IDLE(S, closed, up, b1, b2, b3, i)
BUSY(B, open, stop, false, b2, b3, i) → IDLE(B, closed, stop, false, b2, b3, i)
BUSY(FS, closed, down, b1, b2, b3, i) → IDLE(F, closed, down, b1, b2, 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(F, d, stop, b1, true, b3, i) → IDLE(F, open, stop, b1, false, b3, i)
BUSY(S, closed, stop, b1, true, false, i) → IDLE(S, closed, down, b1, true, false, i)
BUSY(S, closed, down, b1, b2, true, i) → IDLE(S, closed, stop, b1, b2, true, i)
BUSY(S, d, stop, b1, b2, true, i) → IDLE(S, open, stop, b1, b2, false, i)
BUSY(B, closed, up, true, b2, b3, i) → IDLE(B, closed, stop, true, b2, b3, i)
IDLE(fl, d, m, b1, b2, b3, empty) → BUSY(fl, d, m, b1, b2, b3, empty)
BUSY(B, closed, stop, false, true, b3, i) → IDLE(B, closed, up, false, true, b3, i)
BUSY(F, closed, stop, false, false, true, i) → IDLE(F, closed, up, false, false, true, i)
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)
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(F, closed, down, b1, false, b3, i) → IDLE(BF, closed, down, b1, false, b3, i)
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, up, b1, false, b3, i) → IDLE(FS, closed, up, b1, false, b3, i)
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
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
BUSY(F, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) → IDLE(F, closed, stop, false, false, false, newbuttons(i1, i2, i3, i))
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)
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, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) → IDLE(B, closed, stop, false, false, false, newbuttons(i1, i2, i3, i))
Used ordering: Polynomial interpretation [25,35]:
BUSY(B, closed, stop, false, false, true, i) → IDLE(B, closed, up, false, false, true, i)
BUSY(B, d, stop, true, b2, b3, i) → IDLE(B, open, stop, false, 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(B, closed, down, b1, b2, b3, i) → IDLE(B, closed, stop, b1, b2, b3, i)
BUSY(S, closed, stop, true, false, false, i) → IDLE(S, closed, down, true, false, false, i)
BUSY(F, closed, stop, true, false, b3, i) → IDLE(F, closed, down, true, false, b3, i)
BUSY(S, open, stop, b1, b2, false, i) → IDLE(S, closed, stop, b1, b2, false, i)
BUSY(S, closed, up, b1, b2, b3, i) → IDLE(S, closed, stop, b1, b2, b3, i)
BUSY(F, open, stop, b1, false, b3, i) → IDLE(F, closed, stop, b1, false, b3, i)
BUSY(BF, closed, down, b1, b2, b3, i) → IDLE(B, closed, down, b1, b2, b3, i)
BUSY(B, closed, up, false, b2, b3, i) → IDLE(BF, closed, up, false, b2, b3, i)
BUSY(FS, closed, up, b1, b2, b3, i) → IDLE(S, closed, up, b1, b2, b3, i)
BUSY(B, open, stop, false, b2, b3, i) → IDLE(B, closed, stop, false, b2, b3, i)
BUSY(FS, closed, down, b1, b2, b3, i) → IDLE(F, closed, down, b1, b2, 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(F, d, stop, b1, true, b3, i) → IDLE(F, open, stop, b1, false, b3, i)
BUSY(S, closed, stop, b1, true, false, i) → IDLE(S, closed, down, b1, true, false, i)
BUSY(S, closed, down, b1, b2, true, i) → IDLE(S, closed, stop, b1, b2, true, i)
BUSY(S, d, stop, b1, b2, true, i) → IDLE(S, open, stop, b1, b2, false, i)
BUSY(B, closed, up, true, b2, b3, i) → IDLE(B, closed, stop, true, b2, b3, i)
IDLE(fl, d, m, b1, b2, b3, empty) → BUSY(fl, d, m, b1, b2, b3, empty)
BUSY(B, closed, stop, false, true, b3, i) → IDLE(B, closed, up, false, true, b3, i)
BUSY(F, closed, stop, false, false, true, i) → IDLE(F, closed, up, false, false, true, i)
BUSY(F, closed, down, b1, false, b3, i) → IDLE(BF, closed, down, b1, false, b3, i)
BUSY(F, closed, up, b1, false, b3, i) → IDLE(FS, closed, up, b1, false, b3, i)
The value of delta used in the strict ordering is 4.
POL(closed) = 0
POL(FS) = 3
POL(or(x1, x2)) = x_2
POL(true) = 0
POL(empty) = 0
POL(newbuttons(x1, x2, x3, x4)) = 4 + (3)x_1 + (3)x_2 + (3)x_3 + (2)x_4
POL(open) = 1
POL(down) = 0
POL(BUSY(x1, x2, x3, x4, x5, x6, x7)) = (2)x_4 + x_5 + (3)x_6 + (2)x_7
POL(S) = 1
POL(BF) = 2
POL(up) = 1
POL(B) = 3
POL(IDLE(x1, x2, x3, x4, x5, x6, x7)) = (2)x_4 + x_5 + (3)x_6 + x_7
POL(false) = 0
POL(F) = 4
POL(stop) = 0
or(false, b) → b
or(true, b) → true
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
BUSY(B, closed, stop, false, false, true, i) → IDLE(B, closed, up, false, false, true, i)
BUSY(F, closed, up, b1, true, b3, i) → IDLE(F, closed, stop, b1, true, b3, i)
BUSY(B, d, stop, true, b2, b3, i) → IDLE(B, open, stop, false, b2, b3, i)
BUSY(F, closed, down, b1, true, b3, i) → IDLE(F, closed, stop, b1, true, b3, i)
BUSY(B, closed, down, b1, b2, b3, i) → IDLE(B, closed, stop, b1, b2, b3, i)
BUSY(F, closed, stop, true, false, b3, i) → IDLE(F, closed, down, true, false, b3, i)
BUSY(S, closed, stop, true, false, false, i) → IDLE(S, closed, down, true, false, false, i)
BUSY(S, open, stop, b1, b2, false, i) → IDLE(S, closed, stop, b1, b2, false, i)
BUSY(F, open, stop, b1, false, b3, i) → IDLE(F, closed, stop, b1, false, b3, i)
BUSY(S, closed, up, b1, b2, b3, i) → IDLE(S, closed, stop, b1, b2, b3, i)
BUSY(BF, closed, down, b1, b2, b3, i) → IDLE(B, closed, down, b1, b2, b3, i)
BUSY(B, closed, up, false, b2, b3, i) → IDLE(BF, closed, up, false, b2, b3, i)
BUSY(FS, closed, up, b1, b2, b3, i) → IDLE(S, closed, up, b1, b2, b3, i)
BUSY(B, open, stop, false, b2, b3, i) → IDLE(B, closed, stop, false, b2, b3, i)
BUSY(FS, closed, down, b1, b2, b3, i) → IDLE(F, closed, down, b1, b2, 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(F, d, stop, b1, true, b3, i) → IDLE(F, open, stop, b1, false, b3, i)
BUSY(S, closed, stop, b1, true, false, i) → IDLE(S, closed, down, b1, true, false, i)
BUSY(S, closed, down, b1, b2, true, i) → IDLE(S, closed, stop, b1, b2, true, i)
BUSY(S, d, stop, b1, b2, true, i) → IDLE(S, open, stop, b1, b2, false, i)
BUSY(B, closed, up, true, b2, b3, i) → IDLE(B, closed, stop, true, b2, b3, i)
IDLE(fl, d, m, b1, b2, b3, empty) → BUSY(fl, d, m, b1, b2, b3, empty)
BUSY(B, closed, stop, false, true, b3, i) → IDLE(B, closed, up, false, true, b3, i)
BUSY(F, closed, stop, false, false, true, i) → IDLE(F, closed, up, false, false, true, i)
BUSY(F, closed, down, b1, false, b3, i) → IDLE(BF, closed, down, b1, false, b3, i)
BUSY(F, closed, up, b1, false, b3, i) → IDLE(FS, closed, up, b1, false, b3, i)
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
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
BUSY(B, d, stop, true, b2, b3, i) → IDLE(B, open, stop, false, b2, b3, i)
Used ordering: Polynomial interpretation [25,35]:
BUSY(B, closed, stop, false, false, true, i) → IDLE(B, closed, up, false, false, true, 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(B, closed, down, b1, b2, b3, i) → IDLE(B, closed, stop, b1, b2, b3, i)
BUSY(F, closed, stop, true, false, b3, i) → IDLE(F, closed, down, true, false, b3, i)
BUSY(S, closed, stop, true, false, false, i) → IDLE(S, closed, down, true, false, false, i)
BUSY(S, open, stop, b1, b2, false, i) → IDLE(S, closed, stop, b1, b2, false, i)
BUSY(F, open, stop, b1, false, b3, i) → IDLE(F, closed, stop, b1, false, b3, i)
BUSY(S, closed, up, b1, b2, b3, i) → IDLE(S, closed, stop, b1, b2, b3, i)
BUSY(BF, closed, down, b1, b2, b3, i) → IDLE(B, closed, down, b1, b2, b3, i)
BUSY(B, closed, up, false, b2, b3, i) → IDLE(BF, closed, up, false, b2, b3, i)
BUSY(FS, closed, up, b1, b2, b3, i) → IDLE(S, closed, up, b1, b2, b3, i)
BUSY(B, open, stop, false, b2, b3, i) → IDLE(B, closed, stop, false, b2, b3, i)
BUSY(FS, closed, down, b1, b2, b3, i) → IDLE(F, closed, down, b1, b2, 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(F, d, stop, b1, true, b3, i) → IDLE(F, open, stop, b1, false, b3, i)
BUSY(S, closed, stop, b1, true, false, i) → IDLE(S, closed, down, b1, true, false, i)
BUSY(S, closed, down, b1, b2, true, i) → IDLE(S, closed, stop, b1, b2, true, i)
BUSY(S, d, stop, b1, b2, true, i) → IDLE(S, open, stop, b1, b2, false, i)
BUSY(B, closed, up, true, b2, b3, i) → IDLE(B, closed, stop, true, b2, b3, i)
IDLE(fl, d, m, b1, b2, b3, empty) → BUSY(fl, d, m, b1, b2, b3, empty)
BUSY(B, closed, stop, false, true, b3, i) → IDLE(B, closed, up, false, true, b3, i)
BUSY(F, closed, stop, false, false, true, i) → IDLE(F, closed, up, false, false, true, i)
BUSY(F, closed, down, b1, false, b3, i) → IDLE(BF, closed, down, b1, false, b3, i)
BUSY(F, closed, up, b1, false, b3, i) → IDLE(FS, closed, up, b1, false, b3, i)
The value of delta used in the strict ordering is 1.
POL(closed) = 0
POL(FS) = 2
POL(true) = 2
POL(empty) = 0
POL(open) = 0
POL(down) = 0
POL(BUSY(x1, x2, x3, x4, x5, x6, x7)) = x_2 + x_4
POL(S) = 1
POL(BF) = 2
POL(up) = 0
POL(B) = 0
POL(IDLE(x1, x2, x3, x4, x5, x6, x7)) = x_2 + x_4
POL(false) = 1
POL(F) = 2
POL(stop) = 0
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
BUSY(B, closed, stop, false, false, true, i) → IDLE(B, closed, up, false, false, true, 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(B, closed, down, b1, b2, b3, i) → IDLE(B, closed, stop, b1, b2, b3, i)
BUSY(S, closed, stop, true, false, false, i) → IDLE(S, closed, down, true, false, false, i)
BUSY(F, closed, stop, true, false, b3, i) → IDLE(F, closed, down, true, false, b3, i)
BUSY(S, open, stop, b1, b2, false, i) → IDLE(S, closed, stop, b1, b2, false, i)
BUSY(S, closed, up, b1, b2, b3, i) → IDLE(S, closed, stop, b1, b2, b3, i)
BUSY(F, open, stop, b1, false, b3, i) → IDLE(F, closed, stop, b1, false, b3, i)
BUSY(BF, closed, down, b1, b2, b3, i) → IDLE(B, closed, down, b1, b2, b3, i)
BUSY(B, closed, up, false, b2, b3, i) → IDLE(BF, closed, up, false, b2, b3, i)
BUSY(FS, closed, up, b1, b2, b3, i) → IDLE(S, closed, up, b1, b2, b3, i)
BUSY(B, open, stop, false, b2, b3, i) → IDLE(B, closed, stop, false, b2, b3, i)
BUSY(FS, closed, down, b1, b2, b3, i) → IDLE(F, closed, down, b1, b2, 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(F, d, stop, b1, true, b3, i) → IDLE(F, open, stop, b1, false, b3, i)
BUSY(S, closed, stop, b1, true, false, i) → IDLE(S, closed, down, b1, true, false, i)
BUSY(S, closed, down, b1, b2, true, i) → IDLE(S, closed, stop, b1, b2, true, i)
BUSY(S, d, stop, b1, b2, true, i) → IDLE(S, open, stop, b1, b2, false, i)
BUSY(B, closed, up, true, b2, b3, i) → IDLE(B, closed, stop, true, b2, b3, i)
IDLE(fl, d, m, b1, b2, b3, empty) → BUSY(fl, d, m, b1, b2, b3, empty)
BUSY(B, closed, stop, false, true, b3, i) → IDLE(B, closed, up, false, true, b3, i)
BUSY(F, closed, stop, false, false, true, i) → IDLE(F, closed, up, false, false, true, i)
BUSY(F, closed, down, b1, false, b3, i) → IDLE(BF, closed, down, b1, false, b3, i)
BUSY(F, closed, up, b1, false, b3, i) → IDLE(FS, closed, up, b1, false, b3, i)
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
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
BUSY(S, d, stop, b1, b2, true, i) → IDLE(S, open, stop, b1, b2, false, i)
Used ordering: Polynomial interpretation [25,35]:
BUSY(B, closed, stop, false, false, true, i) → IDLE(B, closed, up, false, false, true, 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(B, closed, down, b1, b2, b3, i) → IDLE(B, closed, stop, b1, b2, b3, i)
BUSY(S, closed, stop, true, false, false, i) → IDLE(S, closed, down, true, false, false, i)
BUSY(F, closed, stop, true, false, b3, i) → IDLE(F, closed, down, true, false, b3, i)
BUSY(S, open, stop, b1, b2, false, i) → IDLE(S, closed, stop, b1, b2, false, i)
BUSY(S, closed, up, b1, b2, b3, i) → IDLE(S, closed, stop, b1, b2, b3, i)
BUSY(F, open, stop, b1, false, b3, i) → IDLE(F, closed, stop, b1, false, b3, i)
BUSY(BF, closed, down, b1, b2, b3, i) → IDLE(B, closed, down, b1, b2, b3, i)
BUSY(B, closed, up, false, b2, b3, i) → IDLE(BF, closed, up, false, b2, b3, i)
BUSY(FS, closed, up, b1, b2, b3, i) → IDLE(S, closed, up, b1, b2, b3, i)
BUSY(B, open, stop, false, b2, b3, i) → IDLE(B, closed, stop, false, b2, b3, i)
BUSY(FS, closed, down, b1, b2, b3, i) → IDLE(F, closed, down, b1, b2, 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(F, d, stop, b1, true, b3, i) → IDLE(F, open, stop, b1, false, b3, i)
BUSY(S, closed, stop, b1, true, false, i) → IDLE(S, closed, down, b1, true, false, i)
BUSY(S, closed, down, b1, b2, true, i) → IDLE(S, closed, stop, b1, b2, true, i)
BUSY(B, closed, up, true, b2, b3, i) → IDLE(B, closed, stop, true, b2, b3, i)
IDLE(fl, d, m, b1, b2, b3, empty) → BUSY(fl, d, m, b1, b2, b3, empty)
BUSY(B, closed, stop, false, true, b3, i) → IDLE(B, closed, up, false, true, b3, i)
BUSY(F, closed, stop, false, false, true, i) → IDLE(F, closed, up, false, false, true, i)
BUSY(F, closed, down, b1, false, b3, i) → IDLE(BF, closed, down, b1, false, b3, i)
BUSY(F, closed, up, b1, false, b3, i) → IDLE(FS, closed, up, b1, false, b3, i)
The value of delta used in the strict ordering is 2.
POL(closed) = 3
POL(FS) = 3
POL(true) = 4
POL(empty) = 0
POL(open) = 0
POL(down) = 3
POL(BUSY(x1, x2, x3, x4, x5, x6, x7)) = x_6
POL(S) = 3
POL(BF) = 2
POL(up) = 1
POL(B) = 0
POL(IDLE(x1, x2, x3, x4, x5, x6, x7)) = x_6
POL(false) = 2
POL(F) = 1
POL(stop) = 4
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
BUSY(B, closed, stop, false, false, true, i) → IDLE(B, closed, up, false, false, true, 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(B, closed, down, b1, b2, b3, i) → IDLE(B, closed, stop, b1, b2, b3, i)
BUSY(F, closed, stop, true, false, b3, i) → IDLE(F, closed, down, true, false, b3, i)
BUSY(S, closed, stop, true, false, false, i) → IDLE(S, closed, down, true, false, false, i)
BUSY(S, open, stop, b1, b2, false, i) → IDLE(S, closed, stop, b1, b2, false, i)
BUSY(F, open, stop, b1, false, b3, i) → IDLE(F, closed, stop, b1, false, b3, i)
BUSY(S, closed, up, b1, b2, b3, i) → IDLE(S, closed, stop, b1, b2, b3, i)
BUSY(BF, closed, down, b1, b2, b3, i) → IDLE(B, closed, down, b1, b2, b3, i)
BUSY(B, closed, up, false, b2, b3, i) → IDLE(BF, closed, up, false, b2, b3, i)
BUSY(FS, closed, up, b1, b2, b3, i) → IDLE(S, closed, up, b1, b2, b3, i)
BUSY(B, open, stop, false, b2, b3, i) → IDLE(B, closed, stop, false, b2, b3, i)
BUSY(FS, closed, down, b1, b2, b3, i) → IDLE(F, closed, down, b1, b2, 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(F, d, stop, b1, true, b3, i) → IDLE(F, open, stop, b1, false, b3, i)
BUSY(S, closed, stop, b1, true, false, i) → IDLE(S, closed, down, b1, true, false, i)
BUSY(S, closed, down, b1, b2, true, i) → IDLE(S, closed, stop, b1, b2, true, i)
BUSY(B, closed, up, true, b2, b3, i) → IDLE(B, closed, stop, true, b2, b3, i)
IDLE(fl, d, m, b1, b2, b3, empty) → BUSY(fl, d, m, b1, b2, b3, empty)
BUSY(B, closed, stop, false, true, b3, i) → IDLE(B, closed, up, false, true, b3, i)
BUSY(F, closed, stop, false, false, true, i) → IDLE(F, closed, up, false, false, true, i)
BUSY(F, closed, down, b1, false, b3, i) → IDLE(BF, closed, down, b1, false, b3, i)
BUSY(F, closed, up, b1, false, b3, i) → IDLE(FS, closed, up, b1, false, b3, i)
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
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
BUSY(F, d, stop, b1, true, b3, i) → IDLE(F, open, stop, b1, false, b3, i)
Used ordering: Polynomial interpretation [25,35]:
BUSY(B, closed, stop, false, false, true, i) → IDLE(B, closed, up, false, false, true, 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(B, closed, down, b1, b2, b3, i) → IDLE(B, closed, stop, b1, b2, b3, i)
BUSY(F, closed, stop, true, false, b3, i) → IDLE(F, closed, down, true, false, b3, i)
BUSY(S, closed, stop, true, false, false, i) → IDLE(S, closed, down, true, false, false, i)
BUSY(S, open, stop, b1, b2, false, i) → IDLE(S, closed, stop, b1, b2, false, i)
BUSY(F, open, stop, b1, false, b3, i) → IDLE(F, closed, stop, b1, false, b3, i)
BUSY(S, closed, up, b1, b2, b3, i) → IDLE(S, closed, stop, b1, b2, b3, i)
BUSY(BF, closed, down, b1, b2, b3, i) → IDLE(B, closed, down, b1, b2, b3, i)
BUSY(B, closed, up, false, b2, b3, i) → IDLE(BF, closed, up, false, b2, b3, i)
BUSY(FS, closed, up, b1, b2, b3, i) → IDLE(S, closed, up, b1, b2, b3, i)
BUSY(B, open, stop, false, b2, b3, i) → IDLE(B, closed, stop, false, b2, b3, i)
BUSY(FS, closed, down, b1, b2, b3, i) → IDLE(F, closed, down, b1, b2, 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(S, closed, stop, b1, true, false, i) → IDLE(S, closed, down, b1, true, false, i)
BUSY(S, closed, down, b1, b2, true, i) → IDLE(S, closed, stop, b1, b2, true, i)
BUSY(B, closed, up, true, b2, b3, i) → IDLE(B, closed, stop, true, b2, b3, i)
IDLE(fl, d, m, b1, b2, b3, empty) → BUSY(fl, d, m, b1, b2, b3, empty)
BUSY(B, closed, stop, false, true, b3, i) → IDLE(B, closed, up, false, true, b3, i)
BUSY(F, closed, stop, false, false, true, i) → IDLE(F, closed, up, false, false, true, i)
BUSY(F, closed, down, b1, false, b3, i) → IDLE(BF, closed, down, b1, false, b3, i)
BUSY(F, closed, up, b1, false, b3, i) → IDLE(FS, closed, up, b1, false, b3, i)
The value of delta used in the strict ordering is 4.
POL(closed) = 0
POL(FS) = 0
POL(true) = 4
POL(empty) = 0
POL(open) = 4
POL(down) = 0
POL(BUSY(x1, x2, x3, x4, x5, x6, x7)) = (4)x_5 + (2)x_7
POL(S) = 0
POL(BF) = 3
POL(up) = 0
POL(B) = 0
POL(IDLE(x1, x2, x3, x4, x5, x6, x7)) = (4)x_5 + x_7
POL(false) = 3
POL(F) = 2
POL(stop) = 4
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
BUSY(B, closed, stop, false, false, true, i) → IDLE(B, closed, up, false, false, true, i)
BUSY(B, closed, up, false, b2, b3, i) → IDLE(BF, closed, up, false, b2, b3, i)
BUSY(F, closed, up, b1, true, b3, i) → IDLE(F, closed, stop, b1, true, 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, open, stop, false, b2, b3, i) → IDLE(B, closed, stop, false, b2, b3, i)
BUSY(BF, closed, up, b1, b2, b3, i) → IDLE(F, closed, up, b1, b2, b3, i)
BUSY(S, closed, down, b1, b2, false, i) → IDLE(FS, closed, down, b1, b2, false, i)
BUSY(F, closed, down, b1, true, b3, i) → IDLE(F, closed, stop, b1, true, b3, i)
BUSY(S, closed, stop, b1, true, false, i) → IDLE(S, closed, down, b1, true, false, i)
BUSY(S, closed, down, b1, b2, true, i) → IDLE(S, closed, stop, b1, b2, true, i)
BUSY(B, closed, up, true, b2, b3, i) → IDLE(B, closed, stop, true, b2, b3, i)
IDLE(fl, d, m, b1, b2, b3, empty) → BUSY(fl, d, m, b1, b2, b3, empty)
BUSY(B, closed, stop, false, true, b3, i) → IDLE(B, closed, up, false, true, b3, i)
BUSY(F, closed, stop, false, false, true, i) → IDLE(F, closed, up, false, false, true, i)
BUSY(B, closed, down, b1, b2, b3, i) → IDLE(B, closed, stop, b1, b2, b3, i)
BUSY(F, closed, stop, true, false, b3, i) → IDLE(F, closed, down, true, false, b3, i)
BUSY(S, closed, stop, true, false, false, i) → IDLE(S, closed, down, true, false, false, i)
BUSY(F, closed, down, b1, false, b3, i) → IDLE(BF, closed, down, b1, false, b3, i)
BUSY(S, open, stop, b1, b2, false, i) → IDLE(S, closed, stop, b1, b2, false, i)
BUSY(F, open, stop, b1, false, b3, i) → IDLE(F, closed, stop, b1, false, b3, i)
BUSY(S, closed, up, b1, b2, b3, i) → IDLE(S, closed, stop, b1, b2, b3, i)
BUSY(F, closed, up, b1, false, b3, i) → IDLE(FS, closed, up, b1, false, b3, i)
BUSY(BF, closed, down, b1, b2, b3, i) → IDLE(B, closed, down, b1, b2, b3, i)
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
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
BUSY(B, open, stop, false, b2, b3, i) → IDLE(B, closed, stop, false, b2, b3, i)
BUSY(S, open, stop, b1, b2, false, i) → IDLE(S, closed, stop, b1, b2, false, i)
BUSY(F, open, stop, b1, false, b3, i) → IDLE(F, closed, stop, b1, false, b3, i)
Used ordering: Polynomial interpretation [25,35]:
BUSY(B, closed, stop, false, false, true, i) → IDLE(B, closed, up, false, false, true, i)
BUSY(B, closed, up, false, b2, b3, i) → IDLE(BF, closed, up, false, b2, b3, i)
BUSY(F, closed, up, b1, true, b3, i) → IDLE(F, closed, stop, b1, true, 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(BF, closed, up, b1, b2, b3, i) → IDLE(F, closed, up, b1, b2, b3, i)
BUSY(S, closed, down, b1, b2, false, i) → IDLE(FS, closed, down, b1, b2, false, i)
BUSY(F, closed, down, b1, true, b3, i) → IDLE(F, closed, stop, b1, true, b3, i)
BUSY(S, closed, stop, b1, true, false, i) → IDLE(S, closed, down, b1, true, false, i)
BUSY(S, closed, down, b1, b2, true, i) → IDLE(S, closed, stop, b1, b2, true, i)
BUSY(B, closed, up, true, b2, b3, i) → IDLE(B, closed, stop, true, b2, b3, i)
IDLE(fl, d, m, b1, b2, b3, empty) → BUSY(fl, d, m, b1, b2, b3, empty)
BUSY(B, closed, stop, false, true, b3, i) → IDLE(B, closed, up, false, true, b3, i)
BUSY(F, closed, stop, false, false, true, i) → IDLE(F, closed, up, false, false, true, i)
BUSY(B, closed, down, b1, b2, b3, i) → IDLE(B, closed, stop, b1, b2, b3, i)
BUSY(F, closed, stop, true, false, b3, i) → IDLE(F, closed, down, true, false, b3, i)
BUSY(S, closed, stop, true, false, false, i) → IDLE(S, closed, down, true, false, false, i)
BUSY(F, closed, down, b1, false, b3, i) → IDLE(BF, closed, down, b1, false, b3, i)
BUSY(S, closed, up, b1, b2, b3, i) → IDLE(S, closed, stop, b1, b2, b3, i)
BUSY(F, closed, up, b1, false, b3, i) → IDLE(FS, closed, up, b1, false, b3, i)
BUSY(BF, closed, down, b1, b2, b3, i) → IDLE(B, closed, down, b1, b2, b3, i)
The value of delta used in the strict ordering is 2.
POL(closed) = 0
POL(FS) = 1
POL(true) = 0
POL(empty) = 0
POL(open) = 2
POL(down) = 0
POL(BUSY(x1, x2, x3, x4, x5, x6, x7)) = x_2
POL(S) = 4
POL(BF) = 2
POL(up) = 0
POL(B) = 4
POL(IDLE(x1, x2, x3, x4, x5, x6, x7)) = (3)x_2 + x_3
POL(false) = 0
POL(F) = 3
POL(stop) = 0
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
BUSY(B, closed, stop, false, false, true, i) → IDLE(B, closed, up, false, false, true, i)
BUSY(B, closed, up, false, b2, b3, i) → IDLE(BF, closed, up, false, b2, b3, i)
BUSY(F, closed, up, b1, true, b3, i) → IDLE(F, closed, stop, b1, true, 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(BF, closed, up, b1, b2, b3, i) → IDLE(F, closed, up, b1, b2, b3, i)
BUSY(S, closed, down, b1, b2, false, i) → IDLE(FS, closed, down, b1, b2, false, i)
BUSY(F, closed, down, b1, true, b3, i) → IDLE(F, closed, stop, b1, true, b3, i)
BUSY(S, closed, stop, b1, true, false, i) → IDLE(S, closed, down, b1, true, false, i)
BUSY(S, closed, down, b1, b2, true, i) → IDLE(S, closed, stop, b1, b2, true, i)
BUSY(B, closed, up, true, b2, b3, i) → IDLE(B, closed, stop, true, b2, b3, i)
IDLE(fl, d, m, b1, b2, b3, empty) → BUSY(fl, d, m, b1, b2, b3, empty)
BUSY(B, closed, stop, false, true, b3, i) → IDLE(B, closed, up, false, true, b3, i)
BUSY(F, closed, stop, false, false, true, i) → IDLE(F, closed, up, false, false, true, i)
BUSY(B, closed, down, b1, b2, b3, i) → IDLE(B, closed, stop, b1, b2, b3, i)
BUSY(S, closed, stop, true, false, false, i) → IDLE(S, closed, down, true, false, false, i)
BUSY(F, closed, stop, true, false, b3, i) → IDLE(F, closed, down, true, false, b3, i)
BUSY(F, closed, down, b1, false, b3, i) → IDLE(BF, closed, down, b1, false, b3, i)
BUSY(S, closed, up, b1, b2, b3, i) → IDLE(S, closed, stop, b1, b2, b3, i)
BUSY(F, closed, up, b1, false, b3, i) → IDLE(FS, closed, up, b1, false, b3, i)
BUSY(BF, closed, down, b1, b2, b3, i) → IDLE(B, closed, down, b1, b2, b3, i)
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