Term Rewriting System R:
[i, d, b1, b2, b3, fl, i1, i2, i3, m, b]
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

Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

START(i) -> BUSY(F, closed, stop, false, false, false, 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, 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)
IDLE(fl, d, m, b1, b2, b3, newbuttons(i1, i2, i3, i)) -> OR(b1, i1)
IDLE(fl, d, m, b1, b2, b3, newbuttons(i1, i2, i3, i)) -> OR(b2, i2)
IDLE(fl, d, m, b1, b2, b3, newbuttons(i1, i2, i3, i)) -> OR(b3, i3)

Furthermore, R contains one SCC. 


   R
     ↳DPs
       →DP Problem 1
         ↳Remaining Obligation(s)




The following remains to be proven:
Dependency Pairs:

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


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




Termination of R could not be shown.
Duration:
0:01 minutes