MAYBE
Time: 0.094

Problem:
 Equations:
  plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
  plusAC(x2,x3) -> plusAC(x3,x2)
  plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
  plusAC(x3,x2) -> plusAC(x2,x3)
 TRS:
  minus(plusAC(x,y),y) -> x
  dix(zero(),s(y)) -> 0()
  div(s(x),s(y)) -> s(div(minus(x,y),s(y)))
  plusAC(0(),x) -> x
  plusAC(s(x),y) -> s(plusAC(x,y))

Proof:
 DP Processor:
  Equations#:
   plus{AC,#}(plusAC(x2,x3),x4) -> plus{AC,#}(x2,plusAC(x3,x4))
   plus{AC,#}(x2,x3) -> plus{AC,#}(x3,x2)
   plus{AC,#}(x2,plusAC(x3,x4)) -> plus{AC,#}(plusAC(x2,x3),x4)
   plus{AC,#}(x3,x2) -> plus{AC,#}(x2,x3)
  DPs:
   div#(s(x),s(y)) -> minus#(x,y)
   div#(s(x),s(y)) -> div#(minus(x,y),s(y))
   plus{AC,#}(s(x),y) -> plus{AC,#}(x,y)
   plus{AC,#}(x5,plusAC(0(),x)) -> plus{AC,#}(x5,x)
   plus{AC,#}(x6,plusAC(s(x),y)) -> plus{AC,#}(x,y)
   plus{AC,#}(x6,plusAC(s(x),y)) -> plus{AC,#}(x6,s(plusAC(x,y)))
  Equations:
   plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
   plusAC(x2,x3) -> plusAC(x3,x2)
   plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
   plusAC(x3,x2) -> plusAC(x2,x3)
  TRS:
   minus(plusAC(x,y),y) -> x
   dix(zero(),s(y)) -> 0()
   div(s(x),s(y)) -> s(div(minus(x,y),s(y)))
   plusAC(0(),x) -> x
   plusAC(s(x),y) -> s(plusAC(x,y))
  S:
   plus{AC,#}(plusAC(x7,x8),x9) -> plus{AC,#}(x7,x8)
   plus{AC,#}(x7,plusAC(x8,x9)) -> plus{AC,#}(x8,x9)
  AC-EDG Processor:
   Equations#:
    plus{AC,#}(plusAC(x2,x3),x4) -> plus{AC,#}(x2,plusAC(x3,x4))
    plus{AC,#}(x2,x3) -> plus{AC,#}(x3,x2)
    plus{AC,#}(x2,plusAC(x3,x4)) -> plus{AC,#}(plusAC(x2,x3),x4)
    plus{AC,#}(x3,x2) -> plus{AC,#}(x2,x3)
   DPs:
    div#(s(x),s(y)) -> minus#(x,y)
    div#(s(x),s(y)) -> div#(minus(x,y),s(y))
    plus{AC,#}(s(x),y) -> plus{AC,#}(x,y)
    plus{AC,#}(x5,plusAC(0(),x)) -> plus{AC,#}(x5,x)
    plus{AC,#}(x6,plusAC(s(x),y)) -> plus{AC,#}(x,y)
    plus{AC,#}(x6,plusAC(s(x),y)) -> plus{AC,#}(x6,s(plusAC(x,y)))
   Equations:
    plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
    plusAC(x2,x3) -> plusAC(x3,x2)
    plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
    plusAC(x3,x2) -> plusAC(x2,x3)
   TRS:
    minus(plusAC(x,y),y) -> x
    dix(zero(),s(y)) -> 0()
    div(s(x),s(y)) -> s(div(minus(x,y),s(y)))
    plusAC(0(),x) -> x
    plusAC(s(x),y) -> s(plusAC(x,y))
   S:
    plus{AC,#}(plusAC(x7,x8),x9) -> plus{AC,#}(x7,x8)
    plus{AC,#}(x7,plusAC(x8,x9)) -> plus{AC,#}(x8,x9)
   Open