MAYBE
Time: 0.228

Problem:
 Equations:
  plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
  plusAC(x3,x4) -> plusAC(x4,x3)
  plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
  plusAC(x4,x3) -> plusAC(x3,x4)
 TRS:
  minus(x,0()) -> x
  minus(s(x),s(y)) -> minus(x,y)
  minus(minus(x,y),z) -> minus(x,plusAC(y,z))
  quot(0(),s(y)) -> 0()
  quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
  plusAC(0(),y) -> y
  plusAC(s(x),y) -> s(plusAC(x,y))

Proof:
 DP Processor:
  Equations#:
   plus{AC,#}(plusAC(x3,x4),x5) -> plus{AC,#}(x3,plusAC(x4,x5))
   plus{AC,#}(x3,x4) -> plus{AC,#}(x4,x3)
   plus{AC,#}(x3,plusAC(x4,x5)) -> plus{AC,#}(plusAC(x3,x4),x5)
   plus{AC,#}(x4,x3) -> plus{AC,#}(x3,x4)
  DPs:
   minus#(s(x),s(y)) -> minus#(x,y)
   minus#(minus(x,y),z) -> plus{AC,#}(y,z)
   minus#(minus(x,y),z) -> minus#(x,plusAC(y,z))
   quot#(s(x),s(y)) -> minus#(x,y)
   quot#(s(x),s(y)) -> quot#(minus(x,y),s(y))
   plus{AC,#}(s(x),y) -> plus{AC,#}(x,y)
   plus{AC,#}(x6,plusAC(0(),y)) -> plus{AC,#}(x6,y)
   plus{AC,#}(x7,plusAC(s(x),y)) -> plus{AC,#}(x,y)
   plus{AC,#}(x7,plusAC(s(x),y)) -> plus{AC,#}(x7,s(plusAC(x,y)))
  Equations:
   plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
   plusAC(x3,x4) -> plusAC(x4,x3)
   plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
   plusAC(x4,x3) -> plusAC(x3,x4)
  TRS:
   minus(x,0()) -> x
   minus(s(x),s(y)) -> minus(x,y)
   minus(minus(x,y),z) -> minus(x,plusAC(y,z))
   quot(0(),s(y)) -> 0()
   quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
   plusAC(0(),y) -> y
   plusAC(s(x),y) -> s(plusAC(x,y))
  S:
   plus{AC,#}(plusAC(x8,x9),x10) -> plus{AC,#}(x8,x9)
   plus{AC,#}(x8,plusAC(x9,x10)) -> plus{AC,#}(x9,x10)
  AC-EDG Processor:
   Equations#:
    plus{AC,#}(plusAC(x3,x4),x5) -> plus{AC,#}(x3,plusAC(x4,x5))
    plus{AC,#}(x3,x4) -> plus{AC,#}(x4,x3)
    plus{AC,#}(x3,plusAC(x4,x5)) -> plus{AC,#}(plusAC(x3,x4),x5)
    plus{AC,#}(x4,x3) -> plus{AC,#}(x3,x4)
   DPs:
    minus#(s(x),s(y)) -> minus#(x,y)
    minus#(minus(x,y),z) -> plus{AC,#}(y,z)
    minus#(minus(x,y),z) -> minus#(x,plusAC(y,z))
    quot#(s(x),s(y)) -> minus#(x,y)
    quot#(s(x),s(y)) -> quot#(minus(x,y),s(y))
    plus{AC,#}(s(x),y) -> plus{AC,#}(x,y)
    plus{AC,#}(x6,plusAC(0(),y)) -> plus{AC,#}(x6,y)
    plus{AC,#}(x7,plusAC(s(x),y)) -> plus{AC,#}(x,y)
    plus{AC,#}(x7,plusAC(s(x),y)) -> plus{AC,#}(x7,s(plusAC(x,y)))
   Equations:
    plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
    plusAC(x3,x4) -> plusAC(x4,x3)
    plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
    plusAC(x4,x3) -> plusAC(x3,x4)
   TRS:
    minus(x,0()) -> x
    minus(s(x),s(y)) -> minus(x,y)
    minus(minus(x,y),z) -> minus(x,plusAC(y,z))
    quot(0(),s(y)) -> 0()
    quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
    plusAC(0(),y) -> y
    plusAC(s(x),y) -> s(plusAC(x,y))
   S:
    plus{AC,#}(plusAC(x8,x9),x10) -> plus{AC,#}(x8,x9)
    plus{AC,#}(x8,plusAC(x9,x10)) -> plus{AC,#}(x9,x10)
   Open