YES
Time: 0.402

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:
  zero(sharp()) -> sharp()
  plusAC(x,sharp()) -> x
  plusAC(zero(x),zero(y)) -> zero(plusAC(x,y))
  plusAC(zero(x),one(y)) -> one(plusAC(x,y))
  plusAC(one(x),one(y)) -> zero(plusAC(x,plusAC(y,one(sharp()))))

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:
   plus{AC,#}(zero(x),zero(y)) -> plus{AC,#}(x,y)
   plus{AC,#}(zero(x),zero(y)) -> zero#(plusAC(x,y))
   plus{AC,#}(zero(x),one(y)) -> plus{AC,#}(x,y)
   plus{AC,#}(one(x),one(y)) -> plus{AC,#}(y,one(sharp()))
   plus{AC,#}(one(x),one(y)) -> plus{AC,#}(x,plusAC(y,one(sharp())))
   plus{AC,#}(one(x),one(y)) -> zero#(plusAC(x,plusAC(y,one(sharp()))))
   plus{AC,#}(x5,plusAC(x,sharp())) -> plus{AC,#}(x5,x)
   plus{AC,#}(x6,plusAC(zero(x),zero(y))) -> plus{AC,#}(x,y)
   plus{AC,#}(x6,plusAC(zero(x),zero(y))) -> zero#(plusAC(x,y))
   plus{AC,#}(x6,plusAC(zero(x),zero(y))) -> plus{AC,#}(x6,zero(plusAC(x,y)))
   plus{AC,#}(x7,plusAC(zero(x),one(y))) -> plus{AC,#}(x,y)
   plus{AC,#}(x7,plusAC(zero(x),one(y))) -> plus{AC,#}(x7,one(plusAC(x,y)))
   plus{AC,#}(x8,plusAC(one(x),one(y))) -> plus{AC,#}(y,one(sharp()))
   plus{AC,#}(x8,plusAC(one(x),one(y))) -> plus{AC,#}(x,plusAC(y,one(sharp())))
   plus{AC,#}(x8,plusAC(one(x),one(y))) -> zero#(plusAC(x,plusAC(y,one(sharp()))))
   plus{AC,#}(x8,plusAC(one(x),one(y))) -> plus{AC,#}(x8,zero(plusAC(x,plusAC(y,one(sharp())))))
  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:
   zero(sharp()) -> sharp()
   plusAC(x,sharp()) -> x
   plusAC(zero(x),zero(y)) -> zero(plusAC(x,y))
   plusAC(zero(x),one(y)) -> one(plusAC(x,y))
   plusAC(one(x),one(y)) -> zero(plusAC(x,plusAC(y,one(sharp()))))
  S:
   plus{AC,#}(plusAC(x9,x10),x11) -> plus{AC,#}(x9,x10)
   plus{AC,#}(x9,plusAC(x10,x11)) -> plus{AC,#}(x10,x11)
  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:
    plus{AC,#}(zero(x),zero(y)) -> plus{AC,#}(x,y)
    plus{AC,#}(zero(x),zero(y)) -> zero#(plusAC(x,y))
    plus{AC,#}(zero(x),one(y)) -> plus{AC,#}(x,y)
    plus{AC,#}(one(x),one(y)) -> plus{AC,#}(y,one(sharp()))
    plus{AC,#}(one(x),one(y)) -> plus{AC,#}(x,plusAC(y,one(sharp())))
    plus{AC,#}(one(x),one(y)) -> zero#(plusAC(x,plusAC(y,one(sharp()))))
    plus{AC,#}(x5,plusAC(x,sharp())) -> plus{AC,#}(x5,x)
    plus{AC,#}(x6,plusAC(zero(x),zero(y))) -> plus{AC,#}(x,y)
    plus{AC,#}(x6,plusAC(zero(x),zero(y))) -> zero#(plusAC(x,y))
    plus{AC,#}(x6,plusAC(zero(x),zero(y))) -> plus{AC,#}(x6,zero(plusAC(x,y)))
    plus{AC,#}(x7,plusAC(zero(x),one(y))) -> plus{AC,#}(x,y)
    plus{AC,#}(x7,plusAC(zero(x),one(y))) -> plus{AC,#}(x7,one(plusAC(x,y)))
    plus{AC,#}(x8,plusAC(one(x),one(y))) -> plus{AC,#}(y,one(sharp()))
    plus{AC,#}(x8,plusAC(one(x),one(y))) -> plus{AC,#}(x,plusAC(y,one(sharp())))
    plus{AC,#}(x8,plusAC(one(x),one(y))) -> zero#(plusAC(x,plusAC(y,one(sharp()))))
    plus{AC,#}(x8,plusAC(one(x),one(y))) -> plus{AC,#}(x8,zero(plusAC(x,plusAC(y,one(sharp())))))
   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:
    zero(sharp()) -> sharp()
    plusAC(x,sharp()) -> x
    plusAC(zero(x),zero(y)) -> zero(plusAC(x,y))
    plusAC(zero(x),one(y)) -> one(plusAC(x,y))
    plusAC(one(x),one(y)) -> zero(plusAC(x,plusAC(y,one(sharp()))))
   S:
    plus{AC,#}(plusAC(x9,x10),x11) -> plus{AC,#}(x9,x10)
    plus{AC,#}(x9,plusAC(x10,x11)) -> plus{AC,#}(x10,x11)
   SCC Processor:
    #sccs: 1
    #rules: 12
    #arcs: 192/256
    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:
     plus{AC,#}(one(x),one(y)) -> plus{AC,#}(y,one(sharp()))
     plus{AC,#}(x8,plusAC(one(x),one(y))) -> plus{AC,#}(x8,zero(plusAC(x,plusAC(y,one(sharp())))))
     plus{AC,#}(x8,plusAC(one(x),one(y))) -> plus{AC,#}(x,plusAC(y,one(sharp())))
     plus{AC,#}(x8,plusAC(one(x),one(y))) -> plus{AC,#}(y,one(sharp()))
     plus{AC,#}(x7,plusAC(zero(x),one(y))) -> plus{AC,#}(x7,one(plusAC(x,y)))
     plus{AC,#}(x7,plusAC(zero(x),one(y))) -> plus{AC,#}(x,y)
     plus{AC,#}(x6,plusAC(zero(x),zero(y))) -> plus{AC,#}(x6,zero(plusAC(x,y)))
     plus{AC,#}(x6,plusAC(zero(x),zero(y))) -> plus{AC,#}(x,y)
     plus{AC,#}(x5,plusAC(x,sharp())) -> plus{AC,#}(x5,x)
     plus{AC,#}(one(x),one(y)) -> plus{AC,#}(x,plusAC(y,one(sharp())))
     plus{AC,#}(zero(x),one(y)) -> plus{AC,#}(x,y)
     plus{AC,#}(zero(x),zero(y)) -> plus{AC,#}(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:
     zero(sharp()) -> sharp()
     plusAC(x,sharp()) -> x
     plusAC(zero(x),zero(y)) -> zero(plusAC(x,y))
     plusAC(zero(x),one(y)) -> one(plusAC(x,y))
     plusAC(one(x),one(y)) -> zero(plusAC(x,plusAC(y,one(sharp()))))
    S:
     plus{AC,#}(plusAC(x9,x10),x11) -> plus{AC,#}(x9,x10)
     plus{AC,#}(x9,plusAC(x10,x11)) -> plus{AC,#}(x10,x11)
    AC-DP unlabeling:
     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)
     DPs:
      plusAC(one(x),one(y)) -> plusAC(y,one(sharp()))
      plusAC(x8,plusAC(one(x),one(y))) -> plusAC(x8,zero(plusAC(x,plusAC(y,one(sharp())))))
      plusAC(x8,plusAC(one(x),one(y))) -> plusAC(x,plusAC(y,one(sharp())))
      plusAC(x8,plusAC(one(x),one(y))) -> plusAC(y,one(sharp()))
      plusAC(x7,plusAC(zero(x),one(y))) -> plusAC(x7,one(plusAC(x,y)))
      plusAC(x7,plusAC(zero(x),one(y))) -> plusAC(x,y)
      plusAC(x6,plusAC(zero(x),zero(y))) -> plusAC(x6,zero(plusAC(x,y)))
      plusAC(x6,plusAC(zero(x),zero(y))) -> plusAC(x,y)
      plusAC(x5,plusAC(x,sharp())) -> plusAC(x5,x)
      plusAC(one(x),one(y)) -> plusAC(x,plusAC(y,one(sharp())))
      plusAC(zero(x),one(y)) -> plusAC(x,y)
      plusAC(zero(x),zero(y)) -> 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:
      zero(sharp()) -> sharp()
      plusAC(x,sharp()) -> x
      plusAC(zero(x),zero(y)) -> zero(plusAC(x,y))
      plusAC(zero(x),one(y)) -> one(plusAC(x,y))
      plusAC(one(x),one(y)) -> zero(plusAC(x,plusAC(y,one(sharp()))))
     S:
      plusAC(plusAC(x9,x10),x11) -> plusAC(x9,x10)
      plusAC(x9,plusAC(x10,x11)) -> plusAC(x10,x11)
     AC-KBO Processor:
      argument filtering:
       pi(plusAC) = [0,1]
       pi(sharp) = []
       pi(zero) = [0]
       pi(one) = [0]
      precedence:
       plusAC > one ~ zero ~ sharp
       weight function:
        w0 = 2
        w(one) = 5
        w(sharp) = w(plusAC) = 2
        w(zero) = 1
        usable rules:
         zero(sharp()) -> sharp()
         plusAC(x,sharp()) -> x
         plusAC(zero(x),zero(y)) -> zero(plusAC(x,y))
         plusAC(zero(x),one(y)) -> one(plusAC(x,y))
         plusAC(one(x),one(y)) -> zero(plusAC(x,plusAC(y,one(sharp()))))
        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)
         DPs:
          
         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:
          zero(sharp()) -> sharp()
          plusAC(x,sharp()) -> x
          plusAC(zero(x),zero(y)) -> zero(plusAC(x,y))
          plusAC(zero(x),one(y)) -> one(plusAC(x,y))
          plusAC(one(x),one(y)) -> zero(plusAC(x,plusAC(y,one(sharp()))))
         S:
          plusAC(plusAC(x9,x10),x11) -> plusAC(x9,x10)
          plusAC(x9,plusAC(x10,x11)) -> plusAC(x10,x11)
        Qed