YES
Time: 0.080

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:
  plusAC(x,0()) -> x
  plusAC(x,s(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:
   plus{AC,#}(x,s(y)) -> plus{AC,#}(x,y)
   plus{AC,#}(x5,plusAC(x,0())) -> plus{AC,#}(x5,x)
   plus{AC,#}(x6,plusAC(x,s(y))) -> plus{AC,#}(x,y)
   plus{AC,#}(x6,plusAC(x,s(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:
   plusAC(x,0()) -> x
   plusAC(x,s(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-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(x,s(y)) -> plusAC(x,y)
    plusAC(x5,plusAC(x,0())) -> plusAC(x5,x)
    plusAC(x6,plusAC(x,s(y))) -> plusAC(x,y)
    plusAC(x6,plusAC(x,s(y))) -> plusAC(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:
    plusAC(x,0()) -> x
    plusAC(x,s(y)) -> s(plusAC(x,y))
   S:
    plusAC(plusAC(x7,x8),x9) -> plusAC(x7,x8)
    plusAC(x7,plusAC(x8,x9)) -> plusAC(x8,x9)
   AC-KBO Processor:
    argument filtering:
     pi(plusAC) = [0,1]
     pi(0) = []
     pi(s) = [0]
    precedence:
     0 ~ plusAC > s
     weight function:
      w0 = 2
      w(s) = 5
      w(0) = 2
      w(plusAC) = 0
      usable rules:
       plusAC(x,0()) -> x
       plusAC(x,s(y)) -> s(plusAC(x,y))
      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:
        plusAC(x,0()) -> x
        plusAC(x,s(y)) -> s(plusAC(x,y))
       S:
        plusAC(plusAC(x7,x8),x9) -> plusAC(x7,x8)
        plusAC(x7,plusAC(x8,x9)) -> plusAC(x8,x9)
      Qed