YES
Time: 0.086

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))
  double(x) -> plusAC(x,x)

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)
   double#(x) -> plus{AC,#}(x,x)
   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))
   double(x) -> plusAC(x,x)
  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:
    plus{AC,#}(x,s(y)) -> plus{AC,#}(x,y)
    double#(x) -> plus{AC,#}(x,x)
    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))
    double(x) -> plusAC(x,x)
   S:
    plus{AC,#}(plusAC(x7,x8),x9) -> plus{AC,#}(x7,x8)
    plus{AC,#}(x7,plusAC(x8,x9)) -> plus{AC,#}(x8,x9)
   SCC Processor:
    #sccs: 1
    #rules: 4
    #arcs: 20/25
    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,#}(x6,plusAC(x,s(y))) -> plus{AC,#}(x6,s(plusAC(x,y)))
     plus{AC,#}(x6,plusAC(x,s(y))) -> plus{AC,#}(x,y)
     plus{AC,#}(x5,plusAC(x,0())) -> plus{AC,#}(x5,x)
     plus{AC,#}(x,s(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:
     plusAC(x,0()) -> x
     plusAC(x,s(y)) -> s(plusAC(x,y))
     double(x) -> plusAC(x,x)
    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(x6,plusAC(x,s(y))) -> plusAC(x6,s(plusAC(x,y)))
      plusAC(x6,plusAC(x,s(y))) -> plusAC(x,y)
      plusAC(x5,plusAC(x,0())) -> plusAC(x5,x)
      plusAC(x,s(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:
      plusAC(x,0()) -> x
      plusAC(x,s(y)) -> s(plusAC(x,y))
      double(x) -> plusAC(x,x)
     S:
      plusAC(plusAC(x7,x8),x9) -> plusAC(x7,x8)
      plusAC(x7,plusAC(x8,x9)) -> plusAC(x8,x9)
     Usable Rule Processor:
      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(x6,plusAC(x,s(y))) -> plusAC(x6,s(plusAC(x,y)))
       plusAC(x6,plusAC(x,s(y))) -> plusAC(x,y)
       plusAC(x5,plusAC(x,0())) -> plusAC(x5,x)
       plusAC(x,s(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:
       plusAC(x,s(y)) -> s(plusAC(x,y))
       plusAC(x,0()) -> x
      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 = 4
         w(plusAC) = 5
         w(0) = 4
         w(s) = 2
         usable rules:
          plusAC(x,s(y)) -> s(plusAC(x,y))
          plusAC(x,0()) -> x
         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,s(y)) -> s(plusAC(x,y))
           plusAC(x,0()) -> x
          S:
           plusAC(plusAC(x7,x8),x9) -> plusAC(x7,x8)
           plusAC(x7,plusAC(x8,x9)) -> plusAC(x8,x9)
         Qed