YES
Time: 0.151

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:
  s(p(x)) -> x
  p(s(x)) -> x
  minus(x,0()) -> x
  minus(x,s(y)) -> p(minus(x,y))
  minus(x,p(y)) -> s(minus(x,y))
  plusAC(x,0()) -> x
  plusAC(x,s(y)) -> s(plusAC(x,y))
  plusAC(x,p(y)) -> p(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#(x,s(y)) -> minus#(x,y)
   minus#(x,s(y)) -> p#(minus(x,y))
   minus#(x,p(y)) -> minus#(x,y)
   minus#(x,p(y)) -> s#(minus(x,y))
   plus{AC,#}(x,s(y)) -> plus{AC,#}(x,y)
   plus{AC,#}(x,s(y)) -> s#(plusAC(x,y))
   plus{AC,#}(x,p(y)) -> plus{AC,#}(x,y)
   plus{AC,#}(x,p(y)) -> p#(plusAC(x,y))
   plus{AC,#}(x6,plusAC(x,0())) -> plus{AC,#}(x6,x)
   plus{AC,#}(x7,plusAC(x,s(y))) -> plus{AC,#}(x,y)
   plus{AC,#}(x7,plusAC(x,s(y))) -> s#(plusAC(x,y))
   plus{AC,#}(x7,plusAC(x,s(y))) -> plus{AC,#}(x7,s(plusAC(x,y)))
   plus{AC,#}(x8,plusAC(x,p(y))) -> plus{AC,#}(x,y)
   plus{AC,#}(x8,plusAC(x,p(y))) -> p#(plusAC(x,y))
   plus{AC,#}(x8,plusAC(x,p(y))) -> plus{AC,#}(x8,p(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:
   s(p(x)) -> x
   p(s(x)) -> x
   minus(x,0()) -> x
   minus(x,s(y)) -> p(minus(x,y))
   minus(x,p(y)) -> s(minus(x,y))
   plusAC(x,0()) -> x
   plusAC(x,s(y)) -> s(plusAC(x,y))
   plusAC(x,p(y)) -> p(plusAC(x,y))
  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(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#(x,s(y)) -> minus#(x,y)
    minus#(x,s(y)) -> p#(minus(x,y))
    minus#(x,p(y)) -> minus#(x,y)
    minus#(x,p(y)) -> s#(minus(x,y))
    plus{AC,#}(x,s(y)) -> plus{AC,#}(x,y)
    plus{AC,#}(x,s(y)) -> s#(plusAC(x,y))
    plus{AC,#}(x,p(y)) -> plus{AC,#}(x,y)
    plus{AC,#}(x,p(y)) -> p#(plusAC(x,y))
    plus{AC,#}(x6,plusAC(x,0())) -> plus{AC,#}(x6,x)
    plus{AC,#}(x7,plusAC(x,s(y))) -> plus{AC,#}(x,y)
    plus{AC,#}(x7,plusAC(x,s(y))) -> s#(plusAC(x,y))
    plus{AC,#}(x7,plusAC(x,s(y))) -> plus{AC,#}(x7,s(plusAC(x,y)))
    plus{AC,#}(x8,plusAC(x,p(y))) -> plus{AC,#}(x,y)
    plus{AC,#}(x8,plusAC(x,p(y))) -> p#(plusAC(x,y))
    plus{AC,#}(x8,plusAC(x,p(y))) -> plus{AC,#}(x8,p(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:
    s(p(x)) -> x
    p(s(x)) -> x
    minus(x,0()) -> x
    minus(x,s(y)) -> p(minus(x,y))
    minus(x,p(y)) -> s(minus(x,y))
    plusAC(x,0()) -> x
    plusAC(x,s(y)) -> s(plusAC(x,y))
    plusAC(x,p(y)) -> p(plusAC(x,y))
   S:
    plus{AC,#}(plusAC(x9,x10),x11) -> plus{AC,#}(x9,x10)
    plus{AC,#}(x9,plusAC(x10,x11)) -> plus{AC,#}(x10,x11)
   SCC Processor:
    #sccs: 2
    #rules: 9
    #arcs: 85/225
    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#(x,s(y)) -> minus#(x,y)
     minus#(x,p(y)) -> minus#(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:
     s(p(x)) -> x
     p(s(x)) -> x
     minus(x,0()) -> x
     minus(x,s(y)) -> p(minus(x,y))
     minus(x,p(y)) -> s(minus(x,y))
     plusAC(x,0()) -> x
     plusAC(x,s(y)) -> s(plusAC(x,y))
     plusAC(x,p(y)) -> p(plusAC(x,y))
    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(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)
     DPs:
      minus#(x,s(y)) -> minus#(x,y)
      minus#(x,p(y)) -> minus#(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:
      s(p(x)) -> x
      p(s(x)) -> x
      minus(x,0()) -> x
      minus(x,s(y)) -> p(minus(x,y))
      minus(x,p(y)) -> s(minus(x,y))
      plusAC(x,0()) -> x
      plusAC(x,s(y)) -> s(plusAC(x,y))
      plusAC(x,p(y)) -> p(plusAC(x,y))
     S:
      plusAC(plusAC(x9,x10),x11) -> plusAC(x9,x10)
      plusAC(x9,plusAC(x10,x11)) -> plusAC(x10,x11)
     Usable Rule Processor:
      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)
      DPs:
       minus#(x,s(y)) -> minus#(x,y)
       minus#(x,p(y)) -> minus#(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:
       
      S:
       plusAC(plusAC(x9,x10),x11) -> plusAC(x9,x10)
       plusAC(x9,plusAC(x10,x11)) -> plusAC(x10,x11)
      AC-RPO Processor:
       argument filtering:
        pi(plusAC) = []
        pi(p) = 0
        pi(s) = [0]
        pi(minus#) = 1
       precedence:
        minus# > s > p > plusAC
       status:
        minus#:mul  
       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)
        DPs:
         minus#(x,p(y)) -> minus#(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:
         
        S:
         plusAC(plusAC(x9,x10),x11) -> plusAC(x9,x10)
         plusAC(x9,plusAC(x10,x11)) -> plusAC(x10,x11)
       Restore Modifier:
        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)
        DPs:
         minus#(x,p(y)) -> minus#(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:
         
        S:
         plusAC(plusAC(x9,x10),x11) -> plusAC(x9,x10)
         plusAC(x9,plusAC(x10,x11)) -> plusAC(x10,x11)
        AC-DP unlabeling:
         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)
         DPs:
          minus#(x,p(y)) -> minus#(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:
          
         S:
          plusAC(plusAC(x9,x10),x11) -> plusAC(x9,x10)
          plusAC(x9,plusAC(x10,x11)) -> plusAC(x10,x11)
         AC-RPO Processor:
          argument filtering:
           pi(plusAC) = []
           pi(p) = [0]
           pi(minus#) = 1
          precedence:
           minus# > p > plusAC
          status:
           minus#:mul  
          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)
           DPs:
            
           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:
            
           S:
            plusAC(plusAC(x9,x10),x11) -> plusAC(x9,x10)
            plusAC(x9,plusAC(x10,x11)) -> plusAC(x10,x11)
          Qed
    
    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:
     plus{AC,#}(x8,plusAC(x,p(y))) -> plus{AC,#}(x8,p(plusAC(x,y)))
     plus{AC,#}(x8,plusAC(x,p(y))) -> plus{AC,#}(x,y)
     plus{AC,#}(x7,plusAC(x,s(y))) -> plus{AC,#}(x7,s(plusAC(x,y)))
     plus{AC,#}(x7,plusAC(x,s(y))) -> plus{AC,#}(x,y)
     plus{AC,#}(x6,plusAC(x,0())) -> plus{AC,#}(x6,x)
     plus{AC,#}(x,p(y)) -> plus{AC,#}(x,y)
     plus{AC,#}(x,s(y)) -> plus{AC,#}(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:
     s(p(x)) -> x
     p(s(x)) -> x
     minus(x,0()) -> x
     minus(x,s(y)) -> p(minus(x,y))
     minus(x,p(y)) -> s(minus(x,y))
     plusAC(x,0()) -> x
     plusAC(x,s(y)) -> s(plusAC(x,y))
     plusAC(x,p(y)) -> p(plusAC(x,y))
    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(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)
     DPs:
      plusAC(x8,plusAC(x,p(y))) -> plusAC(x8,p(plusAC(x,y)))
      plusAC(x8,plusAC(x,p(y))) -> plusAC(x,y)
      plusAC(x7,plusAC(x,s(y))) -> plusAC(x7,s(plusAC(x,y)))
      plusAC(x7,plusAC(x,s(y))) -> plusAC(x,y)
      plusAC(x6,plusAC(x,0())) -> plusAC(x6,x)
      plusAC(x,p(y)) -> plusAC(x,y)
      plusAC(x,s(y)) -> 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:
      s(p(x)) -> x
      p(s(x)) -> x
      minus(x,0()) -> x
      minus(x,s(y)) -> p(minus(x,y))
      minus(x,p(y)) -> s(minus(x,y))
      plusAC(x,0()) -> x
      plusAC(x,s(y)) -> s(plusAC(x,y))
      plusAC(x,p(y)) -> p(plusAC(x,y))
     S:
      plusAC(plusAC(x9,x10),x11) -> plusAC(x9,x10)
      plusAC(x9,plusAC(x10,x11)) -> plusAC(x10,x11)
     Usable Rule Processor:
      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)
      DPs:
       plusAC(x8,plusAC(x,p(y))) -> plusAC(x8,p(plusAC(x,y)))
       plusAC(x8,plusAC(x,p(y))) -> plusAC(x,y)
       plusAC(x7,plusAC(x,s(y))) -> plusAC(x7,s(plusAC(x,y)))
       plusAC(x7,plusAC(x,s(y))) -> plusAC(x,y)
       plusAC(x6,plusAC(x,0())) -> plusAC(x6,x)
       plusAC(x,p(y)) -> plusAC(x,y)
       plusAC(x,s(y)) -> 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:
       plusAC(x,0()) -> x
       plusAC(x,s(y)) -> s(plusAC(x,y))
       plusAC(x,p(y)) -> p(plusAC(x,y))
       s(p(x)) -> x
       p(s(x)) -> x
      S:
       plusAC(plusAC(x9,x10),x11) -> plusAC(x9,x10)
       plusAC(x9,plusAC(x10,x11)) -> plusAC(x10,x11)
      AC-RPO Processor:
       argument filtering:
        pi(plusAC) = [0,1]
        pi(p) = [0]
        pi(s) = [0]
        pi(0) = []
       precedence:
        plusAC > p > s > 0
       status:
        
       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)
        DPs:
         
        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:
         plusAC(x,0()) -> x
         plusAC(x,s(y)) -> s(plusAC(x,y))
         plusAC(x,p(y)) -> p(plusAC(x,y))
         s(p(x)) -> x
         p(s(x)) -> x
        S:
         plusAC(plusAC(x9,x10),x11) -> plusAC(x9,x10)
         plusAC(x9,plusAC(x10,x11)) -> plusAC(x10,x11)
       Qed