YES
Time: 0.197

Problem:
 Equations:
  pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
  pAC(x3,x4) -> pAC(x4,x3)
  pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
  pAC(x4,x3) -> pAC(x3,x4)
 TRS:
  pAC(x,zero()) -> x
  pAC(i(x),x) -> zero()
  m(one(),x) -> x
  m(x,one()) -> x
  m(x,m(y,z)) -> m(m(x,y),z)
  m(z,pAC(x,y)) -> pAC(m(z,x),m(z,y))
  m(pAC(x,y),z) -> pAC(m(x,z),m(y,z))

Proof:
 DP Processor:
  Equations#:
   p{AC,#}(pAC(x3,x4),x5) -> p{AC,#}(x3,pAC(x4,x5))
   p{AC,#}(x3,x4) -> p{AC,#}(x4,x3)
   p{AC,#}(x3,pAC(x4,x5)) -> p{AC,#}(pAC(x3,x4),x5)
   p{AC,#}(x4,x3) -> p{AC,#}(x3,x4)
  DPs:
   m#(x,m(y,z)) -> m#(x,y)
   m#(x,m(y,z)) -> m#(m(x,y),z)
   m#(z,pAC(x,y)) -> m#(z,y)
   m#(z,pAC(x,y)) -> m#(z,x)
   m#(z,pAC(x,y)) -> p{AC,#}(m(z,x),m(z,y))
   m#(pAC(x,y),z) -> m#(y,z)
   m#(pAC(x,y),z) -> m#(x,z)
   m#(pAC(x,y),z) -> p{AC,#}(m(x,z),m(y,z))
   p{AC,#}(x6,pAC(x,zero())) -> p{AC,#}(x6,x)
   p{AC,#}(x7,pAC(i(x),x)) -> p{AC,#}(x7,zero())
  Equations:
   pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
   pAC(x3,x4) -> pAC(x4,x3)
   pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
   pAC(x4,x3) -> pAC(x3,x4)
  TRS:
   pAC(x,zero()) -> x
   pAC(i(x),x) -> zero()
   m(one(),x) -> x
   m(x,one()) -> x
   m(x,m(y,z)) -> m(m(x,y),z)
   m(z,pAC(x,y)) -> pAC(m(z,x),m(z,y))
   m(pAC(x,y),z) -> pAC(m(x,z),m(y,z))
  S:
   p{AC,#}(pAC(x8,x9),x10) -> p{AC,#}(x8,x9)
   p{AC,#}(x8,pAC(x9,x10)) -> p{AC,#}(x9,x10)
  AC-EDG Processor:
   Equations#:
    p{AC,#}(pAC(x3,x4),x5) -> p{AC,#}(x3,pAC(x4,x5))
    p{AC,#}(x3,x4) -> p{AC,#}(x4,x3)
    p{AC,#}(x3,pAC(x4,x5)) -> p{AC,#}(pAC(x3,x4),x5)
    p{AC,#}(x4,x3) -> p{AC,#}(x3,x4)
   DPs:
    m#(x,m(y,z)) -> m#(x,y)
    m#(x,m(y,z)) -> m#(m(x,y),z)
    m#(z,pAC(x,y)) -> m#(z,y)
    m#(z,pAC(x,y)) -> m#(z,x)
    m#(z,pAC(x,y)) -> p{AC,#}(m(z,x),m(z,y))
    m#(pAC(x,y),z) -> m#(y,z)
    m#(pAC(x,y),z) -> m#(x,z)
    m#(pAC(x,y),z) -> p{AC,#}(m(x,z),m(y,z))
    p{AC,#}(x6,pAC(x,zero())) -> p{AC,#}(x6,x)
    p{AC,#}(x7,pAC(i(x),x)) -> p{AC,#}(x7,zero())
   Equations:
    pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
    pAC(x3,x4) -> pAC(x4,x3)
    pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
    pAC(x4,x3) -> pAC(x3,x4)
   TRS:
    pAC(x,zero()) -> x
    pAC(i(x),x) -> zero()
    m(one(),x) -> x
    m(x,one()) -> x
    m(x,m(y,z)) -> m(m(x,y),z)
    m(z,pAC(x,y)) -> pAC(m(z,x),m(z,y))
    m(pAC(x,y),z) -> pAC(m(x,z),m(y,z))
   S:
    p{AC,#}(pAC(x8,x9),x10) -> p{AC,#}(x8,x9)
    p{AC,#}(x8,pAC(x9,x10)) -> p{AC,#}(x9,x10)
   SCC Processor:
    #sccs: 2
    #rules: 8
    #arcs: 56/100
    Equations#:
     p{AC,#}(pAC(x3,x4),x5) -> p{AC,#}(x3,pAC(x4,x5))
     p{AC,#}(x3,x4) -> p{AC,#}(x4,x3)
     p{AC,#}(x3,pAC(x4,x5)) -> p{AC,#}(pAC(x3,x4),x5)
     p{AC,#}(x4,x3) -> p{AC,#}(x3,x4)
    DPs:
     m#(pAC(x,y),z) -> m#(y,z)
     m#(pAC(x,y),z) -> m#(x,z)
     m#(z,pAC(x,y)) -> m#(z,x)
     m#(z,pAC(x,y)) -> m#(z,y)
     m#(x,m(y,z)) -> m#(m(x,y),z)
     m#(x,m(y,z)) -> m#(x,y)
    Equations:
     pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
     pAC(x3,x4) -> pAC(x4,x3)
     pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
     pAC(x4,x3) -> pAC(x3,x4)
    TRS:
     pAC(x,zero()) -> x
     pAC(i(x),x) -> zero()
     m(one(),x) -> x
     m(x,one()) -> x
     m(x,m(y,z)) -> m(m(x,y),z)
     m(z,pAC(x,y)) -> pAC(m(z,x),m(z,y))
     m(pAC(x,y),z) -> pAC(m(x,z),m(y,z))
    S:
     p{AC,#}(pAC(x8,x9),x10) -> p{AC,#}(x8,x9)
     p{AC,#}(x8,pAC(x9,x10)) -> p{AC,#}(x9,x10)
    AC-DP unlabeling:
     Equations#:
      pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
      pAC(x3,x4) -> pAC(x4,x3)
      pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
      pAC(x4,x3) -> pAC(x3,x4)
     DPs:
      m#(pAC(x,y),z) -> m#(y,z)
      m#(pAC(x,y),z) -> m#(x,z)
      m#(z,pAC(x,y)) -> m#(z,x)
      m#(z,pAC(x,y)) -> m#(z,y)
      m#(x,m(y,z)) -> m#(m(x,y),z)
      m#(x,m(y,z)) -> m#(x,y)
     Equations:
      pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
      pAC(x3,x4) -> pAC(x4,x3)
      pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
      pAC(x4,x3) -> pAC(x3,x4)
     TRS:
      pAC(x,zero()) -> x
      pAC(i(x),x) -> zero()
      m(one(),x) -> x
      m(x,one()) -> x
      m(x,m(y,z)) -> m(m(x,y),z)
      m(z,pAC(x,y)) -> pAC(m(z,x),m(z,y))
      m(pAC(x,y),z) -> pAC(m(x,z),m(y,z))
     S:
      pAC(pAC(x8,x9),x10) -> pAC(x8,x9)
      pAC(x8,pAC(x9,x10)) -> pAC(x9,x10)
     AC-KBO Processor:
      argument filtering:
       pi(pAC) = [0,1]
       pi(zero) = []
       pi(i) = 0
       pi(one) = []
       pi(m) = [0,1]
       pi(m#) = [1]
      precedence:
       m# ~ m ~ one ~ i ~ zero ~ pAC
       weight function:
        w0 = 1
        w(pAC) = 7
        w(m#) = w(one) = w(i) = w(zero) = 1
        w(m) = 0
        usable rules:
         
        problem:
         Equations#:
          pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
          pAC(x3,x4) -> pAC(x4,x3)
          pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
          pAC(x4,x3) -> pAC(x3,x4)
         DPs:
          m#(pAC(x,y),z) -> m#(y,z)
          m#(pAC(x,y),z) -> m#(x,z)
         Equations:
          pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
          pAC(x3,x4) -> pAC(x4,x3)
          pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
          pAC(x4,x3) -> pAC(x3,x4)
         TRS:
          pAC(x,zero()) -> x
          pAC(i(x),x) -> zero()
          m(one(),x) -> x
          m(x,one()) -> x
          m(x,m(y,z)) -> m(m(x,y),z)
          m(z,pAC(x,y)) -> pAC(m(z,x),m(z,y))
          m(pAC(x,y),z) -> pAC(m(x,z),m(y,z))
         S:
          pAC(pAC(x8,x9),x10) -> pAC(x8,x9)
          pAC(x8,pAC(x9,x10)) -> pAC(x9,x10)
        Restore Modifier:
         Equations#:
          pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
          pAC(x3,x4) -> pAC(x4,x3)
          pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
          pAC(x4,x3) -> pAC(x3,x4)
         DPs:
          m#(pAC(x,y),z) -> m#(y,z)
          m#(pAC(x,y),z) -> m#(x,z)
         Equations:
          pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
          pAC(x3,x4) -> pAC(x4,x3)
          pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
          pAC(x4,x3) -> pAC(x3,x4)
         TRS:
          pAC(x,zero()) -> x
          pAC(i(x),x) -> zero()
          m(one(),x) -> x
          m(x,one()) -> x
          m(x,m(y,z)) -> m(m(x,y),z)
          m(z,pAC(x,y)) -> pAC(m(z,x),m(z,y))
          m(pAC(x,y),z) -> pAC(m(x,z),m(y,z))
         S:
          pAC(pAC(x8,x9),x10) -> pAC(x8,x9)
          pAC(x8,pAC(x9,x10)) -> pAC(x9,x10)
         AC-DP unlabeling:
          Equations#:
           pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
           pAC(x3,x4) -> pAC(x4,x3)
           pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
           pAC(x4,x3) -> pAC(x3,x4)
          DPs:
           m#(pAC(x,y),z) -> m#(y,z)
           m#(pAC(x,y),z) -> m#(x,z)
          Equations:
           pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
           pAC(x3,x4) -> pAC(x4,x3)
           pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
           pAC(x4,x3) -> pAC(x3,x4)
          TRS:
           pAC(x,zero()) -> x
           pAC(i(x),x) -> zero()
           m(one(),x) -> x
           m(x,one()) -> x
           m(x,m(y,z)) -> m(m(x,y),z)
           m(z,pAC(x,y)) -> pAC(m(z,x),m(z,y))
           m(pAC(x,y),z) -> pAC(m(x,z),m(y,z))
          S:
           pAC(pAC(x8,x9),x10) -> pAC(x8,x9)
           pAC(x8,pAC(x9,x10)) -> pAC(x9,x10)
          Usable Rule Processor:
           Equations#:
            pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
            pAC(x3,x4) -> pAC(x4,x3)
            pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
            pAC(x4,x3) -> pAC(x3,x4)
           DPs:
            m#(pAC(x,y),z) -> m#(y,z)
            m#(pAC(x,y),z) -> m#(x,z)
           Equations:
            pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
            pAC(x3,x4) -> pAC(x4,x3)
            pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
            pAC(x4,x3) -> pAC(x3,x4)
           TRS:
            
           S:
            pAC(pAC(x8,x9),x10) -> pAC(x8,x9)
            pAC(x8,pAC(x9,x10)) -> pAC(x9,x10)
           AC-KBO Processor:
            argument filtering:
             pi(pAC) = [0,1]
             pi(m#) = [0,1]
            precedence:
             m# ~ pAC
             weight function:
              w0 = 4
              w(m#) = 7
              w(pAC) = 0
              usable rules:
               
              problem:
               Equations#:
                pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
                pAC(x3,x4) -> pAC(x4,x3)
                pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
                pAC(x4,x3) -> pAC(x3,x4)
               DPs:
                
               Equations:
                pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
                pAC(x3,x4) -> pAC(x4,x3)
                pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
                pAC(x4,x3) -> pAC(x3,x4)
               TRS:
                
               S:
                pAC(pAC(x8,x9),x10) -> pAC(x8,x9)
                pAC(x8,pAC(x9,x10)) -> pAC(x9,x10)
              Qed
     
     Equations#:
      p{AC,#}(pAC(x3,x4),x5) -> p{AC,#}(x3,pAC(x4,x5))
      p{AC,#}(x3,x4) -> p{AC,#}(x4,x3)
      p{AC,#}(x3,pAC(x4,x5)) -> p{AC,#}(pAC(x3,x4),x5)
      p{AC,#}(x4,x3) -> p{AC,#}(x3,x4)
     DPs:
      p{AC,#}(x7,pAC(i(x),x)) -> p{AC,#}(x7,zero())
      p{AC,#}(x6,pAC(x,zero())) -> p{AC,#}(x6,x)
     Equations:
      pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
      pAC(x3,x4) -> pAC(x4,x3)
      pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
      pAC(x4,x3) -> pAC(x3,x4)
     TRS:
      pAC(x,zero()) -> x
      pAC(i(x),x) -> zero()
      m(one(),x) -> x
      m(x,one()) -> x
      m(x,m(y,z)) -> m(m(x,y),z)
      m(z,pAC(x,y)) -> pAC(m(z,x),m(z,y))
      m(pAC(x,y),z) -> pAC(m(x,z),m(y,z))
     S:
      p{AC,#}(pAC(x8,x9),x10) -> p{AC,#}(x8,x9)
      p{AC,#}(x8,pAC(x9,x10)) -> p{AC,#}(x9,x10)
     AC-DP unlabeling:
      Equations#:
       pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
       pAC(x3,x4) -> pAC(x4,x3)
       pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
       pAC(x4,x3) -> pAC(x3,x4)
      DPs:
       pAC(x7,pAC(i(x),x)) -> pAC(x7,zero())
       pAC(x6,pAC(x,zero())) -> pAC(x6,x)
      Equations:
       pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
       pAC(x3,x4) -> pAC(x4,x3)
       pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
       pAC(x4,x3) -> pAC(x3,x4)
      TRS:
       pAC(x,zero()) -> x
       pAC(i(x),x) -> zero()
       m(one(),x) -> x
       m(x,one()) -> x
       m(x,m(y,z)) -> m(m(x,y),z)
       m(z,pAC(x,y)) -> pAC(m(z,x),m(z,y))
       m(pAC(x,y),z) -> pAC(m(x,z),m(y,z))
      S:
       pAC(pAC(x8,x9),x10) -> pAC(x8,x9)
       pAC(x8,pAC(x9,x10)) -> pAC(x9,x10)
      Usable Rule Processor:
       Equations#:
        pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
        pAC(x3,x4) -> pAC(x4,x3)
        pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
        pAC(x4,x3) -> pAC(x3,x4)
       DPs:
        pAC(x7,pAC(i(x),x)) -> pAC(x7,zero())
        pAC(x6,pAC(x,zero())) -> pAC(x6,x)
       Equations:
        pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
        pAC(x3,x4) -> pAC(x4,x3)
        pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
        pAC(x4,x3) -> pAC(x3,x4)
       TRS:
        pAC(x,zero()) -> x
        pAC(i(x),x) -> zero()
       S:
        pAC(pAC(x8,x9),x10) -> pAC(x8,x9)
        pAC(x8,pAC(x9,x10)) -> pAC(x9,x10)
       AC-KBO Processor:
        argument filtering:
         pi(pAC) = [0,1]
         pi(zero) = []
         pi(i) = []
        precedence:
         i ~ zero ~ pAC
         weight function:
          w0 = 2
          w(i) = w(zero) = 4
          w(pAC) = 1
          usable rules:
           pAC(x,zero()) -> x
           pAC(i(x),x) -> zero()
          problem:
           Equations#:
            pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
            pAC(x3,x4) -> pAC(x4,x3)
            pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
            pAC(x4,x3) -> pAC(x3,x4)
           DPs:
            
           Equations:
            pAC(pAC(x3,x4),x5) -> pAC(x3,pAC(x4,x5))
            pAC(x3,x4) -> pAC(x4,x3)
            pAC(x3,pAC(x4,x5)) -> pAC(pAC(x3,x4),x5)
            pAC(x4,x3) -> pAC(x3,x4)
           TRS:
            pAC(x,zero()) -> x
            pAC(i(x),x) -> zero()
           S:
            pAC(pAC(x8,x9),x10) -> pAC(x8,x9)
            pAC(x8,pAC(x9,x10)) -> pAC(x9,x10)
          Qed