YES
Time: 0.335

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(z,pAC(x,y)) -> pAC(m(z,x),m(z,y))
  m(pAC(x,y),z) -> pAC(m(x,z),m(y,z))
  b(x,x) -> zero()
  pAC(b(b(x,y),z),pAC(b(b(y,z),x),b(b(z,x),y))) -> zero()
  b(pAC(x,y),z) -> pAC(b(x,z),b(y,z))
  b(x,pAC(y,z)) -> pAC(b(x,y),b(x,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#(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))
   b#(pAC(x,y),z) -> b#(y,z)
   b#(pAC(x,y),z) -> b#(x,z)
   b#(pAC(x,y),z) -> p{AC,#}(b(x,z),b(y,z))
   b#(x,pAC(y,z)) -> b#(x,z)
   b#(x,pAC(y,z)) -> b#(x,y)
   b#(x,pAC(y,z)) -> p{AC,#}(b(x,y),b(x,z))
   p{AC,#}(x6,pAC(x,zero())) -> p{AC,#}(x6,x)
   p{AC,#}(x7,pAC(i(x),x)) -> p{AC,#}(x7,zero())
   p{AC,#}(x8,pAC(b(b(x,y),z),pAC(b(b(y,z),x),b(b(z,x),y)))) -> p{AC,#}(x8,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(z,pAC(x,y)) -> pAC(m(z,x),m(z,y))
   m(pAC(x,y),z) -> pAC(m(x,z),m(y,z))
   b(x,x) -> zero()
   pAC(b(b(x,y),z),pAC(b(b(y,z),x),b(b(z,x),y))) -> zero()
   b(pAC(x,y),z) -> pAC(b(x,z),b(y,z))
   b(x,pAC(y,z)) -> pAC(b(x,y),b(x,z))
  S:
   p{AC,#}(pAC(x9,x10),x11) -> p{AC,#}(x9,x10)
   p{AC,#}(x9,pAC(x10,x11)) -> p{AC,#}(x10,x11)
  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#(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))
    b#(pAC(x,y),z) -> b#(y,z)
    b#(pAC(x,y),z) -> b#(x,z)
    b#(pAC(x,y),z) -> p{AC,#}(b(x,z),b(y,z))
    b#(x,pAC(y,z)) -> b#(x,z)
    b#(x,pAC(y,z)) -> b#(x,y)
    b#(x,pAC(y,z)) -> p{AC,#}(b(x,y),b(x,z))
    p{AC,#}(x6,pAC(x,zero())) -> p{AC,#}(x6,x)
    p{AC,#}(x7,pAC(i(x),x)) -> p{AC,#}(x7,zero())
    p{AC,#}(x8,pAC(b(b(x,y),z),pAC(b(b(y,z),x),b(b(z,x),y)))) -> p{AC,#}(x8,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(z,pAC(x,y)) -> pAC(m(z,x),m(z,y))
    m(pAC(x,y),z) -> pAC(m(x,z),m(y,z))
    b(x,x) -> zero()
    pAC(b(b(x,y),z),pAC(b(b(y,z),x),b(b(z,x),y))) -> zero()
    b(pAC(x,y),z) -> pAC(b(x,z),b(y,z))
    b(x,pAC(y,z)) -> pAC(b(x,y),b(x,z))
   S:
    p{AC,#}(pAC(x9,x10),x11) -> p{AC,#}(x9,x10)
    p{AC,#}(x9,pAC(x10,x11)) -> p{AC,#}(x10,x11)
   SCC Processor:
    #sccs: 3
    #rules: 11
    #arcs: 69/225
    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)
    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(z,pAC(x,y)) -> pAC(m(z,x),m(z,y))
     m(pAC(x,y),z) -> pAC(m(x,z),m(y,z))
     b(x,x) -> zero()
     pAC(b(b(x,y),z),pAC(b(b(y,z),x),b(b(z,x),y))) -> zero()
     b(pAC(x,y),z) -> pAC(b(x,z),b(y,z))
     b(x,pAC(y,z)) -> pAC(b(x,y),b(x,z))
    S:
     p{AC,#}(pAC(x9,x10),x11) -> p{AC,#}(x9,x10)
     p{AC,#}(x9,pAC(x10,x11)) -> p{AC,#}(x10,x11)
    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)
     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(z,pAC(x,y)) -> pAC(m(z,x),m(z,y))
      m(pAC(x,y),z) -> pAC(m(x,z),m(y,z))
      b(x,x) -> zero()
      pAC(b(b(x,y),z),pAC(b(b(y,z),x),b(b(z,x),y))) -> zero()
      b(pAC(x,y),z) -> pAC(b(x,z),b(y,z))
      b(x,pAC(y,z)) -> pAC(b(x,y),b(x,z))
     S:
      pAC(pAC(x9,x10),x11) -> pAC(x9,x10)
      pAC(x9,pAC(x10,x11)) -> pAC(x10,x11)
     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)
       m#(z,pAC(x,y)) -> m#(z,x)
       m#(z,pAC(x,y)) -> m#(z,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:
       
      S:
       pAC(pAC(x9,x10),x11) -> pAC(x9,x10)
       pAC(x9,pAC(x10,x11)) -> pAC(x10,x11)
      AC-KBO Processor:
       argument filtering:
        pi(pAC) = [0,1]
        pi(m#) = 0
       precedence:
        m# ~ pAC
        weight function:
         w0 = 4
         w(m#) = 4
         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:
           m#(z,pAC(x,y)) -> m#(z,x)
           m#(z,pAC(x,y)) -> m#(z,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:
           
          S:
           pAC(pAC(x9,x10),x11) -> pAC(x9,x10)
           pAC(x9,pAC(x10,x11)) -> pAC(x10,x11)
         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#(z,pAC(x,y)) -> m#(z,x)
           m#(z,pAC(x,y)) -> m#(z,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:
           
          S:
           pAC(pAC(x9,x10),x11) -> pAC(x9,x10)
           pAC(x9,pAC(x10,x11)) -> pAC(x10,x11)
          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#(z,pAC(x,y)) -> m#(z,x)
            m#(z,pAC(x,y)) -> m#(z,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:
            
           S:
            pAC(pAC(x9,x10),x11) -> pAC(x9,x10)
            pAC(x9,pAC(x10,x11)) -> pAC(x10,x11)
           AC-KBO Processor:
            argument filtering:
             pi(pAC) = [0,1]
             pi(m#) = [0,1]
            precedence:
             m# ~ pAC
             weight function:
              w0 = 3
              w(m#) = 3
              w(pAC) = 2
              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(x9,x10),x11) -> pAC(x9,x10)
                pAC(x9,pAC(x10,x11)) -> pAC(x10,x11)
              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:
      b#(pAC(x,y),z) -> b#(y,z)
      b#(x,pAC(y,z)) -> b#(x,y)
      b#(x,pAC(y,z)) -> b#(x,z)
      b#(pAC(x,y),z) -> b#(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(z,pAC(x,y)) -> pAC(m(z,x),m(z,y))
      m(pAC(x,y),z) -> pAC(m(x,z),m(y,z))
      b(x,x) -> zero()
      pAC(b(b(x,y),z),pAC(b(b(y,z),x),b(b(z,x),y))) -> zero()
      b(pAC(x,y),z) -> pAC(b(x,z),b(y,z))
      b(x,pAC(y,z)) -> pAC(b(x,y),b(x,z))
     S:
      p{AC,#}(pAC(x9,x10),x11) -> p{AC,#}(x9,x10)
      p{AC,#}(x9,pAC(x10,x11)) -> p{AC,#}(x10,x11)
     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:
       b#(pAC(x,y),z) -> b#(y,z)
       b#(x,pAC(y,z)) -> b#(x,y)
       b#(x,pAC(y,z)) -> b#(x,z)
       b#(pAC(x,y),z) -> b#(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(z,pAC(x,y)) -> pAC(m(z,x),m(z,y))
       m(pAC(x,y),z) -> pAC(m(x,z),m(y,z))
       b(x,x) -> zero()
       pAC(b(b(x,y),z),pAC(b(b(y,z),x),b(b(z,x),y))) -> zero()
       b(pAC(x,y),z) -> pAC(b(x,z),b(y,z))
       b(x,pAC(y,z)) -> pAC(b(x,y),b(x,z))
      S:
       pAC(pAC(x9,x10),x11) -> pAC(x9,x10)
       pAC(x9,pAC(x10,x11)) -> pAC(x10,x11)
      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:
        b#(pAC(x,y),z) -> b#(y,z)
        b#(x,pAC(y,z)) -> b#(x,y)
        b#(x,pAC(y,z)) -> b#(x,z)
        b#(pAC(x,y),z) -> b#(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(x9,x10),x11) -> pAC(x9,x10)
        pAC(x9,pAC(x10,x11)) -> pAC(x10,x11)
       AC-KBO Processor:
        argument filtering:
         pi(pAC) = [0,1]
         pi(b#) = 1
        precedence:
         b# ~ pAC
         weight function:
          w0 = 3
          w(pAC) = 5
          w(b#) = 3
          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:
            b#(pAC(x,y),z) -> b#(y,z)
            b#(pAC(x,y),z) -> b#(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(x9,x10),x11) -> pAC(x9,x10)
            pAC(x9,pAC(x10,x11)) -> pAC(x10,x11)
          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:
            b#(pAC(x,y),z) -> b#(y,z)
            b#(pAC(x,y),z) -> b#(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(x9,x10),x11) -> pAC(x9,x10)
            pAC(x9,pAC(x10,x11)) -> pAC(x10,x11)
           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:
             b#(pAC(x,y),z) -> b#(y,z)
             b#(pAC(x,y),z) -> b#(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(x9,x10),x11) -> pAC(x9,x10)
             pAC(x9,pAC(x10,x11)) -> pAC(x10,x11)
            AC-KBO Processor:
             argument filtering:
              pi(pAC) = [0,1]
              pi(b#) = [0,1]
             precedence:
              b# ~ pAC
              weight function:
               w0 = 2
               w(pAC) = 4
               w(b#) = 2
               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(x9,x10),x11) -> pAC(x9,x10)
                 pAC(x9,pAC(x10,x11)) -> pAC(x10,x11)
               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,#}(x8,pAC(b(b(x,y),z),pAC(b(b(y,z),x),b(b(z,x),y)))) -> p{AC,#}(x8,zero())
       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(z,pAC(x,y)) -> pAC(m(z,x),m(z,y))
       m(pAC(x,y),z) -> pAC(m(x,z),m(y,z))
       b(x,x) -> zero()
       pAC(b(b(x,y),z),pAC(b(b(y,z),x),b(b(z,x),y))) -> zero()
       b(pAC(x,y),z) -> pAC(b(x,z),b(y,z))
       b(x,pAC(y,z)) -> pAC(b(x,y),b(x,z))
      S:
       p{AC,#}(pAC(x9,x10),x11) -> p{AC,#}(x9,x10)
       p{AC,#}(x9,pAC(x10,x11)) -> p{AC,#}(x10,x11)
      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(x8,pAC(b(b(x,y),z),pAC(b(b(y,z),x),b(b(z,x),y)))) -> pAC(x8,zero())
        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(z,pAC(x,y)) -> pAC(m(z,x),m(z,y))
        m(pAC(x,y),z) -> pAC(m(x,z),m(y,z))
        b(x,x) -> zero()
        pAC(b(b(x,y),z),pAC(b(b(y,z),x),b(b(z,x),y))) -> zero()
        b(pAC(x,y),z) -> pAC(b(x,z),b(y,z))
        b(x,pAC(y,z)) -> pAC(b(x,y),b(x,z))
       S:
        pAC(pAC(x9,x10),x11) -> pAC(x9,x10)
        pAC(x9,pAC(x10,x11)) -> pAC(x10,x11)
       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(x8,pAC(b(b(x,y),z),pAC(b(b(y,z),x),b(b(z,x),y)))) -> pAC(x8,zero())
         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()
         pAC(b(b(x,y),z),pAC(b(b(y,z),x),b(b(z,x),y))) -> zero()
        S:
         pAC(pAC(x9,x10),x11) -> pAC(x9,x10)
         pAC(x9,pAC(x10,x11)) -> pAC(x10,x11)
        AC-KBO Processor:
         argument filtering:
          pi(pAC) = [0,1]
          pi(zero) = []
          pi(i) = []
          pi(b) = 0
         precedence:
          b ~ i > pAC > zero
          weight function:
           w0 = 1
           w(i) = 4
           w(zero) = 3
           w(b) = 1
           w(pAC) = 0
           usable rules:
            pAC(x,zero()) -> x
            pAC(i(x),x) -> zero()
            pAC(b(b(x,y),z),pAC(b(b(y,z),x),b(b(z,x),y))) -> 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()
             pAC(b(b(x,y),z),pAC(b(b(y,z),x),b(b(z,x),y))) -> zero()
            S:
             pAC(pAC(x9,x10),x11) -> pAC(x9,x10)
             pAC(x9,pAC(x10,x11)) -> pAC(x10,x11)
           Qed