YES
Time: 0.052

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(x,i(x)) -> zero()
  pAC(i(x),x) -> zero()
  a(a(x)) -> x
  b(b(x)) -> x
  a(b(a(b(a(b(x)))))) -> x

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:
   p{AC,#}(x6,pAC(x,zero())) -> p{AC,#}(x6,x)
   p{AC,#}(x7,pAC(x,i(x))) -> p{AC,#}(x7,zero())
   p{AC,#}(x8,pAC(i(x),x)) -> 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(x,i(x)) -> zero()
   pAC(i(x),x) -> zero()
   a(a(x)) -> x
   b(b(x)) -> x
   a(b(a(b(a(b(x)))))) -> x
  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(x6,pAC(x,zero())) -> pAC(x6,x)
    pAC(x7,pAC(x,i(x))) -> pAC(x7,zero())
    pAC(x8,pAC(i(x),x)) -> pAC(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(x,i(x)) -> zero()
    pAC(i(x),x) -> zero()
    a(a(x)) -> x
    b(b(x)) -> x
    a(b(a(b(a(b(x)))))) -> x
   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(x6,pAC(x,zero())) -> pAC(x6,x)
     pAC(x7,pAC(x,i(x))) -> pAC(x7,zero())
     pAC(x8,pAC(i(x),x)) -> pAC(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(x,i(x)) -> zero()
     pAC(i(x),x) -> 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) = []
     precedence:
      i ~ pAC > zero
      weight function:
       [i](x0) = 3,
       
       [zero] = 4,
       
       [pAC](x0, x1) = x0 + x1 + 1
       usable rules:
        pAC(x,zero()) -> x
        pAC(x,i(x)) -> zero()
        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(x,i(x)) -> zero()
         pAC(i(x),x) -> zero()
        S:
         pAC(pAC(x9,x10),x11) -> pAC(x9,x10)
         pAC(x9,pAC(x10,x11)) -> pAC(x10,x11)
       Qed