YES
Time: 0.554

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(pAC(pAC(pAC(a(),a()),b()),b()),b()) -> pAC(pAC(pAC(a(),a()),a()),b())
  pAC(pAC(pAC(pAC(a(),a()),a()),a()),b()) -> pAC(pAC(pAC(a(),a()),b()),b())

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,#}(pAC(pAC(pAC(a(),a()),b()),b()),b()) -> p{AC,#}(pAC(a(),a()),a())
   p{AC,#}(pAC(pAC(pAC(a(),a()),b()),b()),b()) -> p{AC,#}(pAC(pAC(a(),a()),a()),b())
   p{AC,#}(pAC(pAC(pAC(a(),a()),a()),a()),b()) -> p{AC,#}(pAC(a(),a()),b())
   p{AC,#}(pAC(pAC(pAC(a(),a()),a()),a()),b()) -> p{AC,#}(pAC(pAC(a(),a()),b()),b())
   p{AC,#}(x6,pAC(x,zero())) -> p{AC,#}(x6,x)
   p{AC,#}(x7,pAC(pAC(pAC(pAC(a(),a()),b()),b()),b())) -> p{AC,#}(pAC(a(),a()),a())
   p{AC,#}(x7,pAC(pAC(pAC(pAC(a(),a()),b()),b()),b())) -> p{AC,#}(pAC(pAC(a(),a()),a()),b())
   p{AC,#}(x7,pAC(pAC(pAC(pAC(a(),a()),b()),b()),b())) ->
   p{AC,#}(x7,pAC(pAC(pAC(a(),a()),a()),b()))
   p{AC,#}(x8,pAC(pAC(pAC(pAC(a(),a()),a()),a()),b())) -> p{AC,#}(pAC(a(),a()),b())
   p{AC,#}(x8,pAC(pAC(pAC(pAC(a(),a()),a()),a()),b())) -> p{AC,#}(pAC(pAC(a(),a()),b()),b())
   p{AC,#}(x8,pAC(pAC(pAC(pAC(a(),a()),a()),a()),b())) ->
   p{AC,#}(x8,pAC(pAC(pAC(a(),a()),b()),b()))
  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(pAC(pAC(pAC(a(),a()),b()),b()),b()) -> pAC(pAC(pAC(a(),a()),a()),b())
   pAC(pAC(pAC(pAC(a(),a()),a()),a()),b()) -> pAC(pAC(pAC(a(),a()),b()),b())
  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(pAC(pAC(pAC(a(),a()),b()),b()),b()) -> pAC(pAC(a(),a()),a())
    pAC(pAC(pAC(pAC(a(),a()),b()),b()),b()) -> pAC(pAC(pAC(a(),a()),a()),b())
    pAC(pAC(pAC(pAC(a(),a()),a()),a()),b()) -> pAC(pAC(a(),a()),b())
    pAC(pAC(pAC(pAC(a(),a()),a()),a()),b()) -> pAC(pAC(pAC(a(),a()),b()),b())
    pAC(x6,pAC(x,zero())) -> pAC(x6,x)
    pAC(x7,pAC(pAC(pAC(pAC(a(),a()),b()),b()),b())) -> pAC(pAC(a(),a()),a())
    pAC(x7,pAC(pAC(pAC(pAC(a(),a()),b()),b()),b())) -> pAC(pAC(pAC(a(),a()),a()),b())
    pAC(x7,pAC(pAC(pAC(pAC(a(),a()),b()),b()),b())) -> pAC(x7,pAC(pAC(pAC(a(),a()),a()),b()))
    pAC(x8,pAC(pAC(pAC(pAC(a(),a()),a()),a()),b())) -> pAC(pAC(a(),a()),b())
    pAC(x8,pAC(pAC(pAC(pAC(a(),a()),a()),a()),b())) -> pAC(pAC(pAC(a(),a()),b()),b())
    pAC(x8,pAC(pAC(pAC(pAC(a(),a()),a()),a()),b())) -> pAC(x8,pAC(pAC(pAC(a(),a()),b()),b()))
   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(pAC(pAC(pAC(a(),a()),b()),b()),b()) -> pAC(pAC(pAC(a(),a()),a()),b())
    pAC(pAC(pAC(pAC(a(),a()),a()),a()),b()) -> pAC(pAC(pAC(a(),a()),b()),b())
   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(a) = []
     pi(b) = []
    precedence:
     zero ~ pAC > b ~ a
     weight function:
      w0 = 1
      w(a) = w(pAC) = 7
      w(zero) = 4
      w(b) = 1
      usable rules:
       pAC(x,zero()) -> x
       pAC(pAC(pAC(pAC(a(),a()),b()),b()),b()) -> pAC(pAC(pAC(a(),a()),a()),b())
       pAC(pAC(pAC(pAC(a(),a()),a()),a()),b()) -> pAC(pAC(pAC(a(),a()),b()),b())
      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(pAC(pAC(pAC(a(),a()),b()),b()),b()) -> pAC(pAC(pAC(a(),a()),a()),b())
        pAC(pAC(pAC(pAC(a(),a()),a()),a()),b()) -> pAC(pAC(pAC(a(),a()),b()),b())
       S:
        pAC(pAC(x9,x10),x11) -> pAC(x9,x10)
        pAC(x9,pAC(x10,x11)) -> pAC(x10,x11)
      Qed