YES
Time: 0.186

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

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())
   p{AC,#}(x9,pAC(a(),a())) -> p{AC,#}(x9,zero())
   p{AC,#}(x10,pAC(b(),b())) -> p{AC,#}(x10,zero())
   p{AC,#}(x11,pAC(pAC(pAC(pAC(pAC(a(),b()),a()),b()),a()),b())) -> p{AC,#}(x11,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()
   pAC(a(),a()) -> zero()
   pAC(b(),b()) -> zero()
   pAC(pAC(pAC(pAC(pAC(a(),b()),a()),b()),a()),b()) -> zero()
  S:
   p{AC,#}(pAC(x12,x13),x14) -> p{AC,#}(x12,x13)
   p{AC,#}(x12,pAC(x13,x14)) -> p{AC,#}(x13,x14)
  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())
    pAC(x9,pAC(a(),a())) -> pAC(x9,zero())
    pAC(x10,pAC(b(),b())) -> pAC(x10,zero())
    pAC(x11,pAC(pAC(pAC(pAC(pAC(a(),b()),a()),b()),a()),b())) -> pAC(x11,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()
    pAC(a(),a()) -> zero()
    pAC(b(),b()) -> zero()
    pAC(pAC(pAC(pAC(pAC(a(),b()),a()),b()),a()),b()) -> zero()
   S:
    pAC(pAC(x12,x13),x14) -> pAC(x12,x13)
    pAC(x12,pAC(x13,x14)) -> pAC(x13,x14)
   AC-KBO Processor:
    argument filtering:
     pi(pAC) = [0,1]
     pi(zero) = []
     pi(i) = []
     pi(a) = []
     pi(b) = []
    precedence:
     a > b ~ i ~ pAC > zero
     weight function:
      [b] = 1,
      
      [a] = 2,
      
      [i](x0) = 4,
      
      [zero] = 2,
      
      [pAC](x0, x1) = x0 + x1
      usable rules:
       pAC(x,zero()) -> x
       pAC(x,i(x)) -> zero()
       pAC(i(x),x) -> zero()
       pAC(a(),a()) -> zero()
       pAC(b(),b()) -> zero()
       pAC(pAC(pAC(pAC(pAC(a(),b()),a()),b()),a()),b()) -> 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()
        pAC(a(),a()) -> zero()
        pAC(b(),b()) -> zero()
        pAC(pAC(pAC(pAC(pAC(a(),b()),a()),b()),a()),b()) -> zero()
       S:
        pAC(pAC(x12,x13),x14) -> pAC(x12,x13)
        pAC(x12,pAC(x13,x14)) -> pAC(x13,x14)
      Qed