YES
Time: 0.270

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:
 Matrix Interpretation Processor:
  dimension: 2
  interpretation:
         [0]
   [b] = [0],
   
         [0]
   [a] = [0],
   
            [14]
   [zero] = [0 ],
   
                             [2]
   [pAC](x0, x1) = x0 + x1 + [0]
  orientation:
                       [16]         
   pAC(x,zero()) = x + [0 ] >= x = x
   
                                             [8]    [6]                                 
   pAC(pAC(pAC(pAC(a(),a()),b()),b()),b()) = [0] >= [0] = pAC(pAC(pAC(a(),a()),a()),b())
   
                                             [8]    [6]                                 
   pAC(pAC(pAC(pAC(a(),a()),a()),a()),b()) = [0] >= [0] = 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)
   TRS:
    
  Qed