YES
Time: 0.080

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: 1
  interpretation:
   [b] = 3,
   
   [a] = 1,
   
   [zero] = 12,
   
   [pAC](x0, x1) = x0 + x1 + 4
  orientation:
   pAC(x,zero()) = x + 16 >= x = x
   
   pAC(pAC(pAC(pAC(a(),a()),b()),b()),b()) = 27 >= 18 = pAC(pAC(pAC(a(),a()),a()),b())
   
   pAC(pAC(pAC(pAC(a(),a()),a()),a()),b()) = 23 >= 20 = 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