YES
Time: 0.022

Problem:
 Equations:
  pAC(pAC(x2,x3),x4) -> pAC(x2,pAC(x3,x4))
  pAC(x2,x3) -> pAC(x3,x2)
  pAC(x2,pAC(x3,x4)) -> pAC(pAC(x2,x3),x4)
  pAC(x3,x2) -> pAC(x2,x3)
 TRS:
  pAC(x,one()) -> x
  pAC(x,x) -> x
  pAC(T(x),x) -> T(x)
  T(pAC(x,T(y))) -> pAC(T(pAC(x,y)),T(y))
  L(pAC(x,T(y))) -> pAC(L(pAC(x,y)),L(y))

Proof:
 AC-RPO Processor:
  precedence:
   L > T > one > pAC
  status:
   
  problem:
   Equations:
    pAC(pAC(x2,x3),x4) -> pAC(x2,pAC(x3,x4))
    pAC(x2,x3) -> pAC(x3,x2)
    pAC(x2,pAC(x3,x4)) -> pAC(pAC(x2,x3),x4)
    pAC(x3,x2) -> pAC(x2,x3)
   TRS:
    
  Qed