YES
Time: 0.086

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:
 Matrix Interpretation Processor:
  dimension: 1
  interpretation:
   [b] = 1,
   
   [a] = 1,
   
   [i](x0) = 2x0 + 6,
   
   [zero] = 1,
   
   [pAC](x0, x1) = x0 + x1
  orientation:
   pAC(x,zero()) = x + 1 >= x = x
   
   pAC(x,i(x)) = 3x + 6 >= 1 = zero()
   
   pAC(i(x),x) = 3x + 6 >= 1 = zero()
   
   pAC(a(),a()) = 2 >= 1 = zero()
   
   pAC(b(),b()) = 2 >= 1 = zero()
   
   pAC(pAC(pAC(pAC(pAC(a(),b()),a()),b()),a()),b()) = 6 >= 1 = 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)
   TRS:
    
  Qed