YES
Time: 0.183

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

Proof:
 Matrix Interpretation Processor:
  dimension: 1
  interpretation:
   [b] = 0,
   
   [a] = 2,
   
   [zero] = 0,
   
   [i](x0) = x0 + 1,
   
   [pAC](x0, x1) = x0 + x1 + 2
  orientation:
   pAC(x,i(x)) = 2x + 3 >= 0 = zero()
   
   pAC(i(x),x) = 2x + 3 >= 0 = zero()
   
   pAC(zero(),x) = x + 2 >= x = x
   
   pAC(x,zero()) = x + 2 >= x = x
   
   pAC(a(),pAC(a(),pAC(a(),pAC(a(),pAC(a(),pAC(a(),a())))))) = 26 >= 0 = zero()
   
   pAC(b(),pAC(b(),pAC(b(),pAC(b(),pAC(b(),pAC(b(),b())))))) = 12 >= 0 = zero()
   
   pAC(a(),pAC(b(),pAC(a(),b()))) = 10 >= 0 = zero()
   
   pAC(i(a()),pAC(b(),pAC(i(a()),pAC(b(),pAC(i(a()),b()))))) = 19 >= 0 = 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