YES
Time: 0.926

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: 2
  interpretation:
         [1]
   [b] = [0],
   
         [0]
   [a] = [0],
   
            [4]
   [zero] = [0],
   
             [8 0]     [7]
   [i](x0) = [0 0]x0 + [9],
   
                             [1]
   [pAC](x0, x1) = x0 + x1 + [0]
  orientation:
                 [9 0]    [8]    [4]         
   pAC(x,i(x)) = [0 1]x + [9] >= [0] = zero()
   
                 [9 0]    [8]    [4]         
   pAC(i(x),x) = [0 1]x + [9] >= [0] = zero()
   
                       [5]         
   pAC(zero(),x) = x + [0] >= x = x
   
                       [5]         
   pAC(x,zero()) = x + [0] >= x = x
   
                                                               [6]    [4]         
   pAC(a(),pAC(a(),pAC(a(),pAC(a(),pAC(a(),pAC(a(),a())))))) = [0] >= [0] = zero()
   
                                                               [13]    [4]         
   pAC(b(),pAC(b(),pAC(b(),pAC(b(),pAC(b(),pAC(b(),b())))))) = [0 ] >= [0] = zero()
   
                                    [5]    [4]         
   pAC(a(),pAC(b(),pAC(a(),b()))) = [0] >= [0] = zero()
   
                                                               [29]    [4]         
   pAC(i(a()),pAC(b(),pAC(i(a()),pAC(b(),pAC(i(a()),b()))))) = [27] >= [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