YES
Time: 0.300

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: 2
  interpretation:
         [4]
   [b] = [1],
   
         [4]
   [a] = [1],
   
             [2 0]     [13]
   [i](x0) = [0 0]x0 + [7 ],
   
            [4]
   [zero] = [0],
   
                             [0]
   [pAC](x0, x1) = x0 + x1 + [3]
  orientation:
                       [4]         
   pAC(x,zero()) = x + [3] >= x = x
   
                 [3 0]    [13]    [4]         
   pAC(x,i(x)) = [0 1]x + [10] >= [0] = zero()
   
                 [3 0]    [13]    [4]         
   pAC(i(x),x) = [0 1]x + [10] >= [0] = zero()
   
                  [8]    [4]         
   pAC(a(),a()) = [5] >= [0] = zero()
   
                  [8]    [4]         
   pAC(b(),b()) = [5] >= [0] = zero()
   
                                                      [24]    [4]         
   pAC(pAC(pAC(pAC(pAC(a(),b()),a()),b()),a()),b()) = [21] >= [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