YES
Time: 1.099

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()
  a(a(x)) -> x
  b(b(x)) -> x
  a(b(a(b(a(b(x)))))) -> x

Proof:
 Matrix Interpretation Processor:
  dimension: 2
  interpretation:
             [1 0]     [2]
   [b](x0) = [0 2]x0 + [0],
   
                  [6]
   [a](x0) = x0 + [0],
   
             [1 0]     [0 ]
   [i](x0) = [0 0]x0 + [10],
   
            [2]
   [zero] = [2],
   
                             [6]
   [pAC](x0, x1) = x0 + x1 + [5]
  orientation:
                       [8]         
   pAC(x,zero()) = x + [7] >= x = x
   
                 [2 0]    [6 ]    [2]         
   pAC(x,i(x)) = [0 1]x + [15] >= [2] = zero()
   
                 [2 0]    [6 ]    [2]         
   pAC(i(x),x) = [0 1]x + [15] >= [2] = zero()
   
                 [12]         
   a(a(x)) = x + [0 ] >= x = x
   
             [1 0]    [4]         
   b(b(x)) = [0 4]x + [0] >= x = x
   
                         [1 0]    [24]         
   a(b(a(b(a(b(x)))))) = [0 8]x + [0 ] >= x = x
  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