YES
Time: 0.101

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: 1
  interpretation:
   [b](x0) = 2x0 + 1,
   
   [a](x0) = x0 + 1,
   
   [i](x0) = 8x0,
   
   [zero] = 2,
   
   [pAC](x0, x1) = x0 + x1 + 6
  orientation:
   pAC(x,zero()) = x + 8 >= x = x
   
   pAC(x,i(x)) = 9x + 6 >= 2 = zero()
   
   pAC(i(x),x) = 9x + 6 >= 2 = zero()
   
   a(a(x)) = x + 2 >= x = x
   
   b(b(x)) = 4x + 3 >= x = x
   
   a(b(a(b(a(b(x)))))) = 8x + 14 >= 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