YES
Time: 0.036

Problem:
 Equations:
  
 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:
 AC-KBO Processor:
  precedence:
   i > pAC > b ~ a ~ zero
   weight function:
    w0 = 2
    w(b) = w(zero) = 5
    w(a) = 2
    w(pAC) = 1
    w(i) = 0
   problem:
    Equations:
     
    TRS:
     
   Qed