YES
Time: 0.015

Problem:
 Equations:
  
 TRS:
  if(true(),x,y) -> x
  if(false(),x,y) -> y
  eqAC(0(),0()) -> true()
  eqAC(0(),1()) -> false()
  eqAC(1(),1()) -> true()
  unionAC(empty(),x) -> x
  interAC(x,empty()) -> empty()
  interAC(x,unionAC(y,z)) -> unionAC(interAC(x,y),interAC(x,z))
  interAC(single(x),single(y)) -> if(eqAC(x,y),single(x),empty())

Proof:
 AC-RPO Processor:
  precedence:
   single > empty > 1 > 0 > false > true > interAC > if > eqAC > unionAC
  status:
   if:mul  
  problem:
   Equations:
    
   TRS:
    
  Qed