YES
Time: 0.016

Problem:
 Equations:
  
 TRS:
  +AC(0(),x) -> x
  +AC(s(x),s(y)) -> s(s(+AC(x,y)))
  *AC(0(),x) -> 0()
  *AC(s(x),s(y)) -> s(+AC(+AC(x,y),*AC(x,y)))
  UAC(empty(),b) -> b
  sum(empty()) -> 0()
  sum(singl(x)) -> x
  sum(UAC(x,y)) -> +AC(sum(x),sum(y))
  prod(empty()) -> s(0())
  prod(singl(x)) -> x
  prod(UAC(x,y)) -> *AC(prod(x),prod(y))

Proof:
 AC-RPO Processor:
  precedence:
   prod > singl > sum > empty > 0 > *AC > +AC > s > UAC
  status:
   
  problem:
   Equations:
    
   TRS:
    
  Qed