YES
Time: 0.018

Problem:
 Equations:
  
 TRS:
  plusAC(x,0()) -> x
  plusAC(x,s(y)) -> s(plusAC(x,y))
  sum(nil(),nil()) -> 0()
  sum(cons(x,xs),nil()) -> plusAC(x,sum(xs,nil()))
  sum(nil(),cons(x,xs)) -> plusAC(x,sum(nil(),xs))
  sum(cons(x,xs),cons(y,ys)) -> plusAC(plusAC(x,y),sum(xs,ys))

Proof:
 AC-KBO Processor:
  precedence:
   plusAC > s > nil > sum > cons > 0
   weight function:
    w0 = 2
    w(0) = 10
    w(cons) = 8
    w(s) = 7
    w(sum) = 6
    w(plusAC) = 4
    w(nil) = 2
   problem:
    Equations:
     
    TRS:
     
   Qed