YES
Time: 0.187

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 > nil > cons > s > sum > 0
   weight function:
    [cons](x0, x1) = 5x0 + 6x1 + 8,
    
    [sum](x0, x1) = 3x0 + 8x1,
    
    [nil] = 1,
    
    [s](x0) = x0 + 12,
    
    [0] = 2,
    
    [plusAC](x0, x1) = x0 + x1
   problem:
    Equations:
     
    TRS:
     
   Qed