YES
Time: 0.078

Problem:
 Equations:
  plusAC(plusAC(x4,x5),x6) -> plusAC(x4,plusAC(x5,x6))
  plusAC(x4,x5) -> plusAC(x5,x4)
  plusAC(x4,plusAC(x5,x6)) -> plusAC(plusAC(x4,x5),x6)
  plusAC(x5,x4) -> plusAC(x4,x5)
 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:
   sum > plusAC > cons ~ nil ~ s ~ 0
   weight function:
    [cons](x0, x1) = x0 + x1 + 12,
    
    [sum](x0, x1) = x0 + x1,
    
    [nil] = 4,
    
    [s](x0) = x0 + 15,
    
    [0] = 8,
    
    [plusAC](x0, x1) = x0 + x1 + 12
   problem:
    Equations:
     plusAC(plusAC(x4,x5),x6) -> plusAC(x4,plusAC(x5,x6))
     plusAC(x4,x5) -> plusAC(x5,x4)
     plusAC(x4,plusAC(x5,x6)) -> plusAC(plusAC(x4,x5),x6)
     plusAC(x5,x4) -> plusAC(x4,x5)
    TRS:
     
   Qed