YES
Time: 0.016

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:
    w0 = 4
    w(s) = 15
    w(0) = 8
    w(nil) = 4
    w(cons) = 1
    w(sum) = w(plusAC) = 0
   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