YES
Time: 0.057

Problem:
 Equations:
  appAC(appAC(x5,x6),x7) -> appAC(x5,appAC(x6,x7))
  appAC(x5,x6) -> appAC(x6,x5)
  appAC(x5,appAC(x6,x7)) -> appAC(appAC(x5,x6),x7)
  appAC(x6,x5) -> appAC(x5,x6)
 TRS:
  1() -> s(0())
  2() -> s(1())
  3() -> s(2())
  4() -> s(3())
  5() -> s(4())
  6() -> s(5())
  7() -> s(6())
  8() -> s(7())
  9() -> s(8())
  max'C(0(),x) -> x
  max'C(s(x),s(y)) -> s(max'C(x,y))
  appAC(empty(),X) -> X
  max(singl(x)) -> x
  max(appAC(singl(x),Y)) -> max2(x,Y)
  max2(x,empty()) -> x
  max2(x,singl(y)) -> max'C(x,y)
  max2(x,appAC(singl(y),Z)) -> max2(max'C(x,y),Z)

Proof:
 AC-KBO Processor:
  precedence:
   max2 ~ 9 ~ 5 ~ 4 ~ 3 > 1 > 7 > 8 ~ 6 ~ 2 > max ~ singl ~ empty ~ s ~ 0 ~ max'C ~ appAC
   weight function:
    w0 = 2
    w(max) = 12
    w(9) = 11
    w(8) = 10
    w(7) = 9
    w(6) = 8
    w(5) = 7
    w(4) = 6
    w(3) = 5
    w(singl) = w(empty) = w(2) = w(max'C) = 4
    w(1) = 3
    w(0) = 2
    w(s) = w(appAC) = 1
    w(max2) = 0
   problem:
    Equations:
     appAC(appAC(x5,x6),x7) -> appAC(x5,appAC(x6,x7))
     appAC(x5,x6) -> appAC(x6,x5)
     appAC(x5,appAC(x6,x7)) -> appAC(appAC(x5,x6),x7)
     appAC(x6,x5) -> appAC(x5,x6)
    TRS:
     
   Qed