YES
Time: 0.255

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:
   9 ~ 6 ~ 3 > max2 > 8 ~ 7 ~ 5 ~ 4 > max ~ singl ~ empty ~ 2 ~ s ~ 0 ~ 1 ~ max'C ~ appAC
   weight function:
    [max2](x0, x1) = 5x0 + 3x1 + 15,
    
    [max](x0) = 3x0 + 6,
    
    [singl](x0) = 4x0 + 13,
    
    [empty] = 8,
    
    [9] = 15,
    
    [8] = 14,
    
    [7] = 13,
    
    [6] = 12,
    
    [5] = 11,
    
    [4] = 10,
    
    [3] = 9,
    
    [2] = 8,
    
    [s](x0) = x0 + 1,
    
    [0] = 2,
    
    [1] = 4,
    
    [max'C](x0, x1) = x0 + x1 + 1,
    
    [appAC](x0, x1) = x0 + x1 + 3
   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