YES

TRS:

  eq(0(),0()) -> true()
  eq(0(),s(m)) -> false()
  eq(s(n),0()) -> false()
  eq(s(n),s(m)) -> eq(n,m)
  le(0(),m) -> true()
  le(s(n),0()) -> false()
  le(s(n),s(m)) -> le(n,m)
  min(cons(0(),nil())) -> 0()
  min(cons(s(n),nil())) -> s(n)
  min(cons(n,cons(m,x))) -> if_min(le(n,m),cons(n,cons(m,x)))
  if_min(true(),cons(n,cons(m,x))) -> min(cons(n,x))
  if_min(false(),cons(n,cons(m,x))) -> min(cons(m,x))
  replace(n,m,nil()) -> nil()
  replace(n,m,cons(k,x)) -> if_replace(eq(n,k),n,m,cons(k,x))
  if_replace(true(),n,m,cons(k,x)) -> cons(m,x)
  if_replace(false(),n,m,cons(k,x)) -> cons(k,replace(n,m,x))
  sort(nil()) -> nil()
  sort(cons(n,x)) -> cons(min(cons(n,x)),sort(replace(min(cons(n,x)),n,x)))

max/plus interpretations on N:

  eq_A(x1,x2) = max{20, 1, -1}
  eq#_A(x1,x2) = max{36, 66, 1}
  0_A = 2
  0#_A = 62
  true_A = 20
  true#_A = 2
  s_A(x1) = max{2, 1}
  s#_A(x1) = max{42, -1}
  false_A = 20
  false#_A = 0
  le_A(x1,x2) = max{55, 1, -1}
  le#_A(x1,x2) = max{62, 3, 4}
  min_A(x1) = max{3, 1}
  min#_A(x1) = max{5, 26 + x1}
  cons_A(x1,x2) = max{2, 24, 33 + x2}
  cons#_A(x1,x2) = max{38, 49, 39 + x2}
  nil_A = 2
  nil#_A = 68
  if_min_A(x1,x2) = max{3, 2, 1}
  if_min#_A(x1,x2) = max{4, 7 + x1, 4}
  replace_A(x1,x2,x3) = max{0, -6, -8, x3}
  replace#_A(x1,x2,x3) = max{35, 37, 59, 33 + x3}
  if_replace_A(x1,x2,x3,x4) = max{27, 4 + x1, 25, -6, x4}
  if_replace#_A(x1,x2,x3,x4) = max{66, 36, 66, 58, 32 + x4}
  sort_A(x1) = max{1, 9 + x1}
  sort#_A(x1) = max{60, 67 + x1}

precedence:

  sort > nil > 0 > cons > min = replace > s = le = if_min = if_replace > true > eq > false