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)))

linear polynomial interpretations on N:

  eq_A(x1,x2) = 1
  eq#_A(x1,x2) = 1
  0_A = 1
  0#_A = 1
  true_A = 1
  true#_A = 0
  s_A(x1) = 0
  s#_A(x1) = 3
  false_A = 1
  false#_A = 0
  le_A(x1,x2) = 1
  le#_A(x1,x2) = 1
  min_A(x1) = 1
  min#_A(x1) = 2
  cons_A(x1,x2) = x2 + 3
  cons#_A(x1,x2) = x2
  nil_A = 4
  nil#_A = 2
  if_min_A(x1,x2) = 1
  if_min#_A(x1,x2) = 1
  replace_A(x1,x2,x3) = x3
  replace#_A(x1,x2,x3) = x1 + x3 + 1
  if_replace_A(x1,x2,x3,x4) = x4
  if_replace#_A(x1,x2,x3,x4) = x2 + x4
  sort_A(x1) = x1
  sort#_A(x1) = x1

precedence:

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