YES

TRS:

  f_0(x) -> a()
  f_1(x) -> g_1(x,x)
  g_1(s(x),y) -> b(f_0(y),g_1(x,y))
  f_2(x) -> g_2(x,x)
  g_2(s(x),y) -> b(f_1(y),g_2(x,y))
  f_3(x) -> g_3(x,x)
  g_3(s(x),y) -> b(f_2(y),g_3(x,y))
  f_4(x) -> g_4(x,x)
  g_4(s(x),y) -> b(f_3(y),g_4(x,y))
  f_5(x) -> g_5(x,x)
  g_5(s(x),y) -> b(f_4(y),g_5(x,y))

max/plus interpretations on N:

  f_0_A(x1) = max{0, x1}
  f_0#_A(x1) = max{0, x1}
  a_A = 0
  a#_A = 0
  f_1_A(x1) = max{0, x1}
  f_1#_A(x1) = max{0, x1}
  g_1_A(x1,x2) = max{0, x1, x2}
  g_1#_A(x1,x2) = max{0, x1, x2}
  s_A(x1) = max{0, x1}
  s#_A(x1) = max{0, x1}
  b_A(x1,x2) = max{0, x1, x2}
  b#_A(x1,x2) = max{0, x1, x2}
  f_2_A(x1) = max{0, x1}
  f_2#_A(x1) = max{0, x1}
  g_2_A(x1,x2) = max{0, x1, x2}
  g_2#_A(x1,x2) = max{0, x1, x2}
  f_3_A(x1) = max{0, x1}
  f_3#_A(x1) = max{0, x1}
  g_3_A(x1,x2) = max{0, x1, x2}
  g_3#_A(x1,x2) = max{0, x1, x2}
  f_4_A(x1) = max{0, x1}
  f_4#_A(x1) = max{0, x1}
  g_4_A(x1,x2) = max{0, x1, x2}
  g_4#_A(x1,x2) = max{0, x1, x2}
  f_5_A(x1) = max{0, x1}
  f_5#_A(x1) = max{0, x1}
  g_5_A(x1,x2) = max{0, x1, x2}
  g_5#_A(x1,x2) = max{0, x1, x2}

precedence:

  f_5 > g_5 > f_4 > g_4 > f_3 > g_3 > f_2 > g_2 > f_1 > g_1 > f_0 = s = b > a