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))
  f_6(x) -> g_6(x,x)
  g_6(s(x),y) -> b(f_5(y),g_6(x,y))
  f_7(x) -> g_7(x,x)
  g_7(s(x),y) -> b(f_6(y),g_7(x,y))
  f_8(x) -> g_8(x,x)
  g_8(s(x),y) -> b(f_7(y),g_8(x,y))
  f_9(x) -> g_9(x,x)
  g_9(s(x),y) -> b(f_8(y),g_9(x,y))
  f_10(x) -> g_10(x,x)
  g_10(s(x),y) -> b(f_9(y),g_10(x,y))

max/plus interpretations on N:

  f_0_A(x1) = max{10, 7 + x1}
  f_0#_A(x1) = max{10, 7 + x1}
  a_A = 6
  a#_A = 6
  f_1_A(x1) = max{11, 12 + x1}
  f_1#_A(x1) = max{11, 12 + x1}
  g_1_A(x1,x2) = max{12, 11 + x1, 11 + x2}
  g_1#_A(x1,x2) = max{12, 11 + x1, 11 + x2}
  s_A(x1) = max{39, 41 + x1}
  s#_A(x1) = max{39, 41 + x1}
  b_A(x1,x2) = max{52, 4 + x1, x2}
  b#_A(x1,x2) = max{52, 4 + x1, x2}
  f_2_A(x1) = max{19, 17 + x1}
  f_2#_A(x1) = max{19, 17 + x1}
  g_2_A(x1,x2) = max{19, 11 + x1, 16 + x2}
  g_2#_A(x1,x2) = max{19, 11 + x1, 16 + x2}
  f_3_A(x1) = max{21, 22 + x1}
  f_3#_A(x1) = max{21, 22 + x1}
  g_3_A(x1,x2) = max{22, 11 + x1, 21 + x2}
  g_3#_A(x1,x2) = max{22, 11 + x1, 21 + x2}
  f_4_A(x1) = max{26, 27 + x1}
  f_4#_A(x1) = max{26, 27 + x1}
  g_4_A(x1,x2) = max{27, 11 + x1, 26 + x2}
  g_4#_A(x1,x2) = max{27, 11 + x1, 26 + x2}
  f_5_A(x1) = max{35, 32 + x1}
  f_5#_A(x1) = max{35, 32 + x1}
  g_5_A(x1,x2) = max{35, 11 + x1, 31 + x2}
  g_5#_A(x1,x2) = max{35, 11 + x1, 31 + x2}
  f_6_A(x1) = max{38, 37 + x1}
  f_6#_A(x1) = max{38, 37 + x1}
  g_6_A(x1,x2) = max{38, 11 + x1, 36 + x2}
  g_6#_A(x1,x2) = max{38, 11 + x1, 36 + x2}
  f_7_A(x1) = max{52, 42 + x1}
  f_7#_A(x1) = max{52, 42 + x1}
  g_7_A(x1,x2) = max{52, x1, 41 + x2}
  g_7#_A(x1,x2) = max{52, x1, 41 + x2}
  f_8_A(x1) = max{56, 47 + x1}
  f_8#_A(x1) = max{56, 47 + x1}
  g_8_A(x1,x2) = max{56, 10 + x1, 46 + x2}
  g_8#_A(x1,x2) = max{56, 10 + x1, 46 + x2}
  f_9_A(x1) = max{48, 60 + x1}
  f_9#_A(x1) = max{48, 60 + x1}
  g_9_A(x1,x2) = max{60, 10 + x1, 51 + x2}
  g_9#_A(x1,x2) = max{60, 10 + x1, 51 + x2}
  f_10_A(x1) = max{66, 65 + x1}
  f_10#_A(x1) = max{66, 65 + x1}
  g_10_A(x1,x2) = max{66, 10 + x1, 64 + x2}
  g_10#_A(x1,x2) = max{66, 10 + x1, 64 + x2}

precedence:

  f_10 > g_10 > f_9 > g_9 > f_8 > g_8 > f_7 > g_7 > f_6 > g_6 > f_5 > g_5 > f_4 > g_4 > f_3 > g_3 > f_2 > g_2 > f_1 > a = g_1 > f_0 = s = b