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{1, 2}
  f_0#_A(x1) = max{35, 1}
  a_A = 2
  a#_A = 0
  f_1_A(x1) = max{24, 59}
  f_1#_A(x1) = max{35, 35}
  g_1_A(x1,x2) = max{26, 25, 25}
  g_1#_A(x1,x2) = max{29, 30, 35}
  s_A(x1) = max{78, 38 + x1}
  s#_A(x1) = max{0, 0}
  b_A(x1,x2) = max{26, 3, 4}
  b#_A(x1,x2) = max{35, -53 + x1, 2 + x2}
  f_2_A(x1) = max{52, -1}
  f_2#_A(x1) = max{35, 35}
  g_2_A(x1,x2) = max{4, 4, 26}
  g_2#_A(x1,x2) = max{7, -30, 35}
  f_3_A(x1) = max{1, 26}
  f_3#_A(x1) = max{36, 36}
  g_3_A(x1,x2) = max{2, -1, 26}
  g_3#_A(x1,x2) = max{0, -2, 35}
  f_4_A(x1) = max{35, -20}
  f_4#_A(x1) = max{8, 37}
  g_4_A(x1,x2) = max{35, 6, 6}
  g_4#_A(x1,x2) = max{37, 8, 7}
  f_5_A(x1) = max{3, 54 + x1}
  f_5#_A(x1) = max{39, -71 + x1}
  g_5_A(x1,x2) = max{36, -35 + x1, 4}
  g_5#_A(x1,x2) = max{38, -71 + x1, -72}
  f_6_A(x1) = max{1, 83}
  f_6#_A(x1) = max{85, 7 + x1}
  g_6_A(x1,x2) = max{3, 83, -1}
  g_6#_A(x1,x2) = max{85, 0, 7 + x2}
  f_7_A(x1) = max{26, -1}
  f_7#_A(x1) = max{32, 30 + x1}
  g_7_A(x1,x2) = max{26, 4, 4}
  g_7#_A(x1,x2) = max{31, 7 + x1, 7 + x2}
  f_8_A(x1) = max{87, -1}
  f_8#_A(x1) = max{41, 33 + x1}
  g_8_A(x1,x2) = max{2, -1, 26}
  g_8#_A(x1,x2) = max{29, 41, 33 + x2}
  f_9_A(x1) = max{32, -2}
  f_9#_A(x1) = max{37, 33 + x1}
  g_9_A(x1,x2) = max{0, 32, -1}
  g_9#_A(x1,x2) = max{1, -37 + x1, 33 + x2}
  f_10_A(x1) = max{24, 26 + x1}
  f_10#_A(x1) = max{37, 39 + x1}
  g_10_A(x1,x2) = max{26, 25, -1}
  g_10#_A(x1,x2) = max{38, 36, 34 + x2}

precedence:

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