YES

TRS:

  f(g(i(a(),b(),b'()),c()),d()) -> if(e(),f(.(b(),c()),d'()),f(.(b'(),c()),d'()))
  f(g(h(a(),b()),c()),d()) -> if(e(),f(.(b(),g(h(a(),b()),c())),d()),f(c(),d'()))

max/plus interpretations on N:

  f_A(x1,x2) = max{1, -7, -1}
  f#_A(x1,x2) = max{11, 38 + x1, 15}
  g_A(x1,x2) = max{0, -15 + x1, 0}
  g#_A(x1,x2) = max{77, 41 + x1, 26}
  i_A(x1,x2,x3) = max{15, 3, -1, -5}
  i#_A(x1,x2,x3) = max{5, 23, 7, 22}
  a_A = 0
  a#_A = 1
  b_A = 1
  b#_A = 2
  b'_A = 1
  b'#_A = 16
  c_A = 0
  c#_A = 23
  d_A = 1
  d#_A = 3
  if_A(x1,x2,x3) = max{0, 0, x2, 1}
  if#_A(x1,x2,x3) = max{4, 4, 13 + x2, 9 + x3}
  e_A = 0
  e#_A = 0
  ._A(x1,x2) = max{19, 1, -26}
  .#_A(x1,x2) = max{4, 17, 25}
  d'_A = 2
  d'#_A = 4
  h_A(x1,x2) = max{35, -5, -14}
  h#_A(x1,x2) = max{24, 37, 37}

precedence:

  h > g = i > f > c > a > b' > d > b = if > e = . = d'