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'()))

linear polynomial interpretations on N:

  f_A(x1,x2) = 1
  f#_A(x1,x2) = x1 + x2 + 2
  g_A(x1,x2) = 4
  g#_A(x1,x2) = 8
  i_A(x1,x2,x3) = x1 + x2
  i#_A(x1,x2,x3) = 1
  a_A = 1
  a#_A = 10
  b_A = 1
  b#_A = 3
  b'_A = 1
  b'#_A = 4
  c_A = 1
  c#_A = 5
  d_A = 0
  d#_A = 8
  if_A(x1,x2,x3) = 0
  if#_A(x1,x2,x3) = 0
  e_A = 1
  e#_A = 0
  ._A(x1,x2) = 3
  .#_A(x1,x2) = 5
  d'_A = 4
  d'#_A = 2
  h_A(x1,x2) = 1
  h#_A(x1,x2) = 11

precedence:

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