YES

TRS:

  D(t()) -> s(h())
  D(constant()) -> h()
  D(b(x,y)) -> b(D(x),D(y))
  D(c(x,y)) -> b(c(y,D(x)),c(x,D(y)))
  D(m(x,y)) -> m(D(x),D(y))
  D(opp(x)) -> opp(D(x))
  D(div(x,y)) -> m(div(D(x),y),div(c(x,D(y)),pow(y,2())))
  D(ln(x)) -> div(D(x),x)
  D(pow(x,y)) -> b(c(c(y,pow(x,m(y,1()))),D(x)),c(c(pow(x,y),ln(x)),D(y)))
  b(h(),x) -> x
  b(x,h()) -> x
  b(s(x),s(y)) -> s(s(b(x,y)))
  b(b(x,y),z) -> b(x,b(y,z))

max/plus interpretations on N:

  D_A(x1) = max{0, x1}
  D#_A(x1) = max{0, x1}
  t_A = 0
  t#_A = 0
  s_A(x1) = max{0, x1}
  s#_A(x1) = max{0, x1}
  h_A = 0
  h#_A = 0
  constant_A = 0
  constant#_A = 0
  b_A(x1,x2) = max{0, x1, x2}
  b#_A(x1,x2) = max{0, x1, x2}
  c_A(x1,x2) = max{0, x1, x2}
  c#_A(x1,x2) = max{0, x1, x2}
  m_A(x1,x2) = max{0, x1, x2}
  m#_A(x1,x2) = max{0, x1, x2}
  opp_A(x1) = max{0, x1}
  opp#_A(x1) = max{0, x1}
  div_A(x1,x2) = max{0, x1, x2}
  div#_A(x1,x2) = max{0, x1, x2}
  pow_A(x1,x2) = max{0, x1, x2}
  pow#_A(x1,x2) = max{0, x1, x2}
  2_A = 0
  2#_A = 0
  ln_A(x1) = max{0, x1}
  ln#_A(x1) = max{0, x1}
  1_A = 0
  1#_A = 0

precedence:

  D = t = constant = pow = 2 = 1 > h = b = m = opp = ln > s = div > c