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{7, -2}
  D#_A(x1) = max{10, 4}
  t_A = 1
  t#_A = 11
  s_A(x1) = max{1, 2}
  s#_A(x1) = max{10, -3}
  h_A = 7
  h#_A = 5
  constant_A = 1
  constant#_A = 6
  b_A(x1,x2) = max{1, x1, x2}
  b#_A(x1,x2) = max{10, 10, -2}
  c_A(x1,x2) = max{7, -2, -1}
  c#_A(x1,x2) = max{10, -1, 10}
  m_A(x1,x2) = max{1, 1, -2 + x2}
  m#_A(x1,x2) = max{4, 4, 4}
  opp_A(x1) = max{1, -1 + x1}
  opp#_A(x1) = max{10, 9}
  div_A(x1,x2) = max{1, 1, 1}
  div#_A(x1,x2) = max{2, 0, 1}
  pow_A(x1,x2) = max{1, 1 + x1, 1}
  pow#_A(x1,x2) = max{5, 6, 8 + x2}
  2_A = 1
  2#_A = 3
  ln_A(x1) = max{7, 7 + x1}
  ln#_A(x1) = max{0, 0}
  1_A = 3
  1#_A = 7

precedence:

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