YES

TRS:

  +(x,0()) -> x
  +(x,s(y)) -> s(+(x,y))
  +(0(),y) -> y
  +(s(x),y) -> s(+(x,y))
  +(x,+(y,z)) -> +(+(x,y),z)
  f(g(f(x))) -> f(h(s(0()),x))
  f(g(h(x,y))) -> f(h(s(x),y))
  f(h(x,h(y,z))) -> f(h(+(x,y),z))

linear polynomial interpretations on N:

  +_A(x1,x2) = x1 + x2 + 1
  +#_A(x1,x2) = x2 + 8
  0_A = 1
  0#_A = 0
  s_A(x1) = x1 + 1
  s#_A(x1) = 0
  f_A(x1) = x1 + 4
  f#_A(x1) = x1 + 1
  g_A(x1) = x1 + 3
  g#_A(x1) = 8
  h_A(x1,x2) = x1 + x2 + 4
  h#_A(x1,x2) = 7

precedence:

  g > h > f > + = 0 > s