YES

Problem:
 f(g(x,a(),b())) -> x
 g(f(h(c(),d())),x,y) -> h(k1(x),k2(y))
 k1(a()) -> c()
 k2(b()) -> d()
 f(h(k1(a()),k2(b()))) -> f(h(c(),d()))
 f(h(c(),k2(b()))) -> f(h(c(),d()))
 f(h(k1(a()),d())) -> f(h(c(),d()))

Proof:
 Matrix Interpretation Processor:
  dimension: 1
  interpretation:
   [k2](x0) = x0,
   
   [k1](x0) = 2x0 + 2,
   
   [h](x0, x1) = 2x0 + 2x1,
   
   [d] = 0,
   
   [c] = 0,
   
   [f](x0) = 2x0 + 3,
   
   [g](x0, x1, x2) = 2x0 + 6x1 + 4x2 + 2,
   
   [b] = 3,
   
   [a] = 0
  orientation:
   f(g(x,a(),b())) = 4x + 31 >= x = x
   
   g(f(h(c(),d())),x,y) = 6x + 4y + 8 >= 4x + 2y + 4 = h(k1(x),k2(y))
   
   k1(a()) = 2 >= 0 = c()
   
   k2(b()) = 3 >= 0 = d()
   
   f(h(k1(a()),k2(b()))) = 23 >= 3 = f(h(c(),d()))
   
   f(h(c(),k2(b()))) = 15 >= 3 = f(h(c(),d()))
   
   f(h(k1(a()),d())) = 11 >= 3 = f(h(c(),d()))
  problem:
   
  Qed