YES

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

Proof:
 Matrix Interpretation Processor:
  dimension: 1
  interpretation:
   [q](x0) = 2x0 + 2,
   
   [h](x0, x1) = 2x0 + 2x1 + 1,
   
   [d] = 0,
   
   [c] = 0,
   
   [p](x0) = x0 + 4,
   
   [f](x0) = x0 + 3,
   
   [g](x0, x1, x2) = 4x0 + 6x1 + 3x2 + 1,
   
   [b] = 1,
   
   [a] = 0
  orientation:
   f(g(x,a(),b())) = 4x + 7 >= x = x
   
   p(a()) = 4 >= 0 = c()
   
   g(f(h(c(),d())),x,y) = 6x + 3y + 17 >= 6x + 13 = h(p(x),q(x))
   
   q(b()) = 4 >= 0 = d()
  problem:
   
  Qed