YES

Problem:
 F(x,y) -> c(y)
 G(x) -> x
 f(x) -> g(x)
 g(x) -> c(x)

Proof:
 Polynomial Interpretation Processor:
  dimension: 1
  interpretation:
   [g](x0) = x0 + 1,
   
   [f](x0) = x0 + 4,
   
   [G](x0) = x0 + 1,
   
   [c](x0) = x0,
   
   [F](x0, x1) = 7x0 + 7x1 + 4x0x0 + 1
  orientation:
   F(x,y) = 7x + 4x*x + 7y + 1 >= y = c(y)
   
   G(x) = x + 1 >= x = x
   
   f(x) = x + 4 >= x + 1 = g(x)
   
   g(x) = x + 1 >= x = c(x)
  problem:
   
  Qed