YES

Problem:
 f(x,y) -> x
 g(a()) -> h(a(),b(),a())
 i(x) -> f(x,x)
 h(x,x,y) -> g(x)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [i](x0) = 6x0 + 4,
   
   [h](x0, x1, x2) = x0 + 6x1 + 4x2,
   
   [b] = 0,
   
   [g](x0) = 6x0,
   
   [a] = 3,
   
   [f](x0, x1) = 2x0 + 4x1 + 1
  orientation:
   f(x,y) = 2x + 4y + 1 >= x = x
   
   g(a()) = 18 >= 15 = h(a(),b(),a())
   
   i(x) = 6x + 4 >= 6x + 1 = f(x,x)
   
   h(x,x,y) = 7x + 4y >= 6x = g(x)
  problem:
   h(x,x,y) -> g(x)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [h](x0, x1, x2) = x0 + x1 + 4x2 + 2,
    
    [g](x0) = 2x0
   orientation:
    h(x,x,y) = 2x + 4y + 2 >= 2x = g(x)
   problem:
    
   Qed