YES

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

Proof:
 DP Processor:
  DPs:
   g#(f(x),y) -> h#(x,y)
   h#(x,y) -> g#(x,f(y))
  TRS:
   g(f(x),y) -> f(h(x,y))
   h(x,y) -> g(x,f(y))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [h#](x0, x1) = 4x0 + 2,
    
    [g#](x0, x1) = 2x0 + 1,
    
    [h](x0, x1) = 4x0 + 3,
    
    [g](x0, x1) = 4x0 + 3,
    
    [f](x0) = 2x0 + 1
   orientation:
    g#(f(x),y) = 4x + 3 >= 4x + 2 = h#(x,y)
    
    h#(x,y) = 4x + 2 >= 2x + 1 = g#(x,f(y))
    
    g(f(x),y) = 8x + 7 >= 8x + 7 = f(h(x,y))
    
    h(x,y) = 4x + 3 >= 4x + 3 = g(x,f(y))
   problem:
    DPs:
     
    TRS:
     g(f(x),y) -> f(h(x,y))
     h(x,y) -> g(x,f(y))
   Qed