YES

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

Proof:
 DP Processor:
  DPs:
   f#(g(h(x,y)),f(a(),a())) -> f#(y,a())
   f#(g(h(x,y)),f(a(),a())) -> f#(h(x,x),g(f(y,a())))
  TRS:
   f(g(h(x,y)),f(a(),a())) -> f(h(x,x),g(f(y,a())))
  Usable Rule Processor:
   DPs:
    f#(g(h(x,y)),f(a(),a())) -> f#(y,a())
    f#(g(h(x,y)),f(a(),a())) -> f#(h(x,x),g(f(y,a())))
   TRS:
    
   Arctic Interpretation Processor:
    dimension: 1
    usable rules:
     
    interpretation:
     [f#](x0, x1) = x0 + -8x1 + -3,
     
     [f](x0, x1) = 1x0 + 0,
     
     [a] = 6,
     
     [g](x0) = 4x0 + 0,
     
     [h](x0, x1) = x0 + 3x1 + -4
    orientation:
     f#(g(h(x,y)),f(a(),a())) = 4x + 7y + 0 >= y + -2 = f#(y,a())
     
     f#(g(h(x,y)),f(a(),a())) = 4x + 7y + 0 >= 3x + -3y + -3 = f#(h(x,x),g(f(y,a())))
    problem:
     DPs:
      
     TRS:
      
    Qed