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:
    f5(x,y) -> x
    f5(x,y) -> y
   Restore Modifier:
    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())))
    SCC Processor:
     #sccs: 1
     #rules: 2
     #arcs: 4/4
     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())))
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [f#](x0, x1) = x1,
       
       [f](x0, x1) = x0,
       
       [a] = 1,
       
       [g](x0) = 0,
       
       [h](x0, x1) = 0
      orientation:
       f#(g(h(x,y)),f(a(),a())) = 1 >= 1 = f#(y,a())
       
       f#(g(h(x,y)),f(a(),a())) = 1 >= 0 = f#(h(x,x),g(f(y,a())))
       
       f(g(h(x,y)),f(a(),a())) = 0 >= 0 = f(h(x,x),g(f(y,a())))
      problem:
       DPs:
        f#(g(h(x,y)),f(a(),a())) -> f#(y,a())
       TRS:
        f(g(h(x,y)),f(a(),a())) -> f(h(x,x),g(f(y,a())))
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [f#](x0, x1) = x1 + 1,
        
        [f](x0, x1) = x0 + 1,
        
        [a] = 1,
        
        [g](x0) = 1,
        
        [h](x0, x1) = 1
       orientation:
        f#(g(h(x,y)),f(a(),a())) = 3 >= 2 = f#(y,a())
        
        f(g(h(x,y)),f(a(),a())) = 2 >= 2 = f(h(x,x),g(f(y,a())))
       problem:
        DPs:
         
        TRS:
         f(g(h(x,y)),f(a(),a())) -> f(h(x,x),g(f(y,a())))
       Qed