YES

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

Proof:
 DP Processor:
  DPs:
   g#(a()) -> h#(a(),b(),a())
   i#(x) -> f#(x,x)
   h#(x,x,y) -> g#(x)
  TRS:
   f(x,y) -> x
   g(a()) -> h(a(),b(),a())
   i(x) -> f(x,x)
   h(x,x,y) -> g(x)
  Usable Rule Processor:
   DPs:
    g#(a()) -> h#(a(),b(),a())
    i#(x) -> f#(x,x)
    h#(x,x,y) -> g#(x)
   TRS:
    f10(x,y) -> x
    f10(x,y) -> y
   TDG Processor:
    DPs:
     g#(a()) -> h#(a(),b(),a())
     i#(x) -> f#(x,x)
     h#(x,x,y) -> g#(x)
    TRS:
     f10(x,y) -> x
     f10(x,y) -> y
    graph:
     h#(x,x,y) -> g#(x) -> g#(a()) -> h#(a(),b(),a())
     g#(a()) -> h#(a(),b(),a()) -> h#(x,x,y) -> g#(x)
    Restore Modifier:
     DPs:
      g#(a()) -> h#(a(),b(),a())
      i#(x) -> f#(x,x)
      h#(x,x,y) -> g#(x)
     TRS:
      f(x,y) -> x
      g(a()) -> h(a(),b(),a())
      i(x) -> f(x,x)
      h(x,x,y) -> g(x)
     SCC Processor:
      #sccs: 1
      #rules: 2
      #arcs: 2/9
      DPs:
       h#(x,x,y) -> g#(x)
       g#(a()) -> h#(a(),b(),a())
      TRS:
       f(x,y) -> x
       g(a()) -> h(a(),b(),a())
       i(x) -> f(x,x)
       h(x,x,y) -> g(x)
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [h#](x0, x1, x2) = x1,
        
        [g#](x0) = x0,
        
        [i](x0) = x0,
        
        [h](x0, x1, x2) = x1,
        
        [b] = 0,
        
        [g](x0) = 0,
        
        [a] = 1,
        
        [f](x0, x1) = x0
       orientation:
        h#(x,x,y) = x >= x = g#(x)
        
        g#(a()) = 1 >= 0 = h#(a(),b(),a())
        
        f(x,y) = x >= x = x
        
        g(a()) = 0 >= 0 = h(a(),b(),a())
        
        i(x) = x >= x = f(x,x)
        
        h(x,x,y) = x >= 0 = g(x)
       problem:
        DPs:
         h#(x,x,y) -> g#(x)
        TRS:
         f(x,y) -> x
         g(a()) -> h(a(),b(),a())
         i(x) -> f(x,x)
         h(x,x,y) -> g(x)
       Matrix Interpretation Processor:
        dimension: 1
        interpretation:
         [h#](x0, x1, x2) = 1,
         
         [g#](x0) = 0,
         
         [i](x0) = x0,
         
         [h](x0, x1, x2) = 0,
         
         [b] = 0,
         
         [g](x0) = 0,
         
         [a] = 0,
         
         [f](x0, x1) = x0
        orientation:
         h#(x,x,y) = 1 >= 0 = g#(x)
         
         f(x,y) = x >= x = x
         
         g(a()) = 0 >= 0 = h(a(),b(),a())
         
         i(x) = x >= x = f(x,x)
         
         h(x,x,y) = 0 >= 0 = g(x)
        problem:
         DPs:
          
         TRS:
          f(x,y) -> x
          g(a()) -> h(a(),b(),a())
          i(x) -> f(x,x)
          h(x,x,y) -> g(x)
        Qed