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)
  TDG 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)
   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)
   EDG 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)
    graph:
     h#(x,x,y) -> g#(x) -> g#(a()) -> h#(a(),b(),a())
    SCC Processor:
     #sccs: 0
     #rules: 0
     #arcs: 1/9