YES

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

Proof:
 DP Processor:
  DPs:
   f#(g(x),a()) -> f#(x,g(a()))
   f#(g(x),g(y)) -> h#(g(y),x,g(y))
   h#(g(x),y,z) -> h#(x,y,z)
   h#(g(x),y,z) -> f#(y,h(x,y,z))
  TRS:
   f(a(),g(y)) -> g(g(y))
   f(g(x),a()) -> f(x,g(a()))
   f(g(x),g(y)) -> h(g(y),x,g(y))
   h(g(x),y,z) -> f(y,h(x,y,z))
   h(a(),y,z) -> z
  EDG Processor:
   DPs:
    f#(g(x),a()) -> f#(x,g(a()))
    f#(g(x),g(y)) -> h#(g(y),x,g(y))
    h#(g(x),y,z) -> h#(x,y,z)
    h#(g(x),y,z) -> f#(y,h(x,y,z))
   TRS:
    f(a(),g(y)) -> g(g(y))
    f(g(x),a()) -> f(x,g(a()))
    f(g(x),g(y)) -> h(g(y),x,g(y))
    h(g(x),y,z) -> f(y,h(x,y,z))
    h(a(),y,z) -> z
   graph:
    h#(g(x),y,z) -> h#(x,y,z) -> h#(g(x),y,z) -> h#(x,y,z)
    h#(g(x),y,z) -> h#(x,y,z) -> h#(g(x),y,z) -> f#(y,h(x,y,z))
    h#(g(x),y,z) -> f#(y,h(x,y,z)) -> f#(g(x),a()) -> f#(x,g(a()))
    h#(g(x),y,z) -> f#(y,h(x,y,z)) ->
    f#(g(x),g(y)) -> h#(g(y),x,g(y))
    f#(g(x),g(y)) -> h#(g(y),x,g(y)) -> h#(g(x),y,z) -> h#(x,y,z)
    f#(g(x),g(y)) -> h#(g(y),x,g(y)) -> h#(g(x),y,z) -> f#(y,h(x,y,z))
    f#(g(x),a()) -> f#(x,g(a())) -> f#(g(x),g(y)) -> h#(g(y),x,g(y))
   Subterm Criterion Processor:
    simple projection:
     pi(f#) = 0
     pi(h#) = 1
    problem:
     DPs:
      h#(g(x),y,z) -> h#(x,y,z)
      h#(g(x),y,z) -> f#(y,h(x,y,z))
     TRS:
      f(a(),g(y)) -> g(g(y))
      f(g(x),a()) -> f(x,g(a()))
      f(g(x),g(y)) -> h(g(y),x,g(y))
      h(g(x),y,z) -> f(y,h(x,y,z))
      h(a(),y,z) -> z
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [h#](x0, x1, x2) = 1,
      
      [f#](x0, x1) = 0,
      
      [h](x0, x1, x2) = x2,
      
      [f](x0, x1) = x1,
      
      [g](x0) = 0,
      
      [a] = 0
     orientation:
      h#(g(x),y,z) = 1 >= 1 = h#(x,y,z)
      
      h#(g(x),y,z) = 1 >= 0 = f#(y,h(x,y,z))
      
      f(a(),g(y)) = 0 >= 0 = g(g(y))
      
      f(g(x),a()) = 0 >= 0 = f(x,g(a()))
      
      f(g(x),g(y)) = 0 >= 0 = h(g(y),x,g(y))
      
      h(g(x),y,z) = z >= z = f(y,h(x,y,z))
      
      h(a(),y,z) = z >= z = z
     problem:
      DPs:
       h#(g(x),y,z) -> h#(x,y,z)
      TRS:
       f(a(),g(y)) -> g(g(y))
       f(g(x),a()) -> f(x,g(a()))
       f(g(x),g(y)) -> h(g(y),x,g(y))
       h(g(x),y,z) -> f(y,h(x,y,z))
       h(a(),y,z) -> z
     Subterm Criterion Processor:
      simple projection:
       pi(h#) = 0
      problem:
       DPs:
        
       TRS:
        f(a(),g(y)) -> g(g(y))
        f(g(x),a()) -> f(x,g(a()))
        f(g(x),g(y)) -> h(g(y),x,g(y))
        h(g(x),y,z) -> f(y,h(x,y,z))
        h(a(),y,z) -> z
      Qed