YES

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

Proof:
 DP Processor:
  DPs:
   f#(h(x)) -> i#(x)
   f#(h(x)) -> f#(i(x))
   g#(i(x)) -> h#(x)
   g#(i(x)) -> g#(h(x))
  TRS:
   f(h(x)) -> f(i(x))
   g(i(x)) -> g(h(x))
   h(a()) -> b()
   i(a()) -> b()
  Usable Rule Processor:
   DPs:
    f#(h(x)) -> i#(x)
    f#(h(x)) -> f#(i(x))
    g#(i(x)) -> h#(x)
    g#(i(x)) -> g#(h(x))
   TRS:
    i(a()) -> b()
    h(a()) -> b()
   TDG Processor:
    DPs:
     f#(h(x)) -> i#(x)
     f#(h(x)) -> f#(i(x))
     g#(i(x)) -> h#(x)
     g#(i(x)) -> g#(h(x))
    TRS:
     i(a()) -> b()
     h(a()) -> b()
    graph:
     g#(i(x)) -> g#(h(x)) -> g#(i(x)) -> g#(h(x))
     g#(i(x)) -> g#(h(x)) -> g#(i(x)) -> h#(x)
     f#(h(x)) -> f#(i(x)) -> f#(h(x)) -> f#(i(x))
     f#(h(x)) -> f#(i(x)) -> f#(h(x)) -> i#(x)
    Restore Modifier:
     DPs:
      f#(h(x)) -> i#(x)
      f#(h(x)) -> f#(i(x))
      g#(i(x)) -> h#(x)
      g#(i(x)) -> g#(h(x))
     TRS:
      f(h(x)) -> f(i(x))
      g(i(x)) -> g(h(x))
      h(a()) -> b()
      i(a()) -> b()
     SCC Processor:
      #sccs: 2
      #rules: 2
      #arcs: 4/16
      DPs:
       f#(h(x)) -> f#(i(x))
      TRS:
       f(h(x)) -> f(i(x))
       g(i(x)) -> g(h(x))
       h(a()) -> b()
       i(a()) -> b()
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [f#](x0) = x0,
        
        [b] = 0,
        
        [a] = 0,
        
        [g](x0) = 0,
        
        [i](x0) = 0,
        
        [f](x0) = 0,
        
        [h](x0) = 1
       orientation:
        f#(h(x)) = 1 >= 0 = f#(i(x))
        
        f(h(x)) = 0 >= 0 = f(i(x))
        
        g(i(x)) = 0 >= 0 = g(h(x))
        
        h(a()) = 1 >= 0 = b()
        
        i(a()) = 0 >= 0 = b()
       problem:
        DPs:
         
        TRS:
         f(h(x)) -> f(i(x))
         g(i(x)) -> g(h(x))
         h(a()) -> b()
         i(a()) -> b()
       Qed
      
      DPs:
       g#(i(x)) -> g#(h(x))
      TRS:
       f(h(x)) -> f(i(x))
       g(i(x)) -> g(h(x))
       h(a()) -> b()
       i(a()) -> b()
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [g#](x0) = x0,
        
        [b] = 0,
        
        [a] = 0,
        
        [g](x0) = 0,
        
        [i](x0) = 1,
        
        [f](x0) = 0,
        
        [h](x0) = 0
       orientation:
        g#(i(x)) = 1 >= 0 = g#(h(x))
        
        f(h(x)) = 0 >= 0 = f(i(x))
        
        g(i(x)) = 0 >= 0 = g(h(x))
        
        h(a()) = 0 >= 0 = b()
        
        i(a()) = 1 >= 0 = b()
       problem:
        DPs:
         
        TRS:
         f(h(x)) -> f(i(x))
         g(i(x)) -> g(h(x))
         h(a()) -> b()
         i(a()) -> b()
       Qed