YES

Problem:
 g(a()) -> g(b())
 b() -> f(a(),a())
 f(a(),a()) -> g(d())

Proof:
 DP Processor:
  DPs:
   g#(a()) -> b#()
   g#(a()) -> g#(b())
   b#() -> f#(a(),a())
   f#(a(),a()) -> g#(d())
  TRS:
   g(a()) -> g(b())
   b() -> f(a(),a())
   f(a(),a()) -> g(d())
  Usable Rule Processor:
   DPs:
    g#(a()) -> b#()
    g#(a()) -> g#(b())
    b#() -> f#(a(),a())
    f#(a(),a()) -> g#(d())
   TRS:
    b() -> f(a(),a())
    f(a(),a()) -> g(d())
   TDG Processor:
    DPs:
     g#(a()) -> b#()
     g#(a()) -> g#(b())
     b#() -> f#(a(),a())
     f#(a(),a()) -> g#(d())
    TRS:
     b() -> f(a(),a())
     f(a(),a()) -> g(d())
    graph:
     f#(a(),a()) -> g#(d()) -> g#(a()) -> g#(b())
     f#(a(),a()) -> g#(d()) -> g#(a()) -> b#()
     b#() -> f#(a(),a()) -> f#(a(),a()) -> g#(d())
     g#(a()) -> b#() -> b#() -> f#(a(),a())
     g#(a()) -> g#(b()) -> g#(a()) -> g#(b())
     g#(a()) -> g#(b()) -> g#(a()) -> b#()
    Restore Modifier:
     DPs:
      g#(a()) -> b#()
      g#(a()) -> g#(b())
      b#() -> f#(a(),a())
      f#(a(),a()) -> g#(d())
     TRS:
      g(a()) -> g(b())
      b() -> f(a(),a())
      f(a(),a()) -> g(d())
     SCC Processor:
      #sccs: 1
      #rules: 4
      #arcs: 6/16
      DPs:
       f#(a(),a()) -> g#(d())
       g#(a()) -> b#()
       b#() -> f#(a(),a())
       g#(a()) -> g#(b())
      TRS:
       g(a()) -> g(b())
       b() -> f(a(),a())
       f(a(),a()) -> g(d())
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [f#](x0, x1) = x1,
        
        [b#] = 1,
        
        [g#](x0) = x0 + 1,
        
        [d] = 0,
        
        [f](x0, x1) = 1,
        
        [b] = 1,
        
        [g](x0) = 0,
        
        [a] = 1
       orientation:
        f#(a(),a()) = 1 >= 1 = g#(d())
        
        g#(a()) = 2 >= 1 = b#()
        
        b#() = 1 >= 1 = f#(a(),a())
        
        g#(a()) = 2 >= 2 = g#(b())
        
        g(a()) = 0 >= 0 = g(b())
        
        b() = 1 >= 1 = f(a(),a())
        
        f(a(),a()) = 1 >= 0 = g(d())
       problem:
        DPs:
         f#(a(),a()) -> g#(d())
         b#() -> f#(a(),a())
         g#(a()) -> g#(b())
        TRS:
         g(a()) -> g(b())
         b() -> f(a(),a())
         f(a(),a()) -> g(d())
       Matrix Interpretation Processor:
        dimension: 1
        interpretation:
         [f#](x0, x1) = 0,
         
         [b#] = 0,
         
         [g#](x0) = x0,
         
         [d] = 0,
         
         [f](x0, x1) = 0,
         
         [b] = 0,
         
         [g](x0) = 0,
         
         [a] = 1
        orientation:
         f#(a(),a()) = 0 >= 0 = g#(d())
         
         b#() = 0 >= 0 = f#(a(),a())
         
         g#(a()) = 1 >= 0 = g#(b())
         
         g(a()) = 0 >= 0 = g(b())
         
         b() = 0 >= 0 = f(a(),a())
         
         f(a(),a()) = 0 >= 0 = g(d())
        problem:
         DPs:
          f#(a(),a()) -> g#(d())
          b#() -> f#(a(),a())
         TRS:
          g(a()) -> g(b())
          b() -> f(a(),a())
          f(a(),a()) -> g(d())
        Matrix Interpretation Processor:
         dimension: 1
         interpretation:
          [f#](x0, x1) = 0,
          
          [b#] = 1,
          
          [g#](x0) = 0,
          
          [d] = 0,
          
          [f](x0, x1) = 0,
          
          [b] = 0,
          
          [g](x0) = 0,
          
          [a] = 0
         orientation:
          f#(a(),a()) = 0 >= 0 = g#(d())
          
          b#() = 1 >= 0 = f#(a(),a())
          
          g(a()) = 0 >= 0 = g(b())
          
          b() = 0 >= 0 = f(a(),a())
          
          f(a(),a()) = 0 >= 0 = g(d())
         problem:
          DPs:
           f#(a(),a()) -> g#(d())
          TRS:
           g(a()) -> g(b())
           b() -> f(a(),a())
           f(a(),a()) -> g(d())
         Matrix Interpretation Processor:
          dimension: 1
          interpretation:
           [f#](x0, x1) = 1,
           
           [g#](x0) = 0,
           
           [d] = 0,
           
           [f](x0, x1) = 0,
           
           [b] = 0,
           
           [g](x0) = 0,
           
           [a] = 0
          orientation:
           f#(a(),a()) = 1 >= 0 = g#(d())
           
           g(a()) = 0 >= 0 = g(b())
           
           b() = 0 >= 0 = f(a(),a())
           
           f(a(),a()) = 0 >= 0 = g(d())
          problem:
           DPs:
            
           TRS:
            g(a()) -> g(b())
            b() -> f(a(),a())
            f(a(),a()) -> g(d())
          Qed