YES

Problem:
 f(g(x)) -> g(f(f(x)))
 f(h(x)) -> h(g(x))
 f'(s(x),y,y) -> f'(y,x,s(x))

Proof:
 DP Processor:
  DPs:
   f#(g(x)) -> f#(x)
   f#(g(x)) -> f#(f(x))
   f'#(s(x),y,y) -> f'#(y,x,s(x))
  TRS:
   f(g(x)) -> g(f(f(x)))
   f(h(x)) -> h(g(x))
   f'(s(x),y,y) -> f'(y,x,s(x))
  EDG Processor:
   DPs:
    f#(g(x)) -> f#(x)
    f#(g(x)) -> f#(f(x))
    f'#(s(x),y,y) -> f'#(y,x,s(x))
   TRS:
    f(g(x)) -> g(f(f(x)))
    f(h(x)) -> h(g(x))
    f'(s(x),y,y) -> f'(y,x,s(x))
   graph:
    f'#(s(x),y,y) -> f'#(y,x,s(x)) -> f'#(s(x),y,y) -> f'#(y,x,s(x))
    f#(g(x)) -> f#(f(x)) -> f#(g(x)) -> f#(x)
    f#(g(x)) -> f#(f(x)) -> f#(g(x)) -> f#(f(x))
    f#(g(x)) -> f#(x) -> f#(g(x)) -> f#(x)
    f#(g(x)) -> f#(x) -> f#(g(x)) -> f#(f(x))
   SCC Processor:
    #sccs: 2
    #rules: 3
    #arcs: 5/9
    DPs:
     f#(g(x)) -> f#(f(x))
     f#(g(x)) -> f#(x)
    TRS:
     f(g(x)) -> g(f(f(x)))
     f(h(x)) -> h(g(x))
     f'(s(x),y,y) -> f'(y,x,s(x))
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [f#](x0) = x0 + 1,
      
      [f'](x0, x1, x2) = x0 + x1 + 1,
      
      [s](x0) = x0,
      
      [h](x0) = 1,
      
      [f](x0) = x0,
      
      [g](x0) = x0 + 1
     orientation:
      f#(g(x)) = x + 2 >= x + 1 = f#(f(x))
      
      f#(g(x)) = x + 2 >= x + 1 = f#(x)
      
      f(g(x)) = x + 1 >= x + 1 = g(f(f(x)))
      
      f(h(x)) = 1 >= 1 = h(g(x))
      
      f'(s(x),y,y) = x + y + 1 >= x + y + 1 = f'(y,x,s(x))
     problem:
      DPs:
       
      TRS:
       f(g(x)) -> g(f(f(x)))
       f(h(x)) -> h(g(x))
       f'(s(x),y,y) -> f'(y,x,s(x))
     Qed
    
    DPs:
     f'#(s(x),y,y) -> f'#(y,x,s(x))
    TRS:
     f(g(x)) -> g(f(f(x)))
     f(h(x)) -> h(g(x))
     f'(s(x),y,y) -> f'(y,x,s(x))
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [f'#](x0, x1, x2) = x0 + x1,
      
      [f'](x0, x1, x2) = 0,
      
      [s](x0) = x0 + 1,
      
      [h](x0) = 0,
      
      [f](x0) = 0,
      
      [g](x0) = 0
     orientation:
      f'#(s(x),y,y) = x + y + 1 >= x + y = f'#(y,x,s(x))
      
      f(g(x)) = 0 >= 0 = g(f(f(x)))
      
      f(h(x)) = 0 >= 0 = h(g(x))
      
      f'(s(x),y,y) = 0 >= 0 = f'(y,x,s(x))
     problem:
      DPs:
       
      TRS:
       f(g(x)) -> g(f(f(x)))
       f(h(x)) -> h(g(x))
       f'(s(x),y,y) -> f'(y,x,s(x))
     Qed