YES

Problem:
 f(nil()) -> nil()
 f(.(nil(),y)) -> .(nil(),f(y))
 f(.(.(x,y),z)) -> f(.(x,.(y,z)))
 g(nil()) -> nil()
 g(.(x,nil())) -> .(g(x),nil())
 g(.(x,.(y,z))) -> g(.(.(x,y),z))

Proof:
 DP Processor:
  DPs:
   f#(.(nil(),y)) -> f#(y)
   f#(.(.(x,y),z)) -> f#(.(x,.(y,z)))
   g#(.(x,nil())) -> g#(x)
   g#(.(x,.(y,z))) -> g#(.(.(x,y),z))
  TRS:
   f(nil()) -> nil()
   f(.(nil(),y)) -> .(nil(),f(y))
   f(.(.(x,y),z)) -> f(.(x,.(y,z)))
   g(nil()) -> nil()
   g(.(x,nil())) -> .(g(x),nil())
   g(.(x,.(y,z))) -> g(.(.(x,y),z))
  TDG Processor:
   DPs:
    f#(.(nil(),y)) -> f#(y)
    f#(.(.(x,y),z)) -> f#(.(x,.(y,z)))
    g#(.(x,nil())) -> g#(x)
    g#(.(x,.(y,z))) -> g#(.(.(x,y),z))
   TRS:
    f(nil()) -> nil()
    f(.(nil(),y)) -> .(nil(),f(y))
    f(.(.(x,y),z)) -> f(.(x,.(y,z)))
    g(nil()) -> nil()
    g(.(x,nil())) -> .(g(x),nil())
    g(.(x,.(y,z))) -> g(.(.(x,y),z))
   graph:
    g#(.(x,.(y,z))) -> g#(.(.(x,y),z)) ->
    g#(.(x,.(y,z))) -> g#(.(.(x,y),z))
    g#(.(x,.(y,z))) -> g#(.(.(x,y),z)) -> g#(.(x,nil())) -> g#(x)
    g#(.(x,nil())) -> g#(x) -> g#(.(x,.(y,z))) -> g#(.(.(x,y),z))
    g#(.(x,nil())) -> g#(x) -> g#(.(x,nil())) -> g#(x)
    f#(.(.(x,y),z)) -> f#(.(x,.(y,z))) ->
    f#(.(.(x,y),z)) -> f#(.(x,.(y,z)))
    f#(.(.(x,y),z)) -> f#(.(x,.(y,z))) -> f#(.(nil(),y)) -> f#(y)
    f#(.(nil(),y)) -> f#(y) -> f#(.(.(x,y),z)) -> f#(.(x,.(y,z)))
    f#(.(nil(),y)) -> f#(y) -> f#(.(nil(),y)) -> f#(y)
   SCC Processor:
    #sccs: 2
    #rules: 4
    #arcs: 8/16
    DPs:
     f#(.(.(x,y),z)) -> f#(.(x,.(y,z)))
     f#(.(nil(),y)) -> f#(y)
    TRS:
     f(nil()) -> nil()
     f(.(nil(),y)) -> .(nil(),f(y))
     f(.(.(x,y),z)) -> f(.(x,.(y,z)))
     g(nil()) -> nil()
     g(.(x,nil())) -> .(g(x),nil())
     g(.(x,.(y,z))) -> g(.(.(x,y),z))
    CDG Processor:
     DPs:
      f#(.(.(x,y),z)) -> f#(.(x,.(y,z)))
      f#(.(nil(),y)) -> f#(y)
     TRS:
      f(nil()) -> nil()
      f(.(nil(),y)) -> .(nil(),f(y))
      f(.(.(x,y),z)) -> f(.(x,.(y,z)))
      g(nil()) -> nil()
      g(.(x,nil())) -> .(g(x),nil())
      g(.(x,.(y,z))) -> g(.(.(x,y),z))
     graph:
      f#(.(nil(),y)) -> f#(y) -> f#(.(.(x,y),z)) -> f#(.(x,.(y,z)))
     SCC Processor:
      #sccs: 0
      #rules: 0
      #arcs: 1/4
      
    
    DPs:
     g#(.(x,.(y,z))) -> g#(.(.(x,y),z))
     g#(.(x,nil())) -> g#(x)
    TRS:
     f(nil()) -> nil()
     f(.(nil(),y)) -> .(nil(),f(y))
     f(.(.(x,y),z)) -> f(.(x,.(y,z)))
     g(nil()) -> nil()
     g(.(x,nil())) -> .(g(x),nil())
     g(.(x,.(y,z))) -> g(.(.(x,y),z))
    CDG Processor:
     DPs:
      g#(.(x,.(y,z))) -> g#(.(.(x,y),z))
      g#(.(x,nil())) -> g#(x)
     TRS:
      f(nil()) -> nil()
      f(.(nil(),y)) -> .(nil(),f(y))
      f(.(.(x,y),z)) -> f(.(x,.(y,z)))
      g(nil()) -> nil()
      g(.(x,nil())) -> .(g(x),nil())
      g(.(x,.(y,z))) -> g(.(.(x,y),z))
     graph:
      g#(.(x,nil())) -> g#(x) -> g#(.(x,.(y,z))) -> g#(.(.(x,y),z))
     SCC Processor:
      #sccs: 0
      #rules: 0
      #arcs: 1/4