YES

Problem:
 minus(x,0()) -> x
 minus(s(x),s(y)) -> minus(x,y)
 f(0()) -> s(0())
 f(s(x)) -> minus(s(x),g(f(x)))
 g(0()) -> 0()
 g(s(x)) -> minus(s(x),f(g(x)))

Proof:
 DP Processor:
  DPs:
   minus#(s(x),s(y)) -> minus#(x,y)
   f#(s(x)) -> f#(x)
   f#(s(x)) -> g#(f(x))
   f#(s(x)) -> minus#(s(x),g(f(x)))
   g#(s(x)) -> g#(x)
   g#(s(x)) -> f#(g(x))
   g#(s(x)) -> minus#(s(x),f(g(x)))
  TRS:
   minus(x,0()) -> x
   minus(s(x),s(y)) -> minus(x,y)
   f(0()) -> s(0())
   f(s(x)) -> minus(s(x),g(f(x)))
   g(0()) -> 0()
   g(s(x)) -> minus(s(x),f(g(x)))
  TDG Processor:
   DPs:
    minus#(s(x),s(y)) -> minus#(x,y)
    f#(s(x)) -> f#(x)
    f#(s(x)) -> g#(f(x))
    f#(s(x)) -> minus#(s(x),g(f(x)))
    g#(s(x)) -> g#(x)
    g#(s(x)) -> f#(g(x))
    g#(s(x)) -> minus#(s(x),f(g(x)))
   TRS:
    minus(x,0()) -> x
    minus(s(x),s(y)) -> minus(x,y)
    f(0()) -> s(0())
    f(s(x)) -> minus(s(x),g(f(x)))
    g(0()) -> 0()
    g(s(x)) -> minus(s(x),f(g(x)))
   graph:
    g#(s(x)) -> g#(x) -> g#(s(x)) -> minus#(s(x),f(g(x)))
    g#(s(x)) -> g#(x) -> g#(s(x)) -> f#(g(x))
    g#(s(x)) -> g#(x) -> g#(s(x)) -> g#(x)
    g#(s(x)) -> f#(g(x)) -> f#(s(x)) -> minus#(s(x),g(f(x)))
    g#(s(x)) -> f#(g(x)) -> f#(s(x)) -> g#(f(x))
    g#(s(x)) -> f#(g(x)) -> f#(s(x)) -> f#(x)
    g#(s(x)) -> minus#(s(x),f(g(x))) -> minus#(s(x),s(y)) -> minus#(x,y)
    f#(s(x)) -> g#(f(x)) -> g#(s(x)) -> minus#(s(x),f(g(x)))
    f#(s(x)) -> g#(f(x)) -> g#(s(x)) -> f#(g(x))
    f#(s(x)) -> g#(f(x)) -> g#(s(x)) -> g#(x)
    f#(s(x)) -> f#(x) -> f#(s(x)) -> minus#(s(x),g(f(x)))
    f#(s(x)) -> f#(x) -> f#(s(x)) -> g#(f(x))
    f#(s(x)) -> f#(x) -> f#(s(x)) -> f#(x)
    f#(s(x)) -> minus#(s(x),g(f(x))) ->
    minus#(s(x),s(y)) -> minus#(x,y)
    minus#(s(x),s(y)) -> minus#(x,y) -> minus#(s(x),s(y)) -> minus#(x,y)
   SCC Processor:
    #sccs: 2
    #rules: 5
    #arcs: 15/49
    DPs:
     g#(s(x)) -> g#(x)
     g#(s(x)) -> f#(g(x))
     f#(s(x)) -> f#(x)
     f#(s(x)) -> g#(f(x))
    TRS:
     minus(x,0()) -> x
     minus(s(x),s(y)) -> minus(x,y)
     f(0()) -> s(0())
     f(s(x)) -> minus(s(x),g(f(x)))
     g(0()) -> 0()
     g(s(x)) -> minus(s(x),f(g(x)))
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [g#](x0) = x0,
      
      [f#](x0) = x0 + 0,
      
      [g](x0) = 2x0 + 0,
      
      [f](x0) = 2x0 + 0,
      
      [s](x0) = 2x0 + 0,
      
      [minus](x0, x1) = 2x0 + x1 + 0,
      
      [0] = 1
     orientation:
      g#(s(x)) = 2x + 0 >= x = g#(x)
      
      g#(s(x)) = 2x + 0 >= 2x + 0 = f#(g(x))
      
      f#(s(x)) = 2x + 0 >= x + 0 = f#(x)
      
      f#(s(x)) = 2x + 0 >= 2x + 0 = g#(f(x))
      
      minus(x,0()) = 2x + 1 >= x = x
      
      minus(s(x),s(y)) = 4x + 2y + 2 >= 2x + y + 0 = minus(x,y)
      
      f(0()) = 3 >= 3 = s(0())
      
      f(s(x)) = 4x + 2 >= 4x + 2 = minus(s(x),g(f(x)))
      
      g(0()) = 3 >= 1 = 0()
      
      g(s(x)) = 4x + 2 >= 4x + 2 = minus(s(x),f(g(x)))
     problem:
      DPs:
       g#(s(x)) -> f#(g(x))
       f#(s(x)) -> f#(x)
       f#(s(x)) -> g#(f(x))
      TRS:
       minus(x,0()) -> x
       minus(s(x),s(y)) -> minus(x,y)
       f(0()) -> s(0())
       f(s(x)) -> minus(s(x),g(f(x)))
       g(0()) -> 0()
       g(s(x)) -> minus(s(x),f(g(x)))
     KBO Processor:
      argument filtering:
       pi(0) = []
       pi(minus) = 0
       pi(s) = [0]
       pi(f) = [0]
       pi(g) = 0
       pi(f#) = [0]
       pi(g#) = 0
      weight function:
       w0 = 1
       w(f#) = w(f) = w(s) = w(0) = 1
       w(g#) = w(g) = w(minus) = 0
      precedence:
       f ~ minus > s > g# ~ f# ~ g ~ 0
      problem:
       DPs:
        
       TRS:
        minus(x,0()) -> x
        minus(s(x),s(y)) -> minus(x,y)
        f(0()) -> s(0())
        f(s(x)) -> minus(s(x),g(f(x)))
        g(0()) -> 0()
        g(s(x)) -> minus(s(x),f(g(x)))
      Qed
    
    DPs:
     minus#(s(x),s(y)) -> minus#(x,y)
    TRS:
     minus(x,0()) -> x
     minus(s(x),s(y)) -> minus(x,y)
     f(0()) -> s(0())
     f(s(x)) -> minus(s(x),g(f(x)))
     g(0()) -> 0()
     g(s(x)) -> minus(s(x),f(g(x)))
    Subterm Criterion Processor:
     simple projection:
      pi(minus#) = 1
     problem:
      DPs:
       
      TRS:
       minus(x,0()) -> x
       minus(s(x),s(y)) -> minus(x,y)
       f(0()) -> s(0())
       f(s(x)) -> minus(s(x),g(f(x)))
       g(0()) -> 0()
       g(s(x)) -> minus(s(x),f(g(x)))
     Qed