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)))
    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(minus) = w(0) = 1
      w(g#) = w(g) = 0
     precedence:
      g# ~ f > f# ~ g ~ s ~ minus ~ 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)))
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [minus#](x0, x1) = 3x0 + x1,
      
      [g](x0) = 2x0 + 3,
      
      [f](x0) = 4x0 + 1,
      
      [s](x0) = 1x0 + 0,
      
      [minus](x0, x1) = 1x0,
      
      [0] = 0
     orientation:
      minus#(s(x),s(y)) = 4x + 1y + 3 >= 3x + y = minus#(x,y)
      
      minus(x,0()) = 1x >= x = x
      
      minus(s(x),s(y)) = 2x + 1 >= 1x = minus(x,y)
      
      f(0()) = 4 >= 1 = s(0())
      
      f(s(x)) = 5x + 4 >= 2x + 1 = minus(s(x),g(f(x)))
      
      g(0()) = 3 >= 0 = 0()
      
      g(s(x)) = 3x + 3 >= 2x + 1 = minus(s(x),f(g(x)))
     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