MAYBE

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

Proof:
 DP Processor:
  DPs:
   f#(t(),x,y) -> g#(x,y)
   f#(t(),x,y) -> f#(g(x,y),x,s(y))
   g#(s(x),s(y)) -> g#(x,y)
  TRS:
   f(t(),x,y) -> f(g(x,y),x,s(y))
   g(s(x),0()) -> t()
   g(s(x),s(y)) -> g(x,y)
  TDG Processor:
   DPs:
    f#(t(),x,y) -> g#(x,y)
    f#(t(),x,y) -> f#(g(x,y),x,s(y))
    g#(s(x),s(y)) -> g#(x,y)
   TRS:
    f(t(),x,y) -> f(g(x,y),x,s(y))
    g(s(x),0()) -> t()
    g(s(x),s(y)) -> g(x,y)
   graph:
    g#(s(x),s(y)) -> g#(x,y) -> g#(s(x),s(y)) -> g#(x,y)
    f#(t(),x,y) -> g#(x,y) -> g#(s(x),s(y)) -> g#(x,y)
    f#(t(),x,y) -> f#(g(x,y),x,s(y)) ->
    f#(t(),x,y) -> f#(g(x,y),x,s(y))
    f#(t(),x,y) -> f#(g(x,y),x,s(y)) -> f#(t(),x,y) -> g#(x,y)
   SCC Processor:
    #sccs: 2
    #rules: 2
    #arcs: 4/9
    DPs:
     f#(t(),x,y) -> f#(g(x,y),x,s(y))
    TRS:
     f(t(),x,y) -> f(g(x,y),x,s(y))
     g(s(x),0()) -> t()
     g(s(x),s(y)) -> g(x,y)
    Open
    
    DPs:
     g#(s(x),s(y)) -> g#(x,y)
    TRS:
     f(t(),x,y) -> f(g(x,y),x,s(y))
     g(s(x),0()) -> t()
     g(s(x),s(y)) -> g(x,y)
    KBO Processor:
     argument filtering:
      pi(t) = []
      pi(f) = 1
      pi(g) = 1
      pi(s) = [0]
      pi(0) = []
      pi(g#) = 1
     weight function:
      w0 = 1
      w(g#) = w(0) = w(s) = w(g) = w(f) = w(t) = 1
     precedence:
      g# ~ 0 > s ~ g ~ f ~ t
     problem:
      DPs:
       
      TRS:
       f(t(),x,y) -> f(g(x,y),x,s(y))
       g(s(x),0()) -> t()
       g(s(x),s(y)) -> g(x,y)
     Qed