MAYBE

Problem:
 f(x,y) -> cond(lt(x,y),x,y)
 cond(tt(),x,y) -> f(s(x),s(y))
 lt(0(),y) -> tt()
 lt(s(x),s(y)) -> lt(x,y)

Proof:
 DP Processor:
  DPs:
   f#(x,y) -> lt#(x,y)
   f#(x,y) -> cond#(lt(x,y),x,y)
   cond#(tt(),x,y) -> f#(s(x),s(y))
   lt#(s(x),s(y)) -> lt#(x,y)
  TRS:
   f(x,y) -> cond(lt(x,y),x,y)
   cond(tt(),x,y) -> f(s(x),s(y))
   lt(0(),y) -> tt()
   lt(s(x),s(y)) -> lt(x,y)
  TDG Processor:
   DPs:
    f#(x,y) -> lt#(x,y)
    f#(x,y) -> cond#(lt(x,y),x,y)
    cond#(tt(),x,y) -> f#(s(x),s(y))
    lt#(s(x),s(y)) -> lt#(x,y)
   TRS:
    f(x,y) -> cond(lt(x,y),x,y)
    cond(tt(),x,y) -> f(s(x),s(y))
    lt(0(),y) -> tt()
    lt(s(x),s(y)) -> lt(x,y)
   graph:
    cond#(tt(),x,y) -> f#(s(x),s(y)) ->
    f#(x,y) -> cond#(lt(x,y),x,y)
    cond#(tt(),x,y) -> f#(s(x),s(y)) -> f#(x,y) -> lt#(x,y)
    lt#(s(x),s(y)) -> lt#(x,y) -> lt#(s(x),s(y)) -> lt#(x,y)
    f#(x,y) -> cond#(lt(x,y),x,y) -> cond#(tt(),x,y) -> f#(s(x),s(y))
    f#(x,y) -> lt#(x,y) -> lt#(s(x),s(y)) -> lt#(x,y)
   SCC Processor:
    #sccs: 2
    #rules: 3
    #arcs: 5/16
    DPs:
     cond#(tt(),x,y) -> f#(s(x),s(y))
     f#(x,y) -> cond#(lt(x,y),x,y)
    TRS:
     f(x,y) -> cond(lt(x,y),x,y)
     cond(tt(),x,y) -> f(s(x),s(y))
     lt(0(),y) -> tt()
     lt(s(x),s(y)) -> lt(x,y)
    Open
    
    DPs:
     lt#(s(x),s(y)) -> lt#(x,y)
    TRS:
     f(x,y) -> cond(lt(x,y),x,y)
     cond(tt(),x,y) -> f(s(x),s(y))
     lt(0(),y) -> tt()
     lt(s(x),s(y)) -> lt(x,y)
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [lt#](x0, x1) = 4x1 + 4,
      
      [0] = 0,
      
      [s](x0) = x0 + 5,
      
      [tt] = 0,
      
      [cond](x0, x1, x2) = 4,
      
      [lt](x0, x1) = 6x1,
      
      [f](x0, x1) = 4
     orientation:
      lt#(s(x),s(y)) = 4y + 24 >= 4y + 4 = lt#(x,y)
      
      f(x,y) = 4 >= 4 = cond(lt(x,y),x,y)
      
      cond(tt(),x,y) = 4 >= 4 = f(s(x),s(y))
      
      lt(0(),y) = 6y >= 0 = tt()
      
      lt(s(x),s(y)) = 6y + 30 >= 6y = lt(x,y)
     problem:
      DPs:
       
      TRS:
       f(x,y) -> cond(lt(x,y),x,y)
       cond(tt(),x,y) -> f(s(x),s(y))
       lt(0(),y) -> tt()
       lt(s(x),s(y)) -> lt(x,y)
     Qed