MAYBE

Problem:
 le(0(),y) -> true()
 le(s(x),0()) -> false()
 le(s(x),s(y)) -> le(x,y)
 int(x,y) -> if(le(x,y),x,y)
 if(true(),x,y) -> cons(x,int(s(x),y))
 if(false(),x,y) -> nil()

Proof:
 DP Processor:
  DPs:
   le#(s(x),s(y)) -> le#(x,y)
   int#(x,y) -> le#(x,y)
   int#(x,y) -> if#(le(x,y),x,y)
   if#(true(),x,y) -> int#(s(x),y)
  TRS:
   le(0(),y) -> true()
   le(s(x),0()) -> false()
   le(s(x),s(y)) -> le(x,y)
   int(x,y) -> if(le(x,y),x,y)
   if(true(),x,y) -> cons(x,int(s(x),y))
   if(false(),x,y) -> nil()
  TDG Processor:
   DPs:
    le#(s(x),s(y)) -> le#(x,y)
    int#(x,y) -> le#(x,y)
    int#(x,y) -> if#(le(x,y),x,y)
    if#(true(),x,y) -> int#(s(x),y)
   TRS:
    le(0(),y) -> true()
    le(s(x),0()) -> false()
    le(s(x),s(y)) -> le(x,y)
    int(x,y) -> if(le(x,y),x,y)
    if(true(),x,y) -> cons(x,int(s(x),y))
    if(false(),x,y) -> nil()
   graph:
    if#(true(),x,y) -> int#(s(x),y) -> int#(x,y) -> if#(le(x,y),x,y)
    if#(true(),x,y) -> int#(s(x),y) -> int#(x,y) -> le#(x,y)
    int#(x,y) -> if#(le(x,y),x,y) -> if#(true(),x,y) -> int#(s(x),y)
    int#(x,y) -> le#(x,y) -> le#(s(x),s(y)) -> le#(x,y)
    le#(s(x),s(y)) -> le#(x,y) -> le#(s(x),s(y)) -> le#(x,y)
   SCC Processor:
    #sccs: 2
    #rules: 3
    #arcs: 5/16
    DPs:
     if#(true(),x,y) -> int#(s(x),y)
     int#(x,y) -> if#(le(x,y),x,y)
    TRS:
     le(0(),y) -> true()
     le(s(x),0()) -> false()
     le(s(x),s(y)) -> le(x,y)
     int(x,y) -> if(le(x,y),x,y)
     if(true(),x,y) -> cons(x,int(s(x),y))
     if(false(),x,y) -> nil()
    Open
    
    DPs:
     le#(s(x),s(y)) -> le#(x,y)
    TRS:
     le(0(),y) -> true()
     le(s(x),0()) -> false()
     le(s(x),s(y)) -> le(x,y)
     int(x,y) -> if(le(x,y),x,y)
     if(true(),x,y) -> cons(x,int(s(x),y))
     if(false(),x,y) -> nil()
    Subterm Criterion Processor:
     simple projection:
      pi(le#) = 1
     problem:
      DPs:
       
      TRS:
       le(0(),y) -> true()
       le(s(x),0()) -> false()
       le(s(x),s(y)) -> le(x,y)
       int(x,y) -> if(le(x,y),x,y)
       if(true(),x,y) -> cons(x,int(s(x),y))
       if(false(),x,y) -> nil()
     Qed