MAYBE

Problem:
 leq(0(),y) -> true()
 leq(s(x),0()) -> false()
 leq(s(x),s(y)) -> leq(x,y)
 if(true(),x,y) -> x
 if(false(),x,y) -> y
 -(x,0()) -> x
 -(s(x),s(y)) -> -(x,y)
 mod(0(),y) -> 0()
 mod(s(x),0()) -> 0()
 mod(s(x),s(y)) -> if(leq(y,x),mod(-(s(x),s(y)),s(y)),s(x))

Proof:
 DP Processor:
  DPs:
   leq#(s(x),s(y)) -> leq#(x,y)
   -#(s(x),s(y)) -> -#(x,y)
   mod#(s(x),s(y)) -> -#(s(x),s(y))
   mod#(s(x),s(y)) -> mod#(-(s(x),s(y)),s(y))
   mod#(s(x),s(y)) -> leq#(y,x)
   mod#(s(x),s(y)) -> if#(leq(y,x),mod(-(s(x),s(y)),s(y)),s(x))
  TRS:
   leq(0(),y) -> true()
   leq(s(x),0()) -> false()
   leq(s(x),s(y)) -> leq(x,y)
   if(true(),x,y) -> x
   if(false(),x,y) -> y
   -(x,0()) -> x
   -(s(x),s(y)) -> -(x,y)
   mod(0(),y) -> 0()
   mod(s(x),0()) -> 0()
   mod(s(x),s(y)) -> if(leq(y,x),mod(-(s(x),s(y)),s(y)),s(x))
  Open