MAYBE

Problem:
 le(0(),y) -> true()
 le(s(x),0()) -> false()
 le(s(x),s(y)) -> le(x,y)
 eq(0(),0()) -> true()
 eq(0(),s(y)) -> false()
 eq(s(x),0()) -> false()
 eq(s(x),s(y)) -> eq(x,y)
 if(true(),x,y) -> x
 if(false(),x,y) -> y
 minsort(nil()) -> nil()
 minsort(cons(x,y)) -> cons(min(x,y),minsort(del(min(x,y),cons(x,y))))
 min(x,nil()) -> x
 min(x,cons(y,z)) -> if(le(x,y),min(x,z),min(y,z))
 del(x,nil()) -> nil()
 del(x,cons(y,z)) -> if(eq(x,y),z,cons(y,del(x,z)))

Proof:
 DP Processor:
  DPs:
   le#(s(x),s(y)) -> le#(x,y)
   eq#(s(x),s(y)) -> eq#(x,y)
   minsort#(cons(x,y)) -> del#(min(x,y),cons(x,y))
   minsort#(cons(x,y)) -> minsort#(del(min(x,y),cons(x,y)))
   minsort#(cons(x,y)) -> min#(x,y)
   min#(x,cons(y,z)) -> min#(y,z)
   min#(x,cons(y,z)) -> min#(x,z)
   min#(x,cons(y,z)) -> le#(x,y)
   min#(x,cons(y,z)) -> if#(le(x,y),min(x,z),min(y,z))
   del#(x,cons(y,z)) -> del#(x,z)
   del#(x,cons(y,z)) -> eq#(x,y)
   del#(x,cons(y,z)) -> if#(eq(x,y),z,cons(y,del(x,z)))
  TRS:
   le(0(),y) -> true()
   le(s(x),0()) -> false()
   le(s(x),s(y)) -> le(x,y)
   eq(0(),0()) -> true()
   eq(0(),s(y)) -> false()
   eq(s(x),0()) -> false()
   eq(s(x),s(y)) -> eq(x,y)
   if(true(),x,y) -> x
   if(false(),x,y) -> y
   minsort(nil()) -> nil()
   minsort(cons(x,y)) -> cons(min(x,y),minsort(del(min(x,y),cons(x,y))))
   min(x,nil()) -> x
   min(x,cons(y,z)) -> if(le(x,y),min(x,z),min(y,z))
   del(x,nil()) -> nil()
   del(x,cons(y,z)) -> if(eq(x,y),z,cons(y,del(x,z)))
  Open