MAYBE

Problem:
 ge(x,0()) -> true()
 ge(0(),s(y)) -> false()
 ge(s(x),s(y)) -> ge(x,y)
 minus(x,0()) -> x
 minus(0(),y) -> 0()
 minus(s(x),s(y)) -> minus(x,y)
 id_inc(x) -> x
 id_inc(x) -> s(x)
 quot(x,y) -> div(x,y,0())
 div(x,y,z) -> if(ge(y,s(0())),ge(x,y),x,y,z)
 if(false(),b,x,y,z) -> div_by_zero()
 if(true(),false(),x,y,z) -> z
 if(true(),true(),x,y,z) -> div(minus(x,y),y,id_inc(z))

Proof:
 Open