MAYBE 0.08/0.18 MAYBE 0.08/0.18 0.08/0.18 Problem: 0.08/0.18 le(0(),y) -> true() 0.08/0.18 le(s(x),0()) -> false() 0.08/0.18 le(s(x),s(y)) -> le(x,y) 0.08/0.18 zero(0()) -> true() 0.08/0.18 zero(s(x)) -> false() 0.08/0.18 id(0()) -> 0() 0.08/0.18 id(s(x)) -> s(id(x)) 0.08/0.18 minus(x,0()) -> x 0.08/0.18 minus(s(x),s(y)) -> minus(x,y) 0.08/0.18 mod(x,y) -> if_mod(zero(x),zero(y),le(y,x),id(x),id(y)) 0.08/0.18 if_mod(true(),b1,b2,x,y) -> 0() 0.08/0.18 if_mod(false(),b1,b2,x,y) -> if2(b1,b2,x,y) 0.08/0.18 if2(true(),b2,x,y) -> 0() 0.08/0.18 if2(false(),b2,x,y) -> if3(b2,x,y) 0.08/0.18 if3(true(),x,y) -> mod(minus(x,y),s(y)) 0.08/0.18 if3(false(),x,y) -> x 0.08/0.18 0.08/0.18 Proof: 0.08/0.18 Open 0.08/0.19 EOF