MAYBE 0.09/0.19 MAYBE 0.09/0.19 0.09/0.19 Problem: 0.09/0.19 le(0(),y) -> true() 0.09/0.19 le(s(x),0()) -> false() 0.09/0.19 le(s(x),s(y)) -> le(x,y) 0.09/0.19 inc(0()) -> 0() 0.09/0.19 inc(s(x)) -> s(inc(x)) 0.09/0.19 minus(0(),y) -> 0() 0.09/0.19 minus(x,0()) -> x 0.09/0.19 minus(s(x),s(y)) -> minus(x,y) 0.09/0.19 quot(0(),s(y)) -> 0() 0.09/0.19 quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) 0.09/0.19 log(x) -> log2(x,0()) 0.09/0.19 log2(x,y) -> if(le(x,0()),le(x,s(0())),x,inc(y)) 0.09/0.19 if(true(),b,x,y) -> log_undefined() 0.09/0.19 if(false(),b,x,y) -> if2(b,x,y) 0.09/0.19 if2(true(),x,s(y)) -> y 0.09/0.19 if2(false(),x,y) -> log2(quot(x,s(s(0()))),y) 0.09/0.19 0.09/0.19 Proof: 0.09/0.19 Open 0.09/0.19 EOF