MAYBE Problem: half(0()) -> 0() half(s(0())) -> 0() half(s(s(x))) -> s(half(x)) lastbit(0()) -> 0() lastbit(s(0())) -> s(0()) lastbit(s(s(x))) -> lastbit(x) conv(0()) -> cons(nil(),0()) conv(s(x)) -> cons(conv(half(s(x))),lastbit(s(x))) Proof: DP Processor: DPs: half#(s(s(x))) -> half#(x) lastbit#(s(s(x))) -> lastbit#(x) conv#(s(x)) -> lastbit#(s(x)) conv#(s(x)) -> half#(s(x)) conv#(s(x)) -> conv#(half(s(x))) TRS: half(0()) -> 0() half(s(0())) -> 0() half(s(s(x))) -> s(half(x)) lastbit(0()) -> 0() lastbit(s(0())) -> s(0()) lastbit(s(s(x))) -> lastbit(x) conv(0()) -> cons(nil(),0()) conv(s(x)) -> cons(conv(half(s(x))),lastbit(s(x))) Usable Rule Processor: DPs: half#(s(s(x))) -> half#(x) lastbit#(s(s(x))) -> lastbit#(x) conv#(s(x)) -> lastbit#(s(x)) conv#(s(x)) -> half#(s(x)) conv#(s(x)) -> conv#(half(s(x))) TRS: half(s(0())) -> 0() half(s(s(x))) -> s(half(x)) half(0()) -> 0() TDG Processor: DPs: half#(s(s(x))) -> half#(x) lastbit#(s(s(x))) -> lastbit#(x) conv#(s(x)) -> lastbit#(s(x)) conv#(s(x)) -> half#(s(x)) conv#(s(x)) -> conv#(half(s(x))) TRS: half(s(0())) -> 0() half(s(s(x))) -> s(half(x)) half(0()) -> 0() graph: conv#(s(x)) -> conv#(half(s(x))) -> conv#(s(x)) -> conv#(half(s(x))) conv#(s(x)) -> conv#(half(s(x))) -> conv#(s(x)) -> half#(s(x)) conv#(s(x)) -> conv#(half(s(x))) -> conv#(s(x)) -> lastbit#(s(x)) conv#(s(x)) -> lastbit#(s(x)) -> lastbit#(s(s(x))) -> lastbit#(x) conv#(s(x)) -> half#(s(x)) -> half#(s(s(x))) -> half#(x) lastbit#(s(s(x))) -> lastbit#(x) -> lastbit#(s(s(x))) -> lastbit#(x) half#(s(s(x))) -> half#(x) -> half#(s(s(x))) -> half#(x) CDG Processor: DPs: half#(s(s(x))) -> half#(x) lastbit#(s(s(x))) -> lastbit#(x) conv#(s(x)) -> lastbit#(s(x)) conv#(s(x)) -> half#(s(x)) conv#(s(x)) -> conv#(half(s(x))) TRS: half(s(0())) -> 0() half(s(s(x))) -> s(half(x)) half(0()) -> 0() graph: conv#(s(x)) -> conv#(half(s(x))) -> conv#(s(x)) -> lastbit#(s(x)) conv#(s(x)) -> conv#(half(s(x))) -> conv#(s(x)) -> half#(s(x)) conv#(s(x)) -> conv#(half(s(x))) -> conv#(s(x)) -> conv#(half(s(x))) Restore Modifier: DPs: half#(s(s(x))) -> half#(x) lastbit#(s(s(x))) -> lastbit#(x) conv#(s(x)) -> lastbit#(s(x)) conv#(s(x)) -> half#(s(x)) conv#(s(x)) -> conv#(half(s(x))) TRS: half(0()) -> 0() half(s(0())) -> 0() half(s(s(x))) -> s(half(x)) lastbit(0()) -> 0() lastbit(s(0())) -> s(0()) lastbit(s(s(x))) -> lastbit(x) conv(0()) -> cons(nil(),0()) conv(s(x)) -> cons(conv(half(s(x))),lastbit(s(x))) SCC Processor: #sccs: 1 #rules: 1 #arcs: 3/25 DPs: conv#(s(x)) -> conv#(half(s(x))) TRS: half(0()) -> 0() half(s(0())) -> 0() half(s(s(x))) -> s(half(x)) lastbit(0()) -> 0() lastbit(s(0())) -> s(0()) lastbit(s(s(x))) -> lastbit(x) conv(0()) -> cons(nil(),0()) conv(s(x)) -> cons(conv(half(s(x))),lastbit(s(x))) Open