MAYBE 0.22/0.25 MAYBE 0.22/0.25 0.22/0.25 Problem: 0.22/0.25 active(natsFrom(N)) -> mark(cons(N,natsFrom(s(N)))) 0.22/0.25 active(fst(pair(XS,YS))) -> mark(XS) 0.22/0.25 active(snd(pair(XS,YS))) -> mark(YS) 0.22/0.25 active(splitAt(0(),XS)) -> mark(pair(nil(),XS)) 0.22/0.25 active(splitAt(s(N),cons(X,XS))) -> mark(u(splitAt(N,XS),N,X,XS)) 0.22/0.25 active(u(pair(YS,ZS),N,X,XS)) -> mark(pair(cons(X,YS),ZS)) 0.22/0.25 active(head(cons(N,XS))) -> mark(N) 0.22/0.25 active(tail(cons(N,XS))) -> mark(XS) 0.22/0.25 active(sel(N,XS)) -> mark(head(afterNth(N,XS))) 0.22/0.25 active(take(N,XS)) -> mark(fst(splitAt(N,XS))) 0.22/0.25 active(afterNth(N,XS)) -> mark(snd(splitAt(N,XS))) 0.22/0.25 active(natsFrom(X)) -> natsFrom(active(X)) 0.22/0.25 active(cons(X1,X2)) -> cons(active(X1),X2) 0.22/0.25 active(s(X)) -> s(active(X)) 0.22/0.25 active(fst(X)) -> fst(active(X)) 0.22/0.25 active(pair(X1,X2)) -> pair(active(X1),X2) 0.22/0.25 active(pair(X1,X2)) -> pair(X1,active(X2)) 0.22/0.25 active(snd(X)) -> snd(active(X)) 0.22/0.25 active(splitAt(X1,X2)) -> splitAt(active(X1),X2) 0.22/0.25 active(splitAt(X1,X2)) -> splitAt(X1,active(X2)) 0.22/0.25 active(u(X1,X2,X3,X4)) -> u(active(X1),X2,X3,X4) 0.22/0.25 active(head(X)) -> head(active(X)) 0.22/0.25 active(tail(X)) -> tail(active(X)) 0.22/0.25 active(sel(X1,X2)) -> sel(active(X1),X2) 0.22/0.25 active(sel(X1,X2)) -> sel(X1,active(X2)) 0.22/0.25 active(afterNth(X1,X2)) -> afterNth(active(X1),X2) 0.22/0.25 active(afterNth(X1,X2)) -> afterNth(X1,active(X2)) 0.22/0.25 active(take(X1,X2)) -> take(active(X1),X2) 0.22/0.25 active(take(X1,X2)) -> take(X1,active(X2)) 0.22/0.25 natsFrom(mark(X)) -> mark(natsFrom(X)) 0.22/0.25 cons(mark(X1),X2) -> mark(cons(X1,X2)) 0.22/0.25 s(mark(X)) -> mark(s(X)) 0.22/0.25 fst(mark(X)) -> mark(fst(X)) 0.22/0.25 pair(mark(X1),X2) -> mark(pair(X1,X2)) 0.22/0.25 pair(X1,mark(X2)) -> mark(pair(X1,X2)) 0.22/0.25 snd(mark(X)) -> mark(snd(X)) 0.22/0.25 splitAt(mark(X1),X2) -> mark(splitAt(X1,X2)) 0.22/0.25 splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2)) 0.22/0.25 u(mark(X1),X2,X3,X4) -> mark(u(X1,X2,X3,X4)) 0.22/0.25 head(mark(X)) -> mark(head(X)) 0.22/0.25 tail(mark(X)) -> mark(tail(X)) 0.22/0.25 sel(mark(X1),X2) -> mark(sel(X1,X2)) 0.22/0.25 sel(X1,mark(X2)) -> mark(sel(X1,X2)) 0.22/0.25 afterNth(mark(X1),X2) -> mark(afterNth(X1,X2)) 0.22/0.25 afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2)) 0.22/0.25 take(mark(X1),X2) -> mark(take(X1,X2)) 0.22/0.25 take(X1,mark(X2)) -> mark(take(X1,X2)) 0.22/0.25 proper(natsFrom(X)) -> natsFrom(proper(X)) 0.22/0.25 proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) 0.22/0.25 proper(s(X)) -> s(proper(X)) 0.22/0.25 proper(fst(X)) -> fst(proper(X)) 0.22/0.25 proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) 0.22/0.25 proper(snd(X)) -> snd(proper(X)) 0.22/0.25 proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2)) 0.22/0.25 proper(0()) -> ok(0()) 0.22/0.25 proper(nil()) -> ok(nil()) 0.22/0.25 proper(u(X1,X2,X3,X4)) -> u(proper(X1),proper(X2),proper(X3),proper(X4)) 0.22/0.25 proper(head(X)) -> head(proper(X)) 0.22/0.25 proper(tail(X)) -> tail(proper(X)) 0.22/0.25 proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) 0.22/0.25 proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2)) 0.22/0.25 proper(take(X1,X2)) -> take(proper(X1),proper(X2)) 0.22/0.25 natsFrom(ok(X)) -> ok(natsFrom(X)) 0.22/0.25 cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) 0.22/0.25 s(ok(X)) -> ok(s(X)) 0.22/0.25 fst(ok(X)) -> ok(fst(X)) 0.22/0.25 pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) 0.22/0.25 snd(ok(X)) -> ok(snd(X)) 0.22/0.25 splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2)) 0.22/0.25 u(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(u(X1,X2,X3,X4)) 0.22/0.25 head(ok(X)) -> ok(head(X)) 0.22/0.25 tail(ok(X)) -> ok(tail(X)) 0.22/0.25 sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) 0.22/0.25 afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2)) 0.22/0.25 take(ok(X1),ok(X2)) -> ok(take(X1,X2)) 0.22/0.25 top(mark(X)) -> top(proper(X)) 0.22/0.25 top(ok(X)) -> top(active(X)) 0.22/0.25 0.22/0.25 Proof: 0.22/0.25 Open 0.22/0.26 EOF