MAYBE
0.27/0.34	MAYBE
0.27/0.35	
0.27/0.35	Problem:
0.27/0.35	 active(U11(tt(),N,XS)) -> mark(U12(tt(),N,XS))
0.27/0.35	 active(U12(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
0.27/0.35	 active(U21(tt(),X)) -> mark(U22(tt(),X))
0.27/0.35	 active(U22(tt(),X)) -> mark(X)
0.27/0.35	 active(U31(tt(),N)) -> mark(U32(tt(),N))
0.27/0.35	 active(U32(tt(),N)) -> mark(N)
0.27/0.35	 active(U41(tt(),N,XS)) -> mark(U42(tt(),N,XS))
0.27/0.35	 active(U42(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
0.27/0.35	 active(U51(tt(),Y)) -> mark(U52(tt(),Y))
0.27/0.35	 active(U52(tt(),Y)) -> mark(Y)
0.27/0.35	 active(U61(tt(),N,X,XS)) -> mark(U62(tt(),N,X,XS))
0.27/0.35	 active(U62(tt(),N,X,XS)) -> mark(U63(tt(),N,X,XS))
0.27/0.35	 active(U63(tt(),N,X,XS)) -> mark(U64(splitAt(N,XS),X))
0.27/0.35	 active(U64(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
0.27/0.35	 active(U71(tt(),XS)) -> mark(U72(tt(),XS))
0.27/0.35	 active(U72(tt(),XS)) -> mark(XS)
0.27/0.35	 active(U81(tt(),N,XS)) -> mark(U82(tt(),N,XS))
0.27/0.35	 active(U82(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
0.27/0.35	 active(afterNth(N,XS)) -> mark(U11(tt(),N,XS))
0.27/0.35	 active(fst(pair(X,Y))) -> mark(U21(tt(),X))
0.27/0.35	 active(head(cons(N,XS))) -> mark(U31(tt(),N))
0.27/0.35	 active(natsFrom(N)) -> mark(cons(N,natsFrom(s(N))))
0.27/0.35	 active(sel(N,XS)) -> mark(U41(tt(),N,XS))
0.27/0.35	 active(snd(pair(X,Y))) -> mark(U51(tt(),Y))
0.27/0.35	 active(splitAt(0(),XS)) -> mark(pair(nil(),XS))
0.27/0.35	 active(splitAt(s(N),cons(X,XS))) -> mark(U61(tt(),N,X,XS))
0.27/0.35	 active(tail(cons(N,XS))) -> mark(U71(tt(),XS))
0.27/0.35	 active(take(N,XS)) -> mark(U81(tt(),N,XS))
0.27/0.35	 active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
0.27/0.35	 active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
0.27/0.35	 active(snd(X)) -> snd(active(X))
0.27/0.35	 active(splitAt(X1,X2)) -> splitAt(active(X1),X2)
0.27/0.35	 active(splitAt(X1,X2)) -> splitAt(X1,active(X2))
0.27/0.35	 active(U21(X1,X2)) -> U21(active(X1),X2)
0.27/0.35	 active(U22(X1,X2)) -> U22(active(X1),X2)
0.27/0.35	 active(U31(X1,X2)) -> U31(active(X1),X2)
0.27/0.35	 active(U32(X1,X2)) -> U32(active(X1),X2)
0.27/0.35	 active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
0.27/0.35	 active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
0.27/0.35	 active(head(X)) -> head(active(X))
0.27/0.35	 active(afterNth(X1,X2)) -> afterNth(active(X1),X2)
0.27/0.35	 active(afterNth(X1,X2)) -> afterNth(X1,active(X2))
0.27/0.35	 active(U51(X1,X2)) -> U51(active(X1),X2)
0.27/0.35	 active(U52(X1,X2)) -> U52(active(X1),X2)
0.27/0.35	 active(U61(X1,X2,X3,X4)) -> U61(active(X1),X2,X3,X4)
0.27/0.35	 active(U62(X1,X2,X3,X4)) -> U62(active(X1),X2,X3,X4)
0.27/0.35	 active(U63(X1,X2,X3,X4)) -> U63(active(X1),X2,X3,X4)
0.27/0.35	 active(U64(X1,X2)) -> U64(active(X1),X2)
0.27/0.35	 active(pair(X1,X2)) -> pair(active(X1),X2)
0.27/0.35	 active(pair(X1,X2)) -> pair(X1,active(X2))
0.27/0.35	 active(cons(X1,X2)) -> cons(active(X1),X2)
0.27/0.35	 active(U71(X1,X2)) -> U71(active(X1),X2)
0.27/0.35	 active(U72(X1,X2)) -> U72(active(X1),X2)
0.27/0.35	 active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
0.27/0.35	 active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
0.27/0.35	 active(fst(X)) -> fst(active(X))
0.27/0.35	 active(natsFrom(X)) -> natsFrom(active(X))
0.27/0.35	 active(s(X)) -> s(active(X))
0.27/0.35	 active(sel(X1,X2)) -> sel(active(X1),X2)
0.27/0.35	 active(sel(X1,X2)) -> sel(X1,active(X2))
0.27/0.35	 active(tail(X)) -> tail(active(X))
0.27/0.35	 active(take(X1,X2)) -> take(active(X1),X2)
0.27/0.35	 active(take(X1,X2)) -> take(X1,active(X2))
0.27/0.35	 U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
0.27/0.35	 U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
0.27/0.35	 snd(mark(X)) -> mark(snd(X))
0.27/0.35	 splitAt(mark(X1),X2) -> mark(splitAt(X1,X2))
0.27/0.35	 splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2))
0.27/0.35	 U21(mark(X1),X2) -> mark(U21(X1,X2))
0.27/0.35	 U22(mark(X1),X2) -> mark(U22(X1,X2))
0.27/0.35	 U31(mark(X1),X2) -> mark(U31(X1,X2))
0.27/0.35	 U32(mark(X1),X2) -> mark(U32(X1,X2))
0.27/0.35	 U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
0.27/0.35	 U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
0.27/0.35	 head(mark(X)) -> mark(head(X))
0.27/0.35	 afterNth(mark(X1),X2) -> mark(afterNth(X1,X2))
0.27/0.35	 afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2))
0.27/0.35	 U51(mark(X1),X2) -> mark(U51(X1,X2))
0.27/0.35	 U52(mark(X1),X2) -> mark(U52(X1,X2))
0.27/0.35	 U61(mark(X1),X2,X3,X4) -> mark(U61(X1,X2,X3,X4))
0.27/0.35	 U62(mark(X1),X2,X3,X4) -> mark(U62(X1,X2,X3,X4))
0.27/0.35	 U63(mark(X1),X2,X3,X4) -> mark(U63(X1,X2,X3,X4))
0.27/0.35	 U64(mark(X1),X2) -> mark(U64(X1,X2))
0.27/0.35	 pair(mark(X1),X2) -> mark(pair(X1,X2))
0.27/0.35	 pair(X1,mark(X2)) -> mark(pair(X1,X2))
0.27/0.35	 cons(mark(X1),X2) -> mark(cons(X1,X2))
0.27/0.35	 U71(mark(X1),X2) -> mark(U71(X1,X2))
0.27/0.35	 U72(mark(X1),X2) -> mark(U72(X1,X2))
0.27/0.35	 U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
0.27/0.35	 U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
0.27/0.35	 fst(mark(X)) -> mark(fst(X))
0.27/0.35	 natsFrom(mark(X)) -> mark(natsFrom(X))
0.27/0.35	 s(mark(X)) -> mark(s(X))
0.27/0.35	 sel(mark(X1),X2) -> mark(sel(X1,X2))
0.27/0.35	 sel(X1,mark(X2)) -> mark(sel(X1,X2))
0.27/0.35	 tail(mark(X)) -> mark(tail(X))
0.27/0.35	 take(mark(X1),X2) -> mark(take(X1,X2))
0.27/0.35	 take(X1,mark(X2)) -> mark(take(X1,X2))
0.27/0.35	 proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
0.27/0.35	 proper(tt()) -> ok(tt())
0.27/0.35	 proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
0.27/0.35	 proper(snd(X)) -> snd(proper(X))
0.27/0.35	 proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2))
0.27/0.35	 proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
0.27/0.35	 proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
0.27/0.35	 proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
0.27/0.35	 proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
0.27/0.35	 proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
0.27/0.35	 proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
0.27/0.35	 proper(head(X)) -> head(proper(X))
0.27/0.35	 proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2))
0.27/0.35	 proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
0.27/0.35	 proper(U52(X1,X2)) -> U52(proper(X1),proper(X2))
0.27/0.35	 proper(U61(X1,X2,X3,X4)) -> U61(proper(X1),proper(X2),proper(X3),proper(X4))
0.27/0.35	 proper(U62(X1,X2,X3,X4)) -> U62(proper(X1),proper(X2),proper(X3),proper(X4))
0.27/0.35	 proper(U63(X1,X2,X3,X4)) -> U63(proper(X1),proper(X2),proper(X3),proper(X4))
0.27/0.35	 proper(U64(X1,X2)) -> U64(proper(X1),proper(X2))
0.27/0.35	 proper(pair(X1,X2)) -> pair(proper(X1),proper(X2))
0.27/0.35	 proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
0.27/0.35	 proper(U71(X1,X2)) -> U71(proper(X1),proper(X2))
0.27/0.35	 proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
0.27/0.35	 proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
0.27/0.35	 proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
0.27/0.35	 proper(fst(X)) -> fst(proper(X))
0.27/0.35	 proper(natsFrom(X)) -> natsFrom(proper(X))
0.27/0.35	 proper(s(X)) -> s(proper(X))
0.27/0.35	 proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
0.27/0.35	 proper(0()) -> ok(0())
0.27/0.35	 proper(nil()) -> ok(nil())
0.27/0.35	 proper(tail(X)) -> tail(proper(X))
0.27/0.35	 proper(take(X1,X2)) -> take(proper(X1),proper(X2))
0.27/0.35	 U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
0.27/0.35	 U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
0.27/0.35	 snd(ok(X)) -> ok(snd(X))
0.27/0.35	 splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2))
0.27/0.35	 U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
0.27/0.35	 U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
0.27/0.35	 U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
0.27/0.35	 U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
0.27/0.35	 U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
0.27/0.35	 U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
0.27/0.35	 head(ok(X)) -> ok(head(X))
0.27/0.35	 afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2))
0.27/0.35	 U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
0.27/0.35	 U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
0.27/0.35	 U61(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U61(X1,X2,X3,X4))
0.27/0.35	 U62(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U62(X1,X2,X3,X4))
0.27/0.35	 U63(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U63(X1,X2,X3,X4))
0.27/0.35	 U64(ok(X1),ok(X2)) -> ok(U64(X1,X2))
0.27/0.35	 pair(ok(X1),ok(X2)) -> ok(pair(X1,X2))
0.27/0.35	 cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
0.27/0.35	 U71(ok(X1),ok(X2)) -> ok(U71(X1,X2))
0.27/0.35	 U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
0.27/0.35	 U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
0.27/0.35	 U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
0.27/0.35	 fst(ok(X)) -> ok(fst(X))
0.27/0.35	 natsFrom(ok(X)) -> ok(natsFrom(X))
0.27/0.35	 s(ok(X)) -> ok(s(X))
0.27/0.35	 sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
0.27/0.35	 tail(ok(X)) -> ok(tail(X))
0.27/0.35	 take(ok(X1),ok(X2)) -> ok(take(X1,X2))
0.27/0.35	 top(mark(X)) -> top(proper(X))
0.27/0.35	 top(ok(X)) -> top(active(X))
0.27/0.35	
0.27/0.35	Proof:
0.27/0.35	 Open
0.27/0.35	EOF