MAYBE
0.28/0.33	MAYBE
0.28/0.34	
0.28/0.34	Problem:
0.28/0.34	 active(U101(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
0.28/0.34	 active(U11(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
0.28/0.34	 active(U21(tt(),X)) -> mark(X)
0.28/0.34	 active(U31(tt(),N)) -> mark(N)
0.28/0.34	 active(U41(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
0.28/0.34	 active(U51(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
0.28/0.34	 active(U61(tt(),Y)) -> mark(Y)
0.28/0.34	 active(U71(tt(),XS)) -> mark(pair(nil(),XS))
0.28/0.34	 active(U81(tt(),N,X,XS)) -> mark(U82(splitAt(N,XS),X))
0.28/0.34	 active(U82(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
0.28/0.34	 active(U91(tt(),XS)) -> mark(XS)
0.28/0.34	 active(afterNth(N,XS)) -> mark(U11(and(isNatural(N),isLNat(XS)),N,XS))
0.28/0.34	 active(and(tt(),X)) -> mark(X)
0.28/0.34	 active(fst(pair(X,Y))) -> mark(U21(and(isLNat(X),isLNat(Y)),X))
0.28/0.34	 active(head(cons(N,XS))) -> mark(U31(and(isNatural(N),isLNat(XS)),N))
0.28/0.34	 active(isLNat(nil())) -> mark(tt())
0.28/0.34	 active(isLNat(afterNth(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
0.28/0.34	 active(isLNat(cons(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
0.28/0.34	 active(isLNat(fst(V1))) -> mark(isPLNat(V1))
0.28/0.34	 active(isLNat(natsFrom(V1))) -> mark(isNatural(V1))
0.28/0.34	 active(isLNat(snd(V1))) -> mark(isPLNat(V1))
0.28/0.34	 active(isLNat(tail(V1))) -> mark(isLNat(V1))
0.28/0.34	 active(isLNat(take(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
0.28/0.34	 active(isNatural(0())) -> mark(tt())
0.28/0.34	 active(isNatural(head(V1))) -> mark(isLNat(V1))
0.28/0.34	 active(isNatural(s(V1))) -> mark(isNatural(V1))
0.28/0.34	 active(isNatural(sel(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
0.28/0.34	 active(isPLNat(pair(V1,V2))) -> mark(and(isLNat(V1),isLNat(V2)))
0.28/0.34	 active(isPLNat(splitAt(V1,V2))) -> mark(and(isNatural(V1),isLNat(V2)))
0.28/0.34	 active(natsFrom(N)) -> mark(U41(isNatural(N),N))
0.28/0.34	 active(sel(N,XS)) -> mark(U51(and(isNatural(N),isLNat(XS)),N,XS))
0.28/0.34	 active(snd(pair(X,Y))) -> mark(U61(and(isLNat(X),isLNat(Y)),Y))
0.28/0.34	 active(splitAt(0(),XS)) -> mark(U71(isLNat(XS),XS))
0.28/0.34	 active(splitAt(s(N),cons(X,XS))) ->
0.28/0.34	 mark(U81(and(isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS))
0.28/0.34	 active(tail(cons(N,XS))) -> mark(U91(and(isNatural(N),isLNat(XS)),XS))
0.28/0.34	 active(take(N,XS)) -> mark(U101(and(isNatural(N),isLNat(XS)),N,XS))
0.28/0.34	 active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
0.28/0.34	 active(fst(X)) -> fst(active(X))
0.28/0.34	 active(splitAt(X1,X2)) -> splitAt(active(X1),X2)
0.28/0.34	 active(splitAt(X1,X2)) -> splitAt(X1,active(X2))
0.28/0.34	 active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
0.28/0.34	 active(snd(X)) -> snd(active(X))
0.28/0.34	 active(U21(X1,X2)) -> U21(active(X1),X2)
0.28/0.34	 active(U31(X1,X2)) -> U31(active(X1),X2)
0.28/0.34	 active(U41(X1,X2)) -> U41(active(X1),X2)
0.28/0.34	 active(cons(X1,X2)) -> cons(active(X1),X2)
0.28/0.34	 active(natsFrom(X)) -> natsFrom(active(X))
0.28/0.34	 active(s(X)) -> s(active(X))
0.28/0.34	 active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
0.28/0.34	 active(head(X)) -> head(active(X))
0.28/0.34	 active(afterNth(X1,X2)) -> afterNth(active(X1),X2)
0.28/0.34	 active(afterNth(X1,X2)) -> afterNth(X1,active(X2))
0.28/0.34	 active(U61(X1,X2)) -> U61(active(X1),X2)
0.28/0.34	 active(U71(X1,X2)) -> U71(active(X1),X2)
0.28/0.34	 active(pair(X1,X2)) -> pair(active(X1),X2)
0.28/0.34	 active(pair(X1,X2)) -> pair(X1,active(X2))
0.28/0.34	 active(U81(X1,X2,X3,X4)) -> U81(active(X1),X2,X3,X4)
0.28/0.34	 active(U82(X1,X2)) -> U82(active(X1),X2)
0.28/0.34	 active(U91(X1,X2)) -> U91(active(X1),X2)
0.28/0.34	 active(and(X1,X2)) -> and(active(X1),X2)
0.28/0.34	 active(tail(X)) -> tail(active(X))
0.28/0.34	 active(take(X1,X2)) -> take(active(X1),X2)
0.28/0.34	 active(take(X1,X2)) -> take(X1,active(X2))
0.28/0.34	 active(sel(X1,X2)) -> sel(active(X1),X2)
0.28/0.34	 active(sel(X1,X2)) -> sel(X1,active(X2))
0.28/0.34	 U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
0.28/0.34	 fst(mark(X)) -> mark(fst(X))
0.28/0.34	 splitAt(mark(X1),X2) -> mark(splitAt(X1,X2))
0.28/0.34	 splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2))
0.28/0.34	 U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
0.28/0.34	 snd(mark(X)) -> mark(snd(X))
0.28/0.34	 U21(mark(X1),X2) -> mark(U21(X1,X2))
0.28/0.34	 U31(mark(X1),X2) -> mark(U31(X1,X2))
0.28/0.34	 U41(mark(X1),X2) -> mark(U41(X1,X2))
0.28/0.34	 cons(mark(X1),X2) -> mark(cons(X1,X2))
0.28/0.34	 natsFrom(mark(X)) -> mark(natsFrom(X))
0.28/0.34	 s(mark(X)) -> mark(s(X))
0.28/0.34	 U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
0.28/0.34	 head(mark(X)) -> mark(head(X))
0.28/0.34	 afterNth(mark(X1),X2) -> mark(afterNth(X1,X2))
0.28/0.34	 afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2))
0.28/0.34	 U61(mark(X1),X2) -> mark(U61(X1,X2))
0.28/0.34	 U71(mark(X1),X2) -> mark(U71(X1,X2))
0.28/0.34	 pair(mark(X1),X2) -> mark(pair(X1,X2))
0.28/0.34	 pair(X1,mark(X2)) -> mark(pair(X1,X2))
0.28/0.34	 U81(mark(X1),X2,X3,X4) -> mark(U81(X1,X2,X3,X4))
0.28/0.34	 U82(mark(X1),X2) -> mark(U82(X1,X2))
0.28/0.34	 U91(mark(X1),X2) -> mark(U91(X1,X2))
0.28/0.34	 and(mark(X1),X2) -> mark(and(X1,X2))
0.28/0.34	 tail(mark(X)) -> mark(tail(X))
0.28/0.34	 take(mark(X1),X2) -> mark(take(X1,X2))
0.28/0.34	 take(X1,mark(X2)) -> mark(take(X1,X2))
0.28/0.34	 sel(mark(X1),X2) -> mark(sel(X1,X2))
0.28/0.34	 sel(X1,mark(X2)) -> mark(sel(X1,X2))
0.28/0.34	 proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
0.28/0.34	 proper(tt()) -> ok(tt())
0.28/0.34	 proper(fst(X)) -> fst(proper(X))
0.28/0.34	 proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2))
0.28/0.34	 proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
0.28/0.34	 proper(snd(X)) -> snd(proper(X))
0.28/0.34	 proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
0.28/0.34	 proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
0.28/0.34	 proper(U41(X1,X2)) -> U41(proper(X1),proper(X2))
0.28/0.34	 proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
0.28/0.34	 proper(natsFrom(X)) -> natsFrom(proper(X))
0.28/0.34	 proper(s(X)) -> s(proper(X))
0.28/0.34	 proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
0.28/0.34	 proper(head(X)) -> head(proper(X))
0.28/0.34	 proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2))
0.28/0.34	 proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
0.28/0.34	 proper(U71(X1,X2)) -> U71(proper(X1),proper(X2))
0.28/0.34	 proper(pair(X1,X2)) -> pair(proper(X1),proper(X2))
0.28/0.34	 proper(nil()) -> ok(nil())
0.28/0.34	 proper(U81(X1,X2,X3,X4)) -> U81(proper(X1),proper(X2),proper(X3),proper(X4))
0.28/0.34	 proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
0.28/0.34	 proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
0.28/0.34	 proper(and(X1,X2)) -> and(proper(X1),proper(X2))
0.28/0.34	 proper(isNatural(X)) -> isNatural(proper(X))
0.28/0.34	 proper(isLNat(X)) -> isLNat(proper(X))
0.28/0.34	 proper(isPLNat(X)) -> isPLNat(proper(X))
0.28/0.34	 proper(tail(X)) -> tail(proper(X))
0.28/0.34	 proper(take(X1,X2)) -> take(proper(X1),proper(X2))
0.28/0.34	 proper(0()) -> ok(0())
0.28/0.34	 proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
0.28/0.34	 U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
0.28/0.34	 fst(ok(X)) -> ok(fst(X))
0.28/0.34	 splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2))
0.28/0.34	 U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
0.28/0.34	 snd(ok(X)) -> ok(snd(X))
0.28/0.34	 U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
0.28/0.34	 U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
0.28/0.34	 U41(ok(X1),ok(X2)) -> ok(U41(X1,X2))
0.28/0.34	 cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
0.28/0.34	 natsFrom(ok(X)) -> ok(natsFrom(X))
0.28/0.34	 s(ok(X)) -> ok(s(X))
0.28/0.34	 U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
0.28/0.34	 head(ok(X)) -> ok(head(X))
0.28/0.34	 afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2))
0.28/0.34	 U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
0.28/0.34	 U71(ok(X1),ok(X2)) -> ok(U71(X1,X2))
0.28/0.34	 pair(ok(X1),ok(X2)) -> ok(pair(X1,X2))
0.28/0.34	 U81(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U81(X1,X2,X3,X4))
0.28/0.34	 U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
0.28/0.34	 U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
0.28/0.34	 and(ok(X1),ok(X2)) -> ok(and(X1,X2))
0.28/0.34	 isNatural(ok(X)) -> ok(isNatural(X))
0.28/0.34	 isLNat(ok(X)) -> ok(isLNat(X))
0.28/0.34	 isPLNat(ok(X)) -> ok(isPLNat(X))
0.28/0.34	 tail(ok(X)) -> ok(tail(X))
0.28/0.34	 take(ok(X1),ok(X2)) -> ok(take(X1,X2))
0.28/0.34	 sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
0.28/0.34	 top(mark(X)) -> top(proper(X))
0.28/0.34	 top(ok(X)) -> top(active(X))
0.28/0.34	
0.28/0.34	Proof:
0.28/0.34	 Open
0.28/0.35	EOF