19.99/5.89	WORST_CASE(NON_POLY, ?)
19.99/5.90	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
19.99/5.90	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
19.99/5.90	
19.99/5.90	
19.99/5.90	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
19.99/5.90	
19.99/5.90	(0) CpxTRS
19.99/5.90	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
19.99/5.90	(2) TRS for Loop Detection
19.99/5.90	(3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
19.99/5.90	(4) BEST
19.99/5.90	    (5) proven lower bound
19.99/5.90	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
19.99/5.90	        (7) BOUNDS(n^1, INF)
19.99/5.90	    (8) TRS for Loop Detection
19.99/5.90	        (9) DecreasingLoopProof [FINISHED, 2946 ms]
19.99/5.90	        (10) BOUNDS(EXP, INF)
19.99/5.90	
19.99/5.90	
19.99/5.90	----------------------------------------
19.99/5.90	
19.99/5.90	(0)
19.99/5.90	Obligation:
19.99/5.90	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
19.99/5.90	
19.99/5.90	
19.99/5.90	The TRS R consists of the following rules:
19.99/5.90	
19.99/5.90	   a__U101(tt, V1, V2) -> a__U102(a__isNaturalKind(V1), V1, V2)
19.99/5.90	   a__U102(tt, V1, V2) -> a__U103(a__isLNatKind(V2), V1, V2)
19.99/5.90	   a__U103(tt, V1, V2) -> a__U104(a__isLNatKind(V2), V1, V2)
19.99/5.90	   a__U104(tt, V1, V2) -> a__U105(a__isNatural(V1), V2)
19.99/5.90	   a__U105(tt, V2) -> a__U106(a__isLNat(V2))
19.99/5.90	   a__U106(tt) -> tt
19.99/5.90	   a__U11(tt, N, XS) -> a__U12(a__isNaturalKind(N), N, XS)
19.99/5.90	   a__U111(tt, V2) -> a__U112(a__isLNatKind(V2))
19.99/5.90	   a__U112(tt) -> tt
19.99/5.90	   a__U12(tt, N, XS) -> a__U13(a__isLNat(XS), N, XS)
19.99/5.90	   a__U121(tt, V2) -> a__U122(a__isLNatKind(V2))
19.99/5.90	   a__U122(tt) -> tt
19.99/5.90	   a__U13(tt, N, XS) -> a__U14(a__isLNatKind(XS), N, XS)
19.99/5.90	   a__U131(tt) -> tt
19.99/5.90	   a__U14(tt, N, XS) -> a__snd(a__splitAt(mark(N), mark(XS)))
19.99/5.90	   a__U141(tt) -> tt
19.99/5.90	   a__U151(tt) -> tt
19.99/5.90	   a__U161(tt) -> tt
19.99/5.90	   a__U171(tt, V2) -> a__U172(a__isLNatKind(V2))
19.99/5.90	   a__U172(tt) -> tt
19.99/5.90	   a__U181(tt, V1) -> a__U182(a__isLNatKind(V1), V1)
19.99/5.90	   a__U182(tt, V1) -> a__U183(a__isLNat(V1))
19.99/5.90	   a__U183(tt) -> tt
19.99/5.90	   a__U191(tt, V1) -> a__U192(a__isNaturalKind(V1), V1)
19.99/5.90	   a__U192(tt, V1) -> a__U193(a__isNatural(V1))
19.99/5.90	   a__U193(tt) -> tt
19.99/5.90	   a__U201(tt, V1, V2) -> a__U202(a__isNaturalKind(V1), V1, V2)
19.99/5.90	   a__U202(tt, V1, V2) -> a__U203(a__isLNatKind(V2), V1, V2)
19.99/5.90	   a__U203(tt, V1, V2) -> a__U204(a__isLNatKind(V2), V1, V2)
19.99/5.90	   a__U204(tt, V1, V2) -> a__U205(a__isNatural(V1), V2)
19.99/5.90	   a__U205(tt, V2) -> a__U206(a__isLNat(V2))
19.99/5.90	   a__U206(tt) -> tt
19.99/5.90	   a__U21(tt, X, Y) -> a__U22(a__isLNatKind(X), X, Y)
19.99/5.90	   a__U211(tt) -> tt
19.99/5.90	   a__U22(tt, X, Y) -> a__U23(a__isLNat(Y), X, Y)
19.99/5.90	   a__U221(tt) -> tt
19.99/5.90	   a__U23(tt, X, Y) -> a__U24(a__isLNatKind(Y), X)
19.99/5.90	   a__U231(tt, V2) -> a__U232(a__isLNatKind(V2))
19.99/5.90	   a__U232(tt) -> tt
19.99/5.90	   a__U24(tt, X) -> mark(X)
19.99/5.90	   a__U241(tt, V1, V2) -> a__U242(a__isLNatKind(V1), V1, V2)
19.99/5.90	   a__U242(tt, V1, V2) -> a__U243(a__isLNatKind(V2), V1, V2)
19.99/5.90	   a__U243(tt, V1, V2) -> a__U244(a__isLNatKind(V2), V1, V2)
19.99/5.90	   a__U244(tt, V1, V2) -> a__U245(a__isLNat(V1), V2)
19.99/5.90	   a__U245(tt, V2) -> a__U246(a__isLNat(V2))
19.99/5.90	   a__U246(tt) -> tt
19.99/5.90	   a__U251(tt, V1, V2) -> a__U252(a__isNaturalKind(V1), V1, V2)
19.99/5.90	   a__U252(tt, V1, V2) -> a__U253(a__isLNatKind(V2), V1, V2)
19.99/5.90	   a__U253(tt, V1, V2) -> a__U254(a__isLNatKind(V2), V1, V2)
19.99/5.90	   a__U254(tt, V1, V2) -> a__U255(a__isNatural(V1), V2)
19.99/5.90	   a__U255(tt, V2) -> a__U256(a__isLNat(V2))
20.08/5.90	   a__U256(tt) -> tt
20.08/5.90	   a__U261(tt, V2) -> a__U262(a__isLNatKind(V2))
20.08/5.90	   a__U262(tt) -> tt
20.08/5.90	   a__U271(tt, V2) -> a__U272(a__isLNatKind(V2))
20.08/5.90	   a__U272(tt) -> tt
20.08/5.90	   a__U281(tt, N) -> a__U282(a__isNaturalKind(N), N)
20.08/5.90	   a__U282(tt, N) -> cons(mark(N), natsFrom(s(N)))
20.08/5.90	   a__U291(tt, N, XS) -> a__U292(a__isNaturalKind(N), N, XS)
20.08/5.90	   a__U292(tt, N, XS) -> a__U293(a__isLNat(XS), N, XS)
20.08/5.90	   a__U293(tt, N, XS) -> a__U294(a__isLNatKind(XS), N, XS)
20.08/5.90	   a__U294(tt, N, XS) -> a__head(a__afterNth(mark(N), mark(XS)))
20.08/5.90	   a__U301(tt, X, Y) -> a__U302(a__isLNatKind(X), Y)
20.08/5.90	   a__U302(tt, Y) -> a__U303(a__isLNat(Y), Y)
20.08/5.90	   a__U303(tt, Y) -> a__U304(a__isLNatKind(Y), Y)
20.08/5.90	   a__U304(tt, Y) -> mark(Y)
20.08/5.90	   a__U31(tt, N, XS) -> a__U32(a__isNaturalKind(N), N, XS)
20.08/5.90	   a__U311(tt, XS) -> a__U312(a__isLNatKind(XS), XS)
20.08/5.90	   a__U312(tt, XS) -> pair(nil, mark(XS))
20.08/5.90	   a__U32(tt, N, XS) -> a__U33(a__isLNat(XS), N, XS)
20.08/5.90	   a__U321(tt, N, X, XS) -> a__U322(a__isNaturalKind(N), N, X, XS)
20.08/5.90	   a__U322(tt, N, X, XS) -> a__U323(a__isNatural(X), N, X, XS)
20.08/5.90	   a__U323(tt, N, X, XS) -> a__U324(a__isNaturalKind(X), N, X, XS)
20.08/5.90	   a__U324(tt, N, X, XS) -> a__U325(a__isLNat(XS), N, X, XS)
20.08/5.90	   a__U325(tt, N, X, XS) -> a__U326(a__isLNatKind(XS), N, X, XS)
20.08/5.90	   a__U326(tt, N, X, XS) -> a__U327(a__splitAt(mark(N), mark(XS)), X)
20.08/5.90	   a__U327(pair(YS, ZS), X) -> pair(cons(mark(X), YS), mark(ZS))
20.08/5.90	   a__U33(tt, N, XS) -> a__U34(a__isLNatKind(XS), N)
20.08/5.90	   a__U331(tt, N, XS) -> a__U332(a__isNaturalKind(N), XS)
20.08/5.90	   a__U332(tt, XS) -> a__U333(a__isLNat(XS), XS)
20.08/5.90	   a__U333(tt, XS) -> a__U334(a__isLNatKind(XS), XS)
20.08/5.90	   a__U334(tt, XS) -> mark(XS)
20.08/5.90	   a__U34(tt, N) -> mark(N)
20.08/5.90	   a__U341(tt, N, XS) -> a__U342(a__isNaturalKind(N), N, XS)
20.08/5.90	   a__U342(tt, N, XS) -> a__U343(a__isLNat(XS), N, XS)
20.08/5.90	   a__U343(tt, N, XS) -> a__U344(a__isLNatKind(XS), N, XS)
20.08/5.90	   a__U344(tt, N, XS) -> a__fst(a__splitAt(mark(N), mark(XS)))
20.08/5.90	   a__U41(tt, V1, V2) -> a__U42(a__isNaturalKind(V1), V1, V2)
20.08/5.90	   a__U42(tt, V1, V2) -> a__U43(a__isLNatKind(V2), V1, V2)
20.08/5.90	   a__U43(tt, V1, V2) -> a__U44(a__isLNatKind(V2), V1, V2)
20.08/5.90	   a__U44(tt, V1, V2) -> a__U45(a__isNatural(V1), V2)
20.08/5.90	   a__U45(tt, V2) -> a__U46(a__isLNat(V2))
20.08/5.90	   a__U46(tt) -> tt
20.08/5.90	   a__U51(tt, V1, V2) -> a__U52(a__isNaturalKind(V1), V1, V2)
20.08/5.90	   a__U52(tt, V1, V2) -> a__U53(a__isLNatKind(V2), V1, V2)
20.08/5.90	   a__U53(tt, V1, V2) -> a__U54(a__isLNatKind(V2), V1, V2)
20.08/5.90	   a__U54(tt, V1, V2) -> a__U55(a__isNatural(V1), V2)
20.08/5.90	   a__U55(tt, V2) -> a__U56(a__isLNat(V2))
20.08/5.90	   a__U56(tt) -> tt
20.08/5.90	   a__U61(tt, V1) -> a__U62(a__isPLNatKind(V1), V1)
20.08/5.90	   a__U62(tt, V1) -> a__U63(a__isPLNat(V1))
20.08/5.90	   a__U63(tt) -> tt
20.08/5.90	   a__U71(tt, V1) -> a__U72(a__isNaturalKind(V1), V1)
20.08/5.90	   a__U72(tt, V1) -> a__U73(a__isNatural(V1))
20.08/5.90	   a__U73(tt) -> tt
20.08/5.90	   a__U81(tt, V1) -> a__U82(a__isPLNatKind(V1), V1)
20.08/5.90	   a__U82(tt, V1) -> a__U83(a__isPLNat(V1))
20.08/5.90	   a__U83(tt) -> tt
20.08/5.90	   a__U91(tt, V1) -> a__U92(a__isLNatKind(V1), V1)
20.08/5.90	   a__U92(tt, V1) -> a__U93(a__isLNat(V1))
20.08/5.90	   a__U93(tt) -> tt
20.08/5.90	   a__afterNth(N, XS) -> a__U11(a__isNatural(N), N, XS)
20.08/5.90	   a__fst(pair(X, Y)) -> a__U21(a__isLNat(X), X, Y)
20.08/5.90	   a__head(cons(N, XS)) -> a__U31(a__isNatural(N), N, XS)
20.08/5.90	   a__isLNat(nil) -> tt
20.08/5.90	   a__isLNat(afterNth(V1, V2)) -> a__U41(a__isNaturalKind(V1), V1, V2)
20.08/5.90	   a__isLNat(cons(V1, V2)) -> a__U51(a__isNaturalKind(V1), V1, V2)
20.08/5.90	   a__isLNat(fst(V1)) -> a__U61(a__isPLNatKind(V1), V1)
20.08/5.90	   a__isLNat(natsFrom(V1)) -> a__U71(a__isNaturalKind(V1), V1)
20.08/5.90	   a__isLNat(snd(V1)) -> a__U81(a__isPLNatKind(V1), V1)
20.08/5.90	   a__isLNat(tail(V1)) -> a__U91(a__isLNatKind(V1), V1)
20.08/5.90	   a__isLNat(take(V1, V2)) -> a__U101(a__isNaturalKind(V1), V1, V2)
20.08/5.90	   a__isLNatKind(nil) -> tt
20.08/5.90	   a__isLNatKind(afterNth(V1, V2)) -> a__U111(a__isNaturalKind(V1), V2)
20.08/5.90	   a__isLNatKind(cons(V1, V2)) -> a__U121(a__isNaturalKind(V1), V2)
20.08/5.90	   a__isLNatKind(fst(V1)) -> a__U131(a__isPLNatKind(V1))
20.08/5.90	   a__isLNatKind(natsFrom(V1)) -> a__U141(a__isNaturalKind(V1))
20.08/5.90	   a__isLNatKind(snd(V1)) -> a__U151(a__isPLNatKind(V1))
20.08/5.90	   a__isLNatKind(tail(V1)) -> a__U161(a__isLNatKind(V1))
20.08/5.90	   a__isLNatKind(take(V1, V2)) -> a__U171(a__isNaturalKind(V1), V2)
20.08/5.90	   a__isNatural(0) -> tt
20.08/5.90	   a__isNatural(head(V1)) -> a__U181(a__isLNatKind(V1), V1)
20.08/5.90	   a__isNatural(s(V1)) -> a__U191(a__isNaturalKind(V1), V1)
20.08/5.90	   a__isNatural(sel(V1, V2)) -> a__U201(a__isNaturalKind(V1), V1, V2)
20.08/5.90	   a__isNaturalKind(0) -> tt
20.08/5.90	   a__isNaturalKind(head(V1)) -> a__U211(a__isLNatKind(V1))
20.08/5.90	   a__isNaturalKind(s(V1)) -> a__U221(a__isNaturalKind(V1))
20.08/5.90	   a__isNaturalKind(sel(V1, V2)) -> a__U231(a__isNaturalKind(V1), V2)
20.08/5.90	   a__isPLNat(pair(V1, V2)) -> a__U241(a__isLNatKind(V1), V1, V2)
20.08/5.90	   a__isPLNat(splitAt(V1, V2)) -> a__U251(a__isNaturalKind(V1), V1, V2)
20.08/5.90	   a__isPLNatKind(pair(V1, V2)) -> a__U261(a__isLNatKind(V1), V2)
20.08/5.90	   a__isPLNatKind(splitAt(V1, V2)) -> a__U271(a__isNaturalKind(V1), V2)
20.08/5.90	   a__natsFrom(N) -> a__U281(a__isNatural(N), N)
20.08/5.90	   a__sel(N, XS) -> a__U291(a__isNatural(N), N, XS)
20.08/5.90	   a__snd(pair(X, Y)) -> a__U301(a__isLNat(X), X, Y)
20.08/5.90	   a__splitAt(0, XS) -> a__U311(a__isLNat(XS), XS)
20.08/5.90	   a__splitAt(s(N), cons(X, XS)) -> a__U321(a__isNatural(N), N, X, XS)
20.08/5.90	   a__tail(cons(N, XS)) -> a__U331(a__isNatural(N), N, XS)
20.08/5.90	   a__take(N, XS) -> a__U341(a__isNatural(N), N, XS)
20.08/5.90	   mark(U101(X1, X2, X3)) -> a__U101(mark(X1), X2, X3)
20.08/5.90	   mark(U102(X1, X2, X3)) -> a__U102(mark(X1), X2, X3)
20.08/5.90	   mark(isNaturalKind(X)) -> a__isNaturalKind(X)
20.08/5.90	   mark(U103(X1, X2, X3)) -> a__U103(mark(X1), X2, X3)
20.08/5.90	   mark(isLNatKind(X)) -> a__isLNatKind(X)
20.08/5.90	   mark(U104(X1, X2, X3)) -> a__U104(mark(X1), X2, X3)
20.08/5.90	   mark(U105(X1, X2)) -> a__U105(mark(X1), X2)
20.08/5.90	   mark(isNatural(X)) -> a__isNatural(X)
20.08/5.90	   mark(U106(X)) -> a__U106(mark(X))
20.08/5.90	   mark(isLNat(X)) -> a__isLNat(X)
20.08/5.90	   mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
20.08/5.90	   mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
20.08/5.90	   mark(U111(X1, X2)) -> a__U111(mark(X1), X2)
20.08/5.90	   mark(U112(X)) -> a__U112(mark(X))
20.08/5.90	   mark(U13(X1, X2, X3)) -> a__U13(mark(X1), X2, X3)
20.08/5.90	   mark(U121(X1, X2)) -> a__U121(mark(X1), X2)
20.08/5.90	   mark(U122(X)) -> a__U122(mark(X))
20.08/5.90	   mark(U14(X1, X2, X3)) -> a__U14(mark(X1), X2, X3)
20.08/5.90	   mark(U131(X)) -> a__U131(mark(X))
20.08/5.90	   mark(snd(X)) -> a__snd(mark(X))
20.08/5.90	   mark(splitAt(X1, X2)) -> a__splitAt(mark(X1), mark(X2))
20.08/5.90	   mark(U141(X)) -> a__U141(mark(X))
20.08/5.90	   mark(U151(X)) -> a__U151(mark(X))
20.08/5.90	   mark(U161(X)) -> a__U161(mark(X))
20.08/5.90	   mark(U171(X1, X2)) -> a__U171(mark(X1), X2)
20.08/5.90	   mark(U172(X)) -> a__U172(mark(X))
20.08/5.90	   mark(U181(X1, X2)) -> a__U181(mark(X1), X2)
20.08/5.90	   mark(U182(X1, X2)) -> a__U182(mark(X1), X2)
20.08/5.90	   mark(U183(X)) -> a__U183(mark(X))
20.08/5.90	   mark(U191(X1, X2)) -> a__U191(mark(X1), X2)
20.08/5.90	   mark(U192(X1, X2)) -> a__U192(mark(X1), X2)
20.08/5.90	   mark(U193(X)) -> a__U193(mark(X))
20.08/5.90	   mark(U201(X1, X2, X3)) -> a__U201(mark(X1), X2, X3)
20.08/5.90	   mark(U202(X1, X2, X3)) -> a__U202(mark(X1), X2, X3)
20.08/5.90	   mark(U203(X1, X2, X3)) -> a__U203(mark(X1), X2, X3)
20.08/5.90	   mark(U204(X1, X2, X3)) -> a__U204(mark(X1), X2, X3)
20.08/5.90	   mark(U205(X1, X2)) -> a__U205(mark(X1), X2)
20.08/5.90	   mark(U206(X)) -> a__U206(mark(X))
20.08/5.90	   mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3)
20.08/5.90	   mark(U22(X1, X2, X3)) -> a__U22(mark(X1), X2, X3)
20.08/5.90	   mark(U211(X)) -> a__U211(mark(X))
20.08/5.90	   mark(U23(X1, X2, X3)) -> a__U23(mark(X1), X2, X3)
20.08/5.90	   mark(U221(X)) -> a__U221(mark(X))
20.08/5.90	   mark(U24(X1, X2)) -> a__U24(mark(X1), X2)
20.08/5.90	   mark(U231(X1, X2)) -> a__U231(mark(X1), X2)
20.08/5.90	   mark(U232(X)) -> a__U232(mark(X))
20.08/5.90	   mark(U241(X1, X2, X3)) -> a__U241(mark(X1), X2, X3)
20.08/5.90	   mark(U242(X1, X2, X3)) -> a__U242(mark(X1), X2, X3)
20.08/5.90	   mark(U243(X1, X2, X3)) -> a__U243(mark(X1), X2, X3)
20.08/5.90	   mark(U244(X1, X2, X3)) -> a__U244(mark(X1), X2, X3)
20.08/5.90	   mark(U245(X1, X2)) -> a__U245(mark(X1), X2)
20.08/5.90	   mark(U246(X)) -> a__U246(mark(X))
20.08/5.90	   mark(U251(X1, X2, X3)) -> a__U251(mark(X1), X2, X3)
20.08/5.90	   mark(U252(X1, X2, X3)) -> a__U252(mark(X1), X2, X3)
20.08/5.90	   mark(U253(X1, X2, X3)) -> a__U253(mark(X1), X2, X3)
20.08/5.90	   mark(U254(X1, X2, X3)) -> a__U254(mark(X1), X2, X3)
20.08/5.90	   mark(U255(X1, X2)) -> a__U255(mark(X1), X2)
20.08/5.90	   mark(U256(X)) -> a__U256(mark(X))
20.08/5.90	   mark(U261(X1, X2)) -> a__U261(mark(X1), X2)
20.08/5.90	   mark(U262(X)) -> a__U262(mark(X))
20.08/5.90	   mark(U271(X1, X2)) -> a__U271(mark(X1), X2)
20.08/5.90	   mark(U272(X)) -> a__U272(mark(X))
20.08/5.90	   mark(U281(X1, X2)) -> a__U281(mark(X1), X2)
20.08/5.90	   mark(U282(X1, X2)) -> a__U282(mark(X1), X2)
20.08/5.90	   mark(natsFrom(X)) -> a__natsFrom(mark(X))
20.08/5.90	   mark(U291(X1, X2, X3)) -> a__U291(mark(X1), X2, X3)
20.08/5.90	   mark(U292(X1, X2, X3)) -> a__U292(mark(X1), X2, X3)
20.08/5.90	   mark(U293(X1, X2, X3)) -> a__U293(mark(X1), X2, X3)
20.08/5.90	   mark(U294(X1, X2, X3)) -> a__U294(mark(X1), X2, X3)
20.08/5.90	   mark(head(X)) -> a__head(mark(X))
20.08/5.90	   mark(afterNth(X1, X2)) -> a__afterNth(mark(X1), mark(X2))
20.08/5.90	   mark(U301(X1, X2, X3)) -> a__U301(mark(X1), X2, X3)
20.08/5.90	   mark(U302(X1, X2)) -> a__U302(mark(X1), X2)
20.08/5.90	   mark(U303(X1, X2)) -> a__U303(mark(X1), X2)
20.08/5.90	   mark(U304(X1, X2)) -> a__U304(mark(X1), X2)
20.08/5.90	   mark(U31(X1, X2, X3)) -> a__U31(mark(X1), X2, X3)
20.08/5.90	   mark(U32(X1, X2, X3)) -> a__U32(mark(X1), X2, X3)
20.08/5.90	   mark(U311(X1, X2)) -> a__U311(mark(X1), X2)
20.08/5.90	   mark(U312(X1, X2)) -> a__U312(mark(X1), X2)
20.08/5.90	   mark(U33(X1, X2, X3)) -> a__U33(mark(X1), X2, X3)
20.08/5.90	   mark(U321(X1, X2, X3, X4)) -> a__U321(mark(X1), X2, X3, X4)
20.08/5.90	   mark(U322(X1, X2, X3, X4)) -> a__U322(mark(X1), X2, X3, X4)
20.08/5.90	   mark(U323(X1, X2, X3, X4)) -> a__U323(mark(X1), X2, X3, X4)
20.08/5.90	   mark(U324(X1, X2, X3, X4)) -> a__U324(mark(X1), X2, X3, X4)
20.08/5.90	   mark(U325(X1, X2, X3, X4)) -> a__U325(mark(X1), X2, X3, X4)
20.08/5.91	   mark(U326(X1, X2, X3, X4)) -> a__U326(mark(X1), X2, X3, X4)
20.08/5.91	   mark(U327(X1, X2)) -> a__U327(mark(X1), X2)
20.08/5.91	   mark(U34(X1, X2)) -> a__U34(mark(X1), X2)
20.08/5.91	   mark(U331(X1, X2, X3)) -> a__U331(mark(X1), X2, X3)
20.08/5.91	   mark(U332(X1, X2)) -> a__U332(mark(X1), X2)
20.08/5.91	   mark(U333(X1, X2)) -> a__U333(mark(X1), X2)
20.08/5.91	   mark(U334(X1, X2)) -> a__U334(mark(X1), X2)
20.08/5.91	   mark(U341(X1, X2, X3)) -> a__U341(mark(X1), X2, X3)
20.08/5.91	   mark(U342(X1, X2, X3)) -> a__U342(mark(X1), X2, X3)
20.08/5.91	   mark(U343(X1, X2, X3)) -> a__U343(mark(X1), X2, X3)
20.08/5.91	   mark(U344(X1, X2, X3)) -> a__U344(mark(X1), X2, X3)
20.08/5.91	   mark(fst(X)) -> a__fst(mark(X))
20.08/5.91	   mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
20.08/5.91	   mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3)
20.08/5.91	   mark(U43(X1, X2, X3)) -> a__U43(mark(X1), X2, X3)
20.08/5.91	   mark(U44(X1, X2, X3)) -> a__U44(mark(X1), X2, X3)
20.08/5.91	   mark(U45(X1, X2)) -> a__U45(mark(X1), X2)
20.08/5.91	   mark(U46(X)) -> a__U46(mark(X))
20.08/5.91	   mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3)
20.08/5.91	   mark(U52(X1, X2, X3)) -> a__U52(mark(X1), X2, X3)
20.08/5.91	   mark(U53(X1, X2, X3)) -> a__U53(mark(X1), X2, X3)
20.08/5.91	   mark(U54(X1, X2, X3)) -> a__U54(mark(X1), X2, X3)
20.08/5.91	   mark(U55(X1, X2)) -> a__U55(mark(X1), X2)
20.08/5.91	   mark(U56(X)) -> a__U56(mark(X))
20.08/5.91	   mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
20.08/5.91	   mark(U62(X1, X2)) -> a__U62(mark(X1), X2)
20.08/5.91	   mark(isPLNatKind(X)) -> a__isPLNatKind(X)
20.08/5.91	   mark(U63(X)) -> a__U63(mark(X))
20.08/5.91	   mark(isPLNat(X)) -> a__isPLNat(X)
20.08/5.91	   mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
20.08/5.91	   mark(U72(X1, X2)) -> a__U72(mark(X1), X2)
20.08/5.91	   mark(U73(X)) -> a__U73(mark(X))
20.08/5.91	   mark(U81(X1, X2)) -> a__U81(mark(X1), X2)
20.08/5.91	   mark(U82(X1, X2)) -> a__U82(mark(X1), X2)
20.08/5.91	   mark(U83(X)) -> a__U83(mark(X))
20.08/5.91	   mark(U91(X1, X2)) -> a__U91(mark(X1), X2)
20.08/5.91	   mark(U92(X1, X2)) -> a__U92(mark(X1), X2)
20.08/5.91	   mark(U93(X)) -> a__U93(mark(X))
20.08/5.91	   mark(tail(X)) -> a__tail(mark(X))
20.08/5.91	   mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
20.08/5.91	   mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
20.08/5.91	   mark(tt) -> tt
20.08/5.91	   mark(cons(X1, X2)) -> cons(mark(X1), X2)
20.08/5.91	   mark(s(X)) -> s(mark(X))
20.08/5.91	   mark(pair(X1, X2)) -> pair(mark(X1), mark(X2))
20.08/5.91	   mark(nil) -> nil
20.08/5.91	   mark(0) -> 0
20.08/5.91	   a__U101(X1, X2, X3) -> U101(X1, X2, X3)
20.08/5.91	   a__U102(X1, X2, X3) -> U102(X1, X2, X3)
20.08/5.91	   a__isNaturalKind(X) -> isNaturalKind(X)
20.08/5.91	   a__U103(X1, X2, X3) -> U103(X1, X2, X3)
20.08/5.91	   a__isLNatKind(X) -> isLNatKind(X)
20.08/5.91	   a__U104(X1, X2, X3) -> U104(X1, X2, X3)
20.08/5.91	   a__U105(X1, X2) -> U105(X1, X2)
20.08/5.91	   a__isNatural(X) -> isNatural(X)
20.08/5.91	   a__U106(X) -> U106(X)
20.08/5.91	   a__isLNat(X) -> isLNat(X)
20.08/5.91	   a__U11(X1, X2, X3) -> U11(X1, X2, X3)
20.08/5.91	   a__U12(X1, X2, X3) -> U12(X1, X2, X3)
20.08/5.91	   a__U111(X1, X2) -> U111(X1, X2)
20.08/5.91	   a__U112(X) -> U112(X)
20.08/5.91	   a__U13(X1, X2, X3) -> U13(X1, X2, X3)
20.08/5.91	   a__U121(X1, X2) -> U121(X1, X2)
20.08/5.91	   a__U122(X) -> U122(X)
20.08/5.91	   a__U14(X1, X2, X3) -> U14(X1, X2, X3)
20.08/5.91	   a__U131(X) -> U131(X)
20.08/5.91	   a__snd(X) -> snd(X)
20.08/5.91	   a__splitAt(X1, X2) -> splitAt(X1, X2)
20.08/5.91	   a__U141(X) -> U141(X)
20.08/5.91	   a__U151(X) -> U151(X)
20.08/5.91	   a__U161(X) -> U161(X)
20.08/5.91	   a__U171(X1, X2) -> U171(X1, X2)
20.08/5.91	   a__U172(X) -> U172(X)
20.08/5.91	   a__U181(X1, X2) -> U181(X1, X2)
20.08/5.91	   a__U182(X1, X2) -> U182(X1, X2)
20.08/5.91	   a__U183(X) -> U183(X)
20.08/5.91	   a__U191(X1, X2) -> U191(X1, X2)
20.08/5.91	   a__U192(X1, X2) -> U192(X1, X2)
20.08/5.91	   a__U193(X) -> U193(X)
20.08/5.91	   a__U201(X1, X2, X3) -> U201(X1, X2, X3)
20.08/5.91	   a__U202(X1, X2, X3) -> U202(X1, X2, X3)
20.08/5.91	   a__U203(X1, X2, X3) -> U203(X1, X2, X3)
20.08/5.91	   a__U204(X1, X2, X3) -> U204(X1, X2, X3)
20.08/5.91	   a__U205(X1, X2) -> U205(X1, X2)
20.08/5.91	   a__U206(X) -> U206(X)
20.08/5.91	   a__U21(X1, X2, X3) -> U21(X1, X2, X3)
20.08/5.91	   a__U22(X1, X2, X3) -> U22(X1, X2, X3)
20.08/5.91	   a__U211(X) -> U211(X)
20.08/5.91	   a__U23(X1, X2, X3) -> U23(X1, X2, X3)
20.08/5.91	   a__U221(X) -> U221(X)
20.08/5.91	   a__U24(X1, X2) -> U24(X1, X2)
20.08/5.91	   a__U231(X1, X2) -> U231(X1, X2)
20.08/5.91	   a__U232(X) -> U232(X)
20.08/5.91	   a__U241(X1, X2, X3) -> U241(X1, X2, X3)
20.08/5.91	   a__U242(X1, X2, X3) -> U242(X1, X2, X3)
20.08/5.91	   a__U243(X1, X2, X3) -> U243(X1, X2, X3)
20.08/5.91	   a__U244(X1, X2, X3) -> U244(X1, X2, X3)
20.08/5.91	   a__U245(X1, X2) -> U245(X1, X2)
20.08/5.91	   a__U246(X) -> U246(X)
20.08/5.91	   a__U251(X1, X2, X3) -> U251(X1, X2, X3)
20.08/5.91	   a__U252(X1, X2, X3) -> U252(X1, X2, X3)
20.08/5.91	   a__U253(X1, X2, X3) -> U253(X1, X2, X3)
20.08/5.91	   a__U254(X1, X2, X3) -> U254(X1, X2, X3)
20.08/5.91	   a__U255(X1, X2) -> U255(X1, X2)
20.08/5.91	   a__U256(X) -> U256(X)
20.08/5.91	   a__U261(X1, X2) -> U261(X1, X2)
20.08/5.91	   a__U262(X) -> U262(X)
20.08/5.91	   a__U271(X1, X2) -> U271(X1, X2)
20.08/5.91	   a__U272(X) -> U272(X)
20.08/5.91	   a__U281(X1, X2) -> U281(X1, X2)
20.08/5.91	   a__U282(X1, X2) -> U282(X1, X2)
20.08/5.91	   a__natsFrom(X) -> natsFrom(X)
20.08/5.91	   a__U291(X1, X2, X3) -> U291(X1, X2, X3)
20.08/5.91	   a__U292(X1, X2, X3) -> U292(X1, X2, X3)
20.08/5.91	   a__U293(X1, X2, X3) -> U293(X1, X2, X3)
20.08/5.91	   a__U294(X1, X2, X3) -> U294(X1, X2, X3)
20.08/5.91	   a__head(X) -> head(X)
20.08/5.91	   a__afterNth(X1, X2) -> afterNth(X1, X2)
20.08/5.91	   a__U301(X1, X2, X3) -> U301(X1, X2, X3)
20.08/5.91	   a__U302(X1, X2) -> U302(X1, X2)
20.08/5.91	   a__U303(X1, X2) -> U303(X1, X2)
20.08/5.91	   a__U304(X1, X2) -> U304(X1, X2)
20.08/5.91	   a__U31(X1, X2, X3) -> U31(X1, X2, X3)
20.08/5.91	   a__U32(X1, X2, X3) -> U32(X1, X2, X3)
20.08/5.91	   a__U311(X1, X2) -> U311(X1, X2)
20.08/5.91	   a__U312(X1, X2) -> U312(X1, X2)
20.08/5.91	   a__U33(X1, X2, X3) -> U33(X1, X2, X3)
20.08/5.91	   a__U321(X1, X2, X3, X4) -> U321(X1, X2, X3, X4)
20.08/5.91	   a__U322(X1, X2, X3, X4) -> U322(X1, X2, X3, X4)
20.08/5.91	   a__U323(X1, X2, X3, X4) -> U323(X1, X2, X3, X4)
20.08/5.91	   a__U324(X1, X2, X3, X4) -> U324(X1, X2, X3, X4)
20.08/5.91	   a__U325(X1, X2, X3, X4) -> U325(X1, X2, X3, X4)
20.08/5.91	   a__U326(X1, X2, X3, X4) -> U326(X1, X2, X3, X4)
20.08/5.91	   a__U327(X1, X2) -> U327(X1, X2)
20.08/5.91	   a__U34(X1, X2) -> U34(X1, X2)
20.08/5.91	   a__U331(X1, X2, X3) -> U331(X1, X2, X3)
20.08/5.91	   a__U332(X1, X2) -> U332(X1, X2)
20.08/5.91	   a__U333(X1, X2) -> U333(X1, X2)
20.08/5.91	   a__U334(X1, X2) -> U334(X1, X2)
20.08/5.91	   a__U341(X1, X2, X3) -> U341(X1, X2, X3)
20.08/5.91	   a__U342(X1, X2, X3) -> U342(X1, X2, X3)
20.08/5.91	   a__U343(X1, X2, X3) -> U343(X1, X2, X3)
20.08/5.91	   a__U344(X1, X2, X3) -> U344(X1, X2, X3)
20.08/5.91	   a__fst(X) -> fst(X)
20.08/5.91	   a__U41(X1, X2, X3) -> U41(X1, X2, X3)
20.08/5.91	   a__U42(X1, X2, X3) -> U42(X1, X2, X3)
20.08/5.91	   a__U43(X1, X2, X3) -> U43(X1, X2, X3)
20.08/5.91	   a__U44(X1, X2, X3) -> U44(X1, X2, X3)
20.08/5.91	   a__U45(X1, X2) -> U45(X1, X2)
20.08/5.91	   a__U46(X) -> U46(X)
20.08/5.91	   a__U51(X1, X2, X3) -> U51(X1, X2, X3)
20.08/5.91	   a__U52(X1, X2, X3) -> U52(X1, X2, X3)
20.08/5.91	   a__U53(X1, X2, X3) -> U53(X1, X2, X3)
20.08/5.91	   a__U54(X1, X2, X3) -> U54(X1, X2, X3)
20.08/5.91	   a__U55(X1, X2) -> U55(X1, X2)
20.08/5.91	   a__U56(X) -> U56(X)
20.08/5.91	   a__U61(X1, X2) -> U61(X1, X2)
20.08/5.91	   a__U62(X1, X2) -> U62(X1, X2)
20.08/5.91	   a__isPLNatKind(X) -> isPLNatKind(X)
20.08/5.91	   a__U63(X) -> U63(X)
20.08/5.91	   a__isPLNat(X) -> isPLNat(X)
20.08/5.91	   a__U71(X1, X2) -> U71(X1, X2)
20.08/5.91	   a__U72(X1, X2) -> U72(X1, X2)
20.08/5.91	   a__U73(X) -> U73(X)
20.08/5.91	   a__U81(X1, X2) -> U81(X1, X2)
20.08/5.91	   a__U82(X1, X2) -> U82(X1, X2)
20.08/5.91	   a__U83(X) -> U83(X)
20.08/5.91	   a__U91(X1, X2) -> U91(X1, X2)
20.08/5.91	   a__U92(X1, X2) -> U92(X1, X2)
20.08/5.91	   a__U93(X) -> U93(X)
20.08/5.91	   a__tail(X) -> tail(X)
20.08/5.91	   a__take(X1, X2) -> take(X1, X2)
20.08/5.91	   a__sel(X1, X2) -> sel(X1, X2)
20.08/5.91	
20.08/5.91	S is empty.
20.08/5.91	Rewrite Strategy: FULL
20.08/5.91	----------------------------------------
20.08/5.91	
20.08/5.91	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
20.08/5.91	Transformed a relative TRS into a decreasing-loop problem.
20.08/5.91	----------------------------------------
20.08/5.91	
20.08/5.91	(2)
20.08/5.91	Obligation:
20.08/5.91	Analyzing the following TRS for decreasing loops:
20.08/5.91	
20.08/5.91	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
20.08/5.91	
20.08/5.91	
20.08/5.91	The TRS R consists of the following rules:
20.08/5.91	
20.08/5.91	   a__U101(tt, V1, V2) -> a__U102(a__isNaturalKind(V1), V1, V2)
20.08/5.91	   a__U102(tt, V1, V2) -> a__U103(a__isLNatKind(V2), V1, V2)
20.08/5.91	   a__U103(tt, V1, V2) -> a__U104(a__isLNatKind(V2), V1, V2)
20.08/5.91	   a__U104(tt, V1, V2) -> a__U105(a__isNatural(V1), V2)
20.08/5.91	   a__U105(tt, V2) -> a__U106(a__isLNat(V2))
20.08/5.91	   a__U106(tt) -> tt
20.08/5.91	   a__U11(tt, N, XS) -> a__U12(a__isNaturalKind(N), N, XS)
20.08/5.91	   a__U111(tt, V2) -> a__U112(a__isLNatKind(V2))
20.08/5.91	   a__U112(tt) -> tt
20.08/5.91	   a__U12(tt, N, XS) -> a__U13(a__isLNat(XS), N, XS)
20.08/5.91	   a__U121(tt, V2) -> a__U122(a__isLNatKind(V2))
20.08/5.91	   a__U122(tt) -> tt
20.08/5.91	   a__U13(tt, N, XS) -> a__U14(a__isLNatKind(XS), N, XS)
20.08/5.91	   a__U131(tt) -> tt
20.08/5.91	   a__U14(tt, N, XS) -> a__snd(a__splitAt(mark(N), mark(XS)))
20.08/5.91	   a__U141(tt) -> tt
20.08/5.91	   a__U151(tt) -> tt
20.08/5.91	   a__U161(tt) -> tt
20.08/5.91	   a__U171(tt, V2) -> a__U172(a__isLNatKind(V2))
20.08/5.91	   a__U172(tt) -> tt
20.08/5.91	   a__U181(tt, V1) -> a__U182(a__isLNatKind(V1), V1)
20.08/5.91	   a__U182(tt, V1) -> a__U183(a__isLNat(V1))
20.08/5.91	   a__U183(tt) -> tt
20.08/5.91	   a__U191(tt, V1) -> a__U192(a__isNaturalKind(V1), V1)
20.08/5.91	   a__U192(tt, V1) -> a__U193(a__isNatural(V1))
20.08/5.91	   a__U193(tt) -> tt
20.08/5.91	   a__U201(tt, V1, V2) -> a__U202(a__isNaturalKind(V1), V1, V2)
20.08/5.91	   a__U202(tt, V1, V2) -> a__U203(a__isLNatKind(V2), V1, V2)
20.08/5.91	   a__U203(tt, V1, V2) -> a__U204(a__isLNatKind(V2), V1, V2)
20.08/5.91	   a__U204(tt, V1, V2) -> a__U205(a__isNatural(V1), V2)
20.08/5.91	   a__U205(tt, V2) -> a__U206(a__isLNat(V2))
20.08/5.91	   a__U206(tt) -> tt
20.08/5.91	   a__U21(tt, X, Y) -> a__U22(a__isLNatKind(X), X, Y)
20.08/5.91	   a__U211(tt) -> tt
20.08/5.91	   a__U22(tt, X, Y) -> a__U23(a__isLNat(Y), X, Y)
20.08/5.91	   a__U221(tt) -> tt
20.08/5.91	   a__U23(tt, X, Y) -> a__U24(a__isLNatKind(Y), X)
20.08/5.91	   a__U231(tt, V2) -> a__U232(a__isLNatKind(V2))
20.08/5.91	   a__U232(tt) -> tt
20.08/5.91	   a__U24(tt, X) -> mark(X)
20.08/5.91	   a__U241(tt, V1, V2) -> a__U242(a__isLNatKind(V1), V1, V2)
20.08/5.91	   a__U242(tt, V1, V2) -> a__U243(a__isLNatKind(V2), V1, V2)
20.08/5.91	   a__U243(tt, V1, V2) -> a__U244(a__isLNatKind(V2), V1, V2)
20.08/5.91	   a__U244(tt, V1, V2) -> a__U245(a__isLNat(V1), V2)
20.08/5.91	   a__U245(tt, V2) -> a__U246(a__isLNat(V2))
20.08/5.91	   a__U246(tt) -> tt
20.08/5.91	   a__U251(tt, V1, V2) -> a__U252(a__isNaturalKind(V1), V1, V2)
20.08/5.91	   a__U252(tt, V1, V2) -> a__U253(a__isLNatKind(V2), V1, V2)
20.08/5.91	   a__U253(tt, V1, V2) -> a__U254(a__isLNatKind(V2), V1, V2)
20.08/5.91	   a__U254(tt, V1, V2) -> a__U255(a__isNatural(V1), V2)
20.08/5.91	   a__U255(tt, V2) -> a__U256(a__isLNat(V2))
20.08/5.91	   a__U256(tt) -> tt
20.08/5.91	   a__U261(tt, V2) -> a__U262(a__isLNatKind(V2))
20.08/5.91	   a__U262(tt) -> tt
20.08/5.91	   a__U271(tt, V2) -> a__U272(a__isLNatKind(V2))
20.08/5.91	   a__U272(tt) -> tt
20.08/5.91	   a__U281(tt, N) -> a__U282(a__isNaturalKind(N), N)
20.08/5.91	   a__U282(tt, N) -> cons(mark(N), natsFrom(s(N)))
20.08/5.91	   a__U291(tt, N, XS) -> a__U292(a__isNaturalKind(N), N, XS)
20.08/5.91	   a__U292(tt, N, XS) -> a__U293(a__isLNat(XS), N, XS)
20.08/5.91	   a__U293(tt, N, XS) -> a__U294(a__isLNatKind(XS), N, XS)
20.08/5.91	   a__U294(tt, N, XS) -> a__head(a__afterNth(mark(N), mark(XS)))
20.08/5.91	   a__U301(tt, X, Y) -> a__U302(a__isLNatKind(X), Y)
20.08/5.91	   a__U302(tt, Y) -> a__U303(a__isLNat(Y), Y)
20.08/5.91	   a__U303(tt, Y) -> a__U304(a__isLNatKind(Y), Y)
20.08/5.91	   a__U304(tt, Y) -> mark(Y)
20.08/5.91	   a__U31(tt, N, XS) -> a__U32(a__isNaturalKind(N), N, XS)
20.08/5.91	   a__U311(tt, XS) -> a__U312(a__isLNatKind(XS), XS)
20.08/5.91	   a__U312(tt, XS) -> pair(nil, mark(XS))
20.08/5.91	   a__U32(tt, N, XS) -> a__U33(a__isLNat(XS), N, XS)
20.08/5.91	   a__U321(tt, N, X, XS) -> a__U322(a__isNaturalKind(N), N, X, XS)
20.08/5.91	   a__U322(tt, N, X, XS) -> a__U323(a__isNatural(X), N, X, XS)
20.08/5.91	   a__U323(tt, N, X, XS) -> a__U324(a__isNaturalKind(X), N, X, XS)
20.08/5.91	   a__U324(tt, N, X, XS) -> a__U325(a__isLNat(XS), N, X, XS)
20.08/5.91	   a__U325(tt, N, X, XS) -> a__U326(a__isLNatKind(XS), N, X, XS)
20.08/5.91	   a__U326(tt, N, X, XS) -> a__U327(a__splitAt(mark(N), mark(XS)), X)
20.08/5.91	   a__U327(pair(YS, ZS), X) -> pair(cons(mark(X), YS), mark(ZS))
20.08/5.91	   a__U33(tt, N, XS) -> a__U34(a__isLNatKind(XS), N)
20.08/5.91	   a__U331(tt, N, XS) -> a__U332(a__isNaturalKind(N), XS)
20.08/5.91	   a__U332(tt, XS) -> a__U333(a__isLNat(XS), XS)
20.08/5.91	   a__U333(tt, XS) -> a__U334(a__isLNatKind(XS), XS)
20.08/5.91	   a__U334(tt, XS) -> mark(XS)
20.08/5.91	   a__U34(tt, N) -> mark(N)
20.08/5.91	   a__U341(tt, N, XS) -> a__U342(a__isNaturalKind(N), N, XS)
20.08/5.91	   a__U342(tt, N, XS) -> a__U343(a__isLNat(XS), N, XS)
20.08/5.91	   a__U343(tt, N, XS) -> a__U344(a__isLNatKind(XS), N, XS)
20.08/5.91	   a__U344(tt, N, XS) -> a__fst(a__splitAt(mark(N), mark(XS)))
20.08/5.91	   a__U41(tt, V1, V2) -> a__U42(a__isNaturalKind(V1), V1, V2)
20.08/5.91	   a__U42(tt, V1, V2) -> a__U43(a__isLNatKind(V2), V1, V2)
20.08/5.91	   a__U43(tt, V1, V2) -> a__U44(a__isLNatKind(V2), V1, V2)
20.08/5.91	   a__U44(tt, V1, V2) -> a__U45(a__isNatural(V1), V2)
20.08/5.91	   a__U45(tt, V2) -> a__U46(a__isLNat(V2))
20.08/5.91	   a__U46(tt) -> tt
20.08/5.91	   a__U51(tt, V1, V2) -> a__U52(a__isNaturalKind(V1), V1, V2)
20.08/5.91	   a__U52(tt, V1, V2) -> a__U53(a__isLNatKind(V2), V1, V2)
20.08/5.91	   a__U53(tt, V1, V2) -> a__U54(a__isLNatKind(V2), V1, V2)
20.08/5.91	   a__U54(tt, V1, V2) -> a__U55(a__isNatural(V1), V2)
20.08/5.91	   a__U55(tt, V2) -> a__U56(a__isLNat(V2))
20.08/5.91	   a__U56(tt) -> tt
20.08/5.91	   a__U61(tt, V1) -> a__U62(a__isPLNatKind(V1), V1)
20.08/5.91	   a__U62(tt, V1) -> a__U63(a__isPLNat(V1))
20.08/5.91	   a__U63(tt) -> tt
20.08/5.91	   a__U71(tt, V1) -> a__U72(a__isNaturalKind(V1), V1)
20.08/5.91	   a__U72(tt, V1) -> a__U73(a__isNatural(V1))
20.08/5.91	   a__U73(tt) -> tt
20.08/5.91	   a__U81(tt, V1) -> a__U82(a__isPLNatKind(V1), V1)
20.08/5.91	   a__U82(tt, V1) -> a__U83(a__isPLNat(V1))
20.08/5.91	   a__U83(tt) -> tt
20.08/5.91	   a__U91(tt, V1) -> a__U92(a__isLNatKind(V1), V1)
20.08/5.91	   a__U92(tt, V1) -> a__U93(a__isLNat(V1))
20.08/5.91	   a__U93(tt) -> tt
20.08/5.91	   a__afterNth(N, XS) -> a__U11(a__isNatural(N), N, XS)
20.08/5.91	   a__fst(pair(X, Y)) -> a__U21(a__isLNat(X), X, Y)
20.08/5.91	   a__head(cons(N, XS)) -> a__U31(a__isNatural(N), N, XS)
20.08/5.91	   a__isLNat(nil) -> tt
20.08/5.91	   a__isLNat(afterNth(V1, V2)) -> a__U41(a__isNaturalKind(V1), V1, V2)
20.08/5.91	   a__isLNat(cons(V1, V2)) -> a__U51(a__isNaturalKind(V1), V1, V2)
20.08/5.91	   a__isLNat(fst(V1)) -> a__U61(a__isPLNatKind(V1), V1)
20.08/5.91	   a__isLNat(natsFrom(V1)) -> a__U71(a__isNaturalKind(V1), V1)
20.08/5.91	   a__isLNat(snd(V1)) -> a__U81(a__isPLNatKind(V1), V1)
20.08/5.91	   a__isLNat(tail(V1)) -> a__U91(a__isLNatKind(V1), V1)
20.08/5.91	   a__isLNat(take(V1, V2)) -> a__U101(a__isNaturalKind(V1), V1, V2)
20.08/5.91	   a__isLNatKind(nil) -> tt
20.08/5.91	   a__isLNatKind(afterNth(V1, V2)) -> a__U111(a__isNaturalKind(V1), V2)
20.08/5.91	   a__isLNatKind(cons(V1, V2)) -> a__U121(a__isNaturalKind(V1), V2)
20.08/5.91	   a__isLNatKind(fst(V1)) -> a__U131(a__isPLNatKind(V1))
20.08/5.91	   a__isLNatKind(natsFrom(V1)) -> a__U141(a__isNaturalKind(V1))
20.08/5.91	   a__isLNatKind(snd(V1)) -> a__U151(a__isPLNatKind(V1))
20.08/5.91	   a__isLNatKind(tail(V1)) -> a__U161(a__isLNatKind(V1))
20.08/5.91	   a__isLNatKind(take(V1, V2)) -> a__U171(a__isNaturalKind(V1), V2)
20.08/5.91	   a__isNatural(0) -> tt
20.08/5.91	   a__isNatural(head(V1)) -> a__U181(a__isLNatKind(V1), V1)
20.08/5.91	   a__isNatural(s(V1)) -> a__U191(a__isNaturalKind(V1), V1)
20.08/5.91	   a__isNatural(sel(V1, V2)) -> a__U201(a__isNaturalKind(V1), V1, V2)
20.08/5.91	   a__isNaturalKind(0) -> tt
20.08/5.91	   a__isNaturalKind(head(V1)) -> a__U211(a__isLNatKind(V1))
20.08/5.91	   a__isNaturalKind(s(V1)) -> a__U221(a__isNaturalKind(V1))
20.08/5.91	   a__isNaturalKind(sel(V1, V2)) -> a__U231(a__isNaturalKind(V1), V2)
20.08/5.91	   a__isPLNat(pair(V1, V2)) -> a__U241(a__isLNatKind(V1), V1, V2)
20.08/5.91	   a__isPLNat(splitAt(V1, V2)) -> a__U251(a__isNaturalKind(V1), V1, V2)
20.08/5.91	   a__isPLNatKind(pair(V1, V2)) -> a__U261(a__isLNatKind(V1), V2)
20.08/5.91	   a__isPLNatKind(splitAt(V1, V2)) -> a__U271(a__isNaturalKind(V1), V2)
20.08/5.91	   a__natsFrom(N) -> a__U281(a__isNatural(N), N)
20.08/5.91	   a__sel(N, XS) -> a__U291(a__isNatural(N), N, XS)
20.08/5.91	   a__snd(pair(X, Y)) -> a__U301(a__isLNat(X), X, Y)
20.08/5.91	   a__splitAt(0, XS) -> a__U311(a__isLNat(XS), XS)
20.08/5.91	   a__splitAt(s(N), cons(X, XS)) -> a__U321(a__isNatural(N), N, X, XS)
20.08/5.91	   a__tail(cons(N, XS)) -> a__U331(a__isNatural(N), N, XS)
20.08/5.91	   a__take(N, XS) -> a__U341(a__isNatural(N), N, XS)
20.08/5.91	   mark(U101(X1, X2, X3)) -> a__U101(mark(X1), X2, X3)
20.08/5.91	   mark(U102(X1, X2, X3)) -> a__U102(mark(X1), X2, X3)
20.08/5.91	   mark(isNaturalKind(X)) -> a__isNaturalKind(X)
20.08/5.91	   mark(U103(X1, X2, X3)) -> a__U103(mark(X1), X2, X3)
20.08/5.91	   mark(isLNatKind(X)) -> a__isLNatKind(X)
20.08/5.91	   mark(U104(X1, X2, X3)) -> a__U104(mark(X1), X2, X3)
20.08/5.91	   mark(U105(X1, X2)) -> a__U105(mark(X1), X2)
20.08/5.91	   mark(isNatural(X)) -> a__isNatural(X)
20.08/5.91	   mark(U106(X)) -> a__U106(mark(X))
20.08/5.91	   mark(isLNat(X)) -> a__isLNat(X)
20.08/5.91	   mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
20.08/5.91	   mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
20.08/5.91	   mark(U111(X1, X2)) -> a__U111(mark(X1), X2)
20.08/5.91	   mark(U112(X)) -> a__U112(mark(X))
20.08/5.91	   mark(U13(X1, X2, X3)) -> a__U13(mark(X1), X2, X3)
20.08/5.91	   mark(U121(X1, X2)) -> a__U121(mark(X1), X2)
20.08/5.91	   mark(U122(X)) -> a__U122(mark(X))
20.08/5.91	   mark(U14(X1, X2, X3)) -> a__U14(mark(X1), X2, X3)
20.08/5.91	   mark(U131(X)) -> a__U131(mark(X))
20.08/5.91	   mark(snd(X)) -> a__snd(mark(X))
20.08/5.91	   mark(splitAt(X1, X2)) -> a__splitAt(mark(X1), mark(X2))
20.08/5.91	   mark(U141(X)) -> a__U141(mark(X))
20.08/5.91	   mark(U151(X)) -> a__U151(mark(X))
20.08/5.91	   mark(U161(X)) -> a__U161(mark(X))
20.08/5.91	   mark(U171(X1, X2)) -> a__U171(mark(X1), X2)
20.08/5.91	   mark(U172(X)) -> a__U172(mark(X))
20.08/5.91	   mark(U181(X1, X2)) -> a__U181(mark(X1), X2)
20.08/5.91	   mark(U182(X1, X2)) -> a__U182(mark(X1), X2)
20.08/5.91	   mark(U183(X)) -> a__U183(mark(X))
20.08/5.91	   mark(U191(X1, X2)) -> a__U191(mark(X1), X2)
20.08/5.91	   mark(U192(X1, X2)) -> a__U192(mark(X1), X2)
20.08/5.91	   mark(U193(X)) -> a__U193(mark(X))
20.08/5.91	   mark(U201(X1, X2, X3)) -> a__U201(mark(X1), X2, X3)
20.08/5.91	   mark(U202(X1, X2, X3)) -> a__U202(mark(X1), X2, X3)
20.08/5.91	   mark(U203(X1, X2, X3)) -> a__U203(mark(X1), X2, X3)
20.08/5.91	   mark(U204(X1, X2, X3)) -> a__U204(mark(X1), X2, X3)
20.08/5.91	   mark(U205(X1, X2)) -> a__U205(mark(X1), X2)
20.08/5.91	   mark(U206(X)) -> a__U206(mark(X))
20.08/5.91	   mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3)
20.08/5.91	   mark(U22(X1, X2, X3)) -> a__U22(mark(X1), X2, X3)
20.08/5.91	   mark(U211(X)) -> a__U211(mark(X))
20.08/5.91	   mark(U23(X1, X2, X3)) -> a__U23(mark(X1), X2, X3)
20.08/5.91	   mark(U221(X)) -> a__U221(mark(X))
20.08/5.91	   mark(U24(X1, X2)) -> a__U24(mark(X1), X2)
20.08/5.91	   mark(U231(X1, X2)) -> a__U231(mark(X1), X2)
20.08/5.91	   mark(U232(X)) -> a__U232(mark(X))
20.08/5.91	   mark(U241(X1, X2, X3)) -> a__U241(mark(X1), X2, X3)
20.08/5.91	   mark(U242(X1, X2, X3)) -> a__U242(mark(X1), X2, X3)
20.08/5.91	   mark(U243(X1, X2, X3)) -> a__U243(mark(X1), X2, X3)
20.08/5.91	   mark(U244(X1, X2, X3)) -> a__U244(mark(X1), X2, X3)
20.08/5.91	   mark(U245(X1, X2)) -> a__U245(mark(X1), X2)
20.08/5.91	   mark(U246(X)) -> a__U246(mark(X))
20.08/5.91	   mark(U251(X1, X2, X3)) -> a__U251(mark(X1), X2, X3)
20.08/5.91	   mark(U252(X1, X2, X3)) -> a__U252(mark(X1), X2, X3)
20.08/5.91	   mark(U253(X1, X2, X3)) -> a__U253(mark(X1), X2, X3)
20.08/5.91	   mark(U254(X1, X2, X3)) -> a__U254(mark(X1), X2, X3)
20.08/5.91	   mark(U255(X1, X2)) -> a__U255(mark(X1), X2)
20.08/5.91	   mark(U256(X)) -> a__U256(mark(X))
20.08/5.91	   mark(U261(X1, X2)) -> a__U261(mark(X1), X2)
20.08/5.91	   mark(U262(X)) -> a__U262(mark(X))
20.08/5.91	   mark(U271(X1, X2)) -> a__U271(mark(X1), X2)
20.08/5.91	   mark(U272(X)) -> a__U272(mark(X))
20.08/5.91	   mark(U281(X1, X2)) -> a__U281(mark(X1), X2)
20.08/5.91	   mark(U282(X1, X2)) -> a__U282(mark(X1), X2)
20.08/5.91	   mark(natsFrom(X)) -> a__natsFrom(mark(X))
20.08/5.91	   mark(U291(X1, X2, X3)) -> a__U291(mark(X1), X2, X3)
20.08/5.91	   mark(U292(X1, X2, X3)) -> a__U292(mark(X1), X2, X3)
20.08/5.91	   mark(U293(X1, X2, X3)) -> a__U293(mark(X1), X2, X3)
20.08/5.91	   mark(U294(X1, X2, X3)) -> a__U294(mark(X1), X2, X3)
20.08/5.91	   mark(head(X)) -> a__head(mark(X))
20.08/5.91	   mark(afterNth(X1, X2)) -> a__afterNth(mark(X1), mark(X2))
20.08/5.91	   mark(U301(X1, X2, X3)) -> a__U301(mark(X1), X2, X3)
20.08/5.91	   mark(U302(X1, X2)) -> a__U302(mark(X1), X2)
20.08/5.91	   mark(U303(X1, X2)) -> a__U303(mark(X1), X2)
20.08/5.91	   mark(U304(X1, X2)) -> a__U304(mark(X1), X2)
20.08/5.91	   mark(U31(X1, X2, X3)) -> a__U31(mark(X1), X2, X3)
20.08/5.91	   mark(U32(X1, X2, X3)) -> a__U32(mark(X1), X2, X3)
20.08/5.91	   mark(U311(X1, X2)) -> a__U311(mark(X1), X2)
20.08/5.91	   mark(U312(X1, X2)) -> a__U312(mark(X1), X2)
20.08/5.91	   mark(U33(X1, X2, X3)) -> a__U33(mark(X1), X2, X3)
20.08/5.91	   mark(U321(X1, X2, X3, X4)) -> a__U321(mark(X1), X2, X3, X4)
20.08/5.91	   mark(U322(X1, X2, X3, X4)) -> a__U322(mark(X1), X2, X3, X4)
20.08/5.91	   mark(U323(X1, X2, X3, X4)) -> a__U323(mark(X1), X2, X3, X4)
20.08/5.91	   mark(U324(X1, X2, X3, X4)) -> a__U324(mark(X1), X2, X3, X4)
20.08/5.91	   mark(U325(X1, X2, X3, X4)) -> a__U325(mark(X1), X2, X3, X4)
20.08/5.91	   mark(U326(X1, X2, X3, X4)) -> a__U326(mark(X1), X2, X3, X4)
20.08/5.91	   mark(U327(X1, X2)) -> a__U327(mark(X1), X2)
20.08/5.91	   mark(U34(X1, X2)) -> a__U34(mark(X1), X2)
20.08/5.91	   mark(U331(X1, X2, X3)) -> a__U331(mark(X1), X2, X3)
20.08/5.91	   mark(U332(X1, X2)) -> a__U332(mark(X1), X2)
20.08/5.91	   mark(U333(X1, X2)) -> a__U333(mark(X1), X2)
20.08/5.91	   mark(U334(X1, X2)) -> a__U334(mark(X1), X2)
20.08/5.91	   mark(U341(X1, X2, X3)) -> a__U341(mark(X1), X2, X3)
20.08/5.91	   mark(U342(X1, X2, X3)) -> a__U342(mark(X1), X2, X3)
20.08/5.91	   mark(U343(X1, X2, X3)) -> a__U343(mark(X1), X2, X3)
20.08/5.91	   mark(U344(X1, X2, X3)) -> a__U344(mark(X1), X2, X3)
20.08/5.91	   mark(fst(X)) -> a__fst(mark(X))
20.08/5.91	   mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
20.08/5.91	   mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3)
20.08/5.91	   mark(U43(X1, X2, X3)) -> a__U43(mark(X1), X2, X3)
20.08/5.91	   mark(U44(X1, X2, X3)) -> a__U44(mark(X1), X2, X3)
20.08/5.91	   mark(U45(X1, X2)) -> a__U45(mark(X1), X2)
20.08/5.91	   mark(U46(X)) -> a__U46(mark(X))
20.08/5.91	   mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3)
20.08/5.91	   mark(U52(X1, X2, X3)) -> a__U52(mark(X1), X2, X3)
20.08/5.91	   mark(U53(X1, X2, X3)) -> a__U53(mark(X1), X2, X3)
20.08/5.91	   mark(U54(X1, X2, X3)) -> a__U54(mark(X1), X2, X3)
20.08/5.91	   mark(U55(X1, X2)) -> a__U55(mark(X1), X2)
20.08/5.91	   mark(U56(X)) -> a__U56(mark(X))
20.08/5.91	   mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
20.08/5.91	   mark(U62(X1, X2)) -> a__U62(mark(X1), X2)
20.08/5.91	   mark(isPLNatKind(X)) -> a__isPLNatKind(X)
20.08/5.91	   mark(U63(X)) -> a__U63(mark(X))
20.08/5.91	   mark(isPLNat(X)) -> a__isPLNat(X)
20.08/5.91	   mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
20.08/5.91	   mark(U72(X1, X2)) -> a__U72(mark(X1), X2)
20.08/5.91	   mark(U73(X)) -> a__U73(mark(X))
20.08/5.91	   mark(U81(X1, X2)) -> a__U81(mark(X1), X2)
20.08/5.91	   mark(U82(X1, X2)) -> a__U82(mark(X1), X2)
20.08/5.91	   mark(U83(X)) -> a__U83(mark(X))
20.08/5.91	   mark(U91(X1, X2)) -> a__U91(mark(X1), X2)
20.08/5.91	   mark(U92(X1, X2)) -> a__U92(mark(X1), X2)
20.08/5.91	   mark(U93(X)) -> a__U93(mark(X))
20.08/5.91	   mark(tail(X)) -> a__tail(mark(X))
20.08/5.91	   mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
20.08/5.91	   mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
20.08/5.91	   mark(tt) -> tt
20.08/5.91	   mark(cons(X1, X2)) -> cons(mark(X1), X2)
20.08/5.91	   mark(s(X)) -> s(mark(X))
20.08/5.91	   mark(pair(X1, X2)) -> pair(mark(X1), mark(X2))
20.08/5.91	   mark(nil) -> nil
20.08/5.91	   mark(0) -> 0
20.08/5.91	   a__U101(X1, X2, X3) -> U101(X1, X2, X3)
20.08/5.91	   a__U102(X1, X2, X3) -> U102(X1, X2, X3)
20.08/5.91	   a__isNaturalKind(X) -> isNaturalKind(X)
20.08/5.91	   a__U103(X1, X2, X3) -> U103(X1, X2, X3)
20.08/5.91	   a__isLNatKind(X) -> isLNatKind(X)
20.08/5.91	   a__U104(X1, X2, X3) -> U104(X1, X2, X3)
20.08/5.91	   a__U105(X1, X2) -> U105(X1, X2)
20.08/5.91	   a__isNatural(X) -> isNatural(X)
20.08/5.91	   a__U106(X) -> U106(X)
20.08/5.91	   a__isLNat(X) -> isLNat(X)
20.08/5.91	   a__U11(X1, X2, X3) -> U11(X1, X2, X3)
20.08/5.91	   a__U12(X1, X2, X3) -> U12(X1, X2, X3)
20.08/5.91	   a__U111(X1, X2) -> U111(X1, X2)
20.08/5.91	   a__U112(X) -> U112(X)
20.08/5.91	   a__U13(X1, X2, X3) -> U13(X1, X2, X3)
20.08/5.91	   a__U121(X1, X2) -> U121(X1, X2)
20.08/5.91	   a__U122(X) -> U122(X)
20.08/5.91	   a__U14(X1, X2, X3) -> U14(X1, X2, X3)
20.08/5.91	   a__U131(X) -> U131(X)
20.08/5.91	   a__snd(X) -> snd(X)
20.08/5.91	   a__splitAt(X1, X2) -> splitAt(X1, X2)
20.08/5.91	   a__U141(X) -> U141(X)
20.08/5.91	   a__U151(X) -> U151(X)
20.08/5.91	   a__U161(X) -> U161(X)
20.08/5.91	   a__U171(X1, X2) -> U171(X1, X2)
20.08/5.91	   a__U172(X) -> U172(X)
20.08/5.91	   a__U181(X1, X2) -> U181(X1, X2)
20.08/5.91	   a__U182(X1, X2) -> U182(X1, X2)
20.08/5.91	   a__U183(X) -> U183(X)
20.08/5.91	   a__U191(X1, X2) -> U191(X1, X2)
20.08/5.91	   a__U192(X1, X2) -> U192(X1, X2)
20.08/5.91	   a__U193(X) -> U193(X)
20.08/5.91	   a__U201(X1, X2, X3) -> U201(X1, X2, X3)
20.08/5.91	   a__U202(X1, X2, X3) -> U202(X1, X2, X3)
20.08/5.91	   a__U203(X1, X2, X3) -> U203(X1, X2, X3)
20.08/5.91	   a__U204(X1, X2, X3) -> U204(X1, X2, X3)
20.08/5.91	   a__U205(X1, X2) -> U205(X1, X2)
20.08/5.91	   a__U206(X) -> U206(X)
20.08/5.91	   a__U21(X1, X2, X3) -> U21(X1, X2, X3)
20.08/5.91	   a__U22(X1, X2, X3) -> U22(X1, X2, X3)
20.08/5.91	   a__U211(X) -> U211(X)
20.08/5.91	   a__U23(X1, X2, X3) -> U23(X1, X2, X3)
20.08/5.91	   a__U221(X) -> U221(X)
20.08/5.91	   a__U24(X1, X2) -> U24(X1, X2)
20.08/5.91	   a__U231(X1, X2) -> U231(X1, X2)
20.08/5.91	   a__U232(X) -> U232(X)
20.08/5.91	   a__U241(X1, X2, X3) -> U241(X1, X2, X3)
20.08/5.91	   a__U242(X1, X2, X3) -> U242(X1, X2, X3)
20.08/5.91	   a__U243(X1, X2, X3) -> U243(X1, X2, X3)
20.08/5.91	   a__U244(X1, X2, X3) -> U244(X1, X2, X3)
20.08/5.91	   a__U245(X1, X2) -> U245(X1, X2)
20.08/5.91	   a__U246(X) -> U246(X)
20.08/5.91	   a__U251(X1, X2, X3) -> U251(X1, X2, X3)
20.08/5.91	   a__U252(X1, X2, X3) -> U252(X1, X2, X3)
20.08/5.91	   a__U253(X1, X2, X3) -> U253(X1, X2, X3)
20.08/5.91	   a__U254(X1, X2, X3) -> U254(X1, X2, X3)
20.08/5.91	   a__U255(X1, X2) -> U255(X1, X2)
20.08/5.91	   a__U256(X) -> U256(X)
20.08/5.91	   a__U261(X1, X2) -> U261(X1, X2)
20.08/5.91	   a__U262(X) -> U262(X)
20.08/5.91	   a__U271(X1, X2) -> U271(X1, X2)
20.08/5.91	   a__U272(X) -> U272(X)
20.08/5.91	   a__U281(X1, X2) -> U281(X1, X2)
20.08/5.91	   a__U282(X1, X2) -> U282(X1, X2)
20.08/5.91	   a__natsFrom(X) -> natsFrom(X)
20.08/5.91	   a__U291(X1, X2, X3) -> U291(X1, X2, X3)
20.08/5.91	   a__U292(X1, X2, X3) -> U292(X1, X2, X3)
20.08/5.91	   a__U293(X1, X2, X3) -> U293(X1, X2, X3)
20.08/5.91	   a__U294(X1, X2, X3) -> U294(X1, X2, X3)
20.08/5.91	   a__head(X) -> head(X)
20.08/5.91	   a__afterNth(X1, X2) -> afterNth(X1, X2)
20.08/5.91	   a__U301(X1, X2, X3) -> U301(X1, X2, X3)
20.08/5.91	   a__U302(X1, X2) -> U302(X1, X2)
20.08/5.91	   a__U303(X1, X2) -> U303(X1, X2)
20.08/5.91	   a__U304(X1, X2) -> U304(X1, X2)
20.08/5.91	   a__U31(X1, X2, X3) -> U31(X1, X2, X3)
20.08/5.91	   a__U32(X1, X2, X3) -> U32(X1, X2, X3)
20.08/5.91	   a__U311(X1, X2) -> U311(X1, X2)
20.08/5.91	   a__U312(X1, X2) -> U312(X1, X2)
20.08/5.91	   a__U33(X1, X2, X3) -> U33(X1, X2, X3)
20.08/5.91	   a__U321(X1, X2, X3, X4) -> U321(X1, X2, X3, X4)
20.08/5.91	   a__U322(X1, X2, X3, X4) -> U322(X1, X2, X3, X4)
20.08/5.91	   a__U323(X1, X2, X3, X4) -> U323(X1, X2, X3, X4)
20.08/5.91	   a__U324(X1, X2, X3, X4) -> U324(X1, X2, X3, X4)
20.08/5.91	   a__U325(X1, X2, X3, X4) -> U325(X1, X2, X3, X4)
20.08/5.91	   a__U326(X1, X2, X3, X4) -> U326(X1, X2, X3, X4)
20.08/5.91	   a__U327(X1, X2) -> U327(X1, X2)
20.08/5.91	   a__U34(X1, X2) -> U34(X1, X2)
20.08/5.91	   a__U331(X1, X2, X3) -> U331(X1, X2, X3)
20.08/5.91	   a__U332(X1, X2) -> U332(X1, X2)
20.08/5.91	   a__U333(X1, X2) -> U333(X1, X2)
20.08/5.91	   a__U334(X1, X2) -> U334(X1, X2)
20.08/5.91	   a__U341(X1, X2, X3) -> U341(X1, X2, X3)
20.08/5.91	   a__U342(X1, X2, X3) -> U342(X1, X2, X3)
20.08/5.91	   a__U343(X1, X2, X3) -> U343(X1, X2, X3)
20.08/5.91	   a__U344(X1, X2, X3) -> U344(X1, X2, X3)
20.08/5.91	   a__fst(X) -> fst(X)
20.08/5.91	   a__U41(X1, X2, X3) -> U41(X1, X2, X3)
20.08/5.91	   a__U42(X1, X2, X3) -> U42(X1, X2, X3)
20.08/5.91	   a__U43(X1, X2, X3) -> U43(X1, X2, X3)
20.08/5.91	   a__U44(X1, X2, X3) -> U44(X1, X2, X3)
20.08/5.91	   a__U45(X1, X2) -> U45(X1, X2)
20.08/5.91	   a__U46(X) -> U46(X)
20.08/5.91	   a__U51(X1, X2, X3) -> U51(X1, X2, X3)
20.08/5.91	   a__U52(X1, X2, X3) -> U52(X1, X2, X3)
20.08/5.91	   a__U53(X1, X2, X3) -> U53(X1, X2, X3)
20.08/5.91	   a__U54(X1, X2, X3) -> U54(X1, X2, X3)
20.08/5.91	   a__U55(X1, X2) -> U55(X1, X2)
20.08/5.91	   a__U56(X) -> U56(X)
20.08/5.91	   a__U61(X1, X2) -> U61(X1, X2)
20.08/5.91	   a__U62(X1, X2) -> U62(X1, X2)
20.08/5.91	   a__isPLNatKind(X) -> isPLNatKind(X)
20.08/5.91	   a__U63(X) -> U63(X)
20.08/5.91	   a__isPLNat(X) -> isPLNat(X)
20.08/5.91	   a__U71(X1, X2) -> U71(X1, X2)
20.08/5.91	   a__U72(X1, X2) -> U72(X1, X2)
20.08/5.91	   a__U73(X) -> U73(X)
20.08/5.91	   a__U81(X1, X2) -> U81(X1, X2)
20.08/5.91	   a__U82(X1, X2) -> U82(X1, X2)
20.08/5.91	   a__U83(X) -> U83(X)
20.08/5.91	   a__U91(X1, X2) -> U91(X1, X2)
20.08/5.91	   a__U92(X1, X2) -> U92(X1, X2)
20.08/5.91	   a__U93(X) -> U93(X)
20.08/5.91	   a__tail(X) -> tail(X)
20.08/5.91	   a__take(X1, X2) -> take(X1, X2)
20.08/5.91	   a__sel(X1, X2) -> sel(X1, X2)
20.08/5.91	
20.08/5.91	S is empty.
20.08/5.91	Rewrite Strategy: FULL
20.08/5.91	----------------------------------------
20.08/5.91	
20.08/5.91	(3) DecreasingLoopProof (LOWER BOUND(ID))
20.08/5.91	The following loop(s) give(s) rise to the lower bound Omega(n^1):
20.08/5.91	
20.08/5.91	The rewrite sequence
20.08/5.91	
20.08/5.91	mark(U55(X1, X2)) ->^+ a__U55(mark(X1), X2)
20.08/5.91	
20.08/5.91	gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
20.08/5.91	
20.08/5.91	The pumping substitution is [X1 / U55(X1, X2)].
20.08/5.91	
20.08/5.91	The result substitution is [ ].
20.08/5.91	
20.08/5.91	
20.08/5.91	
20.08/5.91	
20.08/5.91	----------------------------------------
20.08/5.91	
20.08/5.91	(4)
20.08/5.91	Complex Obligation (BEST)
20.08/5.91	
20.08/5.91	----------------------------------------
20.08/5.91	
20.08/5.91	(5)
20.08/5.91	Obligation:
20.08/5.91	Proved the lower bound n^1 for the following obligation:
20.08/5.91	
20.08/5.91	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
20.08/5.91	
20.08/5.91	
20.08/5.91	The TRS R consists of the following rules:
20.08/5.91	
20.08/5.91	   a__U101(tt, V1, V2) -> a__U102(a__isNaturalKind(V1), V1, V2)
20.08/5.91	   a__U102(tt, V1, V2) -> a__U103(a__isLNatKind(V2), V1, V2)
20.08/5.91	   a__U103(tt, V1, V2) -> a__U104(a__isLNatKind(V2), V1, V2)
20.08/5.91	   a__U104(tt, V1, V2) -> a__U105(a__isNatural(V1), V2)
20.08/5.91	   a__U105(tt, V2) -> a__U106(a__isLNat(V2))
20.08/5.91	   a__U106(tt) -> tt
20.08/5.91	   a__U11(tt, N, XS) -> a__U12(a__isNaturalKind(N), N, XS)
20.08/5.91	   a__U111(tt, V2) -> a__U112(a__isLNatKind(V2))
20.08/5.91	   a__U112(tt) -> tt
20.08/5.91	   a__U12(tt, N, XS) -> a__U13(a__isLNat(XS), N, XS)
20.08/5.91	   a__U121(tt, V2) -> a__U122(a__isLNatKind(V2))
20.08/5.91	   a__U122(tt) -> tt
20.08/5.91	   a__U13(tt, N, XS) -> a__U14(a__isLNatKind(XS), N, XS)
20.08/5.91	   a__U131(tt) -> tt
20.08/5.91	   a__U14(tt, N, XS) -> a__snd(a__splitAt(mark(N), mark(XS)))
20.08/5.91	   a__U141(tt) -> tt
20.08/5.91	   a__U151(tt) -> tt
20.08/5.91	   a__U161(tt) -> tt
20.08/5.91	   a__U171(tt, V2) -> a__U172(a__isLNatKind(V2))
20.08/5.91	   a__U172(tt) -> tt
20.08/5.91	   a__U181(tt, V1) -> a__U182(a__isLNatKind(V1), V1)
20.08/5.91	   a__U182(tt, V1) -> a__U183(a__isLNat(V1))
20.08/5.91	   a__U183(tt) -> tt
20.08/5.91	   a__U191(tt, V1) -> a__U192(a__isNaturalKind(V1), V1)
20.08/5.91	   a__U192(tt, V1) -> a__U193(a__isNatural(V1))
20.08/5.91	   a__U193(tt) -> tt
20.08/5.91	   a__U201(tt, V1, V2) -> a__U202(a__isNaturalKind(V1), V1, V2)
20.08/5.91	   a__U202(tt, V1, V2) -> a__U203(a__isLNatKind(V2), V1, V2)
20.08/5.91	   a__U203(tt, V1, V2) -> a__U204(a__isLNatKind(V2), V1, V2)
20.08/5.91	   a__U204(tt, V1, V2) -> a__U205(a__isNatural(V1), V2)
20.08/5.91	   a__U205(tt, V2) -> a__U206(a__isLNat(V2))
20.08/5.91	   a__U206(tt) -> tt
20.08/5.91	   a__U21(tt, X, Y) -> a__U22(a__isLNatKind(X), X, Y)
20.08/5.91	   a__U211(tt) -> tt
20.08/5.91	   a__U22(tt, X, Y) -> a__U23(a__isLNat(Y), X, Y)
20.08/5.91	   a__U221(tt) -> tt
20.08/5.91	   a__U23(tt, X, Y) -> a__U24(a__isLNatKind(Y), X)
20.08/5.91	   a__U231(tt, V2) -> a__U232(a__isLNatKind(V2))
20.08/5.91	   a__U232(tt) -> tt
20.08/5.91	   a__U24(tt, X) -> mark(X)
20.08/5.91	   a__U241(tt, V1, V2) -> a__U242(a__isLNatKind(V1), V1, V2)
20.08/5.91	   a__U242(tt, V1, V2) -> a__U243(a__isLNatKind(V2), V1, V2)
20.08/5.91	   a__U243(tt, V1, V2) -> a__U244(a__isLNatKind(V2), V1, V2)
20.08/5.91	   a__U244(tt, V1, V2) -> a__U245(a__isLNat(V1), V2)
20.08/5.91	   a__U245(tt, V2) -> a__U246(a__isLNat(V2))
20.08/5.91	   a__U246(tt) -> tt
20.08/5.91	   a__U251(tt, V1, V2) -> a__U252(a__isNaturalKind(V1), V1, V2)
20.08/5.91	   a__U252(tt, V1, V2) -> a__U253(a__isLNatKind(V2), V1, V2)
20.08/5.91	   a__U253(tt, V1, V2) -> a__U254(a__isLNatKind(V2), V1, V2)
20.08/5.91	   a__U254(tt, V1, V2) -> a__U255(a__isNatural(V1), V2)
20.08/5.91	   a__U255(tt, V2) -> a__U256(a__isLNat(V2))
20.08/5.91	   a__U256(tt) -> tt
20.08/5.91	   a__U261(tt, V2) -> a__U262(a__isLNatKind(V2))
20.08/5.91	   a__U262(tt) -> tt
20.08/5.91	   a__U271(tt, V2) -> a__U272(a__isLNatKind(V2))
20.08/5.91	   a__U272(tt) -> tt
20.08/5.91	   a__U281(tt, N) -> a__U282(a__isNaturalKind(N), N)
20.08/5.91	   a__U282(tt, N) -> cons(mark(N), natsFrom(s(N)))
20.08/5.91	   a__U291(tt, N, XS) -> a__U292(a__isNaturalKind(N), N, XS)
20.08/5.91	   a__U292(tt, N, XS) -> a__U293(a__isLNat(XS), N, XS)
20.08/5.91	   a__U293(tt, N, XS) -> a__U294(a__isLNatKind(XS), N, XS)
20.08/5.91	   a__U294(tt, N, XS) -> a__head(a__afterNth(mark(N), mark(XS)))
20.08/5.93	   a__U301(tt, X, Y) -> a__U302(a__isLNatKind(X), Y)
20.08/5.93	   a__U302(tt, Y) -> a__U303(a__isLNat(Y), Y)
20.08/5.93	   a__U303(tt, Y) -> a__U304(a__isLNatKind(Y), Y)
20.08/5.93	   a__U304(tt, Y) -> mark(Y)
20.08/5.93	   a__U31(tt, N, XS) -> a__U32(a__isNaturalKind(N), N, XS)
20.08/5.93	   a__U311(tt, XS) -> a__U312(a__isLNatKind(XS), XS)
20.08/5.93	   a__U312(tt, XS) -> pair(nil, mark(XS))
20.08/5.93	   a__U32(tt, N, XS) -> a__U33(a__isLNat(XS), N, XS)
20.08/5.93	   a__U321(tt, N, X, XS) -> a__U322(a__isNaturalKind(N), N, X, XS)
20.08/5.93	   a__U322(tt, N, X, XS) -> a__U323(a__isNatural(X), N, X, XS)
20.08/5.93	   a__U323(tt, N, X, XS) -> a__U324(a__isNaturalKind(X), N, X, XS)
20.08/5.93	   a__U324(tt, N, X, XS) -> a__U325(a__isLNat(XS), N, X, XS)
20.08/5.93	   a__U325(tt, N, X, XS) -> a__U326(a__isLNatKind(XS), N, X, XS)
20.08/5.93	   a__U326(tt, N, X, XS) -> a__U327(a__splitAt(mark(N), mark(XS)), X)
20.08/5.93	   a__U327(pair(YS, ZS), X) -> pair(cons(mark(X), YS), mark(ZS))
20.08/5.93	   a__U33(tt, N, XS) -> a__U34(a__isLNatKind(XS), N)
20.08/5.93	   a__U331(tt, N, XS) -> a__U332(a__isNaturalKind(N), XS)
20.08/5.93	   a__U332(tt, XS) -> a__U333(a__isLNat(XS), XS)
20.08/5.93	   a__U333(tt, XS) -> a__U334(a__isLNatKind(XS), XS)
20.08/5.93	   a__U334(tt, XS) -> mark(XS)
20.08/5.93	   a__U34(tt, N) -> mark(N)
20.08/5.93	   a__U341(tt, N, XS) -> a__U342(a__isNaturalKind(N), N, XS)
20.08/5.93	   a__U342(tt, N, XS) -> a__U343(a__isLNat(XS), N, XS)
20.08/5.93	   a__U343(tt, N, XS) -> a__U344(a__isLNatKind(XS), N, XS)
20.08/5.93	   a__U344(tt, N, XS) -> a__fst(a__splitAt(mark(N), mark(XS)))
20.08/5.93	   a__U41(tt, V1, V2) -> a__U42(a__isNaturalKind(V1), V1, V2)
20.08/5.93	   a__U42(tt, V1, V2) -> a__U43(a__isLNatKind(V2), V1, V2)
20.08/5.93	   a__U43(tt, V1, V2) -> a__U44(a__isLNatKind(V2), V1, V2)
20.08/5.93	   a__U44(tt, V1, V2) -> a__U45(a__isNatural(V1), V2)
20.08/5.93	   a__U45(tt, V2) -> a__U46(a__isLNat(V2))
20.08/5.93	   a__U46(tt) -> tt
20.08/5.93	   a__U51(tt, V1, V2) -> a__U52(a__isNaturalKind(V1), V1, V2)
20.08/5.93	   a__U52(tt, V1, V2) -> a__U53(a__isLNatKind(V2), V1, V2)
20.08/5.93	   a__U53(tt, V1, V2) -> a__U54(a__isLNatKind(V2), V1, V2)
20.08/5.93	   a__U54(tt, V1, V2) -> a__U55(a__isNatural(V1), V2)
20.08/5.93	   a__U55(tt, V2) -> a__U56(a__isLNat(V2))
20.08/5.93	   a__U56(tt) -> tt
20.08/5.93	   a__U61(tt, V1) -> a__U62(a__isPLNatKind(V1), V1)
20.08/5.93	   a__U62(tt, V1) -> a__U63(a__isPLNat(V1))
20.08/5.93	   a__U63(tt) -> tt
20.08/5.93	   a__U71(tt, V1) -> a__U72(a__isNaturalKind(V1), V1)
20.08/5.93	   a__U72(tt, V1) -> a__U73(a__isNatural(V1))
20.08/5.93	   a__U73(tt) -> tt
20.08/5.93	   a__U81(tt, V1) -> a__U82(a__isPLNatKind(V1), V1)
20.08/5.93	   a__U82(tt, V1) -> a__U83(a__isPLNat(V1))
20.08/5.93	   a__U83(tt) -> tt
20.08/5.93	   a__U91(tt, V1) -> a__U92(a__isLNatKind(V1), V1)
20.08/5.93	   a__U92(tt, V1) -> a__U93(a__isLNat(V1))
20.08/5.93	   a__U93(tt) -> tt
20.08/5.93	   a__afterNth(N, XS) -> a__U11(a__isNatural(N), N, XS)
20.08/5.93	   a__fst(pair(X, Y)) -> a__U21(a__isLNat(X), X, Y)
20.08/5.93	   a__head(cons(N, XS)) -> a__U31(a__isNatural(N), N, XS)
20.08/5.93	   a__isLNat(nil) -> tt
20.08/5.93	   a__isLNat(afterNth(V1, V2)) -> a__U41(a__isNaturalKind(V1), V1, V2)
20.08/5.93	   a__isLNat(cons(V1, V2)) -> a__U51(a__isNaturalKind(V1), V1, V2)
20.08/5.93	   a__isLNat(fst(V1)) -> a__U61(a__isPLNatKind(V1), V1)
20.08/5.93	   a__isLNat(natsFrom(V1)) -> a__U71(a__isNaturalKind(V1), V1)
20.08/5.93	   a__isLNat(snd(V1)) -> a__U81(a__isPLNatKind(V1), V1)
20.08/5.93	   a__isLNat(tail(V1)) -> a__U91(a__isLNatKind(V1), V1)
20.08/5.93	   a__isLNat(take(V1, V2)) -> a__U101(a__isNaturalKind(V1), V1, V2)
20.08/5.93	   a__isLNatKind(nil) -> tt
20.08/5.93	   a__isLNatKind(afterNth(V1, V2)) -> a__U111(a__isNaturalKind(V1), V2)
20.08/5.93	   a__isLNatKind(cons(V1, V2)) -> a__U121(a__isNaturalKind(V1), V2)
20.08/5.93	   a__isLNatKind(fst(V1)) -> a__U131(a__isPLNatKind(V1))
20.08/5.93	   a__isLNatKind(natsFrom(V1)) -> a__U141(a__isNaturalKind(V1))
20.08/5.93	   a__isLNatKind(snd(V1)) -> a__U151(a__isPLNatKind(V1))
20.08/5.93	   a__isLNatKind(tail(V1)) -> a__U161(a__isLNatKind(V1))
20.08/5.93	   a__isLNatKind(take(V1, V2)) -> a__U171(a__isNaturalKind(V1), V2)
20.08/5.93	   a__isNatural(0) -> tt
20.08/5.93	   a__isNatural(head(V1)) -> a__U181(a__isLNatKind(V1), V1)
20.08/5.93	   a__isNatural(s(V1)) -> a__U191(a__isNaturalKind(V1), V1)
20.08/5.93	   a__isNatural(sel(V1, V2)) -> a__U201(a__isNaturalKind(V1), V1, V2)
20.08/5.93	   a__isNaturalKind(0) -> tt
20.08/5.93	   a__isNaturalKind(head(V1)) -> a__U211(a__isLNatKind(V1))
20.08/5.93	   a__isNaturalKind(s(V1)) -> a__U221(a__isNaturalKind(V1))
20.08/5.93	   a__isNaturalKind(sel(V1, V2)) -> a__U231(a__isNaturalKind(V1), V2)
20.08/5.93	   a__isPLNat(pair(V1, V2)) -> a__U241(a__isLNatKind(V1), V1, V2)
20.08/5.93	   a__isPLNat(splitAt(V1, V2)) -> a__U251(a__isNaturalKind(V1), V1, V2)
20.08/5.93	   a__isPLNatKind(pair(V1, V2)) -> a__U261(a__isLNatKind(V1), V2)
20.08/5.93	   a__isPLNatKind(splitAt(V1, V2)) -> a__U271(a__isNaturalKind(V1), V2)
20.08/5.93	   a__natsFrom(N) -> a__U281(a__isNatural(N), N)
20.08/5.93	   a__sel(N, XS) -> a__U291(a__isNatural(N), N, XS)
20.08/5.93	   a__snd(pair(X, Y)) -> a__U301(a__isLNat(X), X, Y)
20.08/5.93	   a__splitAt(0, XS) -> a__U311(a__isLNat(XS), XS)
20.08/5.93	   a__splitAt(s(N), cons(X, XS)) -> a__U321(a__isNatural(N), N, X, XS)
20.08/5.93	   a__tail(cons(N, XS)) -> a__U331(a__isNatural(N), N, XS)
20.08/5.93	   a__take(N, XS) -> a__U341(a__isNatural(N), N, XS)
20.08/5.93	   mark(U101(X1, X2, X3)) -> a__U101(mark(X1), X2, X3)
20.08/5.93	   mark(U102(X1, X2, X3)) -> a__U102(mark(X1), X2, X3)
20.08/5.93	   mark(isNaturalKind(X)) -> a__isNaturalKind(X)
20.08/5.93	   mark(U103(X1, X2, X3)) -> a__U103(mark(X1), X2, X3)
20.08/5.93	   mark(isLNatKind(X)) -> a__isLNatKind(X)
20.08/5.93	   mark(U104(X1, X2, X3)) -> a__U104(mark(X1), X2, X3)
20.08/5.93	   mark(U105(X1, X2)) -> a__U105(mark(X1), X2)
20.08/5.93	   mark(isNatural(X)) -> a__isNatural(X)
20.08/5.93	   mark(U106(X)) -> a__U106(mark(X))
20.08/5.93	   mark(isLNat(X)) -> a__isLNat(X)
20.08/5.93	   mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
20.08/5.93	   mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
20.08/5.93	   mark(U111(X1, X2)) -> a__U111(mark(X1), X2)
20.08/5.93	   mark(U112(X)) -> a__U112(mark(X))
20.08/5.93	   mark(U13(X1, X2, X3)) -> a__U13(mark(X1), X2, X3)
20.08/5.93	   mark(U121(X1, X2)) -> a__U121(mark(X1), X2)
20.08/5.93	   mark(U122(X)) -> a__U122(mark(X))
20.08/5.93	   mark(U14(X1, X2, X3)) -> a__U14(mark(X1), X2, X3)
20.08/5.93	   mark(U131(X)) -> a__U131(mark(X))
20.08/5.93	   mark(snd(X)) -> a__snd(mark(X))
20.08/5.93	   mark(splitAt(X1, X2)) -> a__splitAt(mark(X1), mark(X2))
20.08/5.93	   mark(U141(X)) -> a__U141(mark(X))
20.08/5.93	   mark(U151(X)) -> a__U151(mark(X))
20.08/5.93	   mark(U161(X)) -> a__U161(mark(X))
20.08/5.93	   mark(U171(X1, X2)) -> a__U171(mark(X1), X2)
20.08/5.93	   mark(U172(X)) -> a__U172(mark(X))
20.08/5.93	   mark(U181(X1, X2)) -> a__U181(mark(X1), X2)
20.08/5.93	   mark(U182(X1, X2)) -> a__U182(mark(X1), X2)
20.08/5.93	   mark(U183(X)) -> a__U183(mark(X))
20.08/5.93	   mark(U191(X1, X2)) -> a__U191(mark(X1), X2)
20.08/5.93	   mark(U192(X1, X2)) -> a__U192(mark(X1), X2)
20.08/5.93	   mark(U193(X)) -> a__U193(mark(X))
20.08/5.93	   mark(U201(X1, X2, X3)) -> a__U201(mark(X1), X2, X3)
20.08/5.93	   mark(U202(X1, X2, X3)) -> a__U202(mark(X1), X2, X3)
20.08/5.93	   mark(U203(X1, X2, X3)) -> a__U203(mark(X1), X2, X3)
20.08/5.93	   mark(U204(X1, X2, X3)) -> a__U204(mark(X1), X2, X3)
20.08/5.93	   mark(U205(X1, X2)) -> a__U205(mark(X1), X2)
20.08/5.93	   mark(U206(X)) -> a__U206(mark(X))
20.08/5.93	   mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3)
20.08/5.93	   mark(U22(X1, X2, X3)) -> a__U22(mark(X1), X2, X3)
20.08/5.93	   mark(U211(X)) -> a__U211(mark(X))
20.08/5.93	   mark(U23(X1, X2, X3)) -> a__U23(mark(X1), X2, X3)
20.08/5.93	   mark(U221(X)) -> a__U221(mark(X))
20.08/5.93	   mark(U24(X1, X2)) -> a__U24(mark(X1), X2)
20.08/5.93	   mark(U231(X1, X2)) -> a__U231(mark(X1), X2)
20.08/5.93	   mark(U232(X)) -> a__U232(mark(X))
20.08/5.93	   mark(U241(X1, X2, X3)) -> a__U241(mark(X1), X2, X3)
20.08/5.93	   mark(U242(X1, X2, X3)) -> a__U242(mark(X1), X2, X3)
20.08/5.93	   mark(U243(X1, X2, X3)) -> a__U243(mark(X1), X2, X3)
20.08/5.93	   mark(U244(X1, X2, X3)) -> a__U244(mark(X1), X2, X3)
20.08/5.93	   mark(U245(X1, X2)) -> a__U245(mark(X1), X2)
20.08/5.93	   mark(U246(X)) -> a__U246(mark(X))
20.08/5.93	   mark(U251(X1, X2, X3)) -> a__U251(mark(X1), X2, X3)
20.08/5.93	   mark(U252(X1, X2, X3)) -> a__U252(mark(X1), X2, X3)
20.08/5.93	   mark(U253(X1, X2, X3)) -> a__U253(mark(X1), X2, X3)
20.08/5.93	   mark(U254(X1, X2, X3)) -> a__U254(mark(X1), X2, X3)
20.08/5.93	   mark(U255(X1, X2)) -> a__U255(mark(X1), X2)
20.08/5.93	   mark(U256(X)) -> a__U256(mark(X))
20.08/5.93	   mark(U261(X1, X2)) -> a__U261(mark(X1), X2)
20.08/5.93	   mark(U262(X)) -> a__U262(mark(X))
20.08/5.93	   mark(U271(X1, X2)) -> a__U271(mark(X1), X2)
20.08/5.93	   mark(U272(X)) -> a__U272(mark(X))
20.08/5.93	   mark(U281(X1, X2)) -> a__U281(mark(X1), X2)
20.08/5.93	   mark(U282(X1, X2)) -> a__U282(mark(X1), X2)
20.08/5.93	   mark(natsFrom(X)) -> a__natsFrom(mark(X))
20.08/5.93	   mark(U291(X1, X2, X3)) -> a__U291(mark(X1), X2, X3)
20.08/5.93	   mark(U292(X1, X2, X3)) -> a__U292(mark(X1), X2, X3)
20.08/5.93	   mark(U293(X1, X2, X3)) -> a__U293(mark(X1), X2, X3)
20.08/5.93	   mark(U294(X1, X2, X3)) -> a__U294(mark(X1), X2, X3)
20.08/5.93	   mark(head(X)) -> a__head(mark(X))
20.08/5.93	   mark(afterNth(X1, X2)) -> a__afterNth(mark(X1), mark(X2))
20.08/5.93	   mark(U301(X1, X2, X3)) -> a__U301(mark(X1), X2, X3)
20.08/5.93	   mark(U302(X1, X2)) -> a__U302(mark(X1), X2)
20.08/5.93	   mark(U303(X1, X2)) -> a__U303(mark(X1), X2)
20.08/5.93	   mark(U304(X1, X2)) -> a__U304(mark(X1), X2)
20.08/5.93	   mark(U31(X1, X2, X3)) -> a__U31(mark(X1), X2, X3)
20.08/5.93	   mark(U32(X1, X2, X3)) -> a__U32(mark(X1), X2, X3)
20.08/5.93	   mark(U311(X1, X2)) -> a__U311(mark(X1), X2)
20.08/5.93	   mark(U312(X1, X2)) -> a__U312(mark(X1), X2)
20.08/5.93	   mark(U33(X1, X2, X3)) -> a__U33(mark(X1), X2, X3)
20.08/5.93	   mark(U321(X1, X2, X3, X4)) -> a__U321(mark(X1), X2, X3, X4)
20.08/5.93	   mark(U322(X1, X2, X3, X4)) -> a__U322(mark(X1), X2, X3, X4)
20.08/5.93	   mark(U323(X1, X2, X3, X4)) -> a__U323(mark(X1), X2, X3, X4)
20.08/5.93	   mark(U324(X1, X2, X3, X4)) -> a__U324(mark(X1), X2, X3, X4)
20.08/5.93	   mark(U325(X1, X2, X3, X4)) -> a__U325(mark(X1), X2, X3, X4)
20.08/5.93	   mark(U326(X1, X2, X3, X4)) -> a__U326(mark(X1), X2, X3, X4)
20.08/5.93	   mark(U327(X1, X2)) -> a__U327(mark(X1), X2)
20.08/5.93	   mark(U34(X1, X2)) -> a__U34(mark(X1), X2)
20.08/5.93	   mark(U331(X1, X2, X3)) -> a__U331(mark(X1), X2, X3)
20.08/5.93	   mark(U332(X1, X2)) -> a__U332(mark(X1), X2)
20.08/5.93	   mark(U333(X1, X2)) -> a__U333(mark(X1), X2)
20.08/5.93	   mark(U334(X1, X2)) -> a__U334(mark(X1), X2)
20.08/5.93	   mark(U341(X1, X2, X3)) -> a__U341(mark(X1), X2, X3)
20.08/5.93	   mark(U342(X1, X2, X3)) -> a__U342(mark(X1), X2, X3)
20.08/5.93	   mark(U343(X1, X2, X3)) -> a__U343(mark(X1), X2, X3)
20.08/5.93	   mark(U344(X1, X2, X3)) -> a__U344(mark(X1), X2, X3)
20.08/5.93	   mark(fst(X)) -> a__fst(mark(X))
20.08/5.93	   mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
20.08/5.93	   mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3)
20.08/5.93	   mark(U43(X1, X2, X3)) -> a__U43(mark(X1), X2, X3)
20.08/5.93	   mark(U44(X1, X2, X3)) -> a__U44(mark(X1), X2, X3)
20.08/5.93	   mark(U45(X1, X2)) -> a__U45(mark(X1), X2)
20.08/5.93	   mark(U46(X)) -> a__U46(mark(X))
20.08/5.93	   mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3)
20.08/5.93	   mark(U52(X1, X2, X3)) -> a__U52(mark(X1), X2, X3)
20.08/5.93	   mark(U53(X1, X2, X3)) -> a__U53(mark(X1), X2, X3)
20.08/5.93	   mark(U54(X1, X2, X3)) -> a__U54(mark(X1), X2, X3)
20.08/5.93	   mark(U55(X1, X2)) -> a__U55(mark(X1), X2)
20.08/5.93	   mark(U56(X)) -> a__U56(mark(X))
20.08/5.93	   mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
20.08/5.93	   mark(U62(X1, X2)) -> a__U62(mark(X1), X2)
20.08/5.93	   mark(isPLNatKind(X)) -> a__isPLNatKind(X)
20.08/5.93	   mark(U63(X)) -> a__U63(mark(X))
20.08/5.93	   mark(isPLNat(X)) -> a__isPLNat(X)
20.08/5.93	   mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
20.08/5.93	   mark(U72(X1, X2)) -> a__U72(mark(X1), X2)
20.08/5.93	   mark(U73(X)) -> a__U73(mark(X))
20.08/5.93	   mark(U81(X1, X2)) -> a__U81(mark(X1), X2)
20.08/5.93	   mark(U82(X1, X2)) -> a__U82(mark(X1), X2)
20.08/5.93	   mark(U83(X)) -> a__U83(mark(X))
20.08/5.93	   mark(U91(X1, X2)) -> a__U91(mark(X1), X2)
20.08/5.93	   mark(U92(X1, X2)) -> a__U92(mark(X1), X2)
20.08/5.93	   mark(U93(X)) -> a__U93(mark(X))
20.08/5.93	   mark(tail(X)) -> a__tail(mark(X))
20.08/5.93	   mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
20.08/5.93	   mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
20.08/5.93	   mark(tt) -> tt
20.08/5.93	   mark(cons(X1, X2)) -> cons(mark(X1), X2)
20.08/5.93	   mark(s(X)) -> s(mark(X))
20.08/5.93	   mark(pair(X1, X2)) -> pair(mark(X1), mark(X2))
20.08/5.93	   mark(nil) -> nil
20.08/5.93	   mark(0) -> 0
20.08/5.93	   a__U101(X1, X2, X3) -> U101(X1, X2, X3)
20.08/5.93	   a__U102(X1, X2, X3) -> U102(X1, X2, X3)
20.08/5.93	   a__isNaturalKind(X) -> isNaturalKind(X)
20.08/5.93	   a__U103(X1, X2, X3) -> U103(X1, X2, X3)
20.08/5.93	   a__isLNatKind(X) -> isLNatKind(X)
20.08/5.93	   a__U104(X1, X2, X3) -> U104(X1, X2, X3)
20.08/5.93	   a__U105(X1, X2) -> U105(X1, X2)
20.08/5.93	   a__isNatural(X) -> isNatural(X)
20.08/5.93	   a__U106(X) -> U106(X)
20.08/5.93	   a__isLNat(X) -> isLNat(X)
20.08/5.93	   a__U11(X1, X2, X3) -> U11(X1, X2, X3)
20.08/5.93	   a__U12(X1, X2, X3) -> U12(X1, X2, X3)
20.08/5.93	   a__U111(X1, X2) -> U111(X1, X2)
20.08/5.93	   a__U112(X) -> U112(X)
20.08/5.93	   a__U13(X1, X2, X3) -> U13(X1, X2, X3)
20.08/5.93	   a__U121(X1, X2) -> U121(X1, X2)
20.08/5.93	   a__U122(X) -> U122(X)
20.08/5.93	   a__U14(X1, X2, X3) -> U14(X1, X2, X3)
20.08/5.93	   a__U131(X) -> U131(X)
20.08/5.93	   a__snd(X) -> snd(X)
20.08/5.93	   a__splitAt(X1, X2) -> splitAt(X1, X2)
20.08/5.93	   a__U141(X) -> U141(X)
20.08/5.93	   a__U151(X) -> U151(X)
20.08/5.93	   a__U161(X) -> U161(X)
20.08/5.93	   a__U171(X1, X2) -> U171(X1, X2)
20.08/5.93	   a__U172(X) -> U172(X)
20.08/5.93	   a__U181(X1, X2) -> U181(X1, X2)
20.08/5.93	   a__U182(X1, X2) -> U182(X1, X2)
20.08/5.93	   a__U183(X) -> U183(X)
20.08/5.93	   a__U191(X1, X2) -> U191(X1, X2)
20.08/5.93	   a__U192(X1, X2) -> U192(X1, X2)
20.08/5.93	   a__U193(X) -> U193(X)
20.08/5.93	   a__U201(X1, X2, X3) -> U201(X1, X2, X3)
20.08/5.93	   a__U202(X1, X2, X3) -> U202(X1, X2, X3)
20.08/5.93	   a__U203(X1, X2, X3) -> U203(X1, X2, X3)
20.08/5.93	   a__U204(X1, X2, X3) -> U204(X1, X2, X3)
20.08/5.93	   a__U205(X1, X2) -> U205(X1, X2)
20.08/5.93	   a__U206(X) -> U206(X)
20.08/5.93	   a__U21(X1, X2, X3) -> U21(X1, X2, X3)
20.08/5.93	   a__U22(X1, X2, X3) -> U22(X1, X2, X3)
20.08/5.93	   a__U211(X) -> U211(X)
20.08/5.93	   a__U23(X1, X2, X3) -> U23(X1, X2, X3)
20.08/5.93	   a__U221(X) -> U221(X)
20.08/5.93	   a__U24(X1, X2) -> U24(X1, X2)
20.08/5.93	   a__U231(X1, X2) -> U231(X1, X2)
20.08/5.93	   a__U232(X) -> U232(X)
20.08/5.93	   a__U241(X1, X2, X3) -> U241(X1, X2, X3)
20.08/5.93	   a__U242(X1, X2, X3) -> U242(X1, X2, X3)
20.08/5.93	   a__U243(X1, X2, X3) -> U243(X1, X2, X3)
20.08/5.93	   a__U244(X1, X2, X3) -> U244(X1, X2, X3)
20.08/5.93	   a__U245(X1, X2) -> U245(X1, X2)
20.08/5.93	   a__U246(X) -> U246(X)
20.08/5.93	   a__U251(X1, X2, X3) -> U251(X1, X2, X3)
20.08/5.93	   a__U252(X1, X2, X3) -> U252(X1, X2, X3)
20.08/5.93	   a__U253(X1, X2, X3) -> U253(X1, X2, X3)
20.08/5.93	   a__U254(X1, X2, X3) -> U254(X1, X2, X3)
20.08/5.93	   a__U255(X1, X2) -> U255(X1, X2)
20.08/5.93	   a__U256(X) -> U256(X)
20.08/5.93	   a__U261(X1, X2) -> U261(X1, X2)
20.08/5.93	   a__U262(X) -> U262(X)
20.08/5.93	   a__U271(X1, X2) -> U271(X1, X2)
20.08/5.93	   a__U272(X) -> U272(X)
20.08/5.93	   a__U281(X1, X2) -> U281(X1, X2)
20.08/5.93	   a__U282(X1, X2) -> U282(X1, X2)
20.08/5.93	   a__natsFrom(X) -> natsFrom(X)
20.08/5.93	   a__U291(X1, X2, X3) -> U291(X1, X2, X3)
20.08/5.93	   a__U292(X1, X2, X3) -> U292(X1, X2, X3)
20.08/5.93	   a__U293(X1, X2, X3) -> U293(X1, X2, X3)
20.08/5.93	   a__U294(X1, X2, X3) -> U294(X1, X2, X3)
20.08/5.93	   a__head(X) -> head(X)
20.08/5.93	   a__afterNth(X1, X2) -> afterNth(X1, X2)
20.08/5.93	   a__U301(X1, X2, X3) -> U301(X1, X2, X3)
20.08/5.93	   a__U302(X1, X2) -> U302(X1, X2)
20.08/5.93	   a__U303(X1, X2) -> U303(X1, X2)
20.08/5.93	   a__U304(X1, X2) -> U304(X1, X2)
20.08/5.93	   a__U31(X1, X2, X3) -> U31(X1, X2, X3)
20.08/5.93	   a__U32(X1, X2, X3) -> U32(X1, X2, X3)
20.08/5.93	   a__U311(X1, X2) -> U311(X1, X2)
20.08/5.93	   a__U312(X1, X2) -> U312(X1, X2)
20.08/5.93	   a__U33(X1, X2, X3) -> U33(X1, X2, X3)
20.08/5.93	   a__U321(X1, X2, X3, X4) -> U321(X1, X2, X3, X4)
20.08/5.93	   a__U322(X1, X2, X3, X4) -> U322(X1, X2, X3, X4)
20.08/5.93	   a__U323(X1, X2, X3, X4) -> U323(X1, X2, X3, X4)
20.08/5.93	   a__U324(X1, X2, X3, X4) -> U324(X1, X2, X3, X4)
20.08/5.93	   a__U325(X1, X2, X3, X4) -> U325(X1, X2, X3, X4)
20.08/5.93	   a__U326(X1, X2, X3, X4) -> U326(X1, X2, X3, X4)
20.08/5.93	   a__U327(X1, X2) -> U327(X1, X2)
20.08/5.93	   a__U34(X1, X2) -> U34(X1, X2)
20.08/5.93	   a__U331(X1, X2, X3) -> U331(X1, X2, X3)
20.08/5.93	   a__U332(X1, X2) -> U332(X1, X2)
20.08/5.93	   a__U333(X1, X2) -> U333(X1, X2)
20.08/5.93	   a__U334(X1, X2) -> U334(X1, X2)
20.08/5.93	   a__U341(X1, X2, X3) -> U341(X1, X2, X3)
20.08/5.93	   a__U342(X1, X2, X3) -> U342(X1, X2, X3)
20.08/5.93	   a__U343(X1, X2, X3) -> U343(X1, X2, X3)
20.08/5.93	   a__U344(X1, X2, X3) -> U344(X1, X2, X3)
20.08/5.93	   a__fst(X) -> fst(X)
20.08/5.93	   a__U41(X1, X2, X3) -> U41(X1, X2, X3)
20.08/5.93	   a__U42(X1, X2, X3) -> U42(X1, X2, X3)
20.08/5.93	   a__U43(X1, X2, X3) -> U43(X1, X2, X3)
20.08/5.93	   a__U44(X1, X2, X3) -> U44(X1, X2, X3)
20.08/5.93	   a__U45(X1, X2) -> U45(X1, X2)
20.08/5.93	   a__U46(X) -> U46(X)
20.08/5.93	   a__U51(X1, X2, X3) -> U51(X1, X2, X3)
20.08/5.93	   a__U52(X1, X2, X3) -> U52(X1, X2, X3)
20.08/5.93	   a__U53(X1, X2, X3) -> U53(X1, X2, X3)
20.08/5.93	   a__U54(X1, X2, X3) -> U54(X1, X2, X3)
20.08/5.93	   a__U55(X1, X2) -> U55(X1, X2)
20.08/5.93	   a__U56(X) -> U56(X)
20.08/5.93	   a__U61(X1, X2) -> U61(X1, X2)
20.08/5.93	   a__U62(X1, X2) -> U62(X1, X2)
20.08/5.93	   a__isPLNatKind(X) -> isPLNatKind(X)
20.08/5.93	   a__U63(X) -> U63(X)
20.08/5.93	   a__isPLNat(X) -> isPLNat(X)
20.08/5.93	   a__U71(X1, X2) -> U71(X1, X2)
20.08/5.93	   a__U72(X1, X2) -> U72(X1, X2)
20.08/5.93	   a__U73(X) -> U73(X)
20.08/5.93	   a__U81(X1, X2) -> U81(X1, X2)
20.08/5.93	   a__U82(X1, X2) -> U82(X1, X2)
20.08/5.93	   a__U83(X) -> U83(X)
20.08/5.93	   a__U91(X1, X2) -> U91(X1, X2)
20.08/5.93	   a__U92(X1, X2) -> U92(X1, X2)
20.08/5.93	   a__U93(X) -> U93(X)
20.08/5.93	   a__tail(X) -> tail(X)
20.08/5.93	   a__take(X1, X2) -> take(X1, X2)
20.08/5.93	   a__sel(X1, X2) -> sel(X1, X2)
20.08/5.93	
20.08/5.93	S is empty.
20.08/5.93	Rewrite Strategy: FULL
20.08/5.93	----------------------------------------
20.08/5.93	
20.08/5.93	(6) LowerBoundPropagationProof (FINISHED)
20.08/5.93	Propagated lower bound.
20.08/5.93	----------------------------------------
20.08/5.93	
20.08/5.93	(7)
20.08/5.93	BOUNDS(n^1, INF)
20.08/5.93	
20.08/5.93	----------------------------------------
20.08/5.93	
20.08/5.93	(8)
20.08/5.93	Obligation:
20.08/5.93	Analyzing the following TRS for decreasing loops:
20.08/5.93	
20.08/5.93	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
20.08/5.93	
20.08/5.93	
20.08/5.93	The TRS R consists of the following rules:
20.08/5.93	
20.08/5.93	   a__U101(tt, V1, V2) -> a__U102(a__isNaturalKind(V1), V1, V2)
20.08/5.93	   a__U102(tt, V1, V2) -> a__U103(a__isLNatKind(V2), V1, V2)
20.08/5.93	   a__U103(tt, V1, V2) -> a__U104(a__isLNatKind(V2), V1, V2)
20.08/5.93	   a__U104(tt, V1, V2) -> a__U105(a__isNatural(V1), V2)
20.08/5.93	   a__U105(tt, V2) -> a__U106(a__isLNat(V2))
20.08/5.93	   a__U106(tt) -> tt
20.08/5.93	   a__U11(tt, N, XS) -> a__U12(a__isNaturalKind(N), N, XS)
20.08/5.93	   a__U111(tt, V2) -> a__U112(a__isLNatKind(V2))
20.08/5.93	   a__U112(tt) -> tt
20.08/5.93	   a__U12(tt, N, XS) -> a__U13(a__isLNat(XS), N, XS)
20.08/5.93	   a__U121(tt, V2) -> a__U122(a__isLNatKind(V2))
20.08/5.93	   a__U122(tt) -> tt
20.08/5.93	   a__U13(tt, N, XS) -> a__U14(a__isLNatKind(XS), N, XS)
20.08/5.93	   a__U131(tt) -> tt
20.08/5.93	   a__U14(tt, N, XS) -> a__snd(a__splitAt(mark(N), mark(XS)))
20.08/5.93	   a__U141(tt) -> tt
20.08/5.93	   a__U151(tt) -> tt
20.08/5.93	   a__U161(tt) -> tt
20.08/5.93	   a__U171(tt, V2) -> a__U172(a__isLNatKind(V2))
20.08/5.93	   a__U172(tt) -> tt
20.08/5.93	   a__U181(tt, V1) -> a__U182(a__isLNatKind(V1), V1)
20.08/5.93	   a__U182(tt, V1) -> a__U183(a__isLNat(V1))
20.08/5.93	   a__U183(tt) -> tt
20.08/5.93	   a__U191(tt, V1) -> a__U192(a__isNaturalKind(V1), V1)
20.08/5.93	   a__U192(tt, V1) -> a__U193(a__isNatural(V1))
20.08/5.93	   a__U193(tt) -> tt
20.08/5.93	   a__U201(tt, V1, V2) -> a__U202(a__isNaturalKind(V1), V1, V2)
20.08/5.93	   a__U202(tt, V1, V2) -> a__U203(a__isLNatKind(V2), V1, V2)
20.08/5.93	   a__U203(tt, V1, V2) -> a__U204(a__isLNatKind(V2), V1, V2)
20.08/5.93	   a__U204(tt, V1, V2) -> a__U205(a__isNatural(V1), V2)
20.08/5.93	   a__U205(tt, V2) -> a__U206(a__isLNat(V2))
20.08/5.93	   a__U206(tt) -> tt
20.08/5.93	   a__U21(tt, X, Y) -> a__U22(a__isLNatKind(X), X, Y)
20.08/5.93	   a__U211(tt) -> tt
20.08/5.93	   a__U22(tt, X, Y) -> a__U23(a__isLNat(Y), X, Y)
20.08/5.93	   a__U221(tt) -> tt
20.08/5.93	   a__U23(tt, X, Y) -> a__U24(a__isLNatKind(Y), X)
20.08/5.93	   a__U231(tt, V2) -> a__U232(a__isLNatKind(V2))
20.08/5.93	   a__U232(tt) -> tt
20.08/5.93	   a__U24(tt, X) -> mark(X)
20.08/5.93	   a__U241(tt, V1, V2) -> a__U242(a__isLNatKind(V1), V1, V2)
20.08/5.93	   a__U242(tt, V1, V2) -> a__U243(a__isLNatKind(V2), V1, V2)
20.08/5.93	   a__U243(tt, V1, V2) -> a__U244(a__isLNatKind(V2), V1, V2)
20.08/5.93	   a__U244(tt, V1, V2) -> a__U245(a__isLNat(V1), V2)
20.08/5.93	   a__U245(tt, V2) -> a__U246(a__isLNat(V2))
20.08/5.93	   a__U246(tt) -> tt
20.08/5.93	   a__U251(tt, V1, V2) -> a__U252(a__isNaturalKind(V1), V1, V2)
20.08/5.93	   a__U252(tt, V1, V2) -> a__U253(a__isLNatKind(V2), V1, V2)
20.08/5.93	   a__U253(tt, V1, V2) -> a__U254(a__isLNatKind(V2), V1, V2)
20.08/5.93	   a__U254(tt, V1, V2) -> a__U255(a__isNatural(V1), V2)
20.08/5.93	   a__U255(tt, V2) -> a__U256(a__isLNat(V2))
20.08/5.93	   a__U256(tt) -> tt
20.08/5.93	   a__U261(tt, V2) -> a__U262(a__isLNatKind(V2))
20.08/5.93	   a__U262(tt) -> tt
20.08/5.93	   a__U271(tt, V2) -> a__U272(a__isLNatKind(V2))
20.08/5.93	   a__U272(tt) -> tt
20.08/5.93	   a__U281(tt, N) -> a__U282(a__isNaturalKind(N), N)
20.08/5.93	   a__U282(tt, N) -> cons(mark(N), natsFrom(s(N)))
20.08/5.93	   a__U291(tt, N, XS) -> a__U292(a__isNaturalKind(N), N, XS)
20.08/5.93	   a__U292(tt, N, XS) -> a__U293(a__isLNat(XS), N, XS)
20.08/5.93	   a__U293(tt, N, XS) -> a__U294(a__isLNatKind(XS), N, XS)
20.08/5.93	   a__U294(tt, N, XS) -> a__head(a__afterNth(mark(N), mark(XS)))
20.08/5.93	   a__U301(tt, X, Y) -> a__U302(a__isLNatKind(X), Y)
20.08/5.93	   a__U302(tt, Y) -> a__U303(a__isLNat(Y), Y)
20.08/5.93	   a__U303(tt, Y) -> a__U304(a__isLNatKind(Y), Y)
20.08/5.93	   a__U304(tt, Y) -> mark(Y)
20.08/5.93	   a__U31(tt, N, XS) -> a__U32(a__isNaturalKind(N), N, XS)
20.08/5.93	   a__U311(tt, XS) -> a__U312(a__isLNatKind(XS), XS)
20.08/5.93	   a__U312(tt, XS) -> pair(nil, mark(XS))
20.08/5.93	   a__U32(tt, N, XS) -> a__U33(a__isLNat(XS), N, XS)
20.08/5.93	   a__U321(tt, N, X, XS) -> a__U322(a__isNaturalKind(N), N, X, XS)
20.08/5.93	   a__U322(tt, N, X, XS) -> a__U323(a__isNatural(X), N, X, XS)
20.08/5.93	   a__U323(tt, N, X, XS) -> a__U324(a__isNaturalKind(X), N, X, XS)
20.08/5.93	   a__U324(tt, N, X, XS) -> a__U325(a__isLNat(XS), N, X, XS)
20.08/5.93	   a__U325(tt, N, X, XS) -> a__U326(a__isLNatKind(XS), N, X, XS)
20.08/5.93	   a__U326(tt, N, X, XS) -> a__U327(a__splitAt(mark(N), mark(XS)), X)
20.08/5.93	   a__U327(pair(YS, ZS), X) -> pair(cons(mark(X), YS), mark(ZS))
20.08/5.93	   a__U33(tt, N, XS) -> a__U34(a__isLNatKind(XS), N)
20.08/5.93	   a__U331(tt, N, XS) -> a__U332(a__isNaturalKind(N), XS)
20.08/5.93	   a__U332(tt, XS) -> a__U333(a__isLNat(XS), XS)
20.08/5.93	   a__U333(tt, XS) -> a__U334(a__isLNatKind(XS), XS)
20.08/5.93	   a__U334(tt, XS) -> mark(XS)
20.08/5.93	   a__U34(tt, N) -> mark(N)
20.08/5.93	   a__U341(tt, N, XS) -> a__U342(a__isNaturalKind(N), N, XS)
20.08/5.93	   a__U342(tt, N, XS) -> a__U343(a__isLNat(XS), N, XS)
20.08/5.93	   a__U343(tt, N, XS) -> a__U344(a__isLNatKind(XS), N, XS)
20.08/5.93	   a__U344(tt, N, XS) -> a__fst(a__splitAt(mark(N), mark(XS)))
20.08/5.93	   a__U41(tt, V1, V2) -> a__U42(a__isNaturalKind(V1), V1, V2)
20.08/5.93	   a__U42(tt, V1, V2) -> a__U43(a__isLNatKind(V2), V1, V2)
20.08/5.93	   a__U43(tt, V1, V2) -> a__U44(a__isLNatKind(V2), V1, V2)
20.08/5.93	   a__U44(tt, V1, V2) -> a__U45(a__isNatural(V1), V2)
20.08/5.93	   a__U45(tt, V2) -> a__U46(a__isLNat(V2))
20.08/5.93	   a__U46(tt) -> tt
20.08/5.93	   a__U51(tt, V1, V2) -> a__U52(a__isNaturalKind(V1), V1, V2)
20.08/5.93	   a__U52(tt, V1, V2) -> a__U53(a__isLNatKind(V2), V1, V2)
20.08/5.93	   a__U53(tt, V1, V2) -> a__U54(a__isLNatKind(V2), V1, V2)
20.08/5.93	   a__U54(tt, V1, V2) -> a__U55(a__isNatural(V1), V2)
20.08/5.93	   a__U55(tt, V2) -> a__U56(a__isLNat(V2))
20.08/5.93	   a__U56(tt) -> tt
20.08/5.93	   a__U61(tt, V1) -> a__U62(a__isPLNatKind(V1), V1)
20.08/5.93	   a__U62(tt, V1) -> a__U63(a__isPLNat(V1))
20.08/5.93	   a__U63(tt) -> tt
20.08/5.93	   a__U71(tt, V1) -> a__U72(a__isNaturalKind(V1), V1)
20.08/5.93	   a__U72(tt, V1) -> a__U73(a__isNatural(V1))
20.08/5.93	   a__U73(tt) -> tt
20.08/5.93	   a__U81(tt, V1) -> a__U82(a__isPLNatKind(V1), V1)
20.08/5.93	   a__U82(tt, V1) -> a__U83(a__isPLNat(V1))
20.08/5.93	   a__U83(tt) -> tt
20.08/5.93	   a__U91(tt, V1) -> a__U92(a__isLNatKind(V1), V1)
20.08/5.93	   a__U92(tt, V1) -> a__U93(a__isLNat(V1))
20.08/5.93	   a__U93(tt) -> tt
20.08/5.93	   a__afterNth(N, XS) -> a__U11(a__isNatural(N), N, XS)
20.08/5.93	   a__fst(pair(X, Y)) -> a__U21(a__isLNat(X), X, Y)
20.08/5.93	   a__head(cons(N, XS)) -> a__U31(a__isNatural(N), N, XS)
20.08/5.93	   a__isLNat(nil) -> tt
20.08/5.93	   a__isLNat(afterNth(V1, V2)) -> a__U41(a__isNaturalKind(V1), V1, V2)
20.08/5.93	   a__isLNat(cons(V1, V2)) -> a__U51(a__isNaturalKind(V1), V1, V2)
20.08/5.93	   a__isLNat(fst(V1)) -> a__U61(a__isPLNatKind(V1), V1)
20.08/5.93	   a__isLNat(natsFrom(V1)) -> a__U71(a__isNaturalKind(V1), V1)
20.08/5.93	   a__isLNat(snd(V1)) -> a__U81(a__isPLNatKind(V1), V1)
20.08/5.93	   a__isLNat(tail(V1)) -> a__U91(a__isLNatKind(V1), V1)
20.08/5.93	   a__isLNat(take(V1, V2)) -> a__U101(a__isNaturalKind(V1), V1, V2)
20.08/5.93	   a__isLNatKind(nil) -> tt
20.08/5.93	   a__isLNatKind(afterNth(V1, V2)) -> a__U111(a__isNaturalKind(V1), V2)
20.08/5.93	   a__isLNatKind(cons(V1, V2)) -> a__U121(a__isNaturalKind(V1), V2)
20.08/5.93	   a__isLNatKind(fst(V1)) -> a__U131(a__isPLNatKind(V1))
20.08/5.93	   a__isLNatKind(natsFrom(V1)) -> a__U141(a__isNaturalKind(V1))
20.08/5.93	   a__isLNatKind(snd(V1)) -> a__U151(a__isPLNatKind(V1))
20.08/5.93	   a__isLNatKind(tail(V1)) -> a__U161(a__isLNatKind(V1))
20.08/5.93	   a__isLNatKind(take(V1, V2)) -> a__U171(a__isNaturalKind(V1), V2)
20.08/5.93	   a__isNatural(0) -> tt
20.08/5.93	   a__isNatural(head(V1)) -> a__U181(a__isLNatKind(V1), V1)
20.08/5.93	   a__isNatural(s(V1)) -> a__U191(a__isNaturalKind(V1), V1)
20.08/5.93	   a__isNatural(sel(V1, V2)) -> a__U201(a__isNaturalKind(V1), V1, V2)
20.08/5.93	   a__isNaturalKind(0) -> tt
20.08/5.93	   a__isNaturalKind(head(V1)) -> a__U211(a__isLNatKind(V1))
20.08/5.93	   a__isNaturalKind(s(V1)) -> a__U221(a__isNaturalKind(V1))
20.08/5.93	   a__isNaturalKind(sel(V1, V2)) -> a__U231(a__isNaturalKind(V1), V2)
20.08/5.93	   a__isPLNat(pair(V1, V2)) -> a__U241(a__isLNatKind(V1), V1, V2)
20.08/5.93	   a__isPLNat(splitAt(V1, V2)) -> a__U251(a__isNaturalKind(V1), V1, V2)
20.08/5.93	   a__isPLNatKind(pair(V1, V2)) -> a__U261(a__isLNatKind(V1), V2)
20.08/5.93	   a__isPLNatKind(splitAt(V1, V2)) -> a__U271(a__isNaturalKind(V1), V2)
20.08/5.93	   a__natsFrom(N) -> a__U281(a__isNatural(N), N)
20.08/5.93	   a__sel(N, XS) -> a__U291(a__isNatural(N), N, XS)
20.08/5.93	   a__snd(pair(X, Y)) -> a__U301(a__isLNat(X), X, Y)
20.08/5.93	   a__splitAt(0, XS) -> a__U311(a__isLNat(XS), XS)
20.08/5.93	   a__splitAt(s(N), cons(X, XS)) -> a__U321(a__isNatural(N), N, X, XS)
20.08/5.93	   a__tail(cons(N, XS)) -> a__U331(a__isNatural(N), N, XS)
20.08/5.93	   a__take(N, XS) -> a__U341(a__isNatural(N), N, XS)
20.08/5.93	   mark(U101(X1, X2, X3)) -> a__U101(mark(X1), X2, X3)
20.08/5.93	   mark(U102(X1, X2, X3)) -> a__U102(mark(X1), X2, X3)
20.08/5.93	   mark(isNaturalKind(X)) -> a__isNaturalKind(X)
20.08/5.93	   mark(U103(X1, X2, X3)) -> a__U103(mark(X1), X2, X3)
20.08/5.93	   mark(isLNatKind(X)) -> a__isLNatKind(X)
20.08/5.93	   mark(U104(X1, X2, X3)) -> a__U104(mark(X1), X2, X3)
20.08/5.93	   mark(U105(X1, X2)) -> a__U105(mark(X1), X2)
20.08/5.93	   mark(isNatural(X)) -> a__isNatural(X)
20.08/5.93	   mark(U106(X)) -> a__U106(mark(X))
20.08/5.93	   mark(isLNat(X)) -> a__isLNat(X)
20.08/5.93	   mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
20.08/5.93	   mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
20.08/5.93	   mark(U111(X1, X2)) -> a__U111(mark(X1), X2)
20.08/5.93	   mark(U112(X)) -> a__U112(mark(X))
20.08/5.93	   mark(U13(X1, X2, X3)) -> a__U13(mark(X1), X2, X3)
20.08/5.93	   mark(U121(X1, X2)) -> a__U121(mark(X1), X2)
20.08/5.93	   mark(U122(X)) -> a__U122(mark(X))
20.08/5.93	   mark(U14(X1, X2, X3)) -> a__U14(mark(X1), X2, X3)
20.08/5.93	   mark(U131(X)) -> a__U131(mark(X))
20.08/5.93	   mark(snd(X)) -> a__snd(mark(X))
20.08/5.93	   mark(splitAt(X1, X2)) -> a__splitAt(mark(X1), mark(X2))
20.08/5.93	   mark(U141(X)) -> a__U141(mark(X))
20.08/5.93	   mark(U151(X)) -> a__U151(mark(X))
20.08/5.93	   mark(U161(X)) -> a__U161(mark(X))
20.08/5.93	   mark(U171(X1, X2)) -> a__U171(mark(X1), X2)
20.08/5.93	   mark(U172(X)) -> a__U172(mark(X))
20.08/5.93	   mark(U181(X1, X2)) -> a__U181(mark(X1), X2)
20.08/5.93	   mark(U182(X1, X2)) -> a__U182(mark(X1), X2)
20.08/5.93	   mark(U183(X)) -> a__U183(mark(X))
20.08/5.93	   mark(U191(X1, X2)) -> a__U191(mark(X1), X2)
20.08/5.93	   mark(U192(X1, X2)) -> a__U192(mark(X1), X2)
20.08/5.93	   mark(U193(X)) -> a__U193(mark(X))
20.08/5.93	   mark(U201(X1, X2, X3)) -> a__U201(mark(X1), X2, X3)
20.08/5.93	   mark(U202(X1, X2, X3)) -> a__U202(mark(X1), X2, X3)
20.08/5.93	   mark(U203(X1, X2, X3)) -> a__U203(mark(X1), X2, X3)
20.08/5.93	   mark(U204(X1, X2, X3)) -> a__U204(mark(X1), X2, X3)
20.08/5.93	   mark(U205(X1, X2)) -> a__U205(mark(X1), X2)
20.08/5.93	   mark(U206(X)) -> a__U206(mark(X))
20.08/5.93	   mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3)
20.08/5.93	   mark(U22(X1, X2, X3)) -> a__U22(mark(X1), X2, X3)
20.08/5.93	   mark(U211(X)) -> a__U211(mark(X))
20.08/5.93	   mark(U23(X1, X2, X3)) -> a__U23(mark(X1), X2, X3)
20.08/5.93	   mark(U221(X)) -> a__U221(mark(X))
20.08/5.93	   mark(U24(X1, X2)) -> a__U24(mark(X1), X2)
20.08/5.93	   mark(U231(X1, X2)) -> a__U231(mark(X1), X2)
20.08/5.93	   mark(U232(X)) -> a__U232(mark(X))
20.08/5.93	   mark(U241(X1, X2, X3)) -> a__U241(mark(X1), X2, X3)
20.08/5.93	   mark(U242(X1, X2, X3)) -> a__U242(mark(X1), X2, X3)
20.08/5.93	   mark(U243(X1, X2, X3)) -> a__U243(mark(X1), X2, X3)
20.08/5.93	   mark(U244(X1, X2, X3)) -> a__U244(mark(X1), X2, X3)
20.08/5.93	   mark(U245(X1, X2)) -> a__U245(mark(X1), X2)
20.08/5.93	   mark(U246(X)) -> a__U246(mark(X))
20.08/5.93	   mark(U251(X1, X2, X3)) -> a__U251(mark(X1), X2, X3)
20.08/5.93	   mark(U252(X1, X2, X3)) -> a__U252(mark(X1), X2, X3)
20.08/5.93	   mark(U253(X1, X2, X3)) -> a__U253(mark(X1), X2, X3)
20.08/5.93	   mark(U254(X1, X2, X3)) -> a__U254(mark(X1), X2, X3)
20.08/5.93	   mark(U255(X1, X2)) -> a__U255(mark(X1), X2)
20.08/5.93	   mark(U256(X)) -> a__U256(mark(X))
20.08/5.93	   mark(U261(X1, X2)) -> a__U261(mark(X1), X2)
20.08/5.93	   mark(U262(X)) -> a__U262(mark(X))
20.08/5.93	   mark(U271(X1, X2)) -> a__U271(mark(X1), X2)
20.08/5.93	   mark(U272(X)) -> a__U272(mark(X))
20.08/5.93	   mark(U281(X1, X2)) -> a__U281(mark(X1), X2)
20.08/5.93	   mark(U282(X1, X2)) -> a__U282(mark(X1), X2)
20.08/5.93	   mark(natsFrom(X)) -> a__natsFrom(mark(X))
20.08/5.93	   mark(U291(X1, X2, X3)) -> a__U291(mark(X1), X2, X3)
20.08/5.93	   mark(U292(X1, X2, X3)) -> a__U292(mark(X1), X2, X3)
20.08/5.93	   mark(U293(X1, X2, X3)) -> a__U293(mark(X1), X2, X3)
20.08/5.93	   mark(U294(X1, X2, X3)) -> a__U294(mark(X1), X2, X3)
20.08/5.93	   mark(head(X)) -> a__head(mark(X))
20.08/5.93	   mark(afterNth(X1, X2)) -> a__afterNth(mark(X1), mark(X2))
20.08/5.93	   mark(U301(X1, X2, X3)) -> a__U301(mark(X1), X2, X3)
20.08/5.93	   mark(U302(X1, X2)) -> a__U302(mark(X1), X2)
20.08/5.93	   mark(U303(X1, X2)) -> a__U303(mark(X1), X2)
20.08/5.93	   mark(U304(X1, X2)) -> a__U304(mark(X1), X2)
20.08/5.93	   mark(U31(X1, X2, X3)) -> a__U31(mark(X1), X2, X3)
20.08/5.93	   mark(U32(X1, X2, X3)) -> a__U32(mark(X1), X2, X3)
20.08/5.93	   mark(U311(X1, X2)) -> a__U311(mark(X1), X2)
20.08/5.93	   mark(U312(X1, X2)) -> a__U312(mark(X1), X2)
20.08/5.93	   mark(U33(X1, X2, X3)) -> a__U33(mark(X1), X2, X3)
20.08/5.93	   mark(U321(X1, X2, X3, X4)) -> a__U321(mark(X1), X2, X3, X4)
20.08/5.93	   mark(U322(X1, X2, X3, X4)) -> a__U322(mark(X1), X2, X3, X4)
20.08/5.93	   mark(U323(X1, X2, X3, X4)) -> a__U323(mark(X1), X2, X3, X4)
20.08/5.93	   mark(U324(X1, X2, X3, X4)) -> a__U324(mark(X1), X2, X3, X4)
20.08/5.93	   mark(U325(X1, X2, X3, X4)) -> a__U325(mark(X1), X2, X3, X4)
20.08/5.93	   mark(U326(X1, X2, X3, X4)) -> a__U326(mark(X1), X2, X3, X4)
20.08/5.93	   mark(U327(X1, X2)) -> a__U327(mark(X1), X2)
20.08/5.93	   mark(U34(X1, X2)) -> a__U34(mark(X1), X2)
20.08/5.93	   mark(U331(X1, X2, X3)) -> a__U331(mark(X1), X2, X3)
20.08/5.93	   mark(U332(X1, X2)) -> a__U332(mark(X1), X2)
20.08/5.93	   mark(U333(X1, X2)) -> a__U333(mark(X1), X2)
20.08/5.93	   mark(U334(X1, X2)) -> a__U334(mark(X1), X2)
20.08/5.93	   mark(U341(X1, X2, X3)) -> a__U341(mark(X1), X2, X3)
20.08/5.93	   mark(U342(X1, X2, X3)) -> a__U342(mark(X1), X2, X3)
20.08/5.93	   mark(U343(X1, X2, X3)) -> a__U343(mark(X1), X2, X3)
20.08/5.93	   mark(U344(X1, X2, X3)) -> a__U344(mark(X1), X2, X3)
20.08/5.93	   mark(fst(X)) -> a__fst(mark(X))
20.08/5.93	   mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
20.08/5.93	   mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3)
20.08/5.93	   mark(U43(X1, X2, X3)) -> a__U43(mark(X1), X2, X3)
20.08/5.93	   mark(U44(X1, X2, X3)) -> a__U44(mark(X1), X2, X3)
20.08/5.93	   mark(U45(X1, X2)) -> a__U45(mark(X1), X2)
20.08/5.93	   mark(U46(X)) -> a__U46(mark(X))
20.08/5.93	   mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3)
20.08/5.93	   mark(U52(X1, X2, X3)) -> a__U52(mark(X1), X2, X3)
20.08/5.93	   mark(U53(X1, X2, X3)) -> a__U53(mark(X1), X2, X3)
20.08/5.93	   mark(U54(X1, X2, X3)) -> a__U54(mark(X1), X2, X3)
20.08/5.93	   mark(U55(X1, X2)) -> a__U55(mark(X1), X2)
20.08/5.93	   mark(U56(X)) -> a__U56(mark(X))
20.08/5.93	   mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
20.08/5.93	   mark(U62(X1, X2)) -> a__U62(mark(X1), X2)
20.08/5.93	   mark(isPLNatKind(X)) -> a__isPLNatKind(X)
20.08/5.93	   mark(U63(X)) -> a__U63(mark(X))
20.08/5.93	   mark(isPLNat(X)) -> a__isPLNat(X)
20.08/5.93	   mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
20.08/5.93	   mark(U72(X1, X2)) -> a__U72(mark(X1), X2)
20.08/5.93	   mark(U73(X)) -> a__U73(mark(X))
20.08/5.93	   mark(U81(X1, X2)) -> a__U81(mark(X1), X2)
20.08/5.93	   mark(U82(X1, X2)) -> a__U82(mark(X1), X2)
20.08/5.93	   mark(U83(X)) -> a__U83(mark(X))
20.08/5.93	   mark(U91(X1, X2)) -> a__U91(mark(X1), X2)
20.08/5.93	   mark(U92(X1, X2)) -> a__U92(mark(X1), X2)
20.08/5.93	   mark(U93(X)) -> a__U93(mark(X))
20.08/5.93	   mark(tail(X)) -> a__tail(mark(X))
20.08/5.93	   mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
20.08/5.93	   mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
20.08/5.93	   mark(tt) -> tt
20.08/5.93	   mark(cons(X1, X2)) -> cons(mark(X1), X2)
20.08/5.93	   mark(s(X)) -> s(mark(X))
20.08/5.93	   mark(pair(X1, X2)) -> pair(mark(X1), mark(X2))
20.08/5.93	   mark(nil) -> nil
20.08/5.93	   mark(0) -> 0
20.08/5.93	   a__U101(X1, X2, X3) -> U101(X1, X2, X3)
20.08/5.93	   a__U102(X1, X2, X3) -> U102(X1, X2, X3)
20.08/5.93	   a__isNaturalKind(X) -> isNaturalKind(X)
20.08/5.93	   a__U103(X1, X2, X3) -> U103(X1, X2, X3)
20.08/5.93	   a__isLNatKind(X) -> isLNatKind(X)
20.08/5.93	   a__U104(X1, X2, X3) -> U104(X1, X2, X3)
20.08/5.93	   a__U105(X1, X2) -> U105(X1, X2)
20.08/5.93	   a__isNatural(X) -> isNatural(X)
20.08/5.93	   a__U106(X) -> U106(X)
20.08/5.93	   a__isLNat(X) -> isLNat(X)
20.08/5.93	   a__U11(X1, X2, X3) -> U11(X1, X2, X3)
20.08/5.93	   a__U12(X1, X2, X3) -> U12(X1, X2, X3)
20.08/5.93	   a__U111(X1, X2) -> U111(X1, X2)
20.08/5.93	   a__U112(X) -> U112(X)
20.08/5.93	   a__U13(X1, X2, X3) -> U13(X1, X2, X3)
20.08/5.93	   a__U121(X1, X2) -> U121(X1, X2)
20.08/5.93	   a__U122(X) -> U122(X)
20.08/5.93	   a__U14(X1, X2, X3) -> U14(X1, X2, X3)
20.08/5.93	   a__U131(X) -> U131(X)
20.08/5.93	   a__snd(X) -> snd(X)
20.08/5.93	   a__splitAt(X1, X2) -> splitAt(X1, X2)
20.08/5.93	   a__U141(X) -> U141(X)
20.08/5.93	   a__U151(X) -> U151(X)
20.08/5.93	   a__U161(X) -> U161(X)
20.08/5.93	   a__U171(X1, X2) -> U171(X1, X2)
20.08/5.93	   a__U172(X) -> U172(X)
20.08/5.93	   a__U181(X1, X2) -> U181(X1, X2)
20.08/5.93	   a__U182(X1, X2) -> U182(X1, X2)
20.08/5.93	   a__U183(X) -> U183(X)
20.08/5.93	   a__U191(X1, X2) -> U191(X1, X2)
20.08/5.93	   a__U192(X1, X2) -> U192(X1, X2)
20.08/5.93	   a__U193(X) -> U193(X)
20.08/5.93	   a__U201(X1, X2, X3) -> U201(X1, X2, X3)
20.08/5.93	   a__U202(X1, X2, X3) -> U202(X1, X2, X3)
20.08/5.93	   a__U203(X1, X2, X3) -> U203(X1, X2, X3)
20.08/5.93	   a__U204(X1, X2, X3) -> U204(X1, X2, X3)
20.08/5.93	   a__U205(X1, X2) -> U205(X1, X2)
20.08/5.93	   a__U206(X) -> U206(X)
20.08/5.93	   a__U21(X1, X2, X3) -> U21(X1, X2, X3)
20.08/5.93	   a__U22(X1, X2, X3) -> U22(X1, X2, X3)
20.08/5.93	   a__U211(X) -> U211(X)
20.08/5.93	   a__U23(X1, X2, X3) -> U23(X1, X2, X3)
20.08/5.93	   a__U221(X) -> U221(X)
20.08/5.93	   a__U24(X1, X2) -> U24(X1, X2)
20.08/5.93	   a__U231(X1, X2) -> U231(X1, X2)
20.08/5.93	   a__U232(X) -> U232(X)
20.08/5.93	   a__U241(X1, X2, X3) -> U241(X1, X2, X3)
20.08/5.93	   a__U242(X1, X2, X3) -> U242(X1, X2, X3)
20.08/5.93	   a__U243(X1, X2, X3) -> U243(X1, X2, X3)
20.08/5.93	   a__U244(X1, X2, X3) -> U244(X1, X2, X3)
20.08/5.93	   a__U245(X1, X2) -> U245(X1, X2)
20.08/5.93	   a__U246(X) -> U246(X)
20.08/5.93	   a__U251(X1, X2, X3) -> U251(X1, X2, X3)
20.08/5.93	   a__U252(X1, X2, X3) -> U252(X1, X2, X3)
20.08/5.93	   a__U253(X1, X2, X3) -> U253(X1, X2, X3)
20.08/5.93	   a__U254(X1, X2, X3) -> U254(X1, X2, X3)
20.08/5.93	   a__U255(X1, X2) -> U255(X1, X2)
20.08/5.93	   a__U256(X) -> U256(X)
20.08/5.93	   a__U261(X1, X2) -> U261(X1, X2)
20.08/5.93	   a__U262(X) -> U262(X)
20.08/5.93	   a__U271(X1, X2) -> U271(X1, X2)
20.08/5.93	   a__U272(X) -> U272(X)
20.08/5.93	   a__U281(X1, X2) -> U281(X1, X2)
20.08/5.93	   a__U282(X1, X2) -> U282(X1, X2)
20.08/5.93	   a__natsFrom(X) -> natsFrom(X)
20.08/5.93	   a__U291(X1, X2, X3) -> U291(X1, X2, X3)
20.08/5.93	   a__U292(X1, X2, X3) -> U292(X1, X2, X3)
20.08/5.93	   a__U293(X1, X2, X3) -> U293(X1, X2, X3)
20.08/5.93	   a__U294(X1, X2, X3) -> U294(X1, X2, X3)
20.08/5.93	   a__head(X) -> head(X)
20.08/5.93	   a__afterNth(X1, X2) -> afterNth(X1, X2)
20.08/5.93	   a__U301(X1, X2, X3) -> U301(X1, X2, X3)
20.08/5.93	   a__U302(X1, X2) -> U302(X1, X2)
20.08/5.93	   a__U303(X1, X2) -> U303(X1, X2)
20.08/5.93	   a__U304(X1, X2) -> U304(X1, X2)
20.08/5.93	   a__U31(X1, X2, X3) -> U31(X1, X2, X3)
20.08/5.93	   a__U32(X1, X2, X3) -> U32(X1, X2, X3)
20.08/5.93	   a__U311(X1, X2) -> U311(X1, X2)
20.08/5.93	   a__U312(X1, X2) -> U312(X1, X2)
20.08/5.93	   a__U33(X1, X2, X3) -> U33(X1, X2, X3)
20.08/5.93	   a__U321(X1, X2, X3, X4) -> U321(X1, X2, X3, X4)
20.08/5.93	   a__U322(X1, X2, X3, X4) -> U322(X1, X2, X3, X4)
20.08/5.93	   a__U323(X1, X2, X3, X4) -> U323(X1, X2, X3, X4)
20.08/5.93	   a__U324(X1, X2, X3, X4) -> U324(X1, X2, X3, X4)
20.08/5.93	   a__U325(X1, X2, X3, X4) -> U325(X1, X2, X3, X4)
20.08/5.93	   a__U326(X1, X2, X3, X4) -> U326(X1, X2, X3, X4)
20.08/5.93	   a__U327(X1, X2) -> U327(X1, X2)
20.08/5.93	   a__U34(X1, X2) -> U34(X1, X2)
20.08/5.93	   a__U331(X1, X2, X3) -> U331(X1, X2, X3)
20.08/5.93	   a__U332(X1, X2) -> U332(X1, X2)
20.08/5.93	   a__U333(X1, X2) -> U333(X1, X2)
20.08/5.93	   a__U334(X1, X2) -> U334(X1, X2)
20.08/5.93	   a__U341(X1, X2, X3) -> U341(X1, X2, X3)
20.08/5.93	   a__U342(X1, X2, X3) -> U342(X1, X2, X3)
20.08/5.93	   a__U343(X1, X2, X3) -> U343(X1, X2, X3)
20.08/5.93	   a__U344(X1, X2, X3) -> U344(X1, X2, X3)
20.08/5.93	   a__fst(X) -> fst(X)
20.08/5.93	   a__U41(X1, X2, X3) -> U41(X1, X2, X3)
20.08/5.93	   a__U42(X1, X2, X3) -> U42(X1, X2, X3)
20.08/5.93	   a__U43(X1, X2, X3) -> U43(X1, X2, X3)
20.08/5.93	   a__U44(X1, X2, X3) -> U44(X1, X2, X3)
20.08/5.93	   a__U45(X1, X2) -> U45(X1, X2)
20.08/5.93	   a__U46(X) -> U46(X)
20.08/5.93	   a__U51(X1, X2, X3) -> U51(X1, X2, X3)
20.08/5.93	   a__U52(X1, X2, X3) -> U52(X1, X2, X3)
20.08/5.93	   a__U53(X1, X2, X3) -> U53(X1, X2, X3)
20.08/5.93	   a__U54(X1, X2, X3) -> U54(X1, X2, X3)
20.08/5.93	   a__U55(X1, X2) -> U55(X1, X2)
20.08/5.93	   a__U56(X) -> U56(X)
20.08/5.93	   a__U61(X1, X2) -> U61(X1, X2)
20.08/5.93	   a__U62(X1, X2) -> U62(X1, X2)
20.08/5.93	   a__isPLNatKind(X) -> isPLNatKind(X)
20.08/5.93	   a__U63(X) -> U63(X)
20.08/5.93	   a__isPLNat(X) -> isPLNat(X)
20.08/5.93	   a__U71(X1, X2) -> U71(X1, X2)
20.08/5.93	   a__U72(X1, X2) -> U72(X1, X2)
20.08/5.93	   a__U73(X) -> U73(X)
20.08/5.93	   a__U81(X1, X2) -> U81(X1, X2)
20.08/5.93	   a__U82(X1, X2) -> U82(X1, X2)
20.08/5.93	   a__U83(X) -> U83(X)
20.08/5.93	   a__U91(X1, X2) -> U91(X1, X2)
20.08/5.93	   a__U92(X1, X2) -> U92(X1, X2)
20.08/5.93	   a__U93(X) -> U93(X)
20.08/5.93	   a__tail(X) -> tail(X)
20.08/5.93	   a__take(X1, X2) -> take(X1, X2)
20.08/5.93	   a__sel(X1, X2) -> sel(X1, X2)
20.08/5.93	
20.08/5.93	S is empty.
20.08/5.93	Rewrite Strategy: FULL
20.08/5.93	----------------------------------------
20.08/5.93	
20.08/5.93	(9) DecreasingLoopProof (FINISHED)
20.08/5.93	The following loop(s) give(s) rise to the lower bound EXP:
20.08/5.93	
20.08/5.93	The rewrite sequence
20.08/5.93	
20.08/5.93	mark(take(X1, X2)) ->^+ a__U341(a__isNatural(mark(X1)), mark(X1), mark(X2))
20.08/5.93	
20.08/5.93	gives rise to a decreasing loop by considering the right hand sides subterm at position [0,0].
20.08/5.93	
20.08/5.93	The pumping substitution is [X1 / take(X1, X2)].
20.08/5.93	
20.08/5.93	The result substitution is [ ].
20.08/5.93	
20.08/5.93	
20.08/5.93	
20.08/5.93	The rewrite sequence
20.08/5.93	
20.08/5.93	mark(take(X1, X2)) ->^+ a__U341(a__isNatural(mark(X1)), mark(X1), mark(X2))
20.08/5.93	
20.08/5.93	gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
20.08/5.93	
20.08/5.93	The pumping substitution is [X1 / take(X1, X2)].
20.08/5.93	
20.08/5.93	The result substitution is [ ].
20.08/5.93	
20.08/5.93	
20.08/5.93	
20.08/5.93	
20.08/5.93	----------------------------------------
20.08/5.93	
20.08/5.93	(10)
20.08/5.93	BOUNDS(EXP, INF)
20.33/6.00	EOF