The TRS could not be proven terminating. The proof attempt took 60002 ms.
Problem 1 remains open; application of the following processors failed [DependencyGraph (timeout)].
| mark#(fst(X)) | → | active#(fst(mark(X))) | active#(U132(tt)) | → | mark#(tt) | |
| active#(U211(tt, XS)) | → | isLNat#(XS) | mark#(U61(X)) | → | U61#(mark(X)) | |
| mark#(U51(X1, X2)) | → | U51#(mark(X1), X2) | mark#(U102(X)) | → | mark#(X) | |
| U221#(X1, active(X2), X3) | → | U221#(X1, X2, X3) | mark#(take(X1, X2)) | → | active#(take(mark(X1), mark(X2))) | |
| U132#(mark(X)) | → | U132#(X) | active#(U191(tt, XS)) | → | pair#(nil, XS) | |
| U91#(active(X)) | → | U91#(X) | active#(head(cons(N, XS))) | → | mark#(U31(isNatural(N), N, XS)) | |
| U51#(mark(X1), X2) | → | U51#(X1, X2) | active#(U221(tt, N, XS)) | → | isLNat#(XS) | |
| U152#(active(X)) | → | U152#(X) | mark#(U121(X)) | → | mark#(X) | |
| mark#(U152(X)) | → | U152#(mark(X)) | mark#(s(X)) | → | mark#(X) | |
| active#(U21(tt, X, Y)) | → | isLNat#(Y) | afterNth#(active(X1), X2) | → | afterNth#(X1, X2) | |
| mark#(U31(X1, X2, X3)) | → | active#(U31(mark(X1), X2, X3)) | U81#(mark(X)) | → | U81#(X) | |
| active#(splitAt(s(N), cons(X, XS))) | → | mark#(U201(isNatural(N), N, X, XS)) | mark#(U142(X)) | → | U142#(mark(X)) | |
| splitAt#(X1, mark(X2)) | → | splitAt#(X1, X2) | mark#(U52(X)) | → | mark#(X) | |
| mark#(U91(X)) | → | U91#(mark(X)) | mark#(U42(X)) | → | active#(U42(mark(X))) | |
| U172#(mark(X1), X2, X3) | → | U172#(X1, X2, X3) | U203#(mark(X1), X2, X3, X4) | → | U203#(X1, X2, X3, X4) | |
| mark#(U151(X1, X2)) | → | U151#(mark(X1), X2) | U12#(X1, active(X2), X3) | → | U12#(X1, X2, X3) | |
| active#(isLNat(cons(V1, V2))) | → | isNatural#(V1) | U12#(X1, X2, mark(X3)) | → | U12#(X1, X2, X3) | |
| U141#(X1, active(X2)) | → | U141#(X1, X2) | active#(U42(tt)) | → | mark#(tt) | |
| mark#(U11(X1, X2, X3)) | → | mark#(X1) | active#(isLNat(afterNth(V1, V2))) | → | isNatural#(V1) | |
| U221#(active(X1), X2, X3) | → | U221#(X1, X2, X3) | natsFrom#(mark(X)) | → | natsFrom#(X) | |
| U31#(active(X1), X2, X3) | → | U31#(X1, X2, X3) | U191#(X1, mark(X2)) | → | U191#(X1, X2) | |
| mark#(U111(X)) | → | mark#(X) | active#(take(N, XS)) | → | isNatural#(N) | |
| active#(splitAt(0, XS)) | → | isLNat#(XS) | active#(U151(tt, V2)) | → | mark#(U152(isLNat(V2))) | |
| mark#(U211(X1, X2)) | → | active#(U211(mark(X1), X2)) | active#(U12(tt, N, XS)) | → | mark#(snd(splitAt(N, XS))) | |
| mark#(U22(X1, X2)) | → | mark#(X1) | mark#(splitAt(X1, X2)) | → | mark#(X1) | |
| isNatural#(mark(X)) | → | isNatural#(X) | active#(fst(pair(X, Y))) | → | U21#(isLNat(X), X, Y) | |
| mark#(isNatural(X)) | → | isNatural#(X) | isPLNat#(active(X)) | → | isPLNat#(X) | |
| U11#(active(X1), X2, X3) | → | U11#(X1, X2, X3) | mark#(U61(X)) | → | mark#(X) | |
| U191#(mark(X1), X2) | → | U191#(X1, X2) | U12#(X1, X2, active(X3)) | → | U12#(X1, X2, X3) | |
| active#(U91(tt)) | → | mark#(tt) | U141#(active(X1), X2) | → | U141#(X1, X2) | |
| active#(U41(tt, V2)) | → | isLNat#(V2) | mark#(natsFrom(X)) | → | mark#(X) | |
| cons#(active(X1), X2) | → | cons#(X1, X2) | mark#(afterNth(X1, X2)) | → | active#(afterNth(mark(X1), mark(X2))) | |
| mark#(U201(X1, X2, X3, X4)) | → | mark#(X1) | U172#(X1, X2, active(X3)) | → | U172#(X1, X2, X3) | |
| active#(U172(tt, N, XS)) | → | afterNth#(N, XS) | active#(U151(tt, V2)) | → | U152#(isLNat(V2)) | |
| mark#(U191(X1, X2)) | → | mark#(X1) | mark#(U101(X1, X2)) | → | mark#(X1) | |
| active#(U222(tt, N, XS)) | → | splitAt#(N, XS) | active#(isPLNat(splitAt(V1, V2))) | → | mark#(U151(isNatural(V1), V2)) | |
| active#(snd(pair(X, Y))) | → | mark#(U181(isLNat(X), Y)) | U181#(X1, active(X2)) | → | U181#(X1, X2) | |
| afterNth#(X1, mark(X2)) | → | afterNth#(X1, X2) | isNatural#(active(X)) | → | isNatural#(X) | |
| mark#(U11(X1, X2, X3)) | → | active#(U11(mark(X1), X2, X3)) | active#(head(cons(N, XS))) | → | isNatural#(N) | |
| mark#(tail(X)) | → | active#(tail(mark(X))) | mark#(U191(X1, X2)) | → | U191#(mark(X1), X2) | |
| U202#(X1, mark(X2), X3, X4) | → | U202#(X1, X2, X3, X4) | mark#(isLNat(X)) | → | active#(isLNat(X)) | |
| mark#(natsFrom(X)) | → | active#(natsFrom(mark(X))) | U71#(mark(X)) | → | U71#(X) | |
| active#(splitAt(s(N), cons(X, XS))) | → | isNatural#(N) | isPLNat#(mark(X)) | → | isPLNat#(X) | |
| U41#(X1, mark(X2)) | → | U41#(X1, X2) | mark#(isPLNat(X)) | → | isPLNat#(X) | |
| mark#(U171(X1, X2, X3)) | → | active#(U171(mark(X1), X2, X3)) | active#(natsFrom(N)) | → | isNatural#(N) | |
| take#(X1, mark(X2)) | → | take#(X1, X2) | mark#(splitAt(X1, X2)) | → | active#(splitAt(mark(X1), mark(X2))) | |
| U131#(X1, mark(X2)) | → | U131#(X1, X2) | mark#(U31(X1, X2, X3)) | → | mark#(X1) | |
| U171#(X1, X2, active(X3)) | → | U171#(X1, X2, X3) | active#(U191(tt, XS)) | → | mark#(pair(nil, XS)) | |
| U203#(X1, X2, X3, active(X4)) | → | U203#(X1, X2, X3, X4) | active#(U101(tt, V2)) | → | U102#(isLNat(V2)) | |
| active#(U203(tt, N, X, XS)) | → | splitAt#(N, XS) | U121#(active(X)) | → | U121#(X) | |
| mark#(U211(X1, X2)) | → | mark#(X1) | mark#(U161(X1, X2)) | → | U161#(mark(X1), X2) | |
| sel#(mark(X1), X2) | → | sel#(X1, X2) | active#(U152(tt)) | → | mark#(tt) | |
| mark#(head(X)) | → | active#(head(mark(X))) | active#(U51(tt, V2)) | → | isLNat#(V2) | |
| active#(isLNat(take(V1, V2))) | → | mark#(U101(isNatural(V1), V2)) | U12#(X1, mark(X2), X3) | → | U12#(X1, X2, X3) | |
| mark#(U181(X1, X2)) | → | mark#(X1) | U221#(X1, X2, active(X3)) | → | U221#(X1, X2, X3) | |
| mark#(U42(X)) | → | mark#(X) | active#(isLNat(fst(V1))) | → | isPLNat#(V1) | |
| U222#(X1, active(X2), X3) | → | U222#(X1, X2, X3) | splitAt#(active(X1), X2) | → | splitAt#(X1, X2) | |
| active#(U61(tt)) | → | mark#(tt) | mark#(nil) | → | active#(nil) | |
| mark#(U61(X)) | → | active#(U61(mark(X))) | U172#(X1, mark(X2), X3) | → | U172#(X1, X2, X3) | |
| take#(X1, active(X2)) | → | take#(X1, X2) | U31#(X1, X2, mark(X3)) | → | U31#(X1, X2, X3) | |
| mark#(isNatural(X)) | → | active#(isNatural(X)) | U101#(mark(X1), X2) | → | U101#(X1, X2) | |
| U41#(mark(X1), X2) | → | U41#(X1, X2) | U202#(X1, X2, mark(X3), X4) | → | U202#(X1, X2, X3, X4) | |
| U101#(X1, active(X2)) | → | U101#(X1, X2) | mark#(cons(X1, X2)) | → | cons#(mark(X1), X2) | |
| mark#(U22(X1, X2)) | → | active#(U22(mark(X1), X2)) | mark#(U172(X1, X2, X3)) | → | U172#(mark(X1), X2, X3) | |
| U151#(X1, active(X2)) | → | U151#(X1, X2) | natsFrom#(active(X)) | → | natsFrom#(X) | |
| U212#(active(X1), X2) | → | U212#(X1, X2) | mark#(U32(X1, X2)) | → | active#(U32(mark(X1), X2)) | |
| active#(U31(tt, N, XS)) | → | U32#(isLNat(XS), N) | mark#(splitAt(X1, X2)) | → | mark#(X2) | |
| active#(U71(tt)) | → | mark#(tt) | active#(U181(tt, Y)) | → | mark#(U182(isLNat(Y), Y)) | |
| U203#(X1, mark(X2), X3, X4) | → | U203#(X1, X2, X3, X4) | active#(isLNat(natsFrom(V1))) | → | U71#(isNatural(V1)) | |
| mark#(U21(X1, X2, X3)) | → | U21#(mark(X1), X2, X3) | active#(U31(tt, N, XS)) | → | mark#(U32(isLNat(XS), N)) | |
| s#(mark(X)) | → | s#(X) | U204#(mark(X1), X2) | → | U204#(X1, X2) | |
| mark#(U202(X1, X2, X3, X4)) | → | active#(U202(mark(X1), X2, X3, X4)) | U32#(active(X1), X2) | → | U32#(X1, X2) | |
| active#(U222(tt, N, XS)) | → | mark#(fst(splitAt(N, XS))) | U52#(mark(X)) | → | U52#(X) | |
| active#(tail(cons(N, XS))) | → | mark#(U211(isNatural(N), XS)) | active#(U51(tt, V2)) | → | U52#(isLNat(V2)) | |
| mark#(U142(X)) | → | mark#(X) | U81#(active(X)) | → | U81#(X) | |
| splitAt#(mark(X1), X2) | → | splitAt#(X1, X2) | active#(U161(tt, N)) | → | natsFrom#(s(N)) | |
| active#(natsFrom(N)) | → | U161#(isNatural(N), N) | active#(isLNat(fst(V1))) | → | mark#(U61(isPLNat(V1))) | |
| mark#(U181(X1, X2)) | → | U181#(mark(X1), X2) | mark#(U22(X1, X2)) | → | U22#(mark(X1), X2) | |
| active#(isLNat(take(V1, V2))) | → | isNatural#(V1) | active#(isLNat(natsFrom(V1))) | → | isNatural#(V1) | |
| mark#(U31(X1, X2, X3)) | → | U31#(mark(X1), X2, X3) | mark#(U221(X1, X2, X3)) | → | active#(U221(mark(X1), X2, X3)) | |
| U131#(active(X1), X2) | → | U131#(X1, X2) | U201#(X1, mark(X2), X3, X4) | → | U201#(X1, X2, X3, X4) | |
| active#(sel(N, XS)) | → | mark#(U171(isNatural(N), N, XS)) | U12#(mark(X1), X2, X3) | → | U12#(X1, X2, X3) | |
| mark#(cons(X1, X2)) | → | mark#(X1) | U203#(X1, X2, X3, mark(X4)) | → | U203#(X1, X2, X3, X4) | |
| pair#(X1, mark(X2)) | → | pair#(X1, X2) | active#(tail(cons(N, XS))) | → | isNatural#(N) | |
| U21#(mark(X1), X2, X3) | → | U21#(X1, X2, X3) | mark#(U51(X1, X2)) | → | active#(U51(mark(X1), X2)) | |
| active#(isLNat(nil)) | → | mark#(tt) | U201#(X1, X2, X3, active(X4)) | → | U201#(X1, X2, X3, X4) | |
| mark#(U101(X1, X2)) | → | U101#(mark(X1), X2) | U61#(active(X)) | → | U61#(X) | |
| mark#(U32(X1, X2)) | → | mark#(X1) | U211#(mark(X1), X2) | → | U211#(X1, X2) | |
| active#(U32(tt, N)) | → | mark#(N) | U151#(active(X1), X2) | → | U151#(X1, X2) | |
| U51#(X1, active(X2)) | → | U51#(X1, X2) | U181#(X1, mark(X2)) | → | U181#(X1, X2) | |
| U151#(mark(X1), X2) | → | U151#(X1, X2) | active#(U121(tt)) | → | mark#(tt) | |
| active#(U211(tt, XS)) | → | mark#(U212(isLNat(XS), XS)) | U22#(mark(X1), X2) | → | U22#(X1, X2) | |
| mark#(tail(X)) | → | tail#(mark(X)) | active#(isNatural(0)) | → | mark#(tt) | |
| mark#(splitAt(X1, X2)) | → | splitAt#(mark(X1), mark(X2)) | active#(U12(tt, N, XS)) | → | snd#(splitAt(N, XS)) | |
| mark#(U152(X)) | → | active#(U152(mark(X))) | U12#(active(X1), X2, X3) | → | U12#(X1, X2, X3) | |
| U142#(mark(X)) | → | U142#(X) | U222#(active(X1), X2, X3) | → | U222#(X1, X2, X3) | |
| splitAt#(X1, active(X2)) | → | splitAt#(X1, X2) | active#(U22(tt, X)) | → | mark#(X) | |
| mark#(0) | → | active#(0) | active#(U161(tt, N)) | → | cons#(N, natsFrom(s(N))) | |
| U61#(mark(X)) | → | U61#(X) | U221#(X1, mark(X2), X3) | → | U221#(X1, X2, X3) | |
| active#(U101(tt, V2)) | → | mark#(U102(isLNat(V2))) | U201#(mark(X1), X2, X3, X4) | → | U201#(X1, X2, X3, X4) | |
| mark#(U71(X)) | → | active#(U71(mark(X))) | U211#(X1, mark(X2)) | → | U211#(X1, X2) | |
| mark#(U203(X1, X2, X3, X4)) | → | U203#(mark(X1), X2, X3, X4) | active#(U31(tt, N, XS)) | → | isLNat#(XS) | |
| U11#(X1, X2, active(X3)) | → | U11#(X1, X2, X3) | U201#(X1, X2, active(X3), X4) | → | U201#(X1, X2, X3, X4) | |
| mark#(U71(X)) | → | mark#(X) | U182#(X1, mark(X2)) | → | U182#(X1, X2) | |
| U204#(X1, mark(X2)) | → | U204#(X1, X2) | mark#(fst(X)) | → | fst#(mark(X)) | |
| mark#(U41(X1, X2)) | → | active#(U41(mark(X1), X2)) | U42#(mark(X)) | → | U42#(X) | |
| active#(isNatural(head(V1))) | → | mark#(U111(isLNat(V1))) | active#(U201(tt, N, X, XS)) | → | mark#(U202(isNatural(X), N, X, XS)) | |
| active#(U171(tt, N, XS)) | → | isLNat#(XS) | mark#(U81(X)) | → | mark#(X) | |
| active#(isLNat(natsFrom(V1))) | → | mark#(U71(isNatural(V1))) | mark#(U201(X1, X2, X3, X4)) | → | active#(U201(mark(X1), X2, X3, X4)) | |
| mark#(U132(X)) | → | U132#(mark(X)) | mark#(U172(X1, X2, X3)) | → | active#(U172(mark(X1), X2, X3)) | |
| active#(U81(tt)) | → | mark#(tt) | U131#(X1, active(X2)) | → | U131#(X1, X2) | |
| mark#(U41(X1, X2)) | → | U41#(mark(X1), X2) | sel#(active(X1), X2) | → | sel#(X1, X2) | |
| mark#(U161(X1, X2)) | → | mark#(X1) | active#(isLNat(cons(V1, V2))) | → | mark#(U51(isNatural(V1), V2)) | |
| U21#(X1, active(X2), X3) | → | U21#(X1, X2, X3) | U181#(mark(X1), X2) | → | U181#(X1, X2) | |
| mark#(U182(X1, X2)) | → | mark#(X1) | mark#(afterNth(X1, X2)) | → | afterNth#(mark(X1), mark(X2)) | |
| mark#(U21(X1, X2, X3)) | → | mark#(X1) | active#(U41(tt, V2)) | → | mark#(U42(isLNat(V2))) | |
| mark#(U102(X)) | → | U102#(mark(X)) | U22#(X1, mark(X2)) | → | U22#(X1, X2) | |
| U182#(active(X1), X2) | → | U182#(X1, X2) | U201#(X1, X2, mark(X3), X4) | → | U201#(X1, X2, X3, X4) | |
| U202#(mark(X1), X2, X3, X4) | → | U202#(X1, X2, X3, X4) | mark#(U182(X1, X2)) | → | U182#(mark(X1), X2) | |
| active#(U141(tt, V2)) | → | isLNat#(V2) | tail#(active(X)) | → | tail#(X) | |
| active#(U172(tt, N, XS)) | → | head#(afterNth(N, XS)) | U201#(X1, X2, X3, mark(X4)) | → | U201#(X1, X2, X3, X4) | |
| U121#(mark(X)) | → | U121#(X) | U191#(active(X1), X2) | → | U191#(X1, X2) | |
| active#(isLNat(tail(V1))) | → | mark#(U91(isLNat(V1))) | mark#(U212(X1, X2)) | → | active#(U212(mark(X1), X2)) | |
| active#(U182(tt, Y)) | → | mark#(Y) | U222#(X1, X2, mark(X3)) | → | U222#(X1, X2, X3) | |
| active#(isLNat(tail(V1))) | → | isLNat#(V1) | mark#(take(X1, X2)) | → | mark#(X2) | |
| mark#(natsFrom(X)) | → | natsFrom#(mark(X)) | mark#(U21(X1, X2, X3)) | → | active#(U21(mark(X1), X2, X3)) | |
| U212#(X1, mark(X2)) | → | U212#(X1, X2) | active#(U203(tt, N, X, XS)) | → | mark#(U204(splitAt(N, XS), X)) | |
| mark#(pair(X1, X2)) | → | active#(pair(mark(X1), mark(X2))) | U161#(X1, active(X2)) | → | U161#(X1, X2) | |
| active#(U101(tt, V2)) | → | isLNat#(V2) | active#(isNatural(sel(V1, V2))) | → | U131#(isNatural(V1), V2) | |
| active#(isNatural(head(V1))) | → | U111#(isLNat(V1)) | mark#(U151(X1, X2)) | → | mark#(X1) | |
| U203#(X1, X2, mark(X3), X4) | → | U203#(X1, X2, X3, X4) | U31#(X1, active(X2), X3) | → | U31#(X1, X2, X3) | |
| mark#(U11(X1, X2, X3)) | → | U11#(mark(X1), X2, X3) | U171#(X1, X2, mark(X3)) | → | U171#(X1, X2, X3) | |
| mark#(U132(X)) | → | mark#(X) | active#(natsFrom(N)) | → | mark#(U161(isNatural(N), N)) | |
| active#(U181(tt, Y)) | → | isLNat#(Y) | mark#(snd(X)) | → | active#(snd(mark(X))) | |
| mark#(U111(X)) | → | active#(U111(mark(X))) | mark#(U12(X1, X2, X3)) | → | active#(U12(mark(X1), X2, X3)) | |
| active#(afterNth(N, XS)) | → | U11#(isNatural(N), N, XS) | active#(isPLNat(pair(V1, V2))) | → | isLNat#(V1) | |
| mark#(sel(X1, X2)) | → | mark#(X1) | mark#(U203(X1, X2, X3, X4)) | → | mark#(X1) | |
| U204#(X1, active(X2)) | → | U204#(X1, X2) | mark#(U81(X)) | → | active#(U81(mark(X))) | |
| active#(isNatural(s(V1))) | → | U121#(isNatural(V1)) | mark#(U204(X1, X2)) | → | mark#(X1) | |
| mark#(U171(X1, X2, X3)) | → | mark#(X1) | active#(splitAt(0, XS)) | → | U191#(isLNat(XS), XS) | |
| mark#(afterNth(X1, X2)) | → | mark#(X1) | active#(isLNat(cons(V1, V2))) | → | U51#(isNatural(V1), V2) | |
| active#(U204(pair(YS, ZS), X)) | → | pair#(cons(X, YS), ZS) | U211#(active(X1), X2) | → | U211#(X1, X2) | |
| active#(U161(tt, N)) | → | s#(N) | active#(isPLNat(pair(V1, V2))) | → | U141#(isLNat(V1), V2) | |
| active#(isNatural(s(V1))) | → | mark#(U121(isNatural(V1))) | U172#(active(X1), X2, X3) | → | U172#(X1, X2, X3) | |
| active#(U204(pair(YS, ZS), X)) | → | cons#(X, YS) | active#(isPLNat(splitAt(V1, V2))) | → | U151#(isNatural(V1), V2) | |
| active#(U172(tt, N, XS)) | → | mark#(head(afterNth(N, XS))) | active#(U151(tt, V2)) | → | isLNat#(V2) | |
| head#(active(X)) | → | head#(X) | mark#(U71(X)) | → | U71#(mark(X)) | |
| active#(isLNat(tail(V1))) | → | U91#(isLNat(V1)) | active#(isNatural(sel(V1, V2))) | → | isNatural#(V1) | |
| mark#(U182(X1, X2)) | → | active#(U182(mark(X1), X2)) | isLNat#(active(X)) | → | isLNat#(X) | |
| U201#(X1, active(X2), X3, X4) | → | U201#(X1, X2, X3, X4) | U202#(X1, X2, X3, active(X4)) | → | U202#(X1, X2, X3, X4) | |
| active#(isLNat(afterNth(V1, V2))) | → | U41#(isNatural(V1), V2) | mark#(head(X)) | → | mark#(X) | |
| U32#(X1, active(X2)) | → | U32#(X1, X2) | active#(U11(tt, N, XS)) | → | mark#(U12(isLNat(XS), N, XS)) | |
| U41#(X1, active(X2)) | → | U41#(X1, X2) | mark#(U41(X1, X2)) | → | mark#(X1) | |
| cons#(X1, mark(X2)) | → | cons#(X1, X2) | U171#(X1, active(X2), X3) | → | U171#(X1, X2, X3) | |
| active#(U201(tt, N, X, XS)) | → | isNatural#(X) | mark#(fst(X)) | → | mark#(X) | |
| active#(U221(tt, N, XS)) | → | U222#(isLNat(XS), N, XS) | active#(sel(N, XS)) | → | isNatural#(N) | |
| snd#(mark(X)) | → | snd#(X) | active#(U202(tt, N, X, XS)) | → | U203#(isLNat(XS), N, X, XS) | |
| mark#(U221(X1, X2, X3)) | → | mark#(X1) | mark#(U131(X1, X2)) | → | active#(U131(mark(X1), X2)) | |
| pair#(X1, active(X2)) | → | pair#(X1, X2) | mark#(snd(X)) | → | mark#(X) | |
| U51#(X1, mark(X2)) | → | U51#(X1, X2) | U31#(X1, X2, active(X3)) | → | U31#(X1, X2, X3) | |
| active#(sel(N, XS)) | → | U171#(isNatural(N), N, XS) | active#(U41(tt, V2)) | → | U42#(isLNat(V2)) | |
| mark#(U172(X1, X2, X3)) | → | mark#(X1) | mark#(U204(X1, X2)) | → | U204#(mark(X1), X2) | |
| U152#(mark(X)) | → | U152#(X) | mark#(take(X1, X2)) | → | mark#(X1) | |
| active#(U111(tt)) | → | mark#(tt) | U212#(X1, active(X2)) | → | U212#(X1, X2) | |
| active#(splitAt(0, XS)) | → | mark#(U191(isLNat(XS), XS)) | U71#(active(X)) | → | U71#(X) | |
| mark#(s(X)) | → | s#(mark(X)) | U182#(mark(X1), X2) | → | U182#(X1, X2) | |
| active#(U202(tt, N, X, XS)) | → | isLNat#(XS) | active#(isLNat(fst(V1))) | → | U61#(isPLNat(V1)) | |
| active#(afterNth(N, XS)) | → | isNatural#(N) | U52#(active(X)) | → | U52#(X) | |
| U171#(X1, mark(X2), X3) | → | U171#(X1, X2, X3) | U172#(X1, active(X2), X3) | → | U172#(X1, X2, X3) | |
| U202#(X1, X2, active(X3), X4) | → | U202#(X1, X2, X3, X4) | afterNth#(mark(X1), X2) | → | afterNth#(X1, X2) | |
| mark#(U131(X1, X2)) | → | mark#(X1) | active#(U21(tt, X, Y)) | → | U22#(isLNat(Y), X) | |
| mark#(sel(X1, X2)) | → | sel#(mark(X1), mark(X2)) | U21#(X1, mark(X2), X3) | → | U21#(X1, X2, X3) | |
| mark#(U131(X1, X2)) | → | U131#(mark(X1), X2) | U11#(mark(X1), X2, X3) | → | U11#(X1, X2, X3) | |
| tail#(mark(X)) | → | tail#(X) | mark#(sel(X1, X2)) | → | active#(sel(mark(X1), mark(X2))) | |
| active#(U221(tt, N, XS)) | → | mark#(U222(isLNat(XS), N, XS)) | cons#(X1, active(X2)) | → | cons#(X1, X2) | |
| active#(U161(tt, N)) | → | mark#(cons(N, natsFrom(s(N)))) | U101#(X1, mark(X2)) | → | U101#(X1, X2) | |
| active#(snd(pair(X, Y))) | → | isLNat#(X) | active#(U201(tt, N, X, XS)) | → | U202#(isNatural(X), N, X, XS) | |
| active#(U52(tt)) | → | mark#(tt) | active#(isLNat(afterNth(V1, V2))) | → | mark#(U41(isNatural(V1), V2)) | |
| active#(isPLNat(pair(V1, V2))) | → | mark#(U141(isLNat(V1), V2)) | take#(mark(X1), X2) | → | take#(X1, X2) | |
| active#(afterNth(N, XS)) | → | mark#(U11(isNatural(N), N, XS)) | U221#(mark(X1), X2, X3) | → | U221#(X1, X2, X3) | |
| active#(U142(tt)) | → | mark#(tt) | mark#(pair(X1, X2)) | → | pair#(mark(X1), mark(X2)) | |
| mark#(U211(X1, X2)) | → | U211#(mark(X1), X2) | active#(U203(tt, N, X, XS)) | → | U204#(splitAt(N, XS), X) | |
| mark#(U204(X1, X2)) | → | active#(U204(mark(X1), X2)) | U11#(X1, X2, mark(X3)) | → | U11#(X1, X2, X3) | |
| mark#(U142(X)) | → | active#(U142(mark(X))) | U202#(X1, X2, X3, mark(X4)) | → | U202#(X1, X2, X3, X4) | |
| mark#(sel(X1, X2)) | → | mark#(X2) | fst#(mark(X)) | → | fst#(X) | |
| active#(U211(tt, XS)) | → | U212#(isLNat(XS), XS) | active#(isPLNat(splitAt(V1, V2))) | → | isNatural#(V1) | |
| afterNth#(X1, active(X2)) | → | afterNth#(X1, X2) | mark#(U12(X1, X2, X3)) | → | mark#(X1) | |
| active#(head(cons(N, XS))) | → | U31#(isNatural(N), N, XS) | U212#(mark(X1), X2) | → | U212#(X1, X2) | |
| U171#(mark(X1), X2, X3) | → | U171#(X1, X2, X3) | active#(isNatural(sel(V1, V2))) | → | mark#(U131(isNatural(V1), V2)) | |
| mark#(isLNat(X)) | → | isLNat#(X) | isLNat#(mark(X)) | → | isLNat#(X) | |
| mark#(head(X)) | → | head#(mark(X)) | mark#(take(X1, X2)) | → | take#(mark(X1), mark(X2)) | |
| U91#(mark(X)) | → | U91#(X) | active#(fst(pair(X, Y))) | → | isLNat#(X) | |
| U171#(active(X1), X2, X3) | → | U171#(X1, X2, X3) | U31#(X1, mark(X2), X3) | → | U31#(X1, X2, X3) | |
| mark#(U101(X1, X2)) | → | active#(U101(mark(X1), X2)) | mark#(pair(X1, X2)) | → | mark#(X2) | |
| U21#(X1, X2, active(X3)) | → | U21#(X1, X2, X3) | U172#(X1, X2, mark(X3)) | → | U172#(X1, X2, X3) | |
| active#(U222(tt, N, XS)) | → | fst#(splitAt(N, XS)) | U102#(mark(X)) | → | U102#(X) | |
| active#(U204(pair(YS, ZS), X)) | → | mark#(pair(cons(X, YS), ZS)) | active#(U212(tt, XS)) | → | mark#(XS) | |
| active#(isLNat(take(V1, V2))) | → | U101#(isNatural(V1), V2) | mark#(U42(X)) | → | U42#(mark(X)) | |
| U22#(active(X1), X2) | → | U22#(X1, X2) | mark#(U91(X)) | → | active#(U91(mark(X))) | |
| active#(U51(tt, V2)) | → | mark#(U52(isLNat(V2))) | U11#(X1, active(X2), X3) | → | U11#(X1, X2, X3) | |
| mark#(U161(X1, X2)) | → | active#(U161(mark(X1), X2)) | mark#(U222(X1, X2, X3)) | → | active#(U222(mark(X1), X2, X3)) | |
| fst#(active(X)) | → | fst#(X) | U41#(active(X1), X2) | → | U41#(X1, X2) | |
| sel#(X1, mark(X2)) | → | sel#(X1, X2) | U222#(X1, X2, active(X3)) | → | U222#(X1, X2, X3) | |
| mark#(U181(X1, X2)) | → | active#(U181(mark(X1), X2)) | active#(U141(tt, V2)) | → | mark#(U142(isLNat(V2))) | |
| mark#(pair(X1, X2)) | → | mark#(X1) | sel#(X1, active(X2)) | → | sel#(X1, X2) | |
| active#(U171(tt, N, XS)) | → | mark#(U172(isLNat(XS), N, XS)) | U21#(active(X1), X2, X3) | → | U21#(X1, X2, X3) | |
| active#(U11(tt, N, XS)) | → | U12#(isLNat(XS), N, XS) | mark#(tail(X)) | → | mark#(X) | |
| mark#(U102(X)) | → | active#(U102(mark(X))) | U161#(X1, mark(X2)) | → | U161#(X1, X2) | |
| mark#(afterNth(X1, X2)) | → | mark#(X2) | mark#(U222(X1, X2, X3)) | → | U222#(mark(X1), X2, X3) | |
| mark#(U132(X)) | → | active#(U132(mark(X))) | mark#(U111(X)) | → | U111#(mark(X)) | |
| pair#(mark(X1), X2) | → | pair#(X1, X2) | active#(U171(tt, N, XS)) | → | U172#(isLNat(XS), N, XS) | |
| mark#(tt) | → | active#(tt) | cons#(mark(X1), X2) | → | cons#(X1, X2) | |
| active#(take(N, XS)) | → | mark#(U221(isNatural(N), N, XS)) | U101#(active(X1), X2) | → | U101#(X1, X2) | |
| U203#(active(X1), X2, X3, X4) | → | U203#(X1, X2, X3, X4) | U111#(mark(X)) | → | U111#(X) | |
| U22#(X1, active(X2)) | → | U22#(X1, X2) | mark#(U52(X)) | → | active#(U52(mark(X))) | |
| U201#(active(X1), X2, X3, X4) | → | U201#(X1, X2, X3, X4) | U221#(X1, X2, mark(X3)) | → | U221#(X1, X2, X3) | |
| U21#(X1, X2, mark(X3)) | → | U21#(X1, X2, X3) | mark#(U141(X1, X2)) | → | active#(U141(mark(X1), X2)) | |
| active#(isLNat(snd(V1))) | → | mark#(U81(isPLNat(V1))) | active#(U21(tt, X, Y)) | → | mark#(U22(isLNat(Y), X)) | |
| active#(isLNat(snd(V1))) | → | U81#(isPLNat(V1)) | active#(U181(tt, Y)) | → | U182#(isLNat(Y), Y) | |
| U203#(X1, active(X2), X3, X4) | → | U203#(X1, X2, X3, X4) | U181#(active(X1), X2) | → | U181#(X1, X2) | |
| mark#(s(X)) | → | active#(s(mark(X))) | head#(mark(X)) | → | head#(X) | |
| active#(U131(tt, V2)) | → | U132#(isLNat(V2)) | active#(take(N, XS)) | → | U221#(isNatural(N), N, XS) | |
| active#(splitAt(s(N), cons(X, XS))) | → | U201#(isNatural(N), N, X, XS) | mark#(U12(X1, X2, X3)) | → | U12#(mark(X1), X2, X3) | |
| snd#(active(X)) | → | snd#(X) | mark#(U141(X1, X2)) | → | U141#(mark(X1), X2) | |
| U141#(X1, mark(X2)) | → | U141#(X1, X2) | mark#(U201(X1, X2, X3, X4)) | → | U201#(mark(X1), X2, X3, X4) | |
| active#(isNatural(s(V1))) | → | isNatural#(V1) | U132#(active(X)) | → | U132#(X) | |
| active#(U102(tt)) | → | mark#(tt) | mark#(U121(X)) | → | U121#(mark(X)) | |
| mark#(cons(X1, X2)) | → | active#(cons(mark(X1), X2)) | mark#(snd(X)) | → | snd#(mark(X)) | |
| active#(U12(tt, N, XS)) | → | splitAt#(N, XS) | U42#(active(X)) | → | U42#(X) | |
| U191#(X1, active(X2)) | → | U191#(X1, X2) | mark#(U52(X)) | → | U52#(mark(X)) | |
| mark#(U212(X1, X2)) | → | mark#(X1) | U131#(mark(X1), X2) | → | U131#(X1, X2) | |
| U151#(X1, mark(X2)) | → | U151#(X1, X2) | pair#(active(X1), X2) | → | pair#(X1, X2) | |
| mark#(U212(X1, X2)) | → | U212#(mark(X1), X2) | U142#(active(X)) | → | U142#(X) | |
| mark#(U32(X1, X2)) | → | U32#(mark(X1), X2) | active#(isNatural(head(V1))) | → | isLNat#(V1) | |
| mark#(U121(X)) | → | active#(U121(mark(X))) | U182#(X1, active(X2)) | → | U182#(X1, X2) | |
| U203#(X1, X2, active(X3), X4) | → | U203#(X1, X2, X3, X4) | U202#(X1, active(X2), X3, X4) | → | U202#(X1, X2, X3, X4) | |
| U222#(mark(X1), X2, X3) | → | U222#(X1, X2, X3) | active#(U131(tt, V2)) | → | mark#(U132(isLNat(V2))) | |
| active#(U11(tt, N, XS)) | → | isLNat#(XS) | U161#(mark(X1), X2) | → | U161#(X1, X2) | |
| mark#(U171(X1, X2, X3)) | → | U171#(mark(X1), X2, X3) | mark#(U202(X1, X2, X3, X4)) | → | mark#(X1) | |
| U51#(active(X1), X2) | → | U51#(X1, X2) | mark#(U203(X1, X2, X3, X4)) | → | active#(U203(mark(X1), X2, X3, X4)) | |
| mark#(U81(X)) | → | U81#(mark(X)) | mark#(U221(X1, X2, X3)) | → | U221#(mark(X1), X2, X3) | |
| mark#(U51(X1, X2)) | → | mark#(X1) | mark#(U151(X1, X2)) | → | active#(U151(mark(X1), X2)) | |
| U32#(X1, mark(X2)) | → | U32#(X1, X2) | active#(isLNat(snd(V1))) | → | isPLNat#(V1) | |
| U102#(active(X)) | → | U102#(X) | mark#(isPLNat(X)) | → | active#(isPLNat(X)) | |
| U211#(X1, active(X2)) | → | U211#(X1, X2) | active#(U141(tt, V2)) | → | U142#(isLNat(V2)) | |
| mark#(U152(X)) | → | mark#(X) | active#(U131(tt, V2)) | → | isLNat#(V2) | |
| U161#(active(X1), X2) | → | U161#(X1, X2) | active#(snd(pair(X, Y))) | → | U181#(isLNat(X), Y) | |
| mark#(U222(X1, X2, X3)) | → | mark#(X1) | mark#(U191(X1, X2)) | → | active#(U191(mark(X1), X2)) | |
| mark#(U141(X1, X2)) | → | mark#(X1) | active#(fst(pair(X, Y))) | → | mark#(U21(isLNat(X), X, Y)) | |
| U204#(active(X1), X2) | → | U204#(X1, X2) | mark#(U202(X1, X2, X3, X4)) | → | U202#(mark(X1), X2, X3, X4) | |
| U111#(active(X)) | → | U111#(X) | U141#(mark(X1), X2) | → | U141#(X1, X2) | |
| U222#(X1, mark(X2), X3) | → | U222#(X1, X2, X3) | U32#(mark(X1), X2) | → | U32#(X1, X2) | |
| U11#(X1, mark(X2), X3) | → | U11#(X1, X2, X3) | active#(tail(cons(N, XS))) | → | U211#(isNatural(N), XS) | |
| s#(active(X)) | → | s#(X) | U202#(active(X1), X2, X3, X4) | → | U202#(X1, X2, X3, X4) | |
| active#(U202(tt, N, X, XS)) | → | mark#(U203(isLNat(XS), N, X, XS)) | U31#(mark(X1), X2, X3) | → | U31#(X1, X2, X3) | |
| mark#(U91(X)) | → | mark#(X) | take#(active(X1), X2) | → | take#(X1, X2) |
| active(U101(tt, V2)) | → | mark(U102(isLNat(V2))) | active(U102(tt)) | → | mark(tt) | |
| active(U11(tt, N, XS)) | → | mark(U12(isLNat(XS), N, XS)) | active(U111(tt)) | → | mark(tt) | |
| active(U12(tt, N, XS)) | → | mark(snd(splitAt(N, XS))) | active(U121(tt)) | → | mark(tt) | |
| active(U131(tt, V2)) | → | mark(U132(isLNat(V2))) | active(U132(tt)) | → | mark(tt) | |
| active(U141(tt, V2)) | → | mark(U142(isLNat(V2))) | active(U142(tt)) | → | mark(tt) | |
| active(U151(tt, V2)) | → | mark(U152(isLNat(V2))) | active(U152(tt)) | → | mark(tt) | |
| active(U161(tt, N)) | → | mark(cons(N, natsFrom(s(N)))) | active(U171(tt, N, XS)) | → | mark(U172(isLNat(XS), N, XS)) | |
| active(U172(tt, N, XS)) | → | mark(head(afterNth(N, XS))) | active(U181(tt, Y)) | → | mark(U182(isLNat(Y), Y)) | |
| active(U182(tt, Y)) | → | mark(Y) | active(U191(tt, XS)) | → | mark(pair(nil, XS)) | |
| active(U201(tt, N, X, XS)) | → | mark(U202(isNatural(X), N, X, XS)) | active(U202(tt, N, X, XS)) | → | mark(U203(isLNat(XS), N, X, XS)) | |
| active(U203(tt, N, X, XS)) | → | mark(U204(splitAt(N, XS), X)) | active(U204(pair(YS, ZS), X)) | → | mark(pair(cons(X, YS), ZS)) | |
| active(U21(tt, X, Y)) | → | mark(U22(isLNat(Y), X)) | active(U211(tt, XS)) | → | mark(U212(isLNat(XS), XS)) | |
| active(U212(tt, XS)) | → | mark(XS) | active(U22(tt, X)) | → | mark(X) | |
| active(U221(tt, N, XS)) | → | mark(U222(isLNat(XS), N, XS)) | active(U222(tt, N, XS)) | → | mark(fst(splitAt(N, XS))) | |
| active(U31(tt, N, XS)) | → | mark(U32(isLNat(XS), N)) | active(U32(tt, N)) | → | mark(N) | |
| active(U41(tt, V2)) | → | mark(U42(isLNat(V2))) | active(U42(tt)) | → | mark(tt) | |
| active(U51(tt, V2)) | → | mark(U52(isLNat(V2))) | active(U52(tt)) | → | mark(tt) | |
| active(U61(tt)) | → | mark(tt) | active(U71(tt)) | → | mark(tt) | |
| active(U81(tt)) | → | mark(tt) | active(U91(tt)) | → | mark(tt) | |
| active(afterNth(N, XS)) | → | mark(U11(isNatural(N), N, XS)) | active(fst(pair(X, Y))) | → | mark(U21(isLNat(X), X, Y)) | |
| active(head(cons(N, XS))) | → | mark(U31(isNatural(N), N, XS)) | active(isLNat(nil)) | → | mark(tt) | |
| active(isLNat(afterNth(V1, V2))) | → | mark(U41(isNatural(V1), V2)) | active(isLNat(cons(V1, V2))) | → | mark(U51(isNatural(V1), V2)) | |
| active(isLNat(fst(V1))) | → | mark(U61(isPLNat(V1))) | active(isLNat(natsFrom(V1))) | → | mark(U71(isNatural(V1))) | |
| active(isLNat(snd(V1))) | → | mark(U81(isPLNat(V1))) | active(isLNat(tail(V1))) | → | mark(U91(isLNat(V1))) | |
| active(isLNat(take(V1, V2))) | → | mark(U101(isNatural(V1), V2)) | active(isNatural(0)) | → | mark(tt) | |
| active(isNatural(head(V1))) | → | mark(U111(isLNat(V1))) | active(isNatural(s(V1))) | → | mark(U121(isNatural(V1))) | |
| active(isNatural(sel(V1, V2))) | → | mark(U131(isNatural(V1), V2)) | active(isPLNat(pair(V1, V2))) | → | mark(U141(isLNat(V1), V2)) | |
| active(isPLNat(splitAt(V1, V2))) | → | mark(U151(isNatural(V1), V2)) | active(natsFrom(N)) | → | mark(U161(isNatural(N), N)) | |
| active(sel(N, XS)) | → | mark(U171(isNatural(N), N, XS)) | active(snd(pair(X, Y))) | → | mark(U181(isLNat(X), Y)) | |
| active(splitAt(0, XS)) | → | mark(U191(isLNat(XS), XS)) | active(splitAt(s(N), cons(X, XS))) | → | mark(U201(isNatural(N), N, X, XS)) | |
| active(tail(cons(N, XS))) | → | mark(U211(isNatural(N), XS)) | active(take(N, XS)) | → | mark(U221(isNatural(N), N, XS)) | |
| mark(U101(X1, X2)) | → | active(U101(mark(X1), X2)) | mark(tt) | → | active(tt) | |
| mark(U102(X)) | → | active(U102(mark(X))) | mark(isLNat(X)) | → | active(isLNat(X)) | |
| mark(U11(X1, X2, X3)) | → | active(U11(mark(X1), X2, X3)) | mark(U12(X1, X2, X3)) | → | active(U12(mark(X1), X2, X3)) | |
| mark(U111(X)) | → | active(U111(mark(X))) | mark(snd(X)) | → | active(snd(mark(X))) | |
| mark(splitAt(X1, X2)) | → | active(splitAt(mark(X1), mark(X2))) | mark(U121(X)) | → | active(U121(mark(X))) | |
| mark(U131(X1, X2)) | → | active(U131(mark(X1), X2)) | mark(U132(X)) | → | active(U132(mark(X))) | |
| mark(U141(X1, X2)) | → | active(U141(mark(X1), X2)) | mark(U142(X)) | → | active(U142(mark(X))) | |
| mark(U151(X1, X2)) | → | active(U151(mark(X1), X2)) | mark(U152(X)) | → | active(U152(mark(X))) | |
| mark(U161(X1, X2)) | → | active(U161(mark(X1), X2)) | mark(cons(X1, X2)) | → | active(cons(mark(X1), X2)) | |
| mark(natsFrom(X)) | → | active(natsFrom(mark(X))) | mark(s(X)) | → | active(s(mark(X))) | |
| mark(U171(X1, X2, X3)) | → | active(U171(mark(X1), X2, X3)) | mark(U172(X1, X2, X3)) | → | active(U172(mark(X1), X2, X3)) | |
| mark(head(X)) | → | active(head(mark(X))) | mark(afterNth(X1, X2)) | → | active(afterNth(mark(X1), mark(X2))) | |
| mark(U181(X1, X2)) | → | active(U181(mark(X1), X2)) | mark(U182(X1, X2)) | → | active(U182(mark(X1), X2)) | |
| mark(U191(X1, X2)) | → | active(U191(mark(X1), X2)) | mark(pair(X1, X2)) | → | active(pair(mark(X1), mark(X2))) | |
| mark(nil) | → | active(nil) | mark(U201(X1, X2, X3, X4)) | → | active(U201(mark(X1), X2, X3, X4)) | |
| mark(U202(X1, X2, X3, X4)) | → | active(U202(mark(X1), X2, X3, X4)) | mark(isNatural(X)) | → | active(isNatural(X)) | |
| mark(U203(X1, X2, X3, X4)) | → | active(U203(mark(X1), X2, X3, X4)) | mark(U204(X1, X2)) | → | active(U204(mark(X1), X2)) | |
| mark(U21(X1, X2, X3)) | → | active(U21(mark(X1), X2, X3)) | mark(U22(X1, X2)) | → | active(U22(mark(X1), X2)) | |
| mark(U211(X1, X2)) | → | active(U211(mark(X1), X2)) | mark(U212(X1, X2)) | → | active(U212(mark(X1), X2)) | |
| mark(U221(X1, X2, X3)) | → | active(U221(mark(X1), X2, X3)) | mark(U222(X1, X2, X3)) | → | active(U222(mark(X1), X2, X3)) | |
| mark(fst(X)) | → | active(fst(mark(X))) | mark(U31(X1, X2, X3)) | → | active(U31(mark(X1), X2, X3)) | |
| mark(U32(X1, X2)) | → | active(U32(mark(X1), X2)) | mark(U41(X1, X2)) | → | active(U41(mark(X1), X2)) | |
| mark(U42(X)) | → | active(U42(mark(X))) | mark(U51(X1, X2)) | → | active(U51(mark(X1), X2)) | |
| mark(U52(X)) | → | active(U52(mark(X))) | mark(U61(X)) | → | active(U61(mark(X))) | |
| mark(U71(X)) | → | active(U71(mark(X))) | mark(U81(X)) | → | active(U81(mark(X))) | |
| mark(U91(X)) | → | active(U91(mark(X))) | mark(isPLNat(X)) | → | active(isPLNat(X)) | |
| mark(tail(X)) | → | active(tail(mark(X))) | mark(take(X1, X2)) | → | active(take(mark(X1), mark(X2))) | |
| mark(0) | → | active(0) | mark(sel(X1, X2)) | → | active(sel(mark(X1), mark(X2))) | |
| U101(mark(X1), X2) | → | U101(X1, X2) | U101(X1, mark(X2)) | → | U101(X1, X2) | |
| U101(active(X1), X2) | → | U101(X1, X2) | U101(X1, active(X2)) | → | U101(X1, X2) | |
| U102(mark(X)) | → | U102(X) | U102(active(X)) | → | U102(X) | |
| isLNat(mark(X)) | → | isLNat(X) | isLNat(active(X)) | → | isLNat(X) | |
| U11(mark(X1), X2, X3) | → | U11(X1, X2, X3) | U11(X1, mark(X2), X3) | → | U11(X1, X2, X3) | |
| U11(X1, X2, mark(X3)) | → | U11(X1, X2, X3) | U11(active(X1), X2, X3) | → | U11(X1, X2, X3) | |
| U11(X1, active(X2), X3) | → | U11(X1, X2, X3) | U11(X1, X2, active(X3)) | → | U11(X1, X2, X3) | |
| U12(mark(X1), X2, X3) | → | U12(X1, X2, X3) | U12(X1, mark(X2), X3) | → | U12(X1, X2, X3) | |
| U12(X1, X2, mark(X3)) | → | U12(X1, X2, X3) | U12(active(X1), X2, X3) | → | U12(X1, X2, X3) | |
| U12(X1, active(X2), X3) | → | U12(X1, X2, X3) | U12(X1, X2, active(X3)) | → | U12(X1, X2, X3) | |
| U111(mark(X)) | → | U111(X) | U111(active(X)) | → | U111(X) | |
| snd(mark(X)) | → | snd(X) | snd(active(X)) | → | snd(X) | |
| splitAt(mark(X1), X2) | → | splitAt(X1, X2) | splitAt(X1, mark(X2)) | → | splitAt(X1, X2) | |
| splitAt(active(X1), X2) | → | splitAt(X1, X2) | splitAt(X1, active(X2)) | → | splitAt(X1, X2) | |
| U121(mark(X)) | → | U121(X) | U121(active(X)) | → | U121(X) | |
| U131(mark(X1), X2) | → | U131(X1, X2) | U131(X1, mark(X2)) | → | U131(X1, X2) | |
| U131(active(X1), X2) | → | U131(X1, X2) | U131(X1, active(X2)) | → | U131(X1, X2) | |
| U132(mark(X)) | → | U132(X) | U132(active(X)) | → | U132(X) | |
| U141(mark(X1), X2) | → | U141(X1, X2) | U141(X1, mark(X2)) | → | U141(X1, X2) | |
| U141(active(X1), X2) | → | U141(X1, X2) | U141(X1, active(X2)) | → | U141(X1, X2) | |
| U142(mark(X)) | → | U142(X) | U142(active(X)) | → | U142(X) | |
| U151(mark(X1), X2) | → | U151(X1, X2) | U151(X1, mark(X2)) | → | U151(X1, X2) | |
| U151(active(X1), X2) | → | U151(X1, X2) | U151(X1, active(X2)) | → | U151(X1, X2) | |
| U152(mark(X)) | → | U152(X) | U152(active(X)) | → | U152(X) | |
| U161(mark(X1), X2) | → | U161(X1, X2) | U161(X1, mark(X2)) | → | U161(X1, X2) | |
| U161(active(X1), X2) | → | U161(X1, X2) | U161(X1, active(X2)) | → | U161(X1, X2) | |
| cons(mark(X1), X2) | → | cons(X1, X2) | cons(X1, mark(X2)) | → | cons(X1, X2) | |
| cons(active(X1), X2) | → | cons(X1, X2) | cons(X1, active(X2)) | → | cons(X1, X2) | |
| natsFrom(mark(X)) | → | natsFrom(X) | natsFrom(active(X)) | → | natsFrom(X) | |
| s(mark(X)) | → | s(X) | s(active(X)) | → | s(X) | |
| U171(mark(X1), X2, X3) | → | U171(X1, X2, X3) | U171(X1, mark(X2), X3) | → | U171(X1, X2, X3) | |
| U171(X1, X2, mark(X3)) | → | U171(X1, X2, X3) | U171(active(X1), X2, X3) | → | U171(X1, X2, X3) | |
| U171(X1, active(X2), X3) | → | U171(X1, X2, X3) | U171(X1, X2, active(X3)) | → | U171(X1, X2, X3) | |
| U172(mark(X1), X2, X3) | → | U172(X1, X2, X3) | U172(X1, mark(X2), X3) | → | U172(X1, X2, X3) | |
| U172(X1, X2, mark(X3)) | → | U172(X1, X2, X3) | U172(active(X1), X2, X3) | → | U172(X1, X2, X3) | |
| U172(X1, active(X2), X3) | → | U172(X1, X2, X3) | U172(X1, X2, active(X3)) | → | U172(X1, X2, X3) | |
| head(mark(X)) | → | head(X) | head(active(X)) | → | head(X) | |
| afterNth(mark(X1), X2) | → | afterNth(X1, X2) | afterNth(X1, mark(X2)) | → | afterNth(X1, X2) | |
| afterNth(active(X1), X2) | → | afterNth(X1, X2) | afterNth(X1, active(X2)) | → | afterNth(X1, X2) | |
| U181(mark(X1), X2) | → | U181(X1, X2) | U181(X1, mark(X2)) | → | U181(X1, X2) | |
| U181(active(X1), X2) | → | U181(X1, X2) | U181(X1, active(X2)) | → | U181(X1, X2) | |
| U182(mark(X1), X2) | → | U182(X1, X2) | U182(X1, mark(X2)) | → | U182(X1, X2) | |
| U182(active(X1), X2) | → | U182(X1, X2) | U182(X1, active(X2)) | → | U182(X1, X2) | |
| U191(mark(X1), X2) | → | U191(X1, X2) | U191(X1, mark(X2)) | → | U191(X1, X2) | |
| U191(active(X1), X2) | → | U191(X1, X2) | U191(X1, active(X2)) | → | U191(X1, X2) | |
| pair(mark(X1), X2) | → | pair(X1, X2) | pair(X1, mark(X2)) | → | pair(X1, X2) | |
| pair(active(X1), X2) | → | pair(X1, X2) | pair(X1, active(X2)) | → | pair(X1, X2) | |
| U201(mark(X1), X2, X3, X4) | → | U201(X1, X2, X3, X4) | U201(X1, mark(X2), X3, X4) | → | U201(X1, X2, X3, X4) | |
| U201(X1, X2, mark(X3), X4) | → | U201(X1, X2, X3, X4) | U201(X1, X2, X3, mark(X4)) | → | U201(X1, X2, X3, X4) | |
| U201(active(X1), X2, X3, X4) | → | U201(X1, X2, X3, X4) | U201(X1, active(X2), X3, X4) | → | U201(X1, X2, X3, X4) | |
| U201(X1, X2, active(X3), X4) | → | U201(X1, X2, X3, X4) | U201(X1, X2, X3, active(X4)) | → | U201(X1, X2, X3, X4) | |
| U202(mark(X1), X2, X3, X4) | → | U202(X1, X2, X3, X4) | U202(X1, mark(X2), X3, X4) | → | U202(X1, X2, X3, X4) | |
| U202(X1, X2, mark(X3), X4) | → | U202(X1, X2, X3, X4) | U202(X1, X2, X3, mark(X4)) | → | U202(X1, X2, X3, X4) | |
| U202(active(X1), X2, X3, X4) | → | U202(X1, X2, X3, X4) | U202(X1, active(X2), X3, X4) | → | U202(X1, X2, X3, X4) | |
| U202(X1, X2, active(X3), X4) | → | U202(X1, X2, X3, X4) | U202(X1, X2, X3, active(X4)) | → | U202(X1, X2, X3, X4) | |
| isNatural(mark(X)) | → | isNatural(X) | isNatural(active(X)) | → | isNatural(X) | |
| U203(mark(X1), X2, X3, X4) | → | U203(X1, X2, X3, X4) | U203(X1, mark(X2), X3, X4) | → | U203(X1, X2, X3, X4) | |
| U203(X1, X2, mark(X3), X4) | → | U203(X1, X2, X3, X4) | U203(X1, X2, X3, mark(X4)) | → | U203(X1, X2, X3, X4) | |
| U203(active(X1), X2, X3, X4) | → | U203(X1, X2, X3, X4) | U203(X1, active(X2), X3, X4) | → | U203(X1, X2, X3, X4) | |
| U203(X1, X2, active(X3), X4) | → | U203(X1, X2, X3, X4) | U203(X1, X2, X3, active(X4)) | → | U203(X1, X2, X3, X4) | |
| U204(mark(X1), X2) | → | U204(X1, X2) | U204(X1, mark(X2)) | → | U204(X1, X2) | |
| U204(active(X1), X2) | → | U204(X1, X2) | U204(X1, active(X2)) | → | U204(X1, X2) | |
| U21(mark(X1), X2, X3) | → | U21(X1, X2, X3) | U21(X1, mark(X2), X3) | → | U21(X1, X2, X3) | |
| U21(X1, X2, mark(X3)) | → | U21(X1, X2, X3) | U21(active(X1), X2, X3) | → | U21(X1, X2, X3) | |
| U21(X1, active(X2), X3) | → | U21(X1, X2, X3) | U21(X1, X2, active(X3)) | → | U21(X1, X2, X3) | |
| U22(mark(X1), X2) | → | U22(X1, X2) | U22(X1, mark(X2)) | → | U22(X1, X2) | |
| U22(active(X1), X2) | → | U22(X1, X2) | U22(X1, active(X2)) | → | U22(X1, X2) | |
| U211(mark(X1), X2) | → | U211(X1, X2) | U211(X1, mark(X2)) | → | U211(X1, X2) | |
| U211(active(X1), X2) | → | U211(X1, X2) | U211(X1, active(X2)) | → | U211(X1, X2) | |
| U212(mark(X1), X2) | → | U212(X1, X2) | U212(X1, mark(X2)) | → | U212(X1, X2) | |
| U212(active(X1), X2) | → | U212(X1, X2) | U212(X1, active(X2)) | → | U212(X1, X2) | |
| U221(mark(X1), X2, X3) | → | U221(X1, X2, X3) | U221(X1, mark(X2), X3) | → | U221(X1, X2, X3) | |
| U221(X1, X2, mark(X3)) | → | U221(X1, X2, X3) | U221(active(X1), X2, X3) | → | U221(X1, X2, X3) | |
| U221(X1, active(X2), X3) | → | U221(X1, X2, X3) | U221(X1, X2, active(X3)) | → | U221(X1, X2, X3) | |
| U222(mark(X1), X2, X3) | → | U222(X1, X2, X3) | U222(X1, mark(X2), X3) | → | U222(X1, X2, X3) | |
| U222(X1, X2, mark(X3)) | → | U222(X1, X2, X3) | U222(active(X1), X2, X3) | → | U222(X1, X2, X3) | |
| U222(X1, active(X2), X3) | → | U222(X1, X2, X3) | U222(X1, X2, active(X3)) | → | U222(X1, X2, X3) | |
| fst(mark(X)) | → | fst(X) | fst(active(X)) | → | fst(X) | |
| U31(mark(X1), X2, X3) | → | U31(X1, X2, X3) | U31(X1, mark(X2), X3) | → | U31(X1, X2, X3) | |
| U31(X1, X2, mark(X3)) | → | U31(X1, X2, X3) | U31(active(X1), X2, X3) | → | U31(X1, X2, X3) | |
| U31(X1, active(X2), X3) | → | U31(X1, X2, X3) | U31(X1, X2, active(X3)) | → | U31(X1, X2, X3) | |
| U32(mark(X1), X2) | → | U32(X1, X2) | U32(X1, mark(X2)) | → | U32(X1, X2) | |
| U32(active(X1), X2) | → | U32(X1, X2) | U32(X1, active(X2)) | → | U32(X1, X2) | |
| U41(mark(X1), X2) | → | U41(X1, X2) | U41(X1, mark(X2)) | → | U41(X1, X2) | |
| U41(active(X1), X2) | → | U41(X1, X2) | U41(X1, active(X2)) | → | U41(X1, X2) | |
| U42(mark(X)) | → | U42(X) | U42(active(X)) | → | U42(X) | |
| U51(mark(X1), X2) | → | U51(X1, X2) | U51(X1, mark(X2)) | → | U51(X1, X2) | |
| U51(active(X1), X2) | → | U51(X1, X2) | U51(X1, active(X2)) | → | U51(X1, X2) | |
| U52(mark(X)) | → | U52(X) | U52(active(X)) | → | U52(X) | |
| U61(mark(X)) | → | U61(X) | U61(active(X)) | → | U61(X) | |
| U71(mark(X)) | → | U71(X) | U71(active(X)) | → | U71(X) | |
| U81(mark(X)) | → | U81(X) | U81(active(X)) | → | U81(X) | |
| U91(mark(X)) | → | U91(X) | U91(active(X)) | → | U91(X) | |
| isPLNat(mark(X)) | → | isPLNat(X) | isPLNat(active(X)) | → | isPLNat(X) | |
| tail(mark(X)) | → | tail(X) | tail(active(X)) | → | tail(X) | |
| take(mark(X1), X2) | → | take(X1, X2) | take(X1, mark(X2)) | → | take(X1, X2) | |
| take(active(X1), X2) | → | take(X1, X2) | take(X1, active(X2)) | → | take(X1, X2) | |
| sel(mark(X1), X2) | → | sel(X1, X2) | sel(X1, mark(X2)) | → | sel(X1, X2) | |
| sel(active(X1), X2) | → | sel(X1, X2) | sel(X1, active(X2)) | → | sel(X1, X2) |
Termination of terms over the following signature is verified: natsFrom, U161, U204, U203, fst, U111, U61, U211, U212, head, U21, U22, U151, mark, isPLNat, U152, tail, U71, U191, 0, U121, U221, isLNat, U222, active, U31, U32, U181, U182, pair, isNatural, U132, U131, U42, U41, U91, cons, snd, U171, U172, splitAt, U201, U142, U202, U141, s, U51, tt, take, U81, U52, U11, U12, afterNth, U102, sel, U101, nil