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)].
| proper#(cons(X1, X2)) | → | proper#(X1) | proper#(U41(X1, X2)) | → | proper#(X1) | |
| active#(U182(X1, X2)) | → | U182#(active(X1), X2) | proper#(tail(X)) | → | proper#(X) | |
| active#(U211(tt, XS)) | → | isLNat#(XS) | proper#(U121(X)) | → | U121#(proper(X)) | |
| proper#(U161(X1, X2)) | → | proper#(X2) | U132#(mark(X)) | → | U132#(X) | |
| active#(U191(tt, XS)) | → | pair#(nil, XS) | U51#(mark(X1), X2) | → | U51#(X1, X2) | |
| isNatural#(ok(X)) | → | isNatural#(X) | active#(U221(tt, N, XS)) | → | isLNat#(XS) | |
| proper#(U11(X1, X2, X3)) | → | proper#(X2) | proper#(U222(X1, X2, X3)) | → | proper#(X2) | |
| active#(U212(X1, X2)) | → | active#(X1) | active#(U21(tt, X, Y)) | → | isLNat#(Y) | |
| proper#(U222(X1, X2, X3)) | → | proper#(X3) | U81#(mark(X)) | → | U81#(X) | |
| splitAt#(X1, mark(X2)) | → | splitAt#(X1, X2) | proper#(U101(X1, X2)) | → | U101#(proper(X1), proper(X2)) | |
| proper#(U211(X1, X2)) | → | proper#(X1) | active#(afterNth(X1, X2)) | → | afterNth#(active(X1), X2) | |
| active#(U12(X1, X2, X3)) | → | active#(X1) | U172#(mark(X1), X2, X3) | → | U172#(X1, X2, X3) | |
| active#(U41(X1, X2)) | → | active#(X1) | U203#(mark(X1), X2, X3, X4) | → | U203#(X1, X2, X3, X4) | |
| active#(isLNat(cons(V1, V2))) | → | isNatural#(V1) | active#(isLNat(afterNth(V1, V2))) | → | isNatural#(V1) | |
| proper#(U12(X1, X2, X3)) | → | proper#(X1) | natsFrom#(mark(X)) | → | natsFrom#(X) | |
| proper#(U21(X1, X2, X3)) | → | proper#(X3) | active#(take(N, XS)) | → | isNatural#(N) | |
| active#(splitAt(0, XS)) | → | isLNat#(XS) | active#(U12(X1, X2, X3)) | → | U12#(active(X1), X2, X3) | |
| active#(snd(X)) | → | snd#(active(X)) | active#(fst(pair(X, Y))) | → | U21#(isLNat(X), X, Y) | |
| active#(U52(X)) | → | active#(X) | active#(U22(X1, X2)) | → | active#(X1) | |
| proper#(U51(X1, X2)) | → | proper#(X2) | proper#(U71(X)) | → | U71#(proper(X)) | |
| U191#(mark(X1), X2) | → | U191#(X1, X2) | isLNat#(ok(X)) | → | isLNat#(X) | |
| active#(sel(X1, X2)) | → | sel#(X1, active(X2)) | active#(U41(tt, V2)) | → | isLNat#(V2) | |
| proper#(U202(X1, X2, X3, X4)) | → | U202#(proper(X1), proper(X2), proper(X3), proper(X4)) | active#(afterNth(X1, X2)) | → | active#(X2) | |
| proper#(U171(X1, X2, X3)) | → | proper#(X2) | proper#(U21(X1, X2, X3)) | → | U21#(proper(X1), proper(X2), proper(X3)) | |
| active#(U172(tt, N, XS)) | → | afterNth#(N, XS) | proper#(pair(X1, X2)) | → | pair#(proper(X1), proper(X2)) | |
| proper#(tail(X)) | → | tail#(proper(X)) | U22#(ok(X1), ok(X2)) | → | U22#(X1, X2) | |
| active#(U151(tt, V2)) | → | U152#(isLNat(V2)) | active#(U161(X1, X2)) | → | active#(X1) | |
| active#(U161(X1, X2)) | → | U161#(active(X1), X2) | proper#(U21(X1, X2, X3)) | → | proper#(X2) | |
| proper#(U212(X1, X2)) | → | proper#(X1) | active#(U222(tt, N, XS)) | → | splitAt#(N, XS) | |
| proper#(U181(X1, X2)) | → | proper#(X2) | afterNth#(X1, mark(X2)) | → | afterNth#(X1, X2) | |
| cons#(ok(X1), ok(X2)) | → | cons#(X1, X2) | proper#(U182(X1, X2)) | → | proper#(X2) | |
| proper#(U201(X1, X2, X3, X4)) | → | proper#(X2) | active#(head(cons(N, XS))) | → | isNatural#(N) | |
| proper#(U51(X1, X2)) | → | U51#(proper(X1), proper(X2)) | proper#(isLNat(X)) | → | isLNat#(proper(X)) | |
| active#(sel(X1, X2)) | → | active#(X2) | active#(U51(X1, X2)) | → | U51#(active(X1), X2) | |
| proper#(afterNth(X1, X2)) | → | proper#(X1) | proper#(U91(X)) | → | proper#(X) | |
| active#(splitAt(s(N), cons(X, XS))) | → | isNatural#(N) | U71#(mark(X)) | → | U71#(X) | |
| proper#(fst(X)) | → | fst#(proper(X)) | proper#(pair(X1, X2)) | → | proper#(X2) | |
| active#(natsFrom(N)) | → | isNatural#(N) | U52#(ok(X)) | → | U52#(X) | |
| take#(X1, mark(X2)) | → | take#(X1, X2) | proper#(U12(X1, X2, X3)) | → | proper#(X3) | |
| U32#(ok(X1), ok(X2)) | → | U32#(X1, X2) | U191#(ok(X1), ok(X2)) | → | U191#(X1, X2) | |
| active#(U101(tt, V2)) | → | U102#(isLNat(V2)) | active#(U203(tt, N, X, XS)) | → | splitAt#(N, XS) | |
| proper#(take(X1, X2)) | → | take#(proper(X1), proper(X2)) | active#(snd(X)) | → | active#(X) | |
| active#(cons(X1, X2)) | → | active#(X1) | sel#(mark(X1), X2) | → | sel#(X1, X2) | |
| active#(U51(tt, V2)) | → | isLNat#(V2) | active#(pair(X1, X2)) | → | pair#(X1, active(X2)) | |
| active#(isLNat(fst(V1))) | → | isPLNat#(V1) | active#(U11(X1, X2, X3)) | → | U11#(active(X1), X2, X3) | |
| U31#(ok(X1), ok(X2), ok(X3)) | → | U31#(X1, X2, X3) | proper#(U61(X)) | → | U61#(proper(X)) | |
| proper#(U42(X)) | → | proper#(X) | proper#(U51(X1, X2)) | → | proper#(X1) | |
| splitAt#(ok(X1), ok(X2)) | → | splitAt#(X1, X2) | proper#(U101(X1, X2)) | → | proper#(X1) | |
| proper#(take(X1, X2)) | → | proper#(X1) | proper#(U201(X1, X2, X3, X4)) | → | proper#(X3) | |
| proper#(U222(X1, X2, X3)) | → | proper#(X1) | U101#(mark(X1), X2) | → | U101#(X1, X2) | |
| U41#(mark(X1), X2) | → | U41#(X1, X2) | proper#(U203(X1, X2, X3, X4)) | → | proper#(X1) | |
| active#(U203(X1, X2, X3, X4)) | → | active#(X1) | U203#(ok(X1), ok(X2), ok(X3), ok(X4)) | → | U203#(X1, X2, X3, X4) | |
| proper#(U151(X1, X2)) | → | proper#(X2) | active#(U31(tt, N, XS)) | → | U32#(isLNat(XS), N) | |
| proper#(take(X1, X2)) | → | proper#(X2) | active#(take(X1, X2)) | → | active#(X1) | |
| proper#(U171(X1, X2, X3)) | → | U171#(proper(X1), proper(X2), proper(X3)) | U102#(ok(X)) | → | U102#(X) | |
| active#(isLNat(natsFrom(V1))) | → | U71#(isNatural(V1)) | s#(mark(X)) | → | s#(X) | |
| proper#(U182(X1, X2)) | → | U182#(proper(X1), proper(X2)) | U204#(mark(X1), X2) | → | U204#(X1, X2) | |
| active#(s(X)) | → | active#(X) | active#(tail(X)) | → | active#(X) | |
| U52#(mark(X)) | → | U52#(X) | active#(U61(X)) | → | active#(X) | |
| active#(U51(tt, V2)) | → | U52#(isLNat(V2)) | proper#(isNatural(X)) | → | proper#(X) | |
| splitAt#(mark(X1), X2) | → | splitAt#(X1, X2) | active#(U161(tt, N)) | → | natsFrom#(s(N)) | |
| proper#(U111(X)) | → | proper#(X) | proper#(U32(X1, X2)) | → | proper#(X2) | |
| active#(take(X1, X2)) | → | take#(active(X1), X2) | active#(U101(X1, X2)) | → | active#(X1) | |
| active#(natsFrom(N)) | → | U161#(isNatural(N), N) | active#(splitAt(X1, X2)) | → | splitAt#(active(X1), X2) | |
| active#(U202(X1, X2, X3, X4)) | → | active#(X1) | active#(splitAt(X1, X2)) | → | splitAt#(X1, active(X2)) | |
| active#(U42(X)) | → | U42#(active(X)) | active#(isLNat(take(V1, V2))) | → | isNatural#(V1) | |
| proper#(U201(X1, X2, X3, X4)) | → | proper#(X4) | active#(isLNat(natsFrom(V1))) | → | isNatural#(V1) | |
| proper#(U91(X)) | → | U91#(proper(X)) | proper#(U142(X)) | → | U142#(proper(X)) | |
| U12#(mark(X1), X2, X3) | → | U12#(X1, X2, X3) | active#(take(X1, X2)) | → | active#(X2) | |
| active#(tail(cons(N, XS))) | → | isNatural#(N) | pair#(X1, mark(X2)) | → | pair#(X1, X2) | |
| U21#(mark(X1), X2, X3) | → | U21#(X1, X2, X3) | active#(U21(X1, X2, X3)) | → | U21#(active(X1), X2, X3) | |
| proper#(U131(X1, X2)) | → | proper#(X1) | proper#(U142(X)) | → | proper#(X) | |
| active#(U31(X1, X2, X3)) | → | active#(X1) | proper#(U131(X1, X2)) | → | proper#(X2) | |
| U211#(mark(X1), X2) | → | U211#(X1, X2) | proper#(isNatural(X)) | → | isNatural#(proper(X)) | |
| U151#(mark(X1), X2) | → | U151#(X1, X2) | U22#(mark(X1), X2) | → | U22#(X1, X2) | |
| proper#(U201(X1, X2, X3, X4)) | → | U201#(proper(X1), proper(X2), proper(X3), proper(X4)) | U101#(ok(X1), ok(X2)) | → | U101#(X1, X2) | |
| active#(afterNth(X1, X2)) | → | afterNth#(X1, active(X2)) | active#(U12(tt, N, XS)) | → | snd#(splitAt(N, XS)) | |
| proper#(U212(X1, X2)) | → | proper#(X2) | top#(ok(X)) | → | active#(X) | |
| U141#(ok(X1), ok(X2)) | → | U141#(X1, X2) | active#(pair(X1, X2)) | → | active#(X1) | |
| U142#(mark(X)) | → | U142#(X) | proper#(isLNat(X)) | → | proper#(X) | |
| proper#(U151(X1, X2)) | → | proper#(X1) | proper#(U202(X1, X2, X3, X4)) | → | proper#(X4) | |
| proper#(U81(X)) | → | U81#(proper(X)) | active#(U161(tt, N)) | → | cons#(N, natsFrom(s(N))) | |
| active#(U172(X1, X2, X3)) | → | U172#(active(X1), X2, X3) | U61#(mark(X)) | → | U61#(X) | |
| pair#(ok(X1), ok(X2)) | → | pair#(X1, X2) | active#(head(X)) | → | head#(active(X)) | |
| U201#(mark(X1), X2, X3, X4) | → | U201#(X1, X2, X3, X4) | proper#(U203(X1, X2, X3, X4)) | → | proper#(X2) | |
| proper#(U11(X1, X2, X3)) | → | proper#(X1) | active#(U32(X1, X2)) | → | active#(X1) | |
| proper#(s(X)) | → | s#(proper(X)) | active#(U131(X1, X2)) | → | U131#(active(X1), X2) | |
| active#(splitAt(X1, X2)) | → | active#(X1) | active#(U31(tt, N, XS)) | → | isLNat#(XS) | |
| proper#(U152(X)) | → | U152#(proper(X)) | top#(ok(X)) | → | top#(active(X)) | |
| active#(U91(X)) | → | active#(X) | U172#(ok(X1), ok(X2), ok(X3)) | → | U172#(X1, X2, X3) | |
| proper#(U102(X)) | → | proper#(X) | U42#(mark(X)) | → | U42#(X) | |
| proper#(U171(X1, X2, X3)) | → | proper#(X1) | active#(U171(tt, N, XS)) | → | isLNat#(XS) | |
| active#(pair(X1, X2)) | → | active#(X2) | snd#(ok(X)) | → | snd#(X) | |
| active#(head(X)) | → | active#(X) | active#(U171(X1, X2, X3)) | → | active#(X1) | |
| active#(U11(X1, X2, X3)) | → | active#(X1) | U181#(mark(X1), X2) | → | U181#(X1, X2) | |
| proper#(U141(X1, X2)) | → | proper#(X2) | proper#(U152(X)) | → | proper#(X) | |
| active#(U221(X1, X2, X3)) | → | active#(X1) | proper#(U181(X1, X2)) | → | proper#(X1) | |
| U132#(ok(X)) | → | U132#(X) | proper#(fst(X)) | → | proper#(X) | |
| U91#(ok(X)) | → | U91#(X) | afterNth#(ok(X1), ok(X2)) | → | afterNth#(X1, X2) | |
| active#(U151(X1, X2)) | → | active#(X1) | U202#(mark(X1), X2, X3, X4) | → | U202#(X1, X2, X3, X4) | |
| active#(U141(tt, V2)) | → | isLNat#(V2) | active#(splitAt(X1, X2)) | → | active#(X2) | |
| active#(U172(tt, N, XS)) | → | head#(afterNth(N, XS)) | proper#(U31(X1, X2, X3)) | → | U31#(proper(X1), proper(X2), proper(X3)) | |
| active#(U211(X1, X2)) | → | active#(X1) | active#(U181(X1, X2)) | → | active#(X1) | |
| U121#(mark(X)) | → | U121#(X) | proper#(U172(X1, X2, X3)) | → | U172#(proper(X1), proper(X2), proper(X3)) | |
| proper#(U81(X)) | → | proper#(X) | proper#(U221(X1, X2, X3)) | → | proper#(X3) | |
| active#(U182(X1, X2)) | → | active#(X1) | active#(isLNat(tail(V1))) | → | isLNat#(V1) | |
| active#(U71(X)) | → | active#(X) | proper#(U203(X1, X2, X3, X4)) | → | proper#(X3) | |
| proper#(U52(X)) | → | proper#(X) | proper#(U41(X1, X2)) | → | proper#(X2) | |
| proper#(U171(X1, X2, X3)) | → | proper#(X3) | active#(U101(tt, V2)) | → | isLNat#(V2) | |
| active#(U51(X1, X2)) | → | active#(X1) | proper#(U11(X1, X2, X3)) | → | proper#(X3) | |
| active#(isNatural(head(V1))) | → | U111#(isLNat(V1)) | active#(isNatural(sel(V1, V2))) | → | U131#(isNatural(V1), V2) | |
| active#(U222(X1, X2, X3)) | → | U222#(active(X1), X2, X3) | proper#(U202(X1, X2, X3, X4)) | → | proper#(X2) | |
| active#(U121(X)) | → | U121#(active(X)) | active#(U221(X1, X2, X3)) | → | U221#(active(X1), X2, X3) | |
| active#(U142(X)) | → | U142#(active(X)) | active#(U211(X1, X2)) | → | U211#(active(X1), X2) | |
| tail#(ok(X)) | → | tail#(X) | proper#(U31(X1, X2, X3)) | → | proper#(X2) | |
| active#(U204(X1, X2)) | → | active#(X1) | active#(U181(tt, Y)) | → | isLNat#(Y) | |
| active#(U101(X1, X2)) | → | U101#(active(X1), X2) | active#(afterNth(N, XS)) | → | U11#(isNatural(N), N, XS) | |
| active#(isPLNat(pair(V1, V2))) | → | isLNat#(V1) | proper#(U202(X1, X2, X3, X4)) | → | proper#(X3) | |
| top#(mark(X)) | → | proper#(X) | active#(isNatural(s(V1))) | → | U121#(isNatural(V1)) | |
| active#(splitAt(0, XS)) | → | U191#(isLNat(XS), XS) | active#(isLNat(cons(V1, V2))) | → | U51#(isNatural(V1), V2) | |
| proper#(U204(X1, X2)) | → | U204#(proper(X1), proper(X2)) | active#(U204(pair(YS, ZS), X)) | → | pair#(cons(X, YS), ZS) | |
| active#(U161(tt, N)) | → | s#(N) | active#(isPLNat(pair(V1, V2))) | → | U141#(isLNat(V1), V2) | |
| sel#(ok(X1), ok(X2)) | → | sel#(X1, X2) | active#(U204(pair(YS, ZS), X)) | → | cons#(X, YS) | |
| active#(U151(tt, V2)) | → | isLNat#(V2) | active#(isPLNat(splitAt(V1, V2))) | → | U151#(isNatural(V1), V2) | |
| proper#(splitAt(X1, X2)) | → | proper#(X2) | active#(isLNat(tail(V1))) | → | U91#(isLNat(V1)) | |
| active#(isNatural(sel(V1, V2))) | → | isNatural#(V1) | active#(U204(X1, X2)) | → | U204#(active(X1), X2) | |
| proper#(head(X)) | → | proper#(X) | active#(U102(X)) | → | active#(X) | |
| active#(U191(X1, X2)) | → | U191#(active(X1), X2) | proper#(U181(X1, X2)) | → | U181#(proper(X1), proper(X2)) | |
| proper#(U191(X1, X2)) | → | proper#(X2) | active#(isLNat(afterNth(V1, V2))) | → | U41#(isNatural(V1), V2) | |
| active#(sel(X1, X2)) | → | active#(X1) | take#(ok(X1), ok(X2)) | → | take#(X1, X2) | |
| active#(U201(tt, N, X, XS)) | → | isNatural#(X) | proper#(U22(X1, X2)) | → | U22#(proper(X1), proper(X2)) | |
| active#(U221(tt, N, XS)) | → | U222#(isLNat(XS), N, XS) | proper#(U212(X1, X2)) | → | U212#(proper(X1), proper(X2)) | |
| active#(U222(X1, X2, X3)) | → | active#(X1) | active#(sel(N, XS)) | → | isNatural#(N) | |
| active#(U52(X)) | → | U52#(active(X)) | active#(sel(X1, X2)) | → | sel#(active(X1), X2) | |
| proper#(isPLNat(X)) | → | isPLNat#(proper(X)) | snd#(mark(X)) | → | snd#(X) | |
| U222#(ok(X1), ok(X2), ok(X3)) | → | U222#(X1, X2, X3) | active#(U202(tt, N, X, XS)) | → | U203#(isLNat(XS), N, X, XS) | |
| active#(U181(X1, X2)) | → | U181#(active(X1), X2) | active#(sel(N, XS)) | → | U171#(isNatural(N), N, XS) | |
| active#(U41(tt, V2)) | → | U42#(isLNat(V2)) | proper#(U121(X)) | → | proper#(X) | |
| active#(U102(X)) | → | U102#(active(X)) | U81#(ok(X)) | → | U81#(X) | |
| proper#(isPLNat(X)) | → | proper#(X) | U152#(mark(X)) | → | U152#(X) | |
| U211#(ok(X1), ok(X2)) | → | U211#(X1, X2) | proper#(U204(X1, X2)) | → | proper#(X2) | |
| active#(U22(X1, X2)) | → | U22#(active(X1), X2) | active#(U152(X)) | → | U152#(active(X)) | |
| active#(U132(X)) | → | U132#(active(X)) | active#(U202(tt, N, X, XS)) | → | isLNat#(XS) | |
| U182#(mark(X1), X2) | → | U182#(X1, X2) | active#(U41(X1, X2)) | → | U41#(active(X1), X2) | |
| active#(U191(X1, X2)) | → | active#(X1) | proper#(U202(X1, X2, X3, X4)) | → | proper#(X1) | |
| active#(afterNth(N, XS)) | → | isNatural#(N) | active#(isLNat(fst(V1))) | → | U61#(isPLNat(V1)) | |
| afterNth#(mark(X1), X2) | → | afterNth#(X1, X2) | proper#(U203(X1, X2, X3, X4)) | → | proper#(X4) | |
| active#(U91(X)) | → | U91#(active(X)) | proper#(U32(X1, X2)) | → | proper#(X1) | |
| active#(U21(tt, X, Y)) | → | U22#(isLNat(Y), X) | proper#(U222(X1, X2, X3)) | → | U222#(proper(X1), proper(X2), proper(X3)) | |
| active#(U61(X)) | → | U61#(active(X)) | active#(pair(X1, X2)) | → | pair#(active(X1), X2) | |
| U201#(ok(X1), ok(X2), ok(X3), ok(X4)) | → | U201#(X1, X2, X3, X4) | U11#(mark(X1), X2, X3) | → | U11#(X1, X2, X3) | |
| U182#(ok(X1), ok(X2)) | → | U182#(X1, X2) | tail#(mark(X)) | → | tail#(X) | |
| U131#(ok(X1), ok(X2)) | → | U131#(X1, X2) | active#(U81(X)) | → | active#(X) | |
| active#(U21(X1, X2, X3)) | → | active#(X1) | proper#(pair(X1, X2)) | → | proper#(X1) | |
| proper#(s(X)) | → | proper#(X) | active#(U132(X)) | → | active#(X) | |
| active#(U131(X1, X2)) | → | active#(X1) | active#(U201(tt, N, X, XS)) | → | U202#(isNatural(X), N, X, XS) | |
| active#(snd(pair(X, Y))) | → | isLNat#(X) | proper#(U221(X1, X2, X3)) | → | proper#(X1) | |
| U171#(ok(X1), ok(X2), ok(X3)) | → | U171#(X1, X2, X3) | proper#(natsFrom(X)) | → | natsFrom#(proper(X)) | |
| proper#(U32(X1, X2)) | → | U32#(proper(X1), proper(X2)) | proper#(U131(X1, X2)) | → | U131#(proper(X1), proper(X2)) | |
| proper#(U203(X1, X2, X3, X4)) | → | U203#(proper(X1), proper(X2), proper(X3), proper(X4)) | take#(mark(X1), X2) | → | take#(X1, X2) | |
| active#(U212(X1, X2)) | → | U212#(active(X1), X2) | U221#(mark(X1), X2, X3) | → | U221#(X1, X2, X3) | |
| proper#(U132(X)) | → | proper#(X) | active#(natsFrom(X)) | → | active#(X) | |
| active#(U203(tt, N, X, XS)) | → | U204#(splitAt(N, XS), X) | proper#(sel(X1, X2)) | → | sel#(proper(X1), proper(X2)) | |
| U204#(ok(X1), ok(X2)) | → | U204#(X1, X2) | U41#(ok(X1), ok(X2)) | → | U41#(X1, X2) | |
| active#(U211(tt, XS)) | → | U212#(isLNat(XS), XS) | fst#(mark(X)) | → | fst#(X) | |
| U152#(ok(X)) | → | U152#(X) | active#(isPLNat(splitAt(V1, V2))) | → | isNatural#(V1) | |
| U221#(ok(X1), ok(X2), ok(X3)) | → | U221#(X1, X2, X3) | U142#(ok(X)) | → | U142#(X) | |
| active#(head(cons(N, XS))) | → | U31#(isNatural(N), N, XS) | active#(natsFrom(X)) | → | natsFrom#(active(X)) | |
| U171#(mark(X1), X2, X3) | → | U171#(X1, X2, X3) | U212#(mark(X1), X2) | → | U212#(X1, X2) | |
| proper#(U61(X)) | → | proper#(X) | active#(fst(X)) | → | fst#(active(X)) | |
| U111#(ok(X)) | → | U111#(X) | proper#(U41(X1, X2)) | → | U41#(proper(X1), proper(X2)) | |
| proper#(U11(X1, X2, X3)) | → | U11#(proper(X1), proper(X2), proper(X3)) | active#(fst(pair(X, Y))) | → | isLNat#(X) | |
| U91#(mark(X)) | → | U91#(X) | proper#(U132(X)) | → | U132#(proper(X)) | |
| active#(U201(X1, X2, X3, X4)) | → | U201#(active(X1), X2, X3, X4) | U212#(ok(X1), ok(X2)) | → | U212#(X1, X2) | |
| proper#(afterNth(X1, X2)) | → | afterNth#(proper(X1), proper(X2)) | active#(U151(X1, X2)) | → | U151#(active(X1), X2) | |
| proper#(splitAt(X1, X2)) | → | proper#(X1) | U21#(ok(X1), ok(X2), ok(X3)) | → | U21#(X1, X2, X3) | |
| proper#(U71(X)) | → | proper#(X) | proper#(U211(X1, X2)) | → | proper#(X2) | |
| proper#(U52(X)) | → | U52#(proper(X)) | U161#(ok(X1), ok(X2)) | → | U161#(X1, X2) | |
| proper#(U221(X1, X2, X3)) | → | proper#(X2) | proper#(snd(X)) | → | snd#(proper(X)) | |
| active#(U222(tt, N, XS)) | → | fst#(splitAt(N, XS)) | U102#(mark(X)) | → | U102#(X) | |
| active#(U111(X)) | → | U111#(active(X)) | U202#(ok(X1), ok(X2), ok(X3), ok(X4)) | → | U202#(X1, X2, X3, X4) | |
| proper#(U42(X)) | → | U42#(proper(X)) | U121#(ok(X)) | → | U121#(X) | |
| active#(isLNat(take(V1, V2))) | → | U101#(isNatural(V1), V2) | active#(U142(X)) | → | active#(X) | |
| proper#(U191(X1, X2)) | → | proper#(X1) | sel#(X1, mark(X2)) | → | sel#(X1, X2) | |
| head#(ok(X)) | → | head#(X) | active#(U11(tt, N, XS)) | → | U12#(isLNat(XS), N, XS) | |
| U11#(ok(X1), ok(X2), ok(X3)) | → | U11#(X1, X2, X3) | proper#(U221(X1, X2, X3)) | → | U221#(proper(X1), proper(X2), proper(X3)) | |
| pair#(mark(X1), X2) | → | pair#(X1, X2) | active#(U171(tt, N, XS)) | → | U172#(isLNat(XS), N, XS) | |
| cons#(mark(X1), X2) | → | cons#(X1, X2) | proper#(U201(X1, X2, X3, X4)) | → | proper#(X1) | |
| active#(U121(X)) | → | active#(X) | U111#(mark(X)) | → | U111#(X) | |
| proper#(U172(X1, X2, X3)) | → | proper#(X3) | active#(U31(X1, X2, X3)) | → | U31#(active(X1), X2, X3) | |
| proper#(U21(X1, X2, X3)) | → | proper#(X1) | natsFrom#(ok(X)) | → | natsFrom#(X) | |
| proper#(sel(X1, X2)) | → | proper#(X2) | U42#(ok(X)) | → | U42#(X) | |
| active#(U181(tt, Y)) | → | U182#(isLNat(Y), Y) | active#(isLNat(snd(V1))) | → | U81#(isPLNat(V1)) | |
| U51#(ok(X1), ok(X2)) | → | U51#(X1, X2) | proper#(U161(X1, X2)) | → | proper#(X1) | |
| head#(mark(X)) | → | head#(X) | proper#(U12(X1, X2, X3)) | → | proper#(X2) | |
| proper#(U12(X1, X2, X3)) | → | U12#(proper(X1), proper(X2), proper(X3)) | active#(U131(tt, V2)) | → | U132#(isLNat(V2)) | |
| isPLNat#(ok(X)) | → | isPLNat#(X) | active#(take(N, XS)) | → | U221#(isNatural(N), N, XS) | |
| active#(s(X)) | → | s#(active(X)) | proper#(U31(X1, X2, X3)) | → | proper#(X1) | |
| s#(ok(X)) | → | s#(X) | active#(splitAt(s(N), cons(X, XS))) | → | U201#(isNatural(N), N, X, XS) | |
| proper#(sel(X1, X2)) | → | proper#(X1) | proper#(U172(X1, X2, X3)) | → | proper#(X1) | |
| active#(U32(X1, X2)) | → | U32#(active(X1), X2) | active#(take(X1, X2)) | → | take#(X1, active(X2)) | |
| active#(isNatural(s(V1))) | → | isNatural#(V1) | proper#(U141(X1, X2)) | → | U141#(proper(X1), proper(X2)) | |
| active#(U141(X1, X2)) | → | U141#(active(X1), X2) | U61#(ok(X)) | → | U61#(X) | |
| active#(U171(X1, X2, X3)) | → | U171#(active(X1), X2, X3) | proper#(natsFrom(X)) | → | proper#(X) | |
| U71#(ok(X)) | → | U71#(X) | proper#(U161(X1, X2)) | → | U161#(proper(X1), proper(X2)) | |
| U181#(ok(X1), ok(X2)) | → | U181#(X1, X2) | active#(U81(X)) | → | U81#(active(X)) | |
| active#(U12(tt, N, XS)) | → | splitAt#(N, XS) | active#(cons(X1, X2)) | → | cons#(active(X1), X2) | |
| active#(tail(X)) | → | tail#(active(X)) | U131#(mark(X1), X2) | → | U131#(X1, X2) | |
| active#(U201(X1, X2, X3, X4)) | → | active#(X1) | active#(U202(X1, X2, X3, X4)) | → | U202#(active(X1), X2, X3, X4) | |
| top#(mark(X)) | → | top#(proper(X)) | active#(U203(X1, X2, X3, X4)) | → | U203#(active(X1), X2, X3, X4) | |
| active#(isNatural(head(V1))) | → | isLNat#(V1) | proper#(cons(X1, X2)) | → | proper#(X2) | |
| proper#(U22(X1, X2)) | → | proper#(X2) | active#(U172(X1, X2, X3)) | → | active#(X1) | |
| proper#(afterNth(X1, X2)) | → | proper#(X2) | proper#(snd(X)) | → | proper#(X) | |
| proper#(head(X)) | → | head#(proper(X)) | U12#(ok(X1), ok(X2), ok(X3)) | → | U12#(X1, X2, X3) | |
| active#(U71(X)) | → | U71#(active(X)) | proper#(splitAt(X1, X2)) | → | splitAt#(proper(X1), proper(X2)) | |
| U222#(mark(X1), X2, X3) | → | U222#(X1, X2, X3) | proper#(U211(X1, X2)) | → | U211#(proper(X1), proper(X2)) | |
| active#(U11(tt, N, XS)) | → | isLNat#(XS) | U161#(mark(X1), X2) | → | U161#(X1, X2) | |
| active#(U42(X)) | → | active#(X) | proper#(U141(X1, X2)) | → | proper#(X1) | |
| proper#(U151(X1, X2)) | → | U151#(proper(X1), proper(X2)) | proper#(U111(X)) | → | U111#(proper(X)) | |
| proper#(U22(X1, X2)) | → | proper#(X1) | U151#(ok(X1), ok(X2)) | → | U151#(X1, X2) | |
| active#(isLNat(snd(V1))) | → | isPLNat#(V1) | active#(afterNth(X1, X2)) | → | active#(X1) | |
| proper#(U101(X1, X2)) | → | proper#(X2) | active#(U111(X)) | → | active#(X) | |
| proper#(U31(X1, X2, X3)) | → | proper#(X3) | active#(U141(tt, V2)) | → | U142#(isLNat(V2)) | |
| active#(U131(tt, V2)) | → | isLNat#(V2) | proper#(U102(X)) | → | U102#(proper(X)) | |
| active#(snd(pair(X, Y))) | → | U181#(isLNat(X), Y) | active#(fst(X)) | → | active#(X) | |
| active#(U152(X)) | → | active#(X) | fst#(ok(X)) | → | fst#(X) | |
| U141#(mark(X1), X2) | → | U141#(X1, X2) | proper#(cons(X1, X2)) | → | cons#(proper(X1), proper(X2)) | |
| active#(U141(X1, X2)) | → | active#(X1) | U32#(mark(X1), X2) | → | U32#(X1, X2) | |
| proper#(U182(X1, X2)) | → | proper#(X1) | active#(tail(cons(N, XS))) | → | U211#(isNatural(N), XS) | |
| proper#(U191(X1, X2)) | → | U191#(proper(X1), proper(X2)) | U31#(mark(X1), X2, X3) | → | U31#(X1, X2, X3) | |
| proper#(U204(X1, X2)) | → | proper#(X1) | proper#(U172(X1, X2, X3)) | → | proper#(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)) | |
| active(U101(X1, X2)) | → | U101(active(X1), X2) | active(U102(X)) | → | U102(active(X)) | |
| active(U11(X1, X2, X3)) | → | U11(active(X1), X2, X3) | active(U12(X1, X2, X3)) | → | U12(active(X1), X2, X3) | |
| active(U111(X)) | → | U111(active(X)) | active(snd(X)) | → | snd(active(X)) | |
| active(splitAt(X1, X2)) | → | splitAt(active(X1), X2) | active(splitAt(X1, X2)) | → | splitAt(X1, active(X2)) | |
| active(U121(X)) | → | U121(active(X)) | active(U131(X1, X2)) | → | U131(active(X1), X2) | |
| active(U132(X)) | → | U132(active(X)) | active(U141(X1, X2)) | → | U141(active(X1), X2) | |
| active(U142(X)) | → | U142(active(X)) | active(U151(X1, X2)) | → | U151(active(X1), X2) | |
| active(U152(X)) | → | U152(active(X)) | active(U161(X1, X2)) | → | U161(active(X1), X2) | |
| active(cons(X1, X2)) | → | cons(active(X1), X2) | active(natsFrom(X)) | → | natsFrom(active(X)) | |
| active(s(X)) | → | s(active(X)) | active(U171(X1, X2, X3)) | → | U171(active(X1), X2, X3) | |
| active(U172(X1, X2, X3)) | → | U172(active(X1), X2, X3) | active(head(X)) | → | head(active(X)) | |
| active(afterNth(X1, X2)) | → | afterNth(active(X1), X2) | active(afterNth(X1, X2)) | → | afterNth(X1, active(X2)) | |
| active(U181(X1, X2)) | → | U181(active(X1), X2) | active(U182(X1, X2)) | → | U182(active(X1), X2) | |
| active(U191(X1, X2)) | → | U191(active(X1), X2) | active(pair(X1, X2)) | → | pair(active(X1), X2) | |
| active(pair(X1, X2)) | → | pair(X1, active(X2)) | active(U201(X1, X2, X3, X4)) | → | U201(active(X1), X2, X3, X4) | |
| active(U202(X1, X2, X3, X4)) | → | U202(active(X1), X2, X3, X4) | active(U203(X1, X2, X3, X4)) | → | U203(active(X1), X2, X3, X4) | |
| active(U204(X1, X2)) | → | U204(active(X1), X2) | active(U21(X1, X2, X3)) | → | U21(active(X1), X2, X3) | |
| active(U22(X1, X2)) | → | U22(active(X1), X2) | active(U211(X1, X2)) | → | U211(active(X1), X2) | |
| active(U212(X1, X2)) | → | U212(active(X1), X2) | active(U221(X1, X2, X3)) | → | U221(active(X1), X2, X3) | |
| active(U222(X1, X2, X3)) | → | U222(active(X1), X2, X3) | active(fst(X)) | → | fst(active(X)) | |
| active(U31(X1, X2, X3)) | → | U31(active(X1), X2, X3) | active(U32(X1, X2)) | → | U32(active(X1), X2) | |
| active(U41(X1, X2)) | → | U41(active(X1), X2) | active(U42(X)) | → | U42(active(X)) | |
| active(U51(X1, X2)) | → | U51(active(X1), X2) | active(U52(X)) | → | U52(active(X)) | |
| active(U61(X)) | → | U61(active(X)) | active(U71(X)) | → | U71(active(X)) | |
| active(U81(X)) | → | U81(active(X)) | active(U91(X)) | → | U91(active(X)) | |
| active(tail(X)) | → | tail(active(X)) | active(take(X1, X2)) | → | take(active(X1), X2) | |
| active(take(X1, X2)) | → | take(X1, active(X2)) | active(sel(X1, X2)) | → | sel(active(X1), X2) | |
| active(sel(X1, X2)) | → | sel(X1, active(X2)) | U101(mark(X1), X2) | → | mark(U101(X1, X2)) | |
| U102(mark(X)) | → | mark(U102(X)) | U11(mark(X1), X2, X3) | → | mark(U11(X1, X2, X3)) | |
| U12(mark(X1), X2, X3) | → | mark(U12(X1, X2, X3)) | U111(mark(X)) | → | mark(U111(X)) | |
| snd(mark(X)) | → | mark(snd(X)) | splitAt(mark(X1), X2) | → | mark(splitAt(X1, X2)) | |
| splitAt(X1, mark(X2)) | → | mark(splitAt(X1, X2)) | U121(mark(X)) | → | mark(U121(X)) | |
| U131(mark(X1), X2) | → | mark(U131(X1, X2)) | U132(mark(X)) | → | mark(U132(X)) | |
| U141(mark(X1), X2) | → | mark(U141(X1, X2)) | U142(mark(X)) | → | mark(U142(X)) | |
| U151(mark(X1), X2) | → | mark(U151(X1, X2)) | U152(mark(X)) | → | mark(U152(X)) | |
| U161(mark(X1), X2) | → | mark(U161(X1, X2)) | cons(mark(X1), X2) | → | mark(cons(X1, X2)) | |
| natsFrom(mark(X)) | → | mark(natsFrom(X)) | s(mark(X)) | → | mark(s(X)) | |
| U171(mark(X1), X2, X3) | → | mark(U171(X1, X2, X3)) | U172(mark(X1), X2, X3) | → | mark(U172(X1, X2, X3)) | |
| head(mark(X)) | → | mark(head(X)) | afterNth(mark(X1), X2) | → | mark(afterNth(X1, X2)) | |
| afterNth(X1, mark(X2)) | → | mark(afterNth(X1, X2)) | U181(mark(X1), X2) | → | mark(U181(X1, X2)) | |
| U182(mark(X1), X2) | → | mark(U182(X1, X2)) | U191(mark(X1), X2) | → | mark(U191(X1, X2)) | |
| pair(mark(X1), X2) | → | mark(pair(X1, X2)) | pair(X1, mark(X2)) | → | mark(pair(X1, X2)) | |
| U201(mark(X1), X2, X3, X4) | → | mark(U201(X1, X2, X3, X4)) | U202(mark(X1), X2, X3, X4) | → | mark(U202(X1, X2, X3, X4)) | |
| U203(mark(X1), X2, X3, X4) | → | mark(U203(X1, X2, X3, X4)) | U204(mark(X1), X2) | → | mark(U204(X1, X2)) | |
| U21(mark(X1), X2, X3) | → | mark(U21(X1, X2, X3)) | U22(mark(X1), X2) | → | mark(U22(X1, X2)) | |
| U211(mark(X1), X2) | → | mark(U211(X1, X2)) | U212(mark(X1), X2) | → | mark(U212(X1, X2)) | |
| U221(mark(X1), X2, X3) | → | mark(U221(X1, X2, X3)) | U222(mark(X1), X2, X3) | → | mark(U222(X1, X2, X3)) | |
| fst(mark(X)) | → | mark(fst(X)) | U31(mark(X1), X2, X3) | → | mark(U31(X1, X2, X3)) | |
| U32(mark(X1), X2) | → | mark(U32(X1, X2)) | U41(mark(X1), X2) | → | mark(U41(X1, X2)) | |
| U42(mark(X)) | → | mark(U42(X)) | U51(mark(X1), X2) | → | mark(U51(X1, X2)) | |
| U52(mark(X)) | → | mark(U52(X)) | U61(mark(X)) | → | mark(U61(X)) | |
| U71(mark(X)) | → | mark(U71(X)) | U81(mark(X)) | → | mark(U81(X)) | |
| U91(mark(X)) | → | mark(U91(X)) | tail(mark(X)) | → | mark(tail(X)) | |
| take(mark(X1), X2) | → | mark(take(X1, X2)) | take(X1, mark(X2)) | → | mark(take(X1, X2)) | |
| sel(mark(X1), X2) | → | mark(sel(X1, X2)) | sel(X1, mark(X2)) | → | mark(sel(X1, X2)) | |
| proper(U101(X1, X2)) | → | U101(proper(X1), proper(X2)) | proper(tt) | → | ok(tt) | |
| proper(U102(X)) | → | U102(proper(X)) | proper(isLNat(X)) | → | isLNat(proper(X)) | |
| proper(U11(X1, X2, X3)) | → | U11(proper(X1), proper(X2), proper(X3)) | proper(U12(X1, X2, X3)) | → | U12(proper(X1), proper(X2), proper(X3)) | |
| proper(U111(X)) | → | U111(proper(X)) | proper(snd(X)) | → | snd(proper(X)) | |
| proper(splitAt(X1, X2)) | → | splitAt(proper(X1), proper(X2)) | proper(U121(X)) | → | U121(proper(X)) | |
| proper(U131(X1, X2)) | → | U131(proper(X1), proper(X2)) | proper(U132(X)) | → | U132(proper(X)) | |
| proper(U141(X1, X2)) | → | U141(proper(X1), proper(X2)) | proper(U142(X)) | → | U142(proper(X)) | |
| proper(U151(X1, X2)) | → | U151(proper(X1), proper(X2)) | proper(U152(X)) | → | U152(proper(X)) | |
| proper(U161(X1, X2)) | → | U161(proper(X1), proper(X2)) | proper(cons(X1, X2)) | → | cons(proper(X1), proper(X2)) | |
| proper(natsFrom(X)) | → | natsFrom(proper(X)) | proper(s(X)) | → | s(proper(X)) | |
| proper(U171(X1, X2, X3)) | → | U171(proper(X1), proper(X2), proper(X3)) | proper(U172(X1, X2, X3)) | → | U172(proper(X1), proper(X2), proper(X3)) | |
| proper(head(X)) | → | head(proper(X)) | proper(afterNth(X1, X2)) | → | afterNth(proper(X1), proper(X2)) | |
| proper(U181(X1, X2)) | → | U181(proper(X1), proper(X2)) | proper(U182(X1, X2)) | → | U182(proper(X1), proper(X2)) | |
| proper(U191(X1, X2)) | → | U191(proper(X1), proper(X2)) | proper(pair(X1, X2)) | → | pair(proper(X1), proper(X2)) | |
| proper(nil) | → | ok(nil) | proper(U201(X1, X2, X3, X4)) | → | U201(proper(X1), proper(X2), proper(X3), proper(X4)) | |
| proper(U202(X1, X2, X3, X4)) | → | U202(proper(X1), proper(X2), proper(X3), proper(X4)) | proper(isNatural(X)) | → | isNatural(proper(X)) | |
| proper(U203(X1, X2, X3, X4)) | → | U203(proper(X1), proper(X2), proper(X3), proper(X4)) | proper(U204(X1, X2)) | → | U204(proper(X1), proper(X2)) | |
| proper(U21(X1, X2, X3)) | → | U21(proper(X1), proper(X2), proper(X3)) | proper(U22(X1, X2)) | → | U22(proper(X1), proper(X2)) | |
| proper(U211(X1, X2)) | → | U211(proper(X1), proper(X2)) | proper(U212(X1, X2)) | → | U212(proper(X1), proper(X2)) | |
| proper(U221(X1, X2, X3)) | → | U221(proper(X1), proper(X2), proper(X3)) | proper(U222(X1, X2, X3)) | → | U222(proper(X1), proper(X2), proper(X3)) | |
| proper(fst(X)) | → | fst(proper(X)) | proper(U31(X1, X2, X3)) | → | U31(proper(X1), proper(X2), proper(X3)) | |
| proper(U32(X1, X2)) | → | U32(proper(X1), proper(X2)) | proper(U41(X1, X2)) | → | U41(proper(X1), proper(X2)) | |
| proper(U42(X)) | → | U42(proper(X)) | proper(U51(X1, X2)) | → | U51(proper(X1), proper(X2)) | |
| proper(U52(X)) | → | U52(proper(X)) | proper(U61(X)) | → | U61(proper(X)) | |
| proper(U71(X)) | → | U71(proper(X)) | proper(U81(X)) | → | U81(proper(X)) | |
| proper(U91(X)) | → | U91(proper(X)) | proper(isPLNat(X)) | → | isPLNat(proper(X)) | |
| proper(tail(X)) | → | tail(proper(X)) | proper(take(X1, X2)) | → | take(proper(X1), proper(X2)) | |
| proper(0) | → | ok(0) | proper(sel(X1, X2)) | → | sel(proper(X1), proper(X2)) | |
| U101(ok(X1), ok(X2)) | → | ok(U101(X1, X2)) | U102(ok(X)) | → | ok(U102(X)) | |
| isLNat(ok(X)) | → | ok(isLNat(X)) | U11(ok(X1), ok(X2), ok(X3)) | → | ok(U11(X1, X2, X3)) | |
| U12(ok(X1), ok(X2), ok(X3)) | → | ok(U12(X1, X2, X3)) | U111(ok(X)) | → | ok(U111(X)) | |
| snd(ok(X)) | → | ok(snd(X)) | splitAt(ok(X1), ok(X2)) | → | ok(splitAt(X1, X2)) | |
| U121(ok(X)) | → | ok(U121(X)) | U131(ok(X1), ok(X2)) | → | ok(U131(X1, X2)) | |
| U132(ok(X)) | → | ok(U132(X)) | U141(ok(X1), ok(X2)) | → | ok(U141(X1, X2)) | |
| U142(ok(X)) | → | ok(U142(X)) | U151(ok(X1), ok(X2)) | → | ok(U151(X1, X2)) | |
| U152(ok(X)) | → | ok(U152(X)) | U161(ok(X1), ok(X2)) | → | ok(U161(X1, X2)) | |
| cons(ok(X1), ok(X2)) | → | ok(cons(X1, X2)) | natsFrom(ok(X)) | → | ok(natsFrom(X)) | |
| s(ok(X)) | → | ok(s(X)) | U171(ok(X1), ok(X2), ok(X3)) | → | ok(U171(X1, X2, X3)) | |
| U172(ok(X1), ok(X2), ok(X3)) | → | ok(U172(X1, X2, X3)) | head(ok(X)) | → | ok(head(X)) | |
| afterNth(ok(X1), ok(X2)) | → | ok(afterNth(X1, X2)) | U181(ok(X1), ok(X2)) | → | ok(U181(X1, X2)) | |
| U182(ok(X1), ok(X2)) | → | ok(U182(X1, X2)) | U191(ok(X1), ok(X2)) | → | ok(U191(X1, X2)) | |
| pair(ok(X1), ok(X2)) | → | ok(pair(X1, X2)) | U201(ok(X1), ok(X2), ok(X3), ok(X4)) | → | ok(U201(X1, X2, X3, X4)) | |
| U202(ok(X1), ok(X2), ok(X3), ok(X4)) | → | ok(U202(X1, X2, X3, X4)) | isNatural(ok(X)) | → | ok(isNatural(X)) | |
| U203(ok(X1), ok(X2), ok(X3), ok(X4)) | → | ok(U203(X1, X2, X3, X4)) | U204(ok(X1), ok(X2)) | → | ok(U204(X1, X2)) | |
| U21(ok(X1), ok(X2), ok(X3)) | → | ok(U21(X1, X2, X3)) | U22(ok(X1), ok(X2)) | → | ok(U22(X1, X2)) | |
| U211(ok(X1), ok(X2)) | → | ok(U211(X1, X2)) | U212(ok(X1), ok(X2)) | → | ok(U212(X1, X2)) | |
| U221(ok(X1), ok(X2), ok(X3)) | → | ok(U221(X1, X2, X3)) | U222(ok(X1), ok(X2), ok(X3)) | → | ok(U222(X1, X2, X3)) | |
| fst(ok(X)) | → | ok(fst(X)) | U31(ok(X1), ok(X2), ok(X3)) | → | ok(U31(X1, X2, X3)) | |
| U32(ok(X1), ok(X2)) | → | ok(U32(X1, X2)) | U41(ok(X1), ok(X2)) | → | ok(U41(X1, X2)) | |
| U42(ok(X)) | → | ok(U42(X)) | U51(ok(X1), ok(X2)) | → | ok(U51(X1, X2)) | |
| U52(ok(X)) | → | ok(U52(X)) | U61(ok(X)) | → | ok(U61(X)) | |
| U71(ok(X)) | → | ok(U71(X)) | U81(ok(X)) | → | ok(U81(X)) | |
| U91(ok(X)) | → | ok(U91(X)) | isPLNat(ok(X)) | → | ok(isPLNat(X)) | |
| tail(ok(X)) | → | ok(tail(X)) | take(ok(X1), ok(X2)) | → | ok(take(X1, X2)) | |
| sel(ok(X1), ok(X2)) | → | ok(sel(X1, X2)) | top(mark(X)) | → | top(proper(X)) | |
| top(ok(X)) | → | top(active(X)) |
Termination of terms over the following signature is verified: natsFrom, U161, U204, U203, fst, U111, U61, U211, U212, ok, proper, 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, top, cons, snd, U171, U172, splitAt, U201, U142, U202, U141, s, U51, tt, take, U81, U52, U11, U12, afterNth, U102, sel, U101, nil