TIMEOUT

The TRS could not be proven terminating. The proof attempt took 60001 ms.

The following DP Processors were used


Problem 1 remains open; application of the following processors failed [DependencyGraph (timeout)].

The following open problems remain:



Open Dependency Pair Problem 1

Dependency Pairs

mark#(fst(X))active#(fst(mark(X)))active#(tail(cons(N, XS)))and#(isNatural(N), isLNat(XS))
U91#(X1, active(X2))U91#(X1, X2)active#(isLNat(take(V1, V2)))mark#(and(isNatural(V1), isLNat(V2)))
active#(U82(pair(YS, ZS), X))mark#(pair(cons(X, YS), ZS))active#(snd(pair(X, Y)))and#(isLNat(X), isLNat(Y))
mark#(U11(X1, X2, X3))U11#(mark(X1), X2, X3)mark#(take(X1, X2))active#(take(mark(X1), mark(X2)))
mark#(snd(X))active#(snd(mark(X)))U21#(X1, active(X2))U21#(X1, X2)
mark#(s(X))mark#(X)mark#(sel(X1, X2))mark#(X1)
active#(isPLNat(pair(V1, V2)))isLNat#(V1)active#(U11(tt, N, XS))splitAt#(N, XS)
afterNth#(active(X1), X2)afterNth#(X1, X2)active#(fst(pair(X, Y)))mark#(U21(and(isLNat(X), isLNat(Y)), X))
active#(tail(cons(N, XS)))U91#(and(isNatural(N), isLNat(XS)), XS)splitAt#(X1, mark(X2))splitAt#(X1, X2)
active#(sel(N, XS))mark#(U51(and(isNatural(N), isLNat(XS)), N, XS))mark#(afterNth(X1, X2))mark#(X1)
and#(mark(X1), X2)and#(X1, X2)U81#(X1, X2, X3, active(X4))U81#(X1, X2, X3, X4)
active#(splitAt(0, XS))U71#(isLNat(XS), XS)active#(isLNat(cons(V1, V2)))mark#(and(isNatural(V1), isLNat(V2)))
active#(isLNat(cons(V1, V2)))isNatural#(V1)active#(take(N, XS))U101#(and(isNatural(N), isLNat(XS)), N, XS)
head#(active(X))head#(X)U82#(X1, active(X2))U82#(X1, X2)
active#(isNatural(sel(V1, V2)))isNatural#(V1)active#(U101(tt, N, XS))fst#(splitAt(N, XS))
active#(isLNat(afterNth(V1, V2)))isNatural#(V1)mark#(U11(X1, X2, X3))mark#(X1)
natsFrom#(mark(X))natsFrom#(X)active#(U71(tt, XS))pair#(nil, XS)
isLNat#(active(X))isLNat#(X)active#(take(N, XS))isNatural#(N)
active#(splitAt(0, XS))isLNat#(XS)active#(U51(tt, N, XS))afterNth#(N, XS)
U91#(X1, mark(X2))U91#(X1, X2)active#(isNatural(s(V1)))mark#(isNatural(V1))
mark#(head(X))mark#(X)mark#(splitAt(X1, X2))mark#(X1)
mark#(U21(X1, X2))active#(U21(mark(X1), X2))active#(splitAt(s(N), cons(X, XS)))isLNat#(XS)
isNatural#(mark(X))isNatural#(X)active#(isLNat(snd(V1)))mark#(isPLNat(V1))
mark#(isNatural(X))isNatural#(X)isPLNat#(active(X))isPLNat#(X)
U11#(active(X1), X2, X3)U11#(X1, X2, X3)active#(isLNat(afterNth(V1, V2)))isLNat#(V2)
active#(U11(tt, N, XS))mark#(snd(splitAt(N, XS)))cons#(X1, mark(X2))cons#(X1, X2)
U41#(X1, active(X2))U41#(X1, X2)mark#(U41(X1, X2))mark#(X1)
U81#(active(X1), X2, X3, X4)U81#(X1, X2, X3, X4)active#(isNatural(sel(V1, V2)))isLNat#(V2)
mark#(fst(X))mark#(X)active#(splitAt(0, XS))mark#(U71(isLNat(XS), XS))
active#(sel(N, XS))isNatural#(N)mark#(U82(X1, X2))mark#(X1)
snd#(mark(X))snd#(X)mark#(U101(X1, X2, X3))U101#(mark(X1), X2, X3)
active#(head(cons(N, XS)))isLNat#(XS)U21#(active(X1), X2)U21#(X1, X2)
U81#(X1, X2, X3, mark(X4))U81#(X1, X2, X3, X4)pair#(X1, active(X2))pair#(X1, X2)
mark#(snd(X))mark#(X)cons#(active(X1), X2)cons#(X1, X2)
mark#(natsFrom(X))mark#(X)mark#(afterNth(X1, X2))active#(afterNth(mark(X1), mark(X2)))
active#(afterNth(N, XS))isLNat#(XS)active#(isLNat(take(V1, V2)))and#(isNatural(V1), isLNat(V2))
mark#(take(X1, X2))mark#(X1)U81#(X1, X2, mark(X3), X4)U81#(X1, X2, X3, X4)
mark#(U81(X1, X2, X3, X4))active#(U81(mark(X1), X2, X3, X4))afterNth#(X1, mark(X2))afterNth#(X1, X2)
active#(splitAt(s(N), cons(X, XS)))and#(isNatural(N), and(isNatural(X), isLNat(XS)))isNatural#(active(X))isNatural#(X)
U81#(X1, X2, active(X3), X4)U81#(X1, X2, X3, X4)U61#(active(X1), X2)U61#(X1, X2)
mark#(s(X))s#(mark(X))active#(head(cons(N, XS)))isNatural#(N)
mark#(U11(X1, X2, X3))active#(U11(mark(X1), X2, X3))active#(head(cons(N, XS)))U31#(and(isNatural(N), isLNat(XS)), N)
mark#(tail(X))active#(tail(mark(X)))active#(afterNth(N, XS))isNatural#(N)
active#(isPLNat(pair(V1, V2)))isLNat#(V2)U91#(mark(X1), X2)U91#(X1, X2)
active#(isLNat(fst(V1)))mark#(isPLNat(V1))U61#(mark(X1), X2)U61#(X1, X2)
afterNth#(mark(X1), X2)afterNth#(X1, X2)mark#(natsFrom(X))active#(natsFrom(mark(X)))
mark#(isLNat(X))active#(isLNat(X))U82#(X1, mark(X2))U82#(X1, X2)
mark#(sel(X1, X2))sel#(mark(X1), mark(X2))active#(splitAt(s(N), cons(X, XS)))isNatural#(N)
U51#(X1, mark(X2), X3)U51#(X1, X2, X3)isPLNat#(mark(X))isPLNat#(X)
U41#(X1, mark(X2))U41#(X1, X2)mark#(isPLNat(X))isPLNat#(X)
active#(isPLNat(pair(V1, V2)))and#(isLNat(V1), isLNat(V2))mark#(and(X1, X2))and#(mark(X1), X2)
U11#(mark(X1), X2, X3)U11#(X1, X2, X3)U101#(active(X1), X2, X3)U101#(X1, X2, X3)
tail#(mark(X))tail#(X)active#(natsFrom(N))isNatural#(N)
take#(X1, mark(X2))take#(X1, X2)mark#(sel(X1, X2))active#(sel(mark(X1), mark(X2)))
mark#(splitAt(X1, X2))active#(splitAt(mark(X1), mark(X2)))mark#(U61(X1, X2))active#(U61(mark(X1), X2))
mark#(U71(X1, X2))mark#(X1)cons#(X1, active(X2))cons#(X1, X2)
active#(snd(pair(X, Y)))isLNat#(X)U51#(active(X1), X2, X3)U51#(X1, X2, X3)
U82#(active(X1), X2)U82#(X1, X2)mark#(U61(X1, X2))mark#(X1)
sel#(mark(X1), X2)sel#(X1, X2)mark#(head(X))active#(head(mark(X)))
take#(mark(X1), X2)take#(X1, X2)mark#(U101(X1, X2, X3))active#(U101(mark(X1), X2, X3))
and#(X1, active(X2))and#(X1, X2)U101#(X1, active(X2), X3)U101#(X1, X2, X3)
mark#(pair(X1, X2))pair#(mark(X1), mark(X2))active#(take(N, XS))isLNat#(XS)
mark#(U82(X1, X2))active#(U82(mark(X1), X2))mark#(U21(X1, X2))U21#(mark(X1), X2)
mark#(U21(X1, X2))mark#(X1)active#(isLNat(fst(V1)))isPLNat#(V1)
U61#(X1, mark(X2))U61#(X1, X2)active#(isLNat(cons(V1, V2)))isLNat#(V2)
splitAt#(active(X1), X2)splitAt#(X1, X2)U11#(X1, X2, mark(X3))U11#(X1, X2, X3)
mark#(nil)active#(nil)take#(X1, active(X2))take#(X1, X2)
mark#(sel(X1, X2))mark#(X2)fst#(mark(X))fst#(X)
U101#(X1, X2, active(X3))U101#(X1, X2, X3)active#(isPLNat(splitAt(V1, V2)))isNatural#(V1)
mark#(isNatural(X))active#(isNatural(X))mark#(U81(X1, X2, X3, X4))mark#(X1)
afterNth#(X1, active(X2))afterNth#(X1, X2)U41#(mark(X1), X2)U41#(X1, X2)
active#(U81(tt, N, X, XS))mark#(U82(splitAt(N, XS), X))active#(U61(tt, Y))mark#(Y)
active#(U51(tt, N, XS))head#(afterNth(N, XS))mark#(cons(X1, X2))cons#(mark(X1), X2)
and#(X1, mark(X2))and#(X1, X2)natsFrom#(active(X))natsFrom#(X)
active#(splitAt(s(N), cons(X, XS)))U81#(and(isNatural(N), and(isNatural(X), isLNat(XS))), N, X, XS)active#(U41(tt, N))mark#(cons(N, natsFrom(s(N))))
active#(splitAt(s(N), cons(X, XS)))isNatural#(X)isLNat#(mark(X))isLNat#(X)
mark#(isLNat(X))isLNat#(X)active#(snd(pair(X, Y)))mark#(U61(and(isLNat(X), isLNat(Y)), Y))
mark#(splitAt(X1, X2))mark#(X2)active#(U101(tt, N, XS))mark#(fst(splitAt(N, XS)))
mark#(head(X))head#(mark(X))mark#(take(X1, X2))take#(mark(X1), mark(X2))
s#(mark(X))s#(X)active#(isLNat(cons(V1, V2)))and#(isNatural(V1), isLNat(V2))
active#(tail(cons(N, XS)))mark#(U91(and(isNatural(N), isLNat(XS)), XS))active#(fst(pair(X, Y)))isLNat#(Y)
active#(tail(cons(N, XS)))isLNat#(XS)mark#(U31(X1, X2))U31#(mark(X1), X2)
active#(fst(pair(X, Y)))isLNat#(X)mark#(U51(X1, X2, X3))U51#(mark(X1), X2, X3)
active#(U31(tt, N))mark#(N)active#(isLNat(afterNth(V1, V2)))mark#(and(isNatural(V1), isLNat(V2)))
mark#(U101(X1, X2, X3))mark#(X1)mark#(U81(X1, X2, X3, X4))U81#(mark(X1), X2, X3, X4)
active#(isLNat(take(V1, V2)))isLNat#(V2)mark#(pair(X1, X2))mark#(X2)
U71#(X1, mark(X2))U71#(X1, X2)splitAt#(mark(X1), X2)splitAt#(X1, X2)
active#(natsFrom(N))U41#(isNatural(N), N)active#(afterNth(N, XS))and#(isNatural(N), isLNat(XS))
active#(isLNat(take(V1, V2)))isNatural#(V1)active#(isLNat(natsFrom(V1)))isNatural#(V1)
active#(afterNth(N, XS))U11#(and(isNatural(N), isLNat(XS)), N, XS)U51#(X1, X2, active(X3))U51#(X1, X2, X3)
mark#(U71(X1, X2))U71#(mark(X1), X2)U11#(X1, active(X2), X3)U11#(X1, X2, X3)
active#(U101(tt, N, XS))splitAt#(N, XS)mark#(cons(X1, X2))mark#(X1)
pair#(X1, mark(X2))pair#(X1, X2)active#(tail(cons(N, XS)))isNatural#(N)
fst#(active(X))fst#(X)U41#(active(X1), X2)U41#(X1, X2)
sel#(X1, mark(X2))sel#(X1, X2)active#(isLNat(nil))mark#(tt)
U81#(X1, mark(X2), X3, X4)U81#(X1, X2, X3, X4)mark#(and(X1, X2))mark#(X1)
active#(isNatural(sel(V1, V2)))and#(isNatural(V1), isLNat(V2))mark#(pair(X1, X2))mark#(X1)
sel#(X1, active(X2))sel#(X1, X2)active#(U82(pair(YS, ZS), X))pair#(cons(X, YS), ZS)
mark#(tail(X))mark#(X)mark#(afterNth(X1, X2))mark#(X2)
mark#(U82(X1, X2))U82#(mark(X1), X2)pair#(mark(X1), X2)pair#(X1, X2)
cons#(mark(X1), X2)cons#(X1, X2)mark#(tt)active#(tt)
U31#(X1, active(X2))U31#(X1, X2)active#(U81(tt, N, X, XS))splitAt#(N, XS)
mark#(U61(X1, X2))U61#(mark(X1), X2)mark#(tail(X))tail#(mark(X))
active#(isNatural(0))mark#(tt)U82#(mark(X1), X2)U82#(X1, X2)
mark#(splitAt(X1, X2))splitAt#(mark(X1), mark(X2))U21#(X1, mark(X2))U21#(X1, X2)
mark#(U51(X1, X2, X3))mark#(X1)U71#(mark(X1), X2)U71#(X1, X2)
U61#(X1, active(X2))U61#(X1, X2)U101#(X1, X2, mark(X3))U101#(X1, X2, X3)
splitAt#(X1, active(X2))splitAt#(X1, X2)mark#(U31(X1, X2))active#(U31(mark(X1), X2))
mark#(U91(X1, X2))U91#(mark(X1), X2)U51#(mark(X1), X2, X3)U51#(X1, X2, X3)
mark#(0)active#(0)mark#(s(X))active#(s(mark(X)))
head#(mark(X))head#(X)active#(isNatural(sel(V1, V2)))mark#(and(isNatural(V1), isLNat(V2)))
active#(snd(pair(X, Y)))isLNat#(Y)active#(isNatural(head(V1)))mark#(isLNat(V1))
active#(isPLNat(pair(V1, V2)))mark#(and(isLNat(V1), isLNat(V2)))snd#(active(X))snd#(X)
active#(head(cons(N, XS)))mark#(U31(and(isNatural(N), isLNat(XS)), N))mark#(U51(X1, X2, X3))active#(U51(mark(X1), X2, X3))
active#(isNatural(s(V1)))isNatural#(V1)U81#(mark(X1), X2, X3, X4)U81#(X1, X2, X3, X4)
U11#(X1, X2, active(X3))U11#(X1, X2, X3)active#(isPLNat(splitAt(V1, V2)))isLNat#(V2)
mark#(cons(X1, X2))active#(cons(mark(X1), X2))mark#(fst(X))fst#(mark(X))
mark#(snd(X))snd#(mark(X))active#(snd(pair(X, Y)))U61#(and(isLNat(X), isLNat(Y)), Y)
mark#(U41(X1, X2))active#(U41(mark(X1), X2))U51#(X1, active(X2), X3)U51#(X1, X2, X3)
active#(isPLNat(splitAt(V1, V2)))mark#(and(isNatural(V1), isLNat(V2)))active#(U41(tt, N))s#(N)
active#(head(cons(N, XS)))and#(isNatural(N), isLNat(XS))U31#(active(X1), X2)U31#(X1, X2)
active#(natsFrom(N))mark#(U41(isNatural(N), N))mark#(U31(X1, X2))mark#(X1)
active#(U81(tt, N, X, XS))U82#(splitAt(N, XS), X)pair#(active(X1), X2)pair#(X1, X2)
mark#(U91(X1, X2))active#(U91(mark(X1), X2))active#(U82(pair(YS, ZS), X))cons#(X, YS)
active#(take(N, XS))and#(isNatural(N), isLNat(XS))active#(U91(tt, XS))mark#(XS)
active#(isNatural(head(V1)))isLNat#(V1)active#(take(N, XS))mark#(U101(and(isNatural(N), isLNat(XS)), N, XS))
active#(afterNth(N, XS))mark#(U11(and(isNatural(N), isLNat(XS)), N, XS))active#(isLNat(afterNth(V1, V2)))and#(isNatural(V1), isLNat(V2))
active#(U41(tt, N))natsFrom#(s(N))mark#(U41(X1, X2))U41#(mark(X1), X2)
sel#(active(X1), X2)sel#(X1, X2)U71#(X1, active(X2))U71#(X1, X2)
active#(fst(pair(X, Y)))and#(isLNat(X), isLNat(Y))mark#(afterNth(X1, X2))afterNth#(mark(X1), mark(X2))
active#(splitAt(s(N), cons(X, XS)))mark#(U81(and(isNatural(N), and(isNatural(X), isLNat(XS))), N, X, XS))active#(sel(N, XS))U51#(and(isNatural(N), isLNat(XS)), N, XS)
active#(isLNat(tail(V1)))mark#(isLNat(V1))and#(active(X1), X2)and#(X1, X2)
mark#(U91(X1, X2))mark#(X1)active#(splitAt(s(N), cons(X, XS)))and#(isNatural(X), isLNat(XS))
active#(U71(tt, XS))mark#(pair(nil, XS))U101#(mark(X1), X2, X3)U101#(X1, X2, X3)
U31#(X1, mark(X2))U31#(X1, X2)active#(isLNat(snd(V1)))isPLNat#(V1)
U91#(active(X1), X2)U91#(X1, X2)active#(isLNat(natsFrom(V1)))mark#(isNatural(V1))
tail#(active(X))tail#(X)mark#(U71(X1, X2))active#(U71(mark(X1), X2))
mark#(and(X1, X2))active#(and(mark(X1), X2))active#(isPLNat(splitAt(V1, V2)))and#(isNatural(V1), isLNat(V2))
active#(sel(N, XS))isLNat#(XS)mark#(isPLNat(X))active#(isPLNat(X))
active#(U51(tt, N, XS))mark#(head(afterNth(N, XS)))active#(U41(tt, N))cons#(N, natsFrom(s(N)))
active#(fst(pair(X, Y)))U21#(and(isLNat(X), isLNat(Y)), X)U81#(X1, active(X2), X3, X4)U81#(X1, X2, X3, X4)
U101#(X1, mark(X2), X3)U101#(X1, X2, X3)U51#(X1, X2, mark(X3))U51#(X1, X2, X3)
active#(and(tt, X))mark#(X)U31#(mark(X1), X2)U31#(X1, X2)
active#(isLNat(tail(V1)))isLNat#(V1)U71#(active(X1), X2)U71#(X1, X2)
U21#(mark(X1), X2)U21#(X1, X2)active#(U21(tt, X))mark#(X)
U11#(X1, mark(X2), X3)U11#(X1, X2, X3)mark#(take(X1, X2))mark#(X2)
s#(active(X))s#(X)active#(sel(N, XS))and#(isNatural(N), isLNat(XS))
active#(U11(tt, N, XS))snd#(splitAt(N, XS))mark#(natsFrom(X))natsFrom#(mark(X))
mark#(pair(X1, X2))active#(pair(mark(X1), mark(X2)))take#(active(X1), X2)take#(X1, X2)

Rewrite Rules

active(U101(tt, N, XS))mark(fst(splitAt(N, XS)))active(U11(tt, N, XS))mark(snd(splitAt(N, XS)))
active(U21(tt, X))mark(X)active(U31(tt, N))mark(N)
active(U41(tt, N))mark(cons(N, natsFrom(s(N))))active(U51(tt, N, XS))mark(head(afterNth(N, XS)))
active(U61(tt, Y))mark(Y)active(U71(tt, XS))mark(pair(nil, XS))
active(U81(tt, N, X, XS))mark(U82(splitAt(N, XS), X))active(U82(pair(YS, ZS), X))mark(pair(cons(X, YS), ZS))
active(U91(tt, XS))mark(XS)active(afterNth(N, XS))mark(U11(and(isNatural(N), isLNat(XS)), N, XS))
active(and(tt, X))mark(X)active(fst(pair(X, Y)))mark(U21(and(isLNat(X), isLNat(Y)), X))
active(head(cons(N, XS)))mark(U31(and(isNatural(N), isLNat(XS)), N))active(isLNat(nil))mark(tt)
active(isLNat(afterNth(V1, V2)))mark(and(isNatural(V1), isLNat(V2)))active(isLNat(cons(V1, V2)))mark(and(isNatural(V1), isLNat(V2)))
active(isLNat(fst(V1)))mark(isPLNat(V1))active(isLNat(natsFrom(V1)))mark(isNatural(V1))
active(isLNat(snd(V1)))mark(isPLNat(V1))active(isLNat(tail(V1)))mark(isLNat(V1))
active(isLNat(take(V1, V2)))mark(and(isNatural(V1), isLNat(V2)))active(isNatural(0))mark(tt)
active(isNatural(head(V1)))mark(isLNat(V1))active(isNatural(s(V1)))mark(isNatural(V1))
active(isNatural(sel(V1, V2)))mark(and(isNatural(V1), isLNat(V2)))active(isPLNat(pair(V1, V2)))mark(and(isLNat(V1), isLNat(V2)))
active(isPLNat(splitAt(V1, V2)))mark(and(isNatural(V1), isLNat(V2)))active(natsFrom(N))mark(U41(isNatural(N), N))
active(sel(N, XS))mark(U51(and(isNatural(N), isLNat(XS)), N, XS))active(snd(pair(X, Y)))mark(U61(and(isLNat(X), isLNat(Y)), Y))
active(splitAt(0, XS))mark(U71(isLNat(XS), XS))active(splitAt(s(N), cons(X, XS)))mark(U81(and(isNatural(N), and(isNatural(X), isLNat(XS))), N, X, XS))
active(tail(cons(N, XS)))mark(U91(and(isNatural(N), isLNat(XS)), XS))active(take(N, XS))mark(U101(and(isNatural(N), isLNat(XS)), N, XS))
mark(U101(X1, X2, X3))active(U101(mark(X1), X2, X3))mark(tt)active(tt)
mark(fst(X))active(fst(mark(X)))mark(splitAt(X1, X2))active(splitAt(mark(X1), mark(X2)))
mark(U11(X1, X2, X3))active(U11(mark(X1), X2, X3))mark(snd(X))active(snd(mark(X)))
mark(U21(X1, X2))active(U21(mark(X1), X2))mark(U31(X1, X2))active(U31(mark(X1), X2))
mark(U41(X1, X2))active(U41(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(U51(X1, X2, X3))active(U51(mark(X1), X2, X3))mark(head(X))active(head(mark(X)))
mark(afterNth(X1, X2))active(afterNth(mark(X1), mark(X2)))mark(U61(X1, X2))active(U61(mark(X1), X2))
mark(U71(X1, X2))active(U71(mark(X1), X2))mark(pair(X1, X2))active(pair(mark(X1), mark(X2)))
mark(nil)active(nil)mark(U81(X1, X2, X3, X4))active(U81(mark(X1), X2, X3, X4))
mark(U82(X1, X2))active(U82(mark(X1), X2))mark(U91(X1, X2))active(U91(mark(X1), X2))
mark(and(X1, X2))active(and(mark(X1), X2))mark(isNatural(X))active(isNatural(X))
mark(isLNat(X))active(isLNat(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, X3)U101(X1, X2, X3)U101(X1, mark(X2), X3)U101(X1, X2, X3)
U101(X1, X2, mark(X3))U101(X1, X2, X3)U101(active(X1), X2, X3)U101(X1, X2, X3)
U101(X1, active(X2), X3)U101(X1, X2, X3)U101(X1, X2, active(X3))U101(X1, X2, X3)
fst(mark(X))fst(X)fst(active(X))fst(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)
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)
snd(mark(X))snd(X)snd(active(X))snd(X)
U21(mark(X1), X2)U21(X1, X2)U21(X1, mark(X2))U21(X1, X2)
U21(active(X1), X2)U21(X1, X2)U21(X1, active(X2))U21(X1, X2)
U31(mark(X1), X2)U31(X1, X2)U31(X1, mark(X2))U31(X1, X2)
U31(active(X1), X2)U31(X1, X2)U31(X1, active(X2))U31(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)
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)
U51(mark(X1), X2, X3)U51(X1, X2, X3)U51(X1, mark(X2), X3)U51(X1, X2, X3)
U51(X1, X2, mark(X3))U51(X1, X2, X3)U51(active(X1), X2, X3)U51(X1, X2, X3)
U51(X1, active(X2), X3)U51(X1, X2, X3)U51(X1, X2, active(X3))U51(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)
U61(mark(X1), X2)U61(X1, X2)U61(X1, mark(X2))U61(X1, X2)
U61(active(X1), X2)U61(X1, X2)U61(X1, active(X2))U61(X1, X2)
U71(mark(X1), X2)U71(X1, X2)U71(X1, mark(X2))U71(X1, X2)
U71(active(X1), X2)U71(X1, X2)U71(X1, active(X2))U71(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)
U81(mark(X1), X2, X3, X4)U81(X1, X2, X3, X4)U81(X1, mark(X2), X3, X4)U81(X1, X2, X3, X4)
U81(X1, X2, mark(X3), X4)U81(X1, X2, X3, X4)U81(X1, X2, X3, mark(X4))U81(X1, X2, X3, X4)
U81(active(X1), X2, X3, X4)U81(X1, X2, X3, X4)U81(X1, active(X2), X3, X4)U81(X1, X2, X3, X4)
U81(X1, X2, active(X3), X4)U81(X1, X2, X3, X4)U81(X1, X2, X3, active(X4))U81(X1, X2, X3, X4)
U82(mark(X1), X2)U82(X1, X2)U82(X1, mark(X2))U82(X1, X2)
U82(active(X1), X2)U82(X1, X2)U82(X1, active(X2))U82(X1, X2)
U91(mark(X1), X2)U91(X1, X2)U91(X1, mark(X2))U91(X1, X2)
U91(active(X1), X2)U91(X1, X2)U91(X1, active(X2))U91(X1, X2)
and(mark(X1), X2)and(X1, X2)and(X1, mark(X2))and(X1, X2)
and(active(X1), X2)and(X1, X2)and(X1, active(X2))and(X1, X2)
isNatural(mark(X))isNatural(X)isNatural(active(X))isNatural(X)
isLNat(mark(X))isLNat(X)isLNat(active(X))isLNat(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)

Original Signature

Termination of terms over the following signature is verified: pair, natsFrom, isNatural, fst, U61, U41, U91, head, U21, snd, cons, mark, isPLNat, tail, splitAt, and, U71, 0, s, U51, tt, take, U82, isLNat, U81, U11, active, U31, afterNth, sel, U101, nil