The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(O(1), O(1)).

(0) Obligation:

Runtime Complexity TRS:
The TRS R consists of the following rules:

active(U11(tt, N, XS)) → mark(U12(tt, N, XS))
active(U12(tt, N, XS)) → mark(snd(splitAt(N, XS)))
active(U21(tt, X)) → mark(U22(tt, X))
active(U22(tt, X)) → mark(X)
active(U31(tt, N)) → mark(U32(tt, N))
active(U32(tt, N)) → mark(N)
active(U41(tt, N, XS)) → mark(U42(tt, N, XS))
active(U42(tt, N, XS)) → mark(head(afterNth(N, XS)))
active(U51(tt, Y)) → mark(U52(tt, Y))
active(U52(tt, Y)) → mark(Y)
active(U61(tt, N, X, XS)) → mark(U62(tt, N, X, XS))
active(U62(tt, N, X, XS)) → mark(U63(tt, N, X, XS))
active(U63(tt, N, X, XS)) → mark(U64(splitAt(N, XS), X))
active(U64(pair(YS, ZS), X)) → mark(pair(cons(X, YS), ZS))
active(U71(tt, XS)) → mark(U72(tt, XS))
active(U72(tt, XS)) → mark(XS)
active(U81(tt, N, XS)) → mark(U82(tt, N, XS))
active(U82(tt, N, XS)) → mark(fst(splitAt(N, XS)))
active(afterNth(N, XS)) → mark(U11(tt, N, XS))
active(fst(pair(X, Y))) → mark(U21(tt, X))
active(head(cons(N, XS))) → mark(U31(tt, N))
active(natsFrom(N)) → mark(cons(N, natsFrom(s(N))))
active(sel(N, XS)) → mark(U41(tt, N, XS))
active(snd(pair(X, Y))) → mark(U51(tt, Y))
active(splitAt(0, XS)) → mark(pair(nil, XS))
active(splitAt(s(N), cons(X, XS))) → mark(U61(tt, N, X, XS))
active(tail(cons(N, XS))) → mark(U71(tt, XS))
active(take(N, XS)) → mark(U81(tt, N, XS))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(snd(X)) → active(snd(mark(X)))
mark(splitAt(X1, X2)) → active(splitAt(mark(X1), mark(X2)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(head(X)) → active(head(mark(X)))
mark(afterNth(X1, X2)) → active(afterNth(mark(X1), mark(X2)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3, X4)) → active(U61(mark(X1), X2, X3, X4))
mark(U62(X1, X2, X3, X4)) → active(U62(mark(X1), X2, X3, X4))
mark(U63(X1, X2, X3, X4)) → active(U63(mark(X1), X2, X3, X4))
mark(U64(X1, X2)) → active(U64(mark(X1), X2))
mark(pair(X1, X2)) → active(pair(mark(X1), mark(X2)))
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(U71(X1, X2)) → active(U71(mark(X1), X2))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U81(X1, X2, X3)) → active(U81(mark(X1), X2, X3))
mark(U82(X1, X2, X3)) → active(U82(mark(X1), X2, X3))
mark(fst(X)) → active(fst(mark(X)))
mark(natsFrom(X)) → active(natsFrom(mark(X)))
mark(s(X)) → active(s(mark(X)))
mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))
mark(0) → active(0)
mark(nil) → active(nil)
mark(tail(X)) → active(tail(mark(X)))
mark(take(X1, X2)) → active(take(mark(X1), mark(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)
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)
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)
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)
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)
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)
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, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(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)
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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3, X4) → U61(X1, X2, X3, X4)
U61(X1, mark(X2), X3, X4) → U61(X1, X2, X3, X4)
U61(X1, X2, mark(X3), X4) → U61(X1, X2, X3, X4)
U61(X1, X2, X3, mark(X4)) → U61(X1, X2, X3, X4)
U61(active(X1), X2, X3, X4) → U61(X1, X2, X3, X4)
U61(X1, active(X2), X3, X4) → U61(X1, X2, X3, X4)
U61(X1, X2, active(X3), X4) → U61(X1, X2, X3, X4)
U61(X1, X2, X3, active(X4)) → U61(X1, X2, X3, X4)
U62(mark(X1), X2, X3, X4) → U62(X1, X2, X3, X4)
U62(X1, mark(X2), X3, X4) → U62(X1, X2, X3, X4)
U62(X1, X2, mark(X3), X4) → U62(X1, X2, X3, X4)
U62(X1, X2, X3, mark(X4)) → U62(X1, X2, X3, X4)
U62(active(X1), X2, X3, X4) → U62(X1, X2, X3, X4)
U62(X1, active(X2), X3, X4) → U62(X1, X2, X3, X4)
U62(X1, X2, active(X3), X4) → U62(X1, X2, X3, X4)
U62(X1, X2, X3, active(X4)) → U62(X1, X2, X3, X4)
U63(mark(X1), X2, X3, X4) → U63(X1, X2, X3, X4)
U63(X1, mark(X2), X3, X4) → U63(X1, X2, X3, X4)
U63(X1, X2, mark(X3), X4) → U63(X1, X2, X3, X4)
U63(X1, X2, X3, mark(X4)) → U63(X1, X2, X3, X4)
U63(active(X1), X2, X3, X4) → U63(X1, X2, X3, X4)
U63(X1, active(X2), X3, X4) → U63(X1, X2, X3, X4)
U63(X1, X2, active(X3), X4) → U63(X1, X2, X3, X4)
U63(X1, X2, X3, active(X4)) → U63(X1, X2, X3, X4)
U64(mark(X1), X2) → U64(X1, X2)
U64(X1, mark(X2)) → U64(X1, X2)
U64(active(X1), X2) → U64(X1, X2)
U64(X1, active(X2)) → U64(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)
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)
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)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U81(mark(X1), X2, X3) → U81(X1, X2, X3)
U81(X1, mark(X2), X3) → U81(X1, X2, X3)
U81(X1, X2, mark(X3)) → U81(X1, X2, X3)
U81(active(X1), X2, X3) → U81(X1, X2, X3)
U81(X1, active(X2), X3) → U81(X1, X2, X3)
U81(X1, X2, active(X3)) → U81(X1, X2, X3)
U82(mark(X1), X2, X3) → U82(X1, X2, X3)
U82(X1, mark(X2), X3) → U82(X1, X2, X3)
U82(X1, X2, mark(X3)) → U82(X1, X2, X3)
U82(active(X1), X2, X3) → U82(X1, X2, X3)
U82(X1, active(X2), X3) → U82(X1, X2, X3)
U82(X1, X2, active(X3)) → U82(X1, X2, X3)
fst(mark(X)) → fst(X)
fst(active(X)) → fst(X)
natsFrom(mark(X)) → natsFrom(X)
natsFrom(active(X)) → natsFrom(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
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)
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)

Rewrite Strategy: INNERMOST

(1) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID) transformation)

Converted CpxTRS to CDT

(2) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1))
active(U12(tt, z0, z1)) → mark(snd(splitAt(z0, z1)))
active(U21(tt, z0)) → mark(U22(tt, z0))
active(U22(tt, z0)) → mark(z0)
active(U31(tt, z0)) → mark(U32(tt, z0))
active(U32(tt, z0)) → mark(z0)
active(U41(tt, z0, z1)) → mark(U42(tt, z0, z1))
active(U42(tt, z0, z1)) → mark(head(afterNth(z0, z1)))
active(U51(tt, z0)) → mark(U52(tt, z0))
active(U52(tt, z0)) → mark(z0)
active(U61(tt, z0, z1, z2)) → mark(U62(tt, z0, z1, z2))
active(U62(tt, z0, z1, z2)) → mark(U63(tt, z0, z1, z2))
active(U63(tt, z0, z1, z2)) → mark(U64(splitAt(z0, z2), z1))
active(U64(pair(z0, z1), z2)) → mark(pair(cons(z2, z0), z1))
active(U71(tt, z0)) → mark(U72(tt, z0))
active(U72(tt, z0)) → mark(z0)
active(U81(tt, z0, z1)) → mark(U82(tt, z0, z1))
active(U82(tt, z0, z1)) → mark(fst(splitAt(z0, z1)))
active(afterNth(z0, z1)) → mark(U11(tt, z0, z1))
active(fst(pair(z0, z1))) → mark(U21(tt, z0))
active(head(cons(z0, z1))) → mark(U31(tt, z0))
active(natsFrom(z0)) → mark(cons(z0, natsFrom(s(z0))))
active(sel(z0, z1)) → mark(U41(tt, z0, z1))
active(snd(pair(z0, z1))) → mark(U51(tt, z1))
active(splitAt(0, z0)) → mark(pair(nil, z0))
active(splitAt(s(z0), cons(z1, z2))) → mark(U61(tt, z0, z1, z2))
active(tail(cons(z0, z1))) → mark(U71(tt, z1))
active(take(z0, z1)) → mark(U81(tt, z0, z1))
mark(U11(z0, z1, z2)) → active(U11(mark(z0), z1, z2))
mark(tt) → active(tt)
mark(U12(z0, z1, z2)) → active(U12(mark(z0), z1, z2))
mark(snd(z0)) → active(snd(mark(z0)))
mark(splitAt(z0, z1)) → active(splitAt(mark(z0), mark(z1)))
mark(U21(z0, z1)) → active(U21(mark(z0), z1))
mark(U22(z0, z1)) → active(U22(mark(z0), z1))
mark(U31(z0, z1)) → active(U31(mark(z0), z1))
mark(U32(z0, z1)) → active(U32(mark(z0), z1))
mark(U41(z0, z1, z2)) → active(U41(mark(z0), z1, z2))
mark(U42(z0, z1, z2)) → active(U42(mark(z0), z1, z2))
mark(head(z0)) → active(head(mark(z0)))
mark(afterNth(z0, z1)) → active(afterNth(mark(z0), mark(z1)))
mark(U51(z0, z1)) → active(U51(mark(z0), z1))
mark(U52(z0, z1)) → active(U52(mark(z0), z1))
mark(U61(z0, z1, z2, z3)) → active(U61(mark(z0), z1, z2, z3))
mark(U62(z0, z1, z2, z3)) → active(U62(mark(z0), z1, z2, z3))
mark(U63(z0, z1, z2, z3)) → active(U63(mark(z0), z1, z2, z3))
mark(U64(z0, z1)) → active(U64(mark(z0), z1))
mark(pair(z0, z1)) → active(pair(mark(z0), mark(z1)))
mark(cons(z0, z1)) → active(cons(mark(z0), z1))
mark(U71(z0, z1)) → active(U71(mark(z0), z1))
mark(U72(z0, z1)) → active(U72(mark(z0), z1))
mark(U81(z0, z1, z2)) → active(U81(mark(z0), z1, z2))
mark(U82(z0, z1, z2)) → active(U82(mark(z0), z1, z2))
mark(fst(z0)) → active(fst(mark(z0)))
mark(natsFrom(z0)) → active(natsFrom(mark(z0)))
mark(s(z0)) → active(s(mark(z0)))
mark(sel(z0, z1)) → active(sel(mark(z0), mark(z1)))
mark(0) → active(0)
mark(nil) → active(nil)
mark(tail(z0)) → active(tail(mark(z0)))
mark(take(z0, z1)) → active(take(mark(z0), mark(z1)))
U11(mark(z0), z1, z2) → U11(z0, z1, z2)
U11(z0, mark(z1), z2) → U11(z0, z1, z2)
U11(z0, z1, mark(z2)) → U11(z0, z1, z2)
U11(active(z0), z1, z2) → U11(z0, z1, z2)
U11(z0, active(z1), z2) → U11(z0, z1, z2)
U11(z0, z1, active(z2)) → U11(z0, z1, z2)
U12(mark(z0), z1, z2) → U12(z0, z1, z2)
U12(z0, mark(z1), z2) → U12(z0, z1, z2)
U12(z0, z1, mark(z2)) → U12(z0, z1, z2)
U12(active(z0), z1, z2) → U12(z0, z1, z2)
U12(z0, active(z1), z2) → U12(z0, z1, z2)
U12(z0, z1, active(z2)) → U12(z0, z1, z2)
snd(mark(z0)) → snd(z0)
snd(active(z0)) → snd(z0)
splitAt(mark(z0), z1) → splitAt(z0, z1)
splitAt(z0, mark(z1)) → splitAt(z0, z1)
splitAt(active(z0), z1) → splitAt(z0, z1)
splitAt(z0, active(z1)) → splitAt(z0, z1)
U21(mark(z0), z1) → U21(z0, z1)
U21(z0, mark(z1)) → U21(z0, z1)
U21(active(z0), z1) → U21(z0, z1)
U21(z0, active(z1)) → U21(z0, z1)
U22(mark(z0), z1) → U22(z0, z1)
U22(z0, mark(z1)) → U22(z0, z1)
U22(active(z0), z1) → U22(z0, z1)
U22(z0, active(z1)) → U22(z0, z1)
U31(mark(z0), z1) → U31(z0, z1)
U31(z0, mark(z1)) → U31(z0, z1)
U31(active(z0), z1) → U31(z0, z1)
U31(z0, active(z1)) → U31(z0, z1)
U32(mark(z0), z1) → U32(z0, z1)
U32(z0, mark(z1)) → U32(z0, z1)
U32(active(z0), z1) → U32(z0, z1)
U32(z0, active(z1)) → U32(z0, z1)
U41(mark(z0), z1, z2) → U41(z0, z1, z2)
U41(z0, mark(z1), z2) → U41(z0, z1, z2)
U41(z0, z1, mark(z2)) → U41(z0, z1, z2)
U41(active(z0), z1, z2) → U41(z0, z1, z2)
U41(z0, active(z1), z2) → U41(z0, z1, z2)
U41(z0, z1, active(z2)) → U41(z0, z1, z2)
U42(mark(z0), z1, z2) → U42(z0, z1, z2)
U42(z0, mark(z1), z2) → U42(z0, z1, z2)
U42(z0, z1, mark(z2)) → U42(z0, z1, z2)
U42(active(z0), z1, z2) → U42(z0, z1, z2)
U42(z0, active(z1), z2) → U42(z0, z1, z2)
U42(z0, z1, active(z2)) → U42(z0, z1, z2)
head(mark(z0)) → head(z0)
head(active(z0)) → head(z0)
afterNth(mark(z0), z1) → afterNth(z0, z1)
afterNth(z0, mark(z1)) → afterNth(z0, z1)
afterNth(active(z0), z1) → afterNth(z0, z1)
afterNth(z0, active(z1)) → afterNth(z0, z1)
U51(mark(z0), z1) → U51(z0, z1)
U51(z0, mark(z1)) → U51(z0, z1)
U51(active(z0), z1) → U51(z0, z1)
U51(z0, active(z1)) → U51(z0, z1)
U52(mark(z0), z1) → U52(z0, z1)
U52(z0, mark(z1)) → U52(z0, z1)
U52(active(z0), z1) → U52(z0, z1)
U52(z0, active(z1)) → U52(z0, z1)
U61(mark(z0), z1, z2, z3) → U61(z0, z1, z2, z3)
U61(z0, mark(z1), z2, z3) → U61(z0, z1, z2, z3)
U61(z0, z1, mark(z2), z3) → U61(z0, z1, z2, z3)
U61(z0, z1, z2, mark(z3)) → U61(z0, z1, z2, z3)
U61(active(z0), z1, z2, z3) → U61(z0, z1, z2, z3)
U61(z0, active(z1), z2, z3) → U61(z0, z1, z2, z3)
U61(z0, z1, active(z2), z3) → U61(z0, z1, z2, z3)
U61(z0, z1, z2, active(z3)) → U61(z0, z1, z2, z3)
U62(mark(z0), z1, z2, z3) → U62(z0, z1, z2, z3)
U62(z0, mark(z1), z2, z3) → U62(z0, z1, z2, z3)
U62(z0, z1, mark(z2), z3) → U62(z0, z1, z2, z3)
U62(z0, z1, z2, mark(z3)) → U62(z0, z1, z2, z3)
U62(active(z0), z1, z2, z3) → U62(z0, z1, z2, z3)
U62(z0, active(z1), z2, z3) → U62(z0, z1, z2, z3)
U62(z0, z1, active(z2), z3) → U62(z0, z1, z2, z3)
U62(z0, z1, z2, active(z3)) → U62(z0, z1, z2, z3)
U63(mark(z0), z1, z2, z3) → U63(z0, z1, z2, z3)
U63(z0, mark(z1), z2, z3) → U63(z0, z1, z2, z3)
U63(z0, z1, mark(z2), z3) → U63(z0, z1, z2, z3)
U63(z0, z1, z2, mark(z3)) → U63(z0, z1, z2, z3)
U63(active(z0), z1, z2, z3) → U63(z0, z1, z2, z3)
U63(z0, active(z1), z2, z3) → U63(z0, z1, z2, z3)
U63(z0, z1, active(z2), z3) → U63(z0, z1, z2, z3)
U63(z0, z1, z2, active(z3)) → U63(z0, z1, z2, z3)
U64(mark(z0), z1) → U64(z0, z1)
U64(z0, mark(z1)) → U64(z0, z1)
U64(active(z0), z1) → U64(z0, z1)
U64(z0, active(z1)) → U64(z0, z1)
pair(mark(z0), z1) → pair(z0, z1)
pair(z0, mark(z1)) → pair(z0, z1)
pair(active(z0), z1) → pair(z0, z1)
pair(z0, active(z1)) → pair(z0, z1)
cons(mark(z0), z1) → cons(z0, z1)
cons(z0, mark(z1)) → cons(z0, z1)
cons(active(z0), z1) → cons(z0, z1)
cons(z0, active(z1)) → cons(z0, z1)
U71(mark(z0), z1) → U71(z0, z1)
U71(z0, mark(z1)) → U71(z0, z1)
U71(active(z0), z1) → U71(z0, z1)
U71(z0, active(z1)) → U71(z0, z1)
U72(mark(z0), z1) → U72(z0, z1)
U72(z0, mark(z1)) → U72(z0, z1)
U72(active(z0), z1) → U72(z0, z1)
U72(z0, active(z1)) → U72(z0, z1)
U81(mark(z0), z1, z2) → U81(z0, z1, z2)
U81(z0, mark(z1), z2) → U81(z0, z1, z2)
U81(z0, z1, mark(z2)) → U81(z0, z1, z2)
U81(active(z0), z1, z2) → U81(z0, z1, z2)
U81(z0, active(z1), z2) → U81(z0, z1, z2)
U81(z0, z1, active(z2)) → U81(z0, z1, z2)
U82(mark(z0), z1, z2) → U82(z0, z1, z2)
U82(z0, mark(z1), z2) → U82(z0, z1, z2)
U82(z0, z1, mark(z2)) → U82(z0, z1, z2)
U82(active(z0), z1, z2) → U82(z0, z1, z2)
U82(z0, active(z1), z2) → U82(z0, z1, z2)
U82(z0, z1, active(z2)) → U82(z0, z1, z2)
fst(mark(z0)) → fst(z0)
fst(active(z0)) → fst(z0)
natsFrom(mark(z0)) → natsFrom(z0)
natsFrom(active(z0)) → natsFrom(z0)
s(mark(z0)) → s(z0)
s(active(z0)) → s(z0)
sel(mark(z0), z1) → sel(z0, z1)
sel(z0, mark(z1)) → sel(z0, z1)
sel(active(z0), z1) → sel(z0, z1)
sel(z0, active(z1)) → sel(z0, z1)
tail(mark(z0)) → tail(z0)
tail(active(z0)) → tail(z0)
take(mark(z0), z1) → take(z0, z1)
take(z0, mark(z1)) → take(z0, z1)
take(active(z0), z1) → take(z0, z1)
take(z0, active(z1)) → take(z0, z1)

Tuples:

ACTIVE(U11(tt, z0, z1)) → c(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1))
ACTIVE(U12(tt, z0, z1)) → c1(MARK(snd(splitAt(z0, z1))), SND(splitAt(z0, z1)), SPLITAT(z0, z1))
ACTIVE(U21(tt, z0)) → c2(MARK(U22(tt, z0)), U22'(tt, z0))
ACTIVE(U22(tt, z0)) → c3(MARK(z0))
ACTIVE(U31(tt, z0)) → c4(MARK(U32(tt, z0)), U32'(tt, z0))
ACTIVE(U32(tt, z0)) → c5(MARK(z0))
ACTIVE(U41(tt, z0, z1)) → c6(MARK(U42(tt, z0, z1)), U42'(tt, z0, z1))
ACTIVE(U42(tt, z0, z1)) → c7(MARK(head(afterNth(z0, z1))), HEAD(afterNth(z0, z1)), AFTERNTH(z0, z1))
ACTIVE(U51(tt, z0)) → c8(MARK(U52(tt, z0)), U52'(tt, z0))
ACTIVE(U52(tt, z0)) → c9(MARK(z0))
ACTIVE(U61(tt, z0, z1, z2)) → c10(MARK(U62(tt, z0, z1, z2)), U62'(tt, z0, z1, z2))
ACTIVE(U62(tt, z0, z1, z2)) → c11(MARK(U63(tt, z0, z1, z2)), U63'(tt, z0, z1, z2))
ACTIVE(U63(tt, z0, z1, z2)) → c12(MARK(U64(splitAt(z0, z2), z1)), U64'(splitAt(z0, z2), z1), SPLITAT(z0, z2))
ACTIVE(U64(pair(z0, z1), z2)) → c13(MARK(pair(cons(z2, z0), z1)), PAIR(cons(z2, z0), z1), CONS(z2, z0))
ACTIVE(U71(tt, z0)) → c14(MARK(U72(tt, z0)), U72'(tt, z0))
ACTIVE(U72(tt, z0)) → c15(MARK(z0))
ACTIVE(U81(tt, z0, z1)) → c16(MARK(U82(tt, z0, z1)), U82'(tt, z0, z1))
ACTIVE(U82(tt, z0, z1)) → c17(MARK(fst(splitAt(z0, z1))), FST(splitAt(z0, z1)), SPLITAT(z0, z1))
ACTIVE(afterNth(z0, z1)) → c18(MARK(U11(tt, z0, z1)), U11'(tt, z0, z1))
ACTIVE(fst(pair(z0, z1))) → c19(MARK(U21(tt, z0)), U21'(tt, z0))
ACTIVE(head(cons(z0, z1))) → c20(MARK(U31(tt, z0)), U31'(tt, z0))
ACTIVE(natsFrom(z0)) → c21(MARK(cons(z0, natsFrom(s(z0)))), CONS(z0, natsFrom(s(z0))), NATSFROM(s(z0)), S(z0))
ACTIVE(sel(z0, z1)) → c22(MARK(U41(tt, z0, z1)), U41'(tt, z0, z1))
ACTIVE(snd(pair(z0, z1))) → c23(MARK(U51(tt, z1)), U51'(tt, z1))
ACTIVE(splitAt(0, z0)) → c24(MARK(pair(nil, z0)), PAIR(nil, z0))
ACTIVE(splitAt(s(z0), cons(z1, z2))) → c25(MARK(U61(tt, z0, z1, z2)), U61'(tt, z0, z1, z2))
ACTIVE(tail(cons(z0, z1))) → c26(MARK(U71(tt, z1)), U71'(tt, z1))
ACTIVE(take(z0, z1)) → c27(MARK(U81(tt, z0, z1)), U81'(tt, z0, z1))
MARK(U11(z0, z1, z2)) → c28(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0))
MARK(tt) → c29(ACTIVE(tt))
MARK(U12(z0, z1, z2)) → c30(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0))
MARK(snd(z0)) → c31(ACTIVE(snd(mark(z0))), SND(mark(z0)), MARK(z0))
MARK(splitAt(z0, z1)) → c32(ACTIVE(splitAt(mark(z0), mark(z1))), SPLITAT(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U21(z0, z1)) → c33(ACTIVE(U21(mark(z0), z1)), U21'(mark(z0), z1), MARK(z0))
MARK(U22(z0, z1)) → c34(ACTIVE(U22(mark(z0), z1)), U22'(mark(z0), z1), MARK(z0))
MARK(U31(z0, z1)) → c35(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0))
MARK(U32(z0, z1)) → c36(ACTIVE(U32(mark(z0), z1)), U32'(mark(z0), z1), MARK(z0))
MARK(U41(z0, z1, z2)) → c37(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0))
MARK(U42(z0, z1, z2)) → c38(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0))
MARK(head(z0)) → c39(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0))
MARK(afterNth(z0, z1)) → c40(ACTIVE(afterNth(mark(z0), mark(z1))), AFTERNTH(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U51(z0, z1)) → c41(ACTIVE(U51(mark(z0), z1)), U51'(mark(z0), z1), MARK(z0))
MARK(U52(z0, z1)) → c42(ACTIVE(U52(mark(z0), z1)), U52'(mark(z0), z1), MARK(z0))
MARK(U61(z0, z1, z2, z3)) → c43(ACTIVE(U61(mark(z0), z1, z2, z3)), U61'(mark(z0), z1, z2, z3), MARK(z0))
MARK(U62(z0, z1, z2, z3)) → c44(ACTIVE(U62(mark(z0), z1, z2, z3)), U62'(mark(z0), z1, z2, z3), MARK(z0))
MARK(U63(z0, z1, z2, z3)) → c45(ACTIVE(U63(mark(z0), z1, z2, z3)), U63'(mark(z0), z1, z2, z3), MARK(z0))
MARK(U64(z0, z1)) → c46(ACTIVE(U64(mark(z0), z1)), U64'(mark(z0), z1), MARK(z0))
MARK(pair(z0, z1)) → c47(ACTIVE(pair(mark(z0), mark(z1))), PAIR(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(cons(z0, z1)) → c48(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0))
MARK(U71(z0, z1)) → c49(ACTIVE(U71(mark(z0), z1)), U71'(mark(z0), z1), MARK(z0))
MARK(U72(z0, z1)) → c50(ACTIVE(U72(mark(z0), z1)), U72'(mark(z0), z1), MARK(z0))
MARK(U81(z0, z1, z2)) → c51(ACTIVE(U81(mark(z0), z1, z2)), U81'(mark(z0), z1, z2), MARK(z0))
MARK(U82(z0, z1, z2)) → c52(ACTIVE(U82(mark(z0), z1, z2)), U82'(mark(z0), z1, z2), MARK(z0))
MARK(fst(z0)) → c53(ACTIVE(fst(mark(z0))), FST(mark(z0)), MARK(z0))
MARK(natsFrom(z0)) → c54(ACTIVE(natsFrom(mark(z0))), NATSFROM(mark(z0)), MARK(z0))
MARK(s(z0)) → c55(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0))
MARK(sel(z0, z1)) → c56(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(0) → c57(ACTIVE(0))
MARK(nil) → c58(ACTIVE(nil))
MARK(tail(z0)) → c59(ACTIVE(tail(mark(z0))), TAIL(mark(z0)), MARK(z0))
MARK(take(z0, z1)) → c60(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1))
U11'(mark(z0), z1, z2) → c61(U11'(z0, z1, z2))
U11'(z0, mark(z1), z2) → c62(U11'(z0, z1, z2))
U11'(z0, z1, mark(z2)) → c63(U11'(z0, z1, z2))
U11'(active(z0), z1, z2) → c64(U11'(z0, z1, z2))
U11'(z0, active(z1), z2) → c65(U11'(z0, z1, z2))
U11'(z0, z1, active(z2)) → c66(U11'(z0, z1, z2))
U12'(mark(z0), z1, z2) → c67(U12'(z0, z1, z2))
U12'(z0, mark(z1), z2) → c68(U12'(z0, z1, z2))
U12'(z0, z1, mark(z2)) → c69(U12'(z0, z1, z2))
U12'(active(z0), z1, z2) → c70(U12'(z0, z1, z2))
U12'(z0, active(z1), z2) → c71(U12'(z0, z1, z2))
U12'(z0, z1, active(z2)) → c72(U12'(z0, z1, z2))
SND(mark(z0)) → c73(SND(z0))
SND(active(z0)) → c74(SND(z0))
SPLITAT(mark(z0), z1) → c75(SPLITAT(z0, z1))
SPLITAT(z0, mark(z1)) → c76(SPLITAT(z0, z1))
SPLITAT(active(z0), z1) → c77(SPLITAT(z0, z1))
SPLITAT(z0, active(z1)) → c78(SPLITAT(z0, z1))
U21'(mark(z0), z1) → c79(U21'(z0, z1))
U21'(z0, mark(z1)) → c80(U21'(z0, z1))
U21'(active(z0), z1) → c81(U21'(z0, z1))
U21'(z0, active(z1)) → c82(U21'(z0, z1))
U22'(mark(z0), z1) → c83(U22'(z0, z1))
U22'(z0, mark(z1)) → c84(U22'(z0, z1))
U22'(active(z0), z1) → c85(U22'(z0, z1))
U22'(z0, active(z1)) → c86(U22'(z0, z1))
U31'(mark(z0), z1) → c87(U31'(z0, z1))
U31'(z0, mark(z1)) → c88(U31'(z0, z1))
U31'(active(z0), z1) → c89(U31'(z0, z1))
U31'(z0, active(z1)) → c90(U31'(z0, z1))
U32'(mark(z0), z1) → c91(U32'(z0, z1))
U32'(z0, mark(z1)) → c92(U32'(z0, z1))
U32'(active(z0), z1) → c93(U32'(z0, z1))
U32'(z0, active(z1)) → c94(U32'(z0, z1))
U41'(mark(z0), z1, z2) → c95(U41'(z0, z1, z2))
U41'(z0, mark(z1), z2) → c96(U41'(z0, z1, z2))
U41'(z0, z1, mark(z2)) → c97(U41'(z0, z1, z2))
U41'(active(z0), z1, z2) → c98(U41'(z0, z1, z2))
U41'(z0, active(z1), z2) → c99(U41'(z0, z1, z2))
U41'(z0, z1, active(z2)) → c100(U41'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c101(U42'(z0, z1, z2))
U42'(z0, mark(z1), z2) → c102(U42'(z0, z1, z2))
U42'(z0, z1, mark(z2)) → c103(U42'(z0, z1, z2))
U42'(active(z0), z1, z2) → c104(U42'(z0, z1, z2))
U42'(z0, active(z1), z2) → c105(U42'(z0, z1, z2))
U42'(z0, z1, active(z2)) → c106(U42'(z0, z1, z2))
HEAD(mark(z0)) → c107(HEAD(z0))
HEAD(active(z0)) → c108(HEAD(z0))
AFTERNTH(mark(z0), z1) → c109(AFTERNTH(z0, z1))
AFTERNTH(z0, mark(z1)) → c110(AFTERNTH(z0, z1))
AFTERNTH(active(z0), z1) → c111(AFTERNTH(z0, z1))
AFTERNTH(z0, active(z1)) → c112(AFTERNTH(z0, z1))
U51'(mark(z0), z1) → c113(U51'(z0, z1))
U51'(z0, mark(z1)) → c114(U51'(z0, z1))
U51'(active(z0), z1) → c115(U51'(z0, z1))
U51'(z0, active(z1)) → c116(U51'(z0, z1))
U52'(mark(z0), z1) → c117(U52'(z0, z1))
U52'(z0, mark(z1)) → c118(U52'(z0, z1))
U52'(active(z0), z1) → c119(U52'(z0, z1))
U52'(z0, active(z1)) → c120(U52'(z0, z1))
U61'(mark(z0), z1, z2, z3) → c121(U61'(z0, z1, z2, z3))
U61'(z0, mark(z1), z2, z3) → c122(U61'(z0, z1, z2, z3))
U61'(z0, z1, mark(z2), z3) → c123(U61'(z0, z1, z2, z3))
U61'(z0, z1, z2, mark(z3)) → c124(U61'(z0, z1, z2, z3))
U61'(active(z0), z1, z2, z3) → c125(U61'(z0, z1, z2, z3))
U61'(z0, active(z1), z2, z3) → c126(U61'(z0, z1, z2, z3))
U61'(z0, z1, active(z2), z3) → c127(U61'(z0, z1, z2, z3))
U61'(z0, z1, z2, active(z3)) → c128(U61'(z0, z1, z2, z3))
U62'(mark(z0), z1, z2, z3) → c129(U62'(z0, z1, z2, z3))
U62'(z0, mark(z1), z2, z3) → c130(U62'(z0, z1, z2, z3))
U62'(z0, z1, mark(z2), z3) → c131(U62'(z0, z1, z2, z3))
U62'(z0, z1, z2, mark(z3)) → c132(U62'(z0, z1, z2, z3))
U62'(active(z0), z1, z2, z3) → c133(U62'(z0, z1, z2, z3))
U62'(z0, active(z1), z2, z3) → c134(U62'(z0, z1, z2, z3))
U62'(z0, z1, active(z2), z3) → c135(U62'(z0, z1, z2, z3))
U62'(z0, z1, z2, active(z3)) → c136(U62'(z0, z1, z2, z3))
U63'(mark(z0), z1, z2, z3) → c137(U63'(z0, z1, z2, z3))
U63'(z0, mark(z1), z2, z3) → c138(U63'(z0, z1, z2, z3))
U63'(z0, z1, mark(z2), z3) → c139(U63'(z0, z1, z2, z3))
U63'(z0, z1, z2, mark(z3)) → c140(U63'(z0, z1, z2, z3))
U63'(active(z0), z1, z2, z3) → c141(U63'(z0, z1, z2, z3))
U63'(z0, active(z1), z2, z3) → c142(U63'(z0, z1, z2, z3))
U63'(z0, z1, active(z2), z3) → c143(U63'(z0, z1, z2, z3))
U63'(z0, z1, z2, active(z3)) → c144(U63'(z0, z1, z2, z3))
U64'(mark(z0), z1) → c145(U64'(z0, z1))
U64'(z0, mark(z1)) → c146(U64'(z0, z1))
U64'(active(z0), z1) → c147(U64'(z0, z1))
U64'(z0, active(z1)) → c148(U64'(z0, z1))
PAIR(mark(z0), z1) → c149(PAIR(z0, z1))
PAIR(z0, mark(z1)) → c150(PAIR(z0, z1))
PAIR(active(z0), z1) → c151(PAIR(z0, z1))
PAIR(z0, active(z1)) → c152(PAIR(z0, z1))
CONS(mark(z0), z1) → c153(CONS(z0, z1))
CONS(z0, mark(z1)) → c154(CONS(z0, z1))
CONS(active(z0), z1) → c155(CONS(z0, z1))
CONS(z0, active(z1)) → c156(CONS(z0, z1))
U71'(mark(z0), z1) → c157(U71'(z0, z1))
U71'(z0, mark(z1)) → c158(U71'(z0, z1))
U71'(active(z0), z1) → c159(U71'(z0, z1))
U71'(z0, active(z1)) → c160(U71'(z0, z1))
U72'(mark(z0), z1) → c161(U72'(z0, z1))
U72'(z0, mark(z1)) → c162(U72'(z0, z1))
U72'(active(z0), z1) → c163(U72'(z0, z1))
U72'(z0, active(z1)) → c164(U72'(z0, z1))
U81'(mark(z0), z1, z2) → c165(U81'(z0, z1, z2))
U81'(z0, mark(z1), z2) → c166(U81'(z0, z1, z2))
U81'(z0, z1, mark(z2)) → c167(U81'(z0, z1, z2))
U81'(active(z0), z1, z2) → c168(U81'(z0, z1, z2))
U81'(z0, active(z1), z2) → c169(U81'(z0, z1, z2))
U81'(z0, z1, active(z2)) → c170(U81'(z0, z1, z2))
U82'(mark(z0), z1, z2) → c171(U82'(z0, z1, z2))
U82'(z0, mark(z1), z2) → c172(U82'(z0, z1, z2))
U82'(z0, z1, mark(z2)) → c173(U82'(z0, z1, z2))
U82'(active(z0), z1, z2) → c174(U82'(z0, z1, z2))
U82'(z0, active(z1), z2) → c175(U82'(z0, z1, z2))
U82'(z0, z1, active(z2)) → c176(U82'(z0, z1, z2))
FST(mark(z0)) → c177(FST(z0))
FST(active(z0)) → c178(FST(z0))
NATSFROM(mark(z0)) → c179(NATSFROM(z0))
NATSFROM(active(z0)) → c180(NATSFROM(z0))
S(mark(z0)) → c181(S(z0))
S(active(z0)) → c182(S(z0))
SEL(mark(z0), z1) → c183(SEL(z0, z1))
SEL(z0, mark(z1)) → c184(SEL(z0, z1))
SEL(active(z0), z1) → c185(SEL(z0, z1))
SEL(z0, active(z1)) → c186(SEL(z0, z1))
TAIL(mark(z0)) → c187(TAIL(z0))
TAIL(active(z0)) → c188(TAIL(z0))
TAKE(mark(z0), z1) → c189(TAKE(z0, z1))
TAKE(z0, mark(z1)) → c190(TAKE(z0, z1))
TAKE(active(z0), z1) → c191(TAKE(z0, z1))
TAKE(z0, active(z1)) → c192(TAKE(z0, z1))

S tuples:

ACTIVE(U11(tt, z0, z1)) → c(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1))
ACTIVE(U12(tt, z0, z1)) → c1(MARK(snd(splitAt(z0, z1))), SND(splitAt(z0, z1)), SPLITAT(z0, z1))
ACTIVE(U21(tt, z0)) → c2(MARK(U22(tt, z0)), U22'(tt, z0))
ACTIVE(U22(tt, z0)) → c3(MARK(z0))
ACTIVE(U31(tt, z0)) → c4(MARK(U32(tt, z0)), U32'(tt, z0))
ACTIVE(U32(tt, z0)) → c5(MARK(z0))
ACTIVE(U41(tt, z0, z1)) → c6(MARK(U42(tt, z0, z1)), U42'(tt, z0, z1))
ACTIVE(U42(tt, z0, z1)) → c7(MARK(head(afterNth(z0, z1))), HEAD(afterNth(z0, z1)), AFTERNTH(z0, z1))
ACTIVE(U51(tt, z0)) → c8(MARK(U52(tt, z0)), U52'(tt, z0))
ACTIVE(U52(tt, z0)) → c9(MARK(z0))
ACTIVE(U61(tt, z0, z1, z2)) → c10(MARK(U62(tt, z0, z1, z2)), U62'(tt, z0, z1, z2))
ACTIVE(U62(tt, z0, z1, z2)) → c11(MARK(U63(tt, z0, z1, z2)), U63'(tt, z0, z1, z2))
ACTIVE(U63(tt, z0, z1, z2)) → c12(MARK(U64(splitAt(z0, z2), z1)), U64'(splitAt(z0, z2), z1), SPLITAT(z0, z2))
ACTIVE(U64(pair(z0, z1), z2)) → c13(MARK(pair(cons(z2, z0), z1)), PAIR(cons(z2, z0), z1), CONS(z2, z0))
ACTIVE(U71(tt, z0)) → c14(MARK(U72(tt, z0)), U72'(tt, z0))
ACTIVE(U72(tt, z0)) → c15(MARK(z0))
ACTIVE(U81(tt, z0, z1)) → c16(MARK(U82(tt, z0, z1)), U82'(tt, z0, z1))
ACTIVE(U82(tt, z0, z1)) → c17(MARK(fst(splitAt(z0, z1))), FST(splitAt(z0, z1)), SPLITAT(z0, z1))
ACTIVE(afterNth(z0, z1)) → c18(MARK(U11(tt, z0, z1)), U11'(tt, z0, z1))
ACTIVE(fst(pair(z0, z1))) → c19(MARK(U21(tt, z0)), U21'(tt, z0))
ACTIVE(head(cons(z0, z1))) → c20(MARK(U31(tt, z0)), U31'(tt, z0))
ACTIVE(natsFrom(z0)) → c21(MARK(cons(z0, natsFrom(s(z0)))), CONS(z0, natsFrom(s(z0))), NATSFROM(s(z0)), S(z0))
ACTIVE(sel(z0, z1)) → c22(MARK(U41(tt, z0, z1)), U41'(tt, z0, z1))
ACTIVE(snd(pair(z0, z1))) → c23(MARK(U51(tt, z1)), U51'(tt, z1))
ACTIVE(splitAt(0, z0)) → c24(MARK(pair(nil, z0)), PAIR(nil, z0))
ACTIVE(splitAt(s(z0), cons(z1, z2))) → c25(MARK(U61(tt, z0, z1, z2)), U61'(tt, z0, z1, z2))
ACTIVE(tail(cons(z0, z1))) → c26(MARK(U71(tt, z1)), U71'(tt, z1))
ACTIVE(take(z0, z1)) → c27(MARK(U81(tt, z0, z1)), U81'(tt, z0, z1))
MARK(U11(z0, z1, z2)) → c28(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0))
MARK(tt) → c29(ACTIVE(tt))
MARK(U12(z0, z1, z2)) → c30(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0))
MARK(snd(z0)) → c31(ACTIVE(snd(mark(z0))), SND(mark(z0)), MARK(z0))
MARK(splitAt(z0, z1)) → c32(ACTIVE(splitAt(mark(z0), mark(z1))), SPLITAT(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U21(z0, z1)) → c33(ACTIVE(U21(mark(z0), z1)), U21'(mark(z0), z1), MARK(z0))
MARK(U22(z0, z1)) → c34(ACTIVE(U22(mark(z0), z1)), U22'(mark(z0), z1), MARK(z0))
MARK(U31(z0, z1)) → c35(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0))
MARK(U32(z0, z1)) → c36(ACTIVE(U32(mark(z0), z1)), U32'(mark(z0), z1), MARK(z0))
MARK(U41(z0, z1, z2)) → c37(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0))
MARK(U42(z0, z1, z2)) → c38(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0))
MARK(head(z0)) → c39(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0))
MARK(afterNth(z0, z1)) → c40(ACTIVE(afterNth(mark(z0), mark(z1))), AFTERNTH(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U51(z0, z1)) → c41(ACTIVE(U51(mark(z0), z1)), U51'(mark(z0), z1), MARK(z0))
MARK(U52(z0, z1)) → c42(ACTIVE(U52(mark(z0), z1)), U52'(mark(z0), z1), MARK(z0))
MARK(U61(z0, z1, z2, z3)) → c43(ACTIVE(U61(mark(z0), z1, z2, z3)), U61'(mark(z0), z1, z2, z3), MARK(z0))
MARK(U62(z0, z1, z2, z3)) → c44(ACTIVE(U62(mark(z0), z1, z2, z3)), U62'(mark(z0), z1, z2, z3), MARK(z0))
MARK(U63(z0, z1, z2, z3)) → c45(ACTIVE(U63(mark(z0), z1, z2, z3)), U63'(mark(z0), z1, z2, z3), MARK(z0))
MARK(U64(z0, z1)) → c46(ACTIVE(U64(mark(z0), z1)), U64'(mark(z0), z1), MARK(z0))
MARK(pair(z0, z1)) → c47(ACTIVE(pair(mark(z0), mark(z1))), PAIR(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(cons(z0, z1)) → c48(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0))
MARK(U71(z0, z1)) → c49(ACTIVE(U71(mark(z0), z1)), U71'(mark(z0), z1), MARK(z0))
MARK(U72(z0, z1)) → c50(ACTIVE(U72(mark(z0), z1)), U72'(mark(z0), z1), MARK(z0))
MARK(U81(z0, z1, z2)) → c51(ACTIVE(U81(mark(z0), z1, z2)), U81'(mark(z0), z1, z2), MARK(z0))
MARK(U82(z0, z1, z2)) → c52(ACTIVE(U82(mark(z0), z1, z2)), U82'(mark(z0), z1, z2), MARK(z0))
MARK(fst(z0)) → c53(ACTIVE(fst(mark(z0))), FST(mark(z0)), MARK(z0))
MARK(natsFrom(z0)) → c54(ACTIVE(natsFrom(mark(z0))), NATSFROM(mark(z0)), MARK(z0))
MARK(s(z0)) → c55(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0))
MARK(sel(z0, z1)) → c56(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(0) → c57(ACTIVE(0))
MARK(nil) → c58(ACTIVE(nil))
MARK(tail(z0)) → c59(ACTIVE(tail(mark(z0))), TAIL(mark(z0)), MARK(z0))
MARK(take(z0, z1)) → c60(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1))
U11'(mark(z0), z1, z2) → c61(U11'(z0, z1, z2))
U11'(z0, mark(z1), z2) → c62(U11'(z0, z1, z2))
U11'(z0, z1, mark(z2)) → c63(U11'(z0, z1, z2))
U11'(active(z0), z1, z2) → c64(U11'(z0, z1, z2))
U11'(z0, active(z1), z2) → c65(U11'(z0, z1, z2))
U11'(z0, z1, active(z2)) → c66(U11'(z0, z1, z2))
U12'(mark(z0), z1, z2) → c67(U12'(z0, z1, z2))
U12'(z0, mark(z1), z2) → c68(U12'(z0, z1, z2))
U12'(z0, z1, mark(z2)) → c69(U12'(z0, z1, z2))
U12'(active(z0), z1, z2) → c70(U12'(z0, z1, z2))
U12'(z0, active(z1), z2) → c71(U12'(z0, z1, z2))
U12'(z0, z1, active(z2)) → c72(U12'(z0, z1, z2))
SND(mark(z0)) → c73(SND(z0))
SND(active(z0)) → c74(SND(z0))
SPLITAT(mark(z0), z1) → c75(SPLITAT(z0, z1))
SPLITAT(z0, mark(z1)) → c76(SPLITAT(z0, z1))
SPLITAT(active(z0), z1) → c77(SPLITAT(z0, z1))
SPLITAT(z0, active(z1)) → c78(SPLITAT(z0, z1))
U21'(mark(z0), z1) → c79(U21'(z0, z1))
U21'(z0, mark(z1)) → c80(U21'(z0, z1))
U21'(active(z0), z1) → c81(U21'(z0, z1))
U21'(z0, active(z1)) → c82(U21'(z0, z1))
U22'(mark(z0), z1) → c83(U22'(z0, z1))
U22'(z0, mark(z1)) → c84(U22'(z0, z1))
U22'(active(z0), z1) → c85(U22'(z0, z1))
U22'(z0, active(z1)) → c86(U22'(z0, z1))
U31'(mark(z0), z1) → c87(U31'(z0, z1))
U31'(z0, mark(z1)) → c88(U31'(z0, z1))
U31'(active(z0), z1) → c89(U31'(z0, z1))
U31'(z0, active(z1)) → c90(U31'(z0, z1))
U32'(mark(z0), z1) → c91(U32'(z0, z1))
U32'(z0, mark(z1)) → c92(U32'(z0, z1))
U32'(active(z0), z1) → c93(U32'(z0, z1))
U32'(z0, active(z1)) → c94(U32'(z0, z1))
U41'(mark(z0), z1, z2) → c95(U41'(z0, z1, z2))
U41'(z0, mark(z1), z2) → c96(U41'(z0, z1, z2))
U41'(z0, z1, mark(z2)) → c97(U41'(z0, z1, z2))
U41'(active(z0), z1, z2) → c98(U41'(z0, z1, z2))
U41'(z0, active(z1), z2) → c99(U41'(z0, z1, z2))
U41'(z0, z1, active(z2)) → c100(U41'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c101(U42'(z0, z1, z2))
U42'(z0, mark(z1), z2) → c102(U42'(z0, z1, z2))
U42'(z0, z1, mark(z2)) → c103(U42'(z0, z1, z2))
U42'(active(z0), z1, z2) → c104(U42'(z0, z1, z2))
U42'(z0, active(z1), z2) → c105(U42'(z0, z1, z2))
U42'(z0, z1, active(z2)) → c106(U42'(z0, z1, z2))
HEAD(mark(z0)) → c107(HEAD(z0))
HEAD(active(z0)) → c108(HEAD(z0))
AFTERNTH(mark(z0), z1) → c109(AFTERNTH(z0, z1))
AFTERNTH(z0, mark(z1)) → c110(AFTERNTH(z0, z1))
AFTERNTH(active(z0), z1) → c111(AFTERNTH(z0, z1))
AFTERNTH(z0, active(z1)) → c112(AFTERNTH(z0, z1))
U51'(mark(z0), z1) → c113(U51'(z0, z1))
U51'(z0, mark(z1)) → c114(U51'(z0, z1))
U51'(active(z0), z1) → c115(U51'(z0, z1))
U51'(z0, active(z1)) → c116(U51'(z0, z1))
U52'(mark(z0), z1) → c117(U52'(z0, z1))
U52'(z0, mark(z1)) → c118(U52'(z0, z1))
U52'(active(z0), z1) → c119(U52'(z0, z1))
U52'(z0, active(z1)) → c120(U52'(z0, z1))
U61'(mark(z0), z1, z2, z3) → c121(U61'(z0, z1, z2, z3))
U61'(z0, mark(z1), z2, z3) → c122(U61'(z0, z1, z2, z3))
U61'(z0, z1, mark(z2), z3) → c123(U61'(z0, z1, z2, z3))
U61'(z0, z1, z2, mark(z3)) → c124(U61'(z0, z1, z2, z3))
U61'(active(z0), z1, z2, z3) → c125(U61'(z0, z1, z2, z3))
U61'(z0, active(z1), z2, z3) → c126(U61'(z0, z1, z2, z3))
U61'(z0, z1, active(z2), z3) → c127(U61'(z0, z1, z2, z3))
U61'(z0, z1, z2, active(z3)) → c128(U61'(z0, z1, z2, z3))
U62'(mark(z0), z1, z2, z3) → c129(U62'(z0, z1, z2, z3))
U62'(z0, mark(z1), z2, z3) → c130(U62'(z0, z1, z2, z3))
U62'(z0, z1, mark(z2), z3) → c131(U62'(z0, z1, z2, z3))
U62'(z0, z1, z2, mark(z3)) → c132(U62'(z0, z1, z2, z3))
U62'(active(z0), z1, z2, z3) → c133(U62'(z0, z1, z2, z3))
U62'(z0, active(z1), z2, z3) → c134(U62'(z0, z1, z2, z3))
U62'(z0, z1, active(z2), z3) → c135(U62'(z0, z1, z2, z3))
U62'(z0, z1, z2, active(z3)) → c136(U62'(z0, z1, z2, z3))
U63'(mark(z0), z1, z2, z3) → c137(U63'(z0, z1, z2, z3))
U63'(z0, mark(z1), z2, z3) → c138(U63'(z0, z1, z2, z3))
U63'(z0, z1, mark(z2), z3) → c139(U63'(z0, z1, z2, z3))
U63'(z0, z1, z2, mark(z3)) → c140(U63'(z0, z1, z2, z3))
U63'(active(z0), z1, z2, z3) → c141(U63'(z0, z1, z2, z3))
U63'(z0, active(z1), z2, z3) → c142(U63'(z0, z1, z2, z3))
U63'(z0, z1, active(z2), z3) → c143(U63'(z0, z1, z2, z3))
U63'(z0, z1, z2, active(z3)) → c144(U63'(z0, z1, z2, z3))
U64'(mark(z0), z1) → c145(U64'(z0, z1))
U64'(z0, mark(z1)) → c146(U64'(z0, z1))
U64'(active(z0), z1) → c147(U64'(z0, z1))
U64'(z0, active(z1)) → c148(U64'(z0, z1))
PAIR(mark(z0), z1) → c149(PAIR(z0, z1))
PAIR(z0, mark(z1)) → c150(PAIR(z0, z1))
PAIR(active(z0), z1) → c151(PAIR(z0, z1))
PAIR(z0, active(z1)) → c152(PAIR(z0, z1))
CONS(mark(z0), z1) → c153(CONS(z0, z1))
CONS(z0, mark(z1)) → c154(CONS(z0, z1))
CONS(active(z0), z1) → c155(CONS(z0, z1))
CONS(z0, active(z1)) → c156(CONS(z0, z1))
U71'(mark(z0), z1) → c157(U71'(z0, z1))
U71'(z0, mark(z1)) → c158(U71'(z0, z1))
U71'(active(z0), z1) → c159(U71'(z0, z1))
U71'(z0, active(z1)) → c160(U71'(z0, z1))
U72'(mark(z0), z1) → c161(U72'(z0, z1))
U72'(z0, mark(z1)) → c162(U72'(z0, z1))
U72'(active(z0), z1) → c163(U72'(z0, z1))
U72'(z0, active(z1)) → c164(U72'(z0, z1))
U81'(mark(z0), z1, z2) → c165(U81'(z0, z1, z2))
U81'(z0, mark(z1), z2) → c166(U81'(z0, z1, z2))
U81'(z0, z1, mark(z2)) → c167(U81'(z0, z1, z2))
U81'(active(z0), z1, z2) → c168(U81'(z0, z1, z2))
U81'(z0, active(z1), z2) → c169(U81'(z0, z1, z2))
U81'(z0, z1, active(z2)) → c170(U81'(z0, z1, z2))
U82'(mark(z0), z1, z2) → c171(U82'(z0, z1, z2))
U82'(z0, mark(z1), z2) → c172(U82'(z0, z1, z2))
U82'(z0, z1, mark(z2)) → c173(U82'(z0, z1, z2))
U82'(active(z0), z1, z2) → c174(U82'(z0, z1, z2))
U82'(z0, active(z1), z2) → c175(U82'(z0, z1, z2))
U82'(z0, z1, active(z2)) → c176(U82'(z0, z1, z2))
FST(mark(z0)) → c177(FST(z0))
FST(active(z0)) → c178(FST(z0))
NATSFROM(mark(z0)) → c179(NATSFROM(z0))
NATSFROM(active(z0)) → c180(NATSFROM(z0))
S(mark(z0)) → c181(S(z0))
S(active(z0)) → c182(S(z0))
SEL(mark(z0), z1) → c183(SEL(z0, z1))
SEL(z0, mark(z1)) → c184(SEL(z0, z1))
SEL(active(z0), z1) → c185(SEL(z0, z1))
SEL(z0, active(z1)) → c186(SEL(z0, z1))
TAIL(mark(z0)) → c187(TAIL(z0))
TAIL(active(z0)) → c188(TAIL(z0))
TAKE(mark(z0), z1) → c189(TAKE(z0, z1))
TAKE(z0, mark(z1)) → c190(TAKE(z0, z1))
TAKE(active(z0), z1) → c191(TAKE(z0, z1))
TAKE(z0, active(z1)) → c192(TAKE(z0, z1))

K tuples:none
Defined Rule Symbols:

active, mark, U11, U12, snd, splitAt, U21, U22, U31, U32, U41, U42, head, afterNth, U51, U52, U61, U62, U63, U64, pair, cons, U71, U72, U81, U82, fst, natsFrom, s, sel, tail, take

Defined Pair Symbols:

ACTIVE, MARK, U11', U12', SND, SPLITAT, U21', U22', U31', U32', U41', U42', HEAD, AFTERNTH, U51', U52', U61', U62', U63', U64', PAIR, CONS, U71', U72', U81', U82', FST, NATSFROM, S, SEL, TAIL, TAKE

Compound Symbols:

c, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c90, c91, c92, c93, c94, c95, c96, c97, c98, c99, c100, c101, c102, c103, c104, c105, c106, c107, c108, c109, c110, c111, c112, c113, c114, c115, c116, c117, c118, c119, c120, c121, c122, c123, c124, c125, c126, c127, c128, c129, c130, c131, c132, c133, c134, c135, c136, c137, c138, c139, c140, c141, c142, c143, c144, c145, c146, c147, c148, c149, c150, c151, c152, c153, c154, c155, c156, c157, c158, c159, c160, c161, c162, c163, c164, c165, c166, c167, c168, c169, c170, c171, c172, c173, c174, c175, c176, c177, c178, c179, c180, c181, c182, c183, c184, c185, c186, c187, c188, c189, c190, c191, c192

(3) CdtUnreachableProof (EQUIVALENT transformation)

The following tuples could be removed as they are not reachable from basic start terms:

ACTIVE(U11(tt, z0, z1)) → c(MARK(U12(tt, z0, z1)), U12'(tt, z0, z1))
ACTIVE(U12(tt, z0, z1)) → c1(MARK(snd(splitAt(z0, z1))), SND(splitAt(z0, z1)), SPLITAT(z0, z1))
ACTIVE(U21(tt, z0)) → c2(MARK(U22(tt, z0)), U22'(tt, z0))
ACTIVE(U22(tt, z0)) → c3(MARK(z0))
ACTIVE(U31(tt, z0)) → c4(MARK(U32(tt, z0)), U32'(tt, z0))
ACTIVE(U32(tt, z0)) → c5(MARK(z0))
ACTIVE(U41(tt, z0, z1)) → c6(MARK(U42(tt, z0, z1)), U42'(tt, z0, z1))
ACTIVE(U42(tt, z0, z1)) → c7(MARK(head(afterNth(z0, z1))), HEAD(afterNth(z0, z1)), AFTERNTH(z0, z1))
ACTIVE(U51(tt, z0)) → c8(MARK(U52(tt, z0)), U52'(tt, z0))
ACTIVE(U52(tt, z0)) → c9(MARK(z0))
ACTIVE(U61(tt, z0, z1, z2)) → c10(MARK(U62(tt, z0, z1, z2)), U62'(tt, z0, z1, z2))
ACTIVE(U62(tt, z0, z1, z2)) → c11(MARK(U63(tt, z0, z1, z2)), U63'(tt, z0, z1, z2))
ACTIVE(U63(tt, z0, z1, z2)) → c12(MARK(U64(splitAt(z0, z2), z1)), U64'(splitAt(z0, z2), z1), SPLITAT(z0, z2))
ACTIVE(U64(pair(z0, z1), z2)) → c13(MARK(pair(cons(z2, z0), z1)), PAIR(cons(z2, z0), z1), CONS(z2, z0))
ACTIVE(U71(tt, z0)) → c14(MARK(U72(tt, z0)), U72'(tt, z0))
ACTIVE(U72(tt, z0)) → c15(MARK(z0))
ACTIVE(U81(tt, z0, z1)) → c16(MARK(U82(tt, z0, z1)), U82'(tt, z0, z1))
ACTIVE(U82(tt, z0, z1)) → c17(MARK(fst(splitAt(z0, z1))), FST(splitAt(z0, z1)), SPLITAT(z0, z1))
ACTIVE(afterNth(z0, z1)) → c18(MARK(U11(tt, z0, z1)), U11'(tt, z0, z1))
ACTIVE(fst(pair(z0, z1))) → c19(MARK(U21(tt, z0)), U21'(tt, z0))
ACTIVE(head(cons(z0, z1))) → c20(MARK(U31(tt, z0)), U31'(tt, z0))
ACTIVE(natsFrom(z0)) → c21(MARK(cons(z0, natsFrom(s(z0)))), CONS(z0, natsFrom(s(z0))), NATSFROM(s(z0)), S(z0))
ACTIVE(sel(z0, z1)) → c22(MARK(U41(tt, z0, z1)), U41'(tt, z0, z1))
ACTIVE(snd(pair(z0, z1))) → c23(MARK(U51(tt, z1)), U51'(tt, z1))
ACTIVE(splitAt(0, z0)) → c24(MARK(pair(nil, z0)), PAIR(nil, z0))
ACTIVE(splitAt(s(z0), cons(z1, z2))) → c25(MARK(U61(tt, z0, z1, z2)), U61'(tt, z0, z1, z2))
ACTIVE(tail(cons(z0, z1))) → c26(MARK(U71(tt, z1)), U71'(tt, z1))
ACTIVE(take(z0, z1)) → c27(MARK(U81(tt, z0, z1)), U81'(tt, z0, z1))
MARK(U11(z0, z1, z2)) → c28(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0))
MARK(U12(z0, z1, z2)) → c30(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0))
MARK(snd(z0)) → c31(ACTIVE(snd(mark(z0))), SND(mark(z0)), MARK(z0))
MARK(splitAt(z0, z1)) → c32(ACTIVE(splitAt(mark(z0), mark(z1))), SPLITAT(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U21(z0, z1)) → c33(ACTIVE(U21(mark(z0), z1)), U21'(mark(z0), z1), MARK(z0))
MARK(U22(z0, z1)) → c34(ACTIVE(U22(mark(z0), z1)), U22'(mark(z0), z1), MARK(z0))
MARK(U31(z0, z1)) → c35(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0))
MARK(U32(z0, z1)) → c36(ACTIVE(U32(mark(z0), z1)), U32'(mark(z0), z1), MARK(z0))
MARK(U41(z0, z1, z2)) → c37(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0))
MARK(U42(z0, z1, z2)) → c38(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0))
MARK(head(z0)) → c39(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0))
MARK(afterNth(z0, z1)) → c40(ACTIVE(afterNth(mark(z0), mark(z1))), AFTERNTH(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U51(z0, z1)) → c41(ACTIVE(U51(mark(z0), z1)), U51'(mark(z0), z1), MARK(z0))
MARK(U52(z0, z1)) → c42(ACTIVE(U52(mark(z0), z1)), U52'(mark(z0), z1), MARK(z0))
MARK(U61(z0, z1, z2, z3)) → c43(ACTIVE(U61(mark(z0), z1, z2, z3)), U61'(mark(z0), z1, z2, z3), MARK(z0))
MARK(U62(z0, z1, z2, z3)) → c44(ACTIVE(U62(mark(z0), z1, z2, z3)), U62'(mark(z0), z1, z2, z3), MARK(z0))
MARK(U63(z0, z1, z2, z3)) → c45(ACTIVE(U63(mark(z0), z1, z2, z3)), U63'(mark(z0), z1, z2, z3), MARK(z0))
MARK(U64(z0, z1)) → c46(ACTIVE(U64(mark(z0), z1)), U64'(mark(z0), z1), MARK(z0))
MARK(pair(z0, z1)) → c47(ACTIVE(pair(mark(z0), mark(z1))), PAIR(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(cons(z0, z1)) → c48(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0))
MARK(U71(z0, z1)) → c49(ACTIVE(U71(mark(z0), z1)), U71'(mark(z0), z1), MARK(z0))
MARK(U72(z0, z1)) → c50(ACTIVE(U72(mark(z0), z1)), U72'(mark(z0), z1), MARK(z0))
MARK(U81(z0, z1, z2)) → c51(ACTIVE(U81(mark(z0), z1, z2)), U81'(mark(z0), z1, z2), MARK(z0))
MARK(U82(z0, z1, z2)) → c52(ACTIVE(U82(mark(z0), z1, z2)), U82'(mark(z0), z1, z2), MARK(z0))
MARK(fst(z0)) → c53(ACTIVE(fst(mark(z0))), FST(mark(z0)), MARK(z0))
MARK(natsFrom(z0)) → c54(ACTIVE(natsFrom(mark(z0))), NATSFROM(mark(z0)), MARK(z0))
MARK(s(z0)) → c55(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0))
MARK(sel(z0, z1)) → c56(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(tail(z0)) → c59(ACTIVE(tail(mark(z0))), TAIL(mark(z0)), MARK(z0))
MARK(take(z0, z1)) → c60(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1))
U11'(mark(z0), z1, z2) → c61(U11'(z0, z1, z2))
U11'(z0, mark(z1), z2) → c62(U11'(z0, z1, z2))
U11'(z0, z1, mark(z2)) → c63(U11'(z0, z1, z2))
U11'(active(z0), z1, z2) → c64(U11'(z0, z1, z2))
U11'(z0, active(z1), z2) → c65(U11'(z0, z1, z2))
U11'(z0, z1, active(z2)) → c66(U11'(z0, z1, z2))
U12'(mark(z0), z1, z2) → c67(U12'(z0, z1, z2))
U12'(z0, mark(z1), z2) → c68(U12'(z0, z1, z2))
U12'(z0, z1, mark(z2)) → c69(U12'(z0, z1, z2))
U12'(active(z0), z1, z2) → c70(U12'(z0, z1, z2))
U12'(z0, active(z1), z2) → c71(U12'(z0, z1, z2))
U12'(z0, z1, active(z2)) → c72(U12'(z0, z1, z2))
SND(mark(z0)) → c73(SND(z0))
SND(active(z0)) → c74(SND(z0))
SPLITAT(mark(z0), z1) → c75(SPLITAT(z0, z1))
SPLITAT(z0, mark(z1)) → c76(SPLITAT(z0, z1))
SPLITAT(active(z0), z1) → c77(SPLITAT(z0, z1))
SPLITAT(z0, active(z1)) → c78(SPLITAT(z0, z1))
U21'(mark(z0), z1) → c79(U21'(z0, z1))
U21'(z0, mark(z1)) → c80(U21'(z0, z1))
U21'(active(z0), z1) → c81(U21'(z0, z1))
U21'(z0, active(z1)) → c82(U21'(z0, z1))
U22'(mark(z0), z1) → c83(U22'(z0, z1))
U22'(z0, mark(z1)) → c84(U22'(z0, z1))
U22'(active(z0), z1) → c85(U22'(z0, z1))
U22'(z0, active(z1)) → c86(U22'(z0, z1))
U31'(mark(z0), z1) → c87(U31'(z0, z1))
U31'(z0, mark(z1)) → c88(U31'(z0, z1))
U31'(active(z0), z1) → c89(U31'(z0, z1))
U31'(z0, active(z1)) → c90(U31'(z0, z1))
U32'(mark(z0), z1) → c91(U32'(z0, z1))
U32'(z0, mark(z1)) → c92(U32'(z0, z1))
U32'(active(z0), z1) → c93(U32'(z0, z1))
U32'(z0, active(z1)) → c94(U32'(z0, z1))
U41'(mark(z0), z1, z2) → c95(U41'(z0, z1, z2))
U41'(z0, mark(z1), z2) → c96(U41'(z0, z1, z2))
U41'(z0, z1, mark(z2)) → c97(U41'(z0, z1, z2))
U41'(active(z0), z1, z2) → c98(U41'(z0, z1, z2))
U41'(z0, active(z1), z2) → c99(U41'(z0, z1, z2))
U41'(z0, z1, active(z2)) → c100(U41'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c101(U42'(z0, z1, z2))
U42'(z0, mark(z1), z2) → c102(U42'(z0, z1, z2))
U42'(z0, z1, mark(z2)) → c103(U42'(z0, z1, z2))
U42'(active(z0), z1, z2) → c104(U42'(z0, z1, z2))
U42'(z0, active(z1), z2) → c105(U42'(z0, z1, z2))
U42'(z0, z1, active(z2)) → c106(U42'(z0, z1, z2))
HEAD(mark(z0)) → c107(HEAD(z0))
HEAD(active(z0)) → c108(HEAD(z0))
AFTERNTH(mark(z0), z1) → c109(AFTERNTH(z0, z1))
AFTERNTH(z0, mark(z1)) → c110(AFTERNTH(z0, z1))
AFTERNTH(active(z0), z1) → c111(AFTERNTH(z0, z1))
AFTERNTH(z0, active(z1)) → c112(AFTERNTH(z0, z1))
U51'(mark(z0), z1) → c113(U51'(z0, z1))
U51'(z0, mark(z1)) → c114(U51'(z0, z1))
U51'(active(z0), z1) → c115(U51'(z0, z1))
U51'(z0, active(z1)) → c116(U51'(z0, z1))
U52'(mark(z0), z1) → c117(U52'(z0, z1))
U52'(z0, mark(z1)) → c118(U52'(z0, z1))
U52'(active(z0), z1) → c119(U52'(z0, z1))
U52'(z0, active(z1)) → c120(U52'(z0, z1))
U61'(mark(z0), z1, z2, z3) → c121(U61'(z0, z1, z2, z3))
U61'(z0, mark(z1), z2, z3) → c122(U61'(z0, z1, z2, z3))
U61'(z0, z1, mark(z2), z3) → c123(U61'(z0, z1, z2, z3))
U61'(z0, z1, z2, mark(z3)) → c124(U61'(z0, z1, z2, z3))
U61'(active(z0), z1, z2, z3) → c125(U61'(z0, z1, z2, z3))
U61'(z0, active(z1), z2, z3) → c126(U61'(z0, z1, z2, z3))
U61'(z0, z1, active(z2), z3) → c127(U61'(z0, z1, z2, z3))
U61'(z0, z1, z2, active(z3)) → c128(U61'(z0, z1, z2, z3))
U62'(mark(z0), z1, z2, z3) → c129(U62'(z0, z1, z2, z3))
U62'(z0, mark(z1), z2, z3) → c130(U62'(z0, z1, z2, z3))
U62'(z0, z1, mark(z2), z3) → c131(U62'(z0, z1, z2, z3))
U62'(z0, z1, z2, mark(z3)) → c132(U62'(z0, z1, z2, z3))
U62'(active(z0), z1, z2, z3) → c133(U62'(z0, z1, z2, z3))
U62'(z0, active(z1), z2, z3) → c134(U62'(z0, z1, z2, z3))
U62'(z0, z1, active(z2), z3) → c135(U62'(z0, z1, z2, z3))
U62'(z0, z1, z2, active(z3)) → c136(U62'(z0, z1, z2, z3))
U63'(mark(z0), z1, z2, z3) → c137(U63'(z0, z1, z2, z3))
U63'(z0, mark(z1), z2, z3) → c138(U63'(z0, z1, z2, z3))
U63'(z0, z1, mark(z2), z3) → c139(U63'(z0, z1, z2, z3))
U63'(z0, z1, z2, mark(z3)) → c140(U63'(z0, z1, z2, z3))
U63'(active(z0), z1, z2, z3) → c141(U63'(z0, z1, z2, z3))
U63'(z0, active(z1), z2, z3) → c142(U63'(z0, z1, z2, z3))
U63'(z0, z1, active(z2), z3) → c143(U63'(z0, z1, z2, z3))
U63'(z0, z1, z2, active(z3)) → c144(U63'(z0, z1, z2, z3))
U64'(mark(z0), z1) → c145(U64'(z0, z1))
U64'(z0, mark(z1)) → c146(U64'(z0, z1))
U64'(active(z0), z1) → c147(U64'(z0, z1))
U64'(z0, active(z1)) → c148(U64'(z0, z1))
PAIR(mark(z0), z1) → c149(PAIR(z0, z1))
PAIR(z0, mark(z1)) → c150(PAIR(z0, z1))
PAIR(active(z0), z1) → c151(PAIR(z0, z1))
PAIR(z0, active(z1)) → c152(PAIR(z0, z1))
CONS(mark(z0), z1) → c153(CONS(z0, z1))
CONS(z0, mark(z1)) → c154(CONS(z0, z1))
CONS(active(z0), z1) → c155(CONS(z0, z1))
CONS(z0, active(z1)) → c156(CONS(z0, z1))
U71'(mark(z0), z1) → c157(U71'(z0, z1))
U71'(z0, mark(z1)) → c158(U71'(z0, z1))
U71'(active(z0), z1) → c159(U71'(z0, z1))
U71'(z0, active(z1)) → c160(U71'(z0, z1))
U72'(mark(z0), z1) → c161(U72'(z0, z1))
U72'(z0, mark(z1)) → c162(U72'(z0, z1))
U72'(active(z0), z1) → c163(U72'(z0, z1))
U72'(z0, active(z1)) → c164(U72'(z0, z1))
U81'(mark(z0), z1, z2) → c165(U81'(z0, z1, z2))
U81'(z0, mark(z1), z2) → c166(U81'(z0, z1, z2))
U81'(z0, z1, mark(z2)) → c167(U81'(z0, z1, z2))
U81'(active(z0), z1, z2) → c168(U81'(z0, z1, z2))
U81'(z0, active(z1), z2) → c169(U81'(z0, z1, z2))
U81'(z0, z1, active(z2)) → c170(U81'(z0, z1, z2))
U82'(mark(z0), z1, z2) → c171(U82'(z0, z1, z2))
U82'(z0, mark(z1), z2) → c172(U82'(z0, z1, z2))
U82'(z0, z1, mark(z2)) → c173(U82'(z0, z1, z2))
U82'(active(z0), z1, z2) → c174(U82'(z0, z1, z2))
U82'(z0, active(z1), z2) → c175(U82'(z0, z1, z2))
U82'(z0, z1, active(z2)) → c176(U82'(z0, z1, z2))
FST(mark(z0)) → c177(FST(z0))
FST(active(z0)) → c178(FST(z0))
NATSFROM(mark(z0)) → c179(NATSFROM(z0))
NATSFROM(active(z0)) → c180(NATSFROM(z0))
S(mark(z0)) → c181(S(z0))
S(active(z0)) → c182(S(z0))
SEL(mark(z0), z1) → c183(SEL(z0, z1))
SEL(z0, mark(z1)) → c184(SEL(z0, z1))
SEL(active(z0), z1) → c185(SEL(z0, z1))
SEL(z0, active(z1)) → c186(SEL(z0, z1))
TAIL(mark(z0)) → c187(TAIL(z0))
TAIL(active(z0)) → c188(TAIL(z0))
TAKE(mark(z0), z1) → c189(TAKE(z0, z1))
TAKE(z0, mark(z1)) → c190(TAKE(z0, z1))
TAKE(active(z0), z1) → c191(TAKE(z0, z1))
TAKE(z0, active(z1)) → c192(TAKE(z0, z1))

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1))
active(U12(tt, z0, z1)) → mark(snd(splitAt(z0, z1)))
active(U21(tt, z0)) → mark(U22(tt, z0))
active(U22(tt, z0)) → mark(z0)
active(U31(tt, z0)) → mark(U32(tt, z0))
active(U32(tt, z0)) → mark(z0)
active(U41(tt, z0, z1)) → mark(U42(tt, z0, z1))
active(U42(tt, z0, z1)) → mark(head(afterNth(z0, z1)))
active(U51(tt, z0)) → mark(U52(tt, z0))
active(U52(tt, z0)) → mark(z0)
active(U61(tt, z0, z1, z2)) → mark(U62(tt, z0, z1, z2))
active(U62(tt, z0, z1, z2)) → mark(U63(tt, z0, z1, z2))
active(U63(tt, z0, z1, z2)) → mark(U64(splitAt(z0, z2), z1))
active(U64(pair(z0, z1), z2)) → mark(pair(cons(z2, z0), z1))
active(U71(tt, z0)) → mark(U72(tt, z0))
active(U72(tt, z0)) → mark(z0)
active(U81(tt, z0, z1)) → mark(U82(tt, z0, z1))
active(U82(tt, z0, z1)) → mark(fst(splitAt(z0, z1)))
active(afterNth(z0, z1)) → mark(U11(tt, z0, z1))
active(fst(pair(z0, z1))) → mark(U21(tt, z0))
active(head(cons(z0, z1))) → mark(U31(tt, z0))
active(natsFrom(z0)) → mark(cons(z0, natsFrom(s(z0))))
active(sel(z0, z1)) → mark(U41(tt, z0, z1))
active(snd(pair(z0, z1))) → mark(U51(tt, z1))
active(splitAt(0, z0)) → mark(pair(nil, z0))
active(splitAt(s(z0), cons(z1, z2))) → mark(U61(tt, z0, z1, z2))
active(tail(cons(z0, z1))) → mark(U71(tt, z1))
active(take(z0, z1)) → mark(U81(tt, z0, z1))
mark(U11(z0, z1, z2)) → active(U11(mark(z0), z1, z2))
mark(tt) → active(tt)
mark(U12(z0, z1, z2)) → active(U12(mark(z0), z1, z2))
mark(snd(z0)) → active(snd(mark(z0)))
mark(splitAt(z0, z1)) → active(splitAt(mark(z0), mark(z1)))
mark(U21(z0, z1)) → active(U21(mark(z0), z1))
mark(U22(z0, z1)) → active(U22(mark(z0), z1))
mark(U31(z0, z1)) → active(U31(mark(z0), z1))
mark(U32(z0, z1)) → active(U32(mark(z0), z1))
mark(U41(z0, z1, z2)) → active(U41(mark(z0), z1, z2))
mark(U42(z0, z1, z2)) → active(U42(mark(z0), z1, z2))
mark(head(z0)) → active(head(mark(z0)))
mark(afterNth(z0, z1)) → active(afterNth(mark(z0), mark(z1)))
mark(U51(z0, z1)) → active(U51(mark(z0), z1))
mark(U52(z0, z1)) → active(U52(mark(z0), z1))
mark(U61(z0, z1, z2, z3)) → active(U61(mark(z0), z1, z2, z3))
mark(U62(z0, z1, z2, z3)) → active(U62(mark(z0), z1, z2, z3))
mark(U63(z0, z1, z2, z3)) → active(U63(mark(z0), z1, z2, z3))
mark(U64(z0, z1)) → active(U64(mark(z0), z1))
mark(pair(z0, z1)) → active(pair(mark(z0), mark(z1)))
mark(cons(z0, z1)) → active(cons(mark(z0), z1))
mark(U71(z0, z1)) → active(U71(mark(z0), z1))
mark(U72(z0, z1)) → active(U72(mark(z0), z1))
mark(U81(z0, z1, z2)) → active(U81(mark(z0), z1, z2))
mark(U82(z0, z1, z2)) → active(U82(mark(z0), z1, z2))
mark(fst(z0)) → active(fst(mark(z0)))
mark(natsFrom(z0)) → active(natsFrom(mark(z0)))
mark(s(z0)) → active(s(mark(z0)))
mark(sel(z0, z1)) → active(sel(mark(z0), mark(z1)))
mark(0) → active(0)
mark(nil) → active(nil)
mark(tail(z0)) → active(tail(mark(z0)))
mark(take(z0, z1)) → active(take(mark(z0), mark(z1)))
U11(mark(z0), z1, z2) → U11(z0, z1, z2)
U11(z0, mark(z1), z2) → U11(z0, z1, z2)
U11(z0, z1, mark(z2)) → U11(z0, z1, z2)
U11(active(z0), z1, z2) → U11(z0, z1, z2)
U11(z0, active(z1), z2) → U11(z0, z1, z2)
U11(z0, z1, active(z2)) → U11(z0, z1, z2)
U12(mark(z0), z1, z2) → U12(z0, z1, z2)
U12(z0, mark(z1), z2) → U12(z0, z1, z2)
U12(z0, z1, mark(z2)) → U12(z0, z1, z2)
U12(active(z0), z1, z2) → U12(z0, z1, z2)
U12(z0, active(z1), z2) → U12(z0, z1, z2)
U12(z0, z1, active(z2)) → U12(z0, z1, z2)
snd(mark(z0)) → snd(z0)
snd(active(z0)) → snd(z0)
splitAt(mark(z0), z1) → splitAt(z0, z1)
splitAt(z0, mark(z1)) → splitAt(z0, z1)
splitAt(active(z0), z1) → splitAt(z0, z1)
splitAt(z0, active(z1)) → splitAt(z0, z1)
U21(mark(z0), z1) → U21(z0, z1)
U21(z0, mark(z1)) → U21(z0, z1)
U21(active(z0), z1) → U21(z0, z1)
U21(z0, active(z1)) → U21(z0, z1)
U22(mark(z0), z1) → U22(z0, z1)
U22(z0, mark(z1)) → U22(z0, z1)
U22(active(z0), z1) → U22(z0, z1)
U22(z0, active(z1)) → U22(z0, z1)
U31(mark(z0), z1) → U31(z0, z1)
U31(z0, mark(z1)) → U31(z0, z1)
U31(active(z0), z1) → U31(z0, z1)
U31(z0, active(z1)) → U31(z0, z1)
U32(mark(z0), z1) → U32(z0, z1)
U32(z0, mark(z1)) → U32(z0, z1)
U32(active(z0), z1) → U32(z0, z1)
U32(z0, active(z1)) → U32(z0, z1)
U41(mark(z0), z1, z2) → U41(z0, z1, z2)
U41(z0, mark(z1), z2) → U41(z0, z1, z2)
U41(z0, z1, mark(z2)) → U41(z0, z1, z2)
U41(active(z0), z1, z2) → U41(z0, z1, z2)
U41(z0, active(z1), z2) → U41(z0, z1, z2)
U41(z0, z1, active(z2)) → U41(z0, z1, z2)
U42(mark(z0), z1, z2) → U42(z0, z1, z2)
U42(z0, mark(z1), z2) → U42(z0, z1, z2)
U42(z0, z1, mark(z2)) → U42(z0, z1, z2)
U42(active(z0), z1, z2) → U42(z0, z1, z2)
U42(z0, active(z1), z2) → U42(z0, z1, z2)
U42(z0, z1, active(z2)) → U42(z0, z1, z2)
head(mark(z0)) → head(z0)
head(active(z0)) → head(z0)
afterNth(mark(z0), z1) → afterNth(z0, z1)
afterNth(z0, mark(z1)) → afterNth(z0, z1)
afterNth(active(z0), z1) → afterNth(z0, z1)
afterNth(z0, active(z1)) → afterNth(z0, z1)
U51(mark(z0), z1) → U51(z0, z1)
U51(z0, mark(z1)) → U51(z0, z1)
U51(active(z0), z1) → U51(z0, z1)
U51(z0, active(z1)) → U51(z0, z1)
U52(mark(z0), z1) → U52(z0, z1)
U52(z0, mark(z1)) → U52(z0, z1)
U52(active(z0), z1) → U52(z0, z1)
U52(z0, active(z1)) → U52(z0, z1)
U61(mark(z0), z1, z2, z3) → U61(z0, z1, z2, z3)
U61(z0, mark(z1), z2, z3) → U61(z0, z1, z2, z3)
U61(z0, z1, mark(z2), z3) → U61(z0, z1, z2, z3)
U61(z0, z1, z2, mark(z3)) → U61(z0, z1, z2, z3)
U61(active(z0), z1, z2, z3) → U61(z0, z1, z2, z3)
U61(z0, active(z1), z2, z3) → U61(z0, z1, z2, z3)
U61(z0, z1, active(z2), z3) → U61(z0, z1, z2, z3)
U61(z0, z1, z2, active(z3)) → U61(z0, z1, z2, z3)
U62(mark(z0), z1, z2, z3) → U62(z0, z1, z2, z3)
U62(z0, mark(z1), z2, z3) → U62(z0, z1, z2, z3)
U62(z0, z1, mark(z2), z3) → U62(z0, z1, z2, z3)
U62(z0, z1, z2, mark(z3)) → U62(z0, z1, z2, z3)
U62(active(z0), z1, z2, z3) → U62(z0, z1, z2, z3)
U62(z0, active(z1), z2, z3) → U62(z0, z1, z2, z3)
U62(z0, z1, active(z2), z3) → U62(z0, z1, z2, z3)
U62(z0, z1, z2, active(z3)) → U62(z0, z1, z2, z3)
U63(mark(z0), z1, z2, z3) → U63(z0, z1, z2, z3)
U63(z0, mark(z1), z2, z3) → U63(z0, z1, z2, z3)
U63(z0, z1, mark(z2), z3) → U63(z0, z1, z2, z3)
U63(z0, z1, z2, mark(z3)) → U63(z0, z1, z2, z3)
U63(active(z0), z1, z2, z3) → U63(z0, z1, z2, z3)
U63(z0, active(z1), z2, z3) → U63(z0, z1, z2, z3)
U63(z0, z1, active(z2), z3) → U63(z0, z1, z2, z3)
U63(z0, z1, z2, active(z3)) → U63(z0, z1, z2, z3)
U64(mark(z0), z1) → U64(z0, z1)
U64(z0, mark(z1)) → U64(z0, z1)
U64(active(z0), z1) → U64(z0, z1)
U64(z0, active(z1)) → U64(z0, z1)
pair(mark(z0), z1) → pair(z0, z1)
pair(z0, mark(z1)) → pair(z0, z1)
pair(active(z0), z1) → pair(z0, z1)
pair(z0, active(z1)) → pair(z0, z1)
cons(mark(z0), z1) → cons(z0, z1)
cons(z0, mark(z1)) → cons(z0, z1)
cons(active(z0), z1) → cons(z0, z1)
cons(z0, active(z1)) → cons(z0, z1)
U71(mark(z0), z1) → U71(z0, z1)
U71(z0, mark(z1)) → U71(z0, z1)
U71(active(z0), z1) → U71(z0, z1)
U71(z0, active(z1)) → U71(z0, z1)
U72(mark(z0), z1) → U72(z0, z1)
U72(z0, mark(z1)) → U72(z0, z1)
U72(active(z0), z1) → U72(z0, z1)
U72(z0, active(z1)) → U72(z0, z1)
U81(mark(z0), z1, z2) → U81(z0, z1, z2)
U81(z0, mark(z1), z2) → U81(z0, z1, z2)
U81(z0, z1, mark(z2)) → U81(z0, z1, z2)
U81(active(z0), z1, z2) → U81(z0, z1, z2)
U81(z0, active(z1), z2) → U81(z0, z1, z2)
U81(z0, z1, active(z2)) → U81(z0, z1, z2)
U82(mark(z0), z1, z2) → U82(z0, z1, z2)
U82(z0, mark(z1), z2) → U82(z0, z1, z2)
U82(z0, z1, mark(z2)) → U82(z0, z1, z2)
U82(active(z0), z1, z2) → U82(z0, z1, z2)
U82(z0, active(z1), z2) → U82(z0, z1, z2)
U82(z0, z1, active(z2)) → U82(z0, z1, z2)
fst(mark(z0)) → fst(z0)
fst(active(z0)) → fst(z0)
natsFrom(mark(z0)) → natsFrom(z0)
natsFrom(active(z0)) → natsFrom(z0)
s(mark(z0)) → s(z0)
s(active(z0)) → s(z0)
sel(mark(z0), z1) → sel(z0, z1)
sel(z0, mark(z1)) → sel(z0, z1)
sel(active(z0), z1) → sel(z0, z1)
sel(z0, active(z1)) → sel(z0, z1)
tail(mark(z0)) → tail(z0)
tail(active(z0)) → tail(z0)
take(mark(z0), z1) → take(z0, z1)
take(z0, mark(z1)) → take(z0, z1)
take(active(z0), z1) → take(z0, z1)
take(z0, active(z1)) → take(z0, z1)

Tuples:

MARK(tt) → c29(ACTIVE(tt))
MARK(0) → c57(ACTIVE(0))
MARK(nil) → c58(ACTIVE(nil))

S tuples:

MARK(tt) → c29(ACTIVE(tt))
MARK(0) → c57(ACTIVE(0))
MARK(nil) → c58(ACTIVE(nil))

K tuples:none
Defined Rule Symbols:

active, mark, U11, U12, snd, splitAt, U21, U22, U31, U32, U41, U42, head, afterNth, U51, U52, U61, U62, U63, U64, pair, cons, U71, U72, U81, U82, fst, natsFrom, s, sel, tail, take

Defined Pair Symbols:

MARK

Compound Symbols:

c29, c57, c58

(5) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

Removed 3 trailing nodes:

MARK(nil) → c58(ACTIVE(nil))
MARK(0) → c57(ACTIVE(0))
MARK(tt) → c29(ACTIVE(tt))

(6) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0, z1)) → mark(U12(tt, z0, z1))
active(U12(tt, z0, z1)) → mark(snd(splitAt(z0, z1)))
active(U21(tt, z0)) → mark(U22(tt, z0))
active(U22(tt, z0)) → mark(z0)
active(U31(tt, z0)) → mark(U32(tt, z0))
active(U32(tt, z0)) → mark(z0)
active(U41(tt, z0, z1)) → mark(U42(tt, z0, z1))
active(U42(tt, z0, z1)) → mark(head(afterNth(z0, z1)))
active(U51(tt, z0)) → mark(U52(tt, z0))
active(U52(tt, z0)) → mark(z0)
active(U61(tt, z0, z1, z2)) → mark(U62(tt, z0, z1, z2))
active(U62(tt, z0, z1, z2)) → mark(U63(tt, z0, z1, z2))
active(U63(tt, z0, z1, z2)) → mark(U64(splitAt(z0, z2), z1))
active(U64(pair(z0, z1), z2)) → mark(pair(cons(z2, z0), z1))
active(U71(tt, z0)) → mark(U72(tt, z0))
active(U72(tt, z0)) → mark(z0)
active(U81(tt, z0, z1)) → mark(U82(tt, z0, z1))
active(U82(tt, z0, z1)) → mark(fst(splitAt(z0, z1)))
active(afterNth(z0, z1)) → mark(U11(tt, z0, z1))
active(fst(pair(z0, z1))) → mark(U21(tt, z0))
active(head(cons(z0, z1))) → mark(U31(tt, z0))
active(natsFrom(z0)) → mark(cons(z0, natsFrom(s(z0))))
active(sel(z0, z1)) → mark(U41(tt, z0, z1))
active(snd(pair(z0, z1))) → mark(U51(tt, z1))
active(splitAt(0, z0)) → mark(pair(nil, z0))
active(splitAt(s(z0), cons(z1, z2))) → mark(U61(tt, z0, z1, z2))
active(tail(cons(z0, z1))) → mark(U71(tt, z1))
active(take(z0, z1)) → mark(U81(tt, z0, z1))
mark(U11(z0, z1, z2)) → active(U11(mark(z0), z1, z2))
mark(tt) → active(tt)
mark(U12(z0, z1, z2)) → active(U12(mark(z0), z1, z2))
mark(snd(z0)) → active(snd(mark(z0)))
mark(splitAt(z0, z1)) → active(splitAt(mark(z0), mark(z1)))
mark(U21(z0, z1)) → active(U21(mark(z0), z1))
mark(U22(z0, z1)) → active(U22(mark(z0), z1))
mark(U31(z0, z1)) → active(U31(mark(z0), z1))
mark(U32(z0, z1)) → active(U32(mark(z0), z1))
mark(U41(z0, z1, z2)) → active(U41(mark(z0), z1, z2))
mark(U42(z0, z1, z2)) → active(U42(mark(z0), z1, z2))
mark(head(z0)) → active(head(mark(z0)))
mark(afterNth(z0, z1)) → active(afterNth(mark(z0), mark(z1)))
mark(U51(z0, z1)) → active(U51(mark(z0), z1))
mark(U52(z0, z1)) → active(U52(mark(z0), z1))
mark(U61(z0, z1, z2, z3)) → active(U61(mark(z0), z1, z2, z3))
mark(U62(z0, z1, z2, z3)) → active(U62(mark(z0), z1, z2, z3))
mark(U63(z0, z1, z2, z3)) → active(U63(mark(z0), z1, z2, z3))
mark(U64(z0, z1)) → active(U64(mark(z0), z1))
mark(pair(z0, z1)) → active(pair(mark(z0), mark(z1)))
mark(cons(z0, z1)) → active(cons(mark(z0), z1))
mark(U71(z0, z1)) → active(U71(mark(z0), z1))
mark(U72(z0, z1)) → active(U72(mark(z0), z1))
mark(U81(z0, z1, z2)) → active(U81(mark(z0), z1, z2))
mark(U82(z0, z1, z2)) → active(U82(mark(z0), z1, z2))
mark(fst(z0)) → active(fst(mark(z0)))
mark(natsFrom(z0)) → active(natsFrom(mark(z0)))
mark(s(z0)) → active(s(mark(z0)))
mark(sel(z0, z1)) → active(sel(mark(z0), mark(z1)))
mark(0) → active(0)
mark(nil) → active(nil)
mark(tail(z0)) → active(tail(mark(z0)))
mark(take(z0, z1)) → active(take(mark(z0), mark(z1)))
U11(mark(z0), z1, z2) → U11(z0, z1, z2)
U11(z0, mark(z1), z2) → U11(z0, z1, z2)
U11(z0, z1, mark(z2)) → U11(z0, z1, z2)
U11(active(z0), z1, z2) → U11(z0, z1, z2)
U11(z0, active(z1), z2) → U11(z0, z1, z2)
U11(z0, z1, active(z2)) → U11(z0, z1, z2)
U12(mark(z0), z1, z2) → U12(z0, z1, z2)
U12(z0, mark(z1), z2) → U12(z0, z1, z2)
U12(z0, z1, mark(z2)) → U12(z0, z1, z2)
U12(active(z0), z1, z2) → U12(z0, z1, z2)
U12(z0, active(z1), z2) → U12(z0, z1, z2)
U12(z0, z1, active(z2)) → U12(z0, z1, z2)
snd(mark(z0)) → snd(z0)
snd(active(z0)) → snd(z0)
splitAt(mark(z0), z1) → splitAt(z0, z1)
splitAt(z0, mark(z1)) → splitAt(z0, z1)
splitAt(active(z0), z1) → splitAt(z0, z1)
splitAt(z0, active(z1)) → splitAt(z0, z1)
U21(mark(z0), z1) → U21(z0, z1)
U21(z0, mark(z1)) → U21(z0, z1)
U21(active(z0), z1) → U21(z0, z1)
U21(z0, active(z1)) → U21(z0, z1)
U22(mark(z0), z1) → U22(z0, z1)
U22(z0, mark(z1)) → U22(z0, z1)
U22(active(z0), z1) → U22(z0, z1)
U22(z0, active(z1)) → U22(z0, z1)
U31(mark(z0), z1) → U31(z0, z1)
U31(z0, mark(z1)) → U31(z0, z1)
U31(active(z0), z1) → U31(z0, z1)
U31(z0, active(z1)) → U31(z0, z1)
U32(mark(z0), z1) → U32(z0, z1)
U32(z0, mark(z1)) → U32(z0, z1)
U32(active(z0), z1) → U32(z0, z1)
U32(z0, active(z1)) → U32(z0, z1)
U41(mark(z0), z1, z2) → U41(z0, z1, z2)
U41(z0, mark(z1), z2) → U41(z0, z1, z2)
U41(z0, z1, mark(z2)) → U41(z0, z1, z2)
U41(active(z0), z1, z2) → U41(z0, z1, z2)
U41(z0, active(z1), z2) → U41(z0, z1, z2)
U41(z0, z1, active(z2)) → U41(z0, z1, z2)
U42(mark(z0), z1, z2) → U42(z0, z1, z2)
U42(z0, mark(z1), z2) → U42(z0, z1, z2)
U42(z0, z1, mark(z2)) → U42(z0, z1, z2)
U42(active(z0), z1, z2) → U42(z0, z1, z2)
U42(z0, active(z1), z2) → U42(z0, z1, z2)
U42(z0, z1, active(z2)) → U42(z0, z1, z2)
head(mark(z0)) → head(z0)
head(active(z0)) → head(z0)
afterNth(mark(z0), z1) → afterNth(z0, z1)
afterNth(z0, mark(z1)) → afterNth(z0, z1)
afterNth(active(z0), z1) → afterNth(z0, z1)
afterNth(z0, active(z1)) → afterNth(z0, z1)
U51(mark(z0), z1) → U51(z0, z1)
U51(z0, mark(z1)) → U51(z0, z1)
U51(active(z0), z1) → U51(z0, z1)
U51(z0, active(z1)) → U51(z0, z1)
U52(mark(z0), z1) → U52(z0, z1)
U52(z0, mark(z1)) → U52(z0, z1)
U52(active(z0), z1) → U52(z0, z1)
U52(z0, active(z1)) → U52(z0, z1)
U61(mark(z0), z1, z2, z3) → U61(z0, z1, z2, z3)
U61(z0, mark(z1), z2, z3) → U61(z0, z1, z2, z3)
U61(z0, z1, mark(z2), z3) → U61(z0, z1, z2, z3)
U61(z0, z1, z2, mark(z3)) → U61(z0, z1, z2, z3)
U61(active(z0), z1, z2, z3) → U61(z0, z1, z2, z3)
U61(z0, active(z1), z2, z3) → U61(z0, z1, z2, z3)
U61(z0, z1, active(z2), z3) → U61(z0, z1, z2, z3)
U61(z0, z1, z2, active(z3)) → U61(z0, z1, z2, z3)
U62(mark(z0), z1, z2, z3) → U62(z0, z1, z2, z3)
U62(z0, mark(z1), z2, z3) → U62(z0, z1, z2, z3)
U62(z0, z1, mark(z2), z3) → U62(z0, z1, z2, z3)
U62(z0, z1, z2, mark(z3)) → U62(z0, z1, z2, z3)
U62(active(z0), z1, z2, z3) → U62(z0, z1, z2, z3)
U62(z0, active(z1), z2, z3) → U62(z0, z1, z2, z3)
U62(z0, z1, active(z2), z3) → U62(z0, z1, z2, z3)
U62(z0, z1, z2, active(z3)) → U62(z0, z1, z2, z3)
U63(mark(z0), z1, z2, z3) → U63(z0, z1, z2, z3)
U63(z0, mark(z1), z2, z3) → U63(z0, z1, z2, z3)
U63(z0, z1, mark(z2), z3) → U63(z0, z1, z2, z3)
U63(z0, z1, z2, mark(z3)) → U63(z0, z1, z2, z3)
U63(active(z0), z1, z2, z3) → U63(z0, z1, z2, z3)
U63(z0, active(z1), z2, z3) → U63(z0, z1, z2, z3)
U63(z0, z1, active(z2), z3) → U63(z0, z1, z2, z3)
U63(z0, z1, z2, active(z3)) → U63(z0, z1, z2, z3)
U64(mark(z0), z1) → U64(z0, z1)
U64(z0, mark(z1)) → U64(z0, z1)
U64(active(z0), z1) → U64(z0, z1)
U64(z0, active(z1)) → U64(z0, z1)
pair(mark(z0), z1) → pair(z0, z1)
pair(z0, mark(z1)) → pair(z0, z1)
pair(active(z0), z1) → pair(z0, z1)
pair(z0, active(z1)) → pair(z0, z1)
cons(mark(z0), z1) → cons(z0, z1)
cons(z0, mark(z1)) → cons(z0, z1)
cons(active(z0), z1) → cons(z0, z1)
cons(z0, active(z1)) → cons(z0, z1)
U71(mark(z0), z1) → U71(z0, z1)
U71(z0, mark(z1)) → U71(z0, z1)
U71(active(z0), z1) → U71(z0, z1)
U71(z0, active(z1)) → U71(z0, z1)
U72(mark(z0), z1) → U72(z0, z1)
U72(z0, mark(z1)) → U72(z0, z1)
U72(active(z0), z1) → U72(z0, z1)
U72(z0, active(z1)) → U72(z0, z1)
U81(mark(z0), z1, z2) → U81(z0, z1, z2)
U81(z0, mark(z1), z2) → U81(z0, z1, z2)
U81(z0, z1, mark(z2)) → U81(z0, z1, z2)
U81(active(z0), z1, z2) → U81(z0, z1, z2)
U81(z0, active(z1), z2) → U81(z0, z1, z2)
U81(z0, z1, active(z2)) → U81(z0, z1, z2)
U82(mark(z0), z1, z2) → U82(z0, z1, z2)
U82(z0, mark(z1), z2) → U82(z0, z1, z2)
U82(z0, z1, mark(z2)) → U82(z0, z1, z2)
U82(active(z0), z1, z2) → U82(z0, z1, z2)
U82(z0, active(z1), z2) → U82(z0, z1, z2)
U82(z0, z1, active(z2)) → U82(z0, z1, z2)
fst(mark(z0)) → fst(z0)
fst(active(z0)) → fst(z0)
natsFrom(mark(z0)) → natsFrom(z0)
natsFrom(active(z0)) → natsFrom(z0)
s(mark(z0)) → s(z0)
s(active(z0)) → s(z0)
sel(mark(z0), z1) → sel(z0, z1)
sel(z0, mark(z1)) → sel(z0, z1)
sel(active(z0), z1) → sel(z0, z1)
sel(z0, active(z1)) → sel(z0, z1)
tail(mark(z0)) → tail(z0)
tail(active(z0)) → tail(z0)
take(mark(z0), z1) → take(z0, z1)
take(z0, mark(z1)) → take(z0, z1)
take(active(z0), z1) → take(z0, z1)
take(z0, active(z1)) → take(z0, z1)

Tuples:none
S tuples:none
K tuples:none
Defined Rule Symbols:

active, mark, U11, U12, snd, splitAt, U21, U22, U31, U32, U41, U42, head, afterNth, U51, U52, U61, U62, U63, U64, pair, cons, U71, U72, U81, U82, fst, natsFrom, s, sel, tail, take

Defined Pair Symbols:none

Compound Symbols:none

(7) SIsEmptyProof (EQUIVALENT transformation)

The set S is empty

(8) BOUNDS(O(1), O(1))