MAYBE
Time: 1.423967
TRS:
{ cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
active cons(X1, X2) -> cons(active X1, X2),
active zeros() -> mark cons(0(), zeros()),
active U12 X -> U12 active X,
active U12 tt() -> mark tt(),
active isNatList cons(V1, V2) -> mark U51(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatList nil() -> mark tt(),
active isNatList take(V1, V2) -> mark U61(and(isNatKind V1, isNatIListKind V2), V1, V2),
active U11(X1, X2) -> U11(active X1, X2),
active U11(tt(), V1) -> mark U12 isNatList V1,
active U22 X -> U22 active X,
active U22 tt() -> mark tt(),
active isNat 0() -> mark tt(),
active isNat s V1 -> mark U21(isNatKind V1, V1),
active isNat length V1 -> mark U11(isNatIListKind V1, V1),
active U21(X1, X2) -> U21(active X1, X2),
active U21(tt(), V1) -> mark U22 isNat V1,
active U32 X -> U32 active X,
active U32 tt() -> mark tt(),
active U31(X1, X2) -> U31(active X1, X2),
active U31(tt(), V) -> mark U32 isNatList V,
active U42(X1, X2) -> U42(active X1, X2),
active U42(tt(), V2) -> mark U43 isNatIList V2,
active U41(X1, X2, X3) -> U41(active X1, X2, X3),
active U41(tt(), V1, V2) -> mark U42(isNat V1, V2),
active U43 X -> U43 active X,
active U43 tt() -> mark tt(),
active isNatIList V -> mark U31(isNatIListKind V, V),
active isNatIList cons(V1, V2) -> mark U41(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatIList zeros() -> mark tt(),
active U52(X1, X2) -> U52(active X1, X2),
active U52(tt(), V2) -> mark U53 isNatList V2,
active U51(X1, X2, X3) -> U51(active X1, X2, X3),
active U51(tt(), V1, V2) -> mark U52(isNat V1, V2),
active U53 X -> U53 active X,
active U53 tt() -> mark tt(),
active U62(X1, X2) -> U62(active X1, X2),
active U62(tt(), V2) -> mark U63 isNatIList V2,
active U61(X1, X2, X3) -> U61(active X1, X2, X3),
active U61(tt(), V1, V2) -> mark U62(isNat V1, V2),
active U63 X -> U63 active X,
active U63 tt() -> mark tt(),
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark U71(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L),
active length nil() -> mark 0(),
active U71(X1, X2) -> U71(active X1, X2),
active U71(tt(), L) -> mark s length L,
active U81 X -> U81 active X,
active U81 tt() -> mark nil(),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark U81 and(isNatIList IL, isNatIListKind IL),
active take(s M, cons(N, IL)) -> mark U91(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N),
active U91(X1, X2, X3, X4) -> U91(active X1, X2, X3, X4),
active U91(tt(), IL, M, N) -> mark cons(N, take(M, IL)),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), X) -> mark X,
active isNatIListKind cons(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatIListKind zeros() -> mark tt(),
active isNatIListKind nil() -> mark tt(),
active isNatIListKind take(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatKind 0() -> mark tt(),
active isNatKind s V1 -> mark isNatKind V1,
active isNatKind length V1 -> mark isNatIListKind V1,
U12 mark X -> mark U12 X,
U12 ok X -> ok U12 X,
isNatList ok X -> ok isNatList X,
U11(mark X1, X2) -> mark U11(X1, X2),
U11(ok X1, ok X2) -> ok U11(X1, X2),
U22 mark X -> mark U22 X,
U22 ok X -> ok U22 X,
isNat ok X -> ok isNat X,
U21(mark X1, X2) -> mark U21(X1, X2),
U21(ok X1, ok X2) -> ok U21(X1, X2),
U32 mark X -> mark U32 X,
U32 ok X -> ok U32 X,
U31(mark X1, X2) -> mark U31(X1, X2),
U31(ok X1, ok X2) -> ok U31(X1, X2),
U42(mark X1, X2) -> mark U42(X1, X2),
U42(ok X1, ok X2) -> ok U42(X1, X2),
U41(mark X1, X2, X3) -> mark U41(X1, X2, X3),
U41(ok X1, ok X2, ok X3) -> ok U41(X1, X2, X3),
U43 mark X -> mark U43 X,
U43 ok X -> ok U43 X,
isNatIList ok X -> ok isNatIList X,
U52(mark X1, X2) -> mark U52(X1, X2),
U52(ok X1, ok X2) -> ok U52(X1, X2),
U51(mark X1, X2, X3) -> mark U51(X1, X2, X3),
U51(ok X1, ok X2, ok X3) -> ok U51(X1, X2, X3),
U53 mark X -> mark U53 X,
U53 ok X -> ok U53 X,
U62(mark X1, X2) -> mark U62(X1, X2),
U62(ok X1, ok X2) -> ok U62(X1, X2),
U61(mark X1, X2, X3) -> mark U61(X1, X2, X3),
U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3),
U63 mark X -> mark U63 X,
U63 ok X -> ok U63 X,
s mark X -> mark s X,
s ok X -> ok s X,
length mark X -> mark length X,
length ok X -> ok length X,
U71(mark X1, X2) -> mark U71(X1, X2),
U71(ok X1, ok X2) -> ok U71(X1, X2),
U81 mark X -> mark U81 X,
U81 ok X -> ok U81 X,
take(X1, mark X2) -> mark take(X1, X2),
take(mark X1, X2) -> mark take(X1, X2),
take(ok X1, ok X2) -> ok take(X1, X2),
U91(mark X1, X2, X3, X4) -> mark U91(X1, X2, X3, X4),
U91(ok X1, ok X2, ok X3, ok X4) -> ok U91(X1, X2, X3, X4),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatIListKind ok X -> ok isNatIListKind X,
isNatKind ok X -> ok isNatKind X,
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper 0() -> ok 0(),
proper zeros() -> ok zeros(),
proper U12 X -> U12 proper X,
proper isNatList X -> isNatList proper X,
proper U11(X1, X2) -> U11(proper X1, proper X2),
proper tt() -> ok tt(),
proper U22 X -> U22 proper X,
proper isNat X -> isNat proper X,
proper U21(X1, X2) -> U21(proper X1, proper X2),
proper U32 X -> U32 proper X,
proper U31(X1, X2) -> U31(proper X1, proper X2),
proper U42(X1, X2) -> U42(proper X1, proper X2),
proper U41(X1, X2, X3) -> U41(proper X1, proper X2, proper X3),
proper U43 X -> U43 proper X,
proper isNatIList X -> isNatIList proper X,
proper U52(X1, X2) -> U52(proper X1, proper X2),
proper U51(X1, X2, X3) -> U51(proper X1, proper X2, proper X3),
proper U53 X -> U53 proper X,
proper U62(X1, X2) -> U62(proper X1, proper X2),
proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3),
proper U63 X -> U63 proper X,
proper s X -> s proper X,
proper length X -> length proper X,
proper U71(X1, X2) -> U71(proper X1, proper X2),
proper nil() -> ok nil(),
proper U81 X -> U81 proper X,
proper take(X1, X2) -> take(proper X1, proper X2),
proper U91(X1, X2, X3, X4) -> U91(proper X1, proper X2, proper X3, proper X4),
proper and(X1, X2) -> and(proper X1, proper X2),
proper isNatIListKind X -> isNatIListKind proper X,
proper isNatKind X -> isNatKind proper X,
top mark X -> top proper X,
top ok X -> top active X}
DP:
DP:
{
cons#(mark X1, X2) -> cons#(X1, X2),
cons#(ok X1, ok X2) -> cons#(X1, X2),
active# cons(X1, X2) -> cons#(active X1, X2),
active# cons(X1, X2) -> active# X1,
active# zeros() -> cons#(0(), zeros()),
active# U12 X -> active# X,
active# U12 X -> U12# active X,
active# isNatList cons(V1, V2) -> U51#(and(isNatKind V1, isNatIListKind V2), V1, V2),
active# isNatList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2),
active# isNatList cons(V1, V2) -> isNatIListKind# V2,
active# isNatList cons(V1, V2) -> isNatKind# V1,
active# isNatList take(V1, V2) -> U61#(and(isNatKind V1, isNatIListKind V2), V1, V2),
active# isNatList take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2),
active# isNatList take(V1, V2) -> isNatIListKind# V2,
active# isNatList take(V1, V2) -> isNatKind# V1,
active# U11(X1, X2) -> active# X1,
active# U11(X1, X2) -> U11#(active X1, X2),
active# U11(tt(), V1) -> U12# isNatList V1,
active# U11(tt(), V1) -> isNatList# V1,
active# U22 X -> active# X,
active# U22 X -> U22# active X,
active# isNat s V1 -> U21#(isNatKind V1, V1),
active# isNat s V1 -> isNatKind# V1,
active# isNat length V1 -> U11#(isNatIListKind V1, V1),
active# isNat length V1 -> isNatIListKind# V1,
active# U21(X1, X2) -> active# X1,
active# U21(X1, X2) -> U21#(active X1, X2),
active# U21(tt(), V1) -> U22# isNat V1,
active# U21(tt(), V1) -> isNat# V1,
active# U32 X -> active# X,
active# U32 X -> U32# active X,
active# U31(X1, X2) -> active# X1,
active# U31(X1, X2) -> U31#(active X1, X2),
active# U31(tt(), V) -> isNatList# V,
active# U31(tt(), V) -> U32# isNatList V,
active# U42(X1, X2) -> active# X1,
active# U42(X1, X2) -> U42#(active X1, X2),
active# U42(tt(), V2) -> U43# isNatIList V2,
active# U42(tt(), V2) -> isNatIList# V2,
active# U41(X1, X2, X3) -> active# X1,
active# U41(X1, X2, X3) -> U41#(active X1, X2, X3),
active# U41(tt(), V1, V2) -> isNat# V1,
active# U41(tt(), V1, V2) -> U42#(isNat V1, V2),
active# U43 X -> active# X,
active# U43 X -> U43# active X,
active# isNatIList V -> U31#(isNatIListKind V, V),
active# isNatIList V -> isNatIListKind# V,
active# isNatIList cons(V1, V2) -> U41#(and(isNatKind V1, isNatIListKind V2), V1, V2),
active# isNatIList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2),
active# isNatIList cons(V1, V2) -> isNatIListKind# V2,
active# isNatIList cons(V1, V2) -> isNatKind# V1,
active# U52(X1, X2) -> active# X1,
active# U52(X1, X2) -> U52#(active X1, X2),
active# U52(tt(), V2) -> isNatList# V2,
active# U52(tt(), V2) -> U53# isNatList V2,
active# U51(X1, X2, X3) -> active# X1,
active# U51(X1, X2, X3) -> U51#(active X1, X2, X3),
active# U51(tt(), V1, V2) -> isNat# V1,
active# U51(tt(), V1, V2) -> U52#(isNat V1, V2),
active# U53 X -> active# X,
active# U53 X -> U53# active X,
active# U62(X1, X2) -> active# X1,
active# U62(X1, X2) -> U62#(active X1, X2),
active# U62(tt(), V2) -> isNatIList# V2,
active# U62(tt(), V2) -> U63# isNatIList V2,
active# U61(X1, X2, X3) -> active# X1,
active# U61(X1, X2, X3) -> U61#(active X1, X2, X3),
active# U61(tt(), V1, V2) -> isNat# V1,
active# U61(tt(), V1, V2) -> U62#(isNat V1, V2),
active# U63 X -> active# X,
active# U63 X -> U63# active X,
active# s X -> active# X,
active# s X -> s# active X,
active# length X -> active# X,
active# length X -> length# active X,
active# length cons(N, L) -> isNatList# L,
active# length cons(N, L) -> isNat# N,
active# length cons(N, L) -> U71#(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L),
active# length cons(N, L) -> and#(isNatList L, isNatIListKind L),
active# length cons(N, L) -> and#(isNat N, isNatKind N),
active# length cons(N, L) -> and#(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)),
active# length cons(N, L) -> isNatIListKind# L,
active# length cons(N, L) -> isNatKind# N,
active# U71(X1, X2) -> active# X1,
active# U71(X1, X2) -> U71#(active X1, X2),
active# U71(tt(), L) -> s# length L,
active# U71(tt(), L) -> length# L,
active# U81 X -> active# X,
active# U81 X -> U81# active X,
active# take(X1, X2) -> active# X1,
active# take(X1, X2) -> active# X2,
active# take(X1, X2) -> take#(X1, active X2),
active# take(X1, X2) -> take#(active X1, X2),
active# take(0(), IL) -> isNatIList# IL,
active# take(0(), IL) -> U81# and(isNatIList IL, isNatIListKind IL),
active# take(0(), IL) -> and#(isNatIList IL, isNatIListKind IL),
active# take(0(), IL) -> isNatIListKind# IL,
active# take(s M, cons(N, IL)) -> isNat# N,
active# take(s M, cons(N, IL)) -> isNat# M,
active# take(s M, cons(N, IL)) -> isNatIList# IL,
active# take(s M, cons(N, IL)) -> U91#(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N),
active# take(s M, cons(N, IL)) -> and#(isNat N, isNatKind N),
active# take(s M, cons(N, IL)) -> and#(isNat M, isNatKind M),
active# take(s M, cons(N, IL)) -> and#(isNatIList IL, isNatIListKind IL),
active# take(s M, cons(N, IL)) -> and#(and(isNat M, isNatKind M), and(isNat N, isNatKind N)),
active# take(s M, cons(N, IL)) -> and#(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))),
active# take(s M, cons(N, IL)) -> isNatIListKind# IL,
active# take(s M, cons(N, IL)) -> isNatKind# N,
active# take(s M, cons(N, IL)) -> isNatKind# M,
active# U91(X1, X2, X3, X4) -> active# X1,
active# U91(X1, X2, X3, X4) -> U91#(active X1, X2, X3, X4),
active# U91(tt(), IL, M, N) -> cons#(N, take(M, IL)),
active# U91(tt(), IL, M, N) -> take#(M, IL),
active# and(X1, X2) -> active# X1,
active# and(X1, X2) -> and#(active X1, X2),
active# isNatIListKind cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2),
active# isNatIListKind cons(V1, V2) -> isNatIListKind# V2,
active# isNatIListKind cons(V1, V2) -> isNatKind# V1,
active# isNatIListKind take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2),
active# isNatIListKind take(V1, V2) -> isNatIListKind# V2,
active# isNatIListKind take(V1, V2) -> isNatKind# V1,
active# isNatKind s V1 -> isNatKind# V1,
active# isNatKind length V1 -> isNatIListKind# V1,
U12# mark X -> U12# X,
U12# ok X -> U12# X,
isNatList# ok X -> isNatList# X,
U11#(mark X1, X2) -> U11#(X1, X2),
U11#(ok X1, ok X2) -> U11#(X1, X2),
U22# mark X -> U22# X,
U22# ok X -> U22# X,
isNat# ok X -> isNat# X,
U21#(mark X1, X2) -> U21#(X1, X2),
U21#(ok X1, ok X2) -> U21#(X1, X2),
U32# mark X -> U32# X,
U32# ok X -> U32# X,
U31#(mark X1, X2) -> U31#(X1, X2),
U31#(ok X1, ok X2) -> U31#(X1, X2),
U42#(mark X1, X2) -> U42#(X1, X2),
U42#(ok X1, ok X2) -> U42#(X1, X2),
U41#(mark X1, X2, X3) -> U41#(X1, X2, X3),
U41#(ok X1, ok X2, ok X3) -> U41#(X1, X2, X3),
U43# mark X -> U43# X,
U43# ok X -> U43# X,
isNatIList# ok X -> isNatIList# X,
U52#(mark X1, X2) -> U52#(X1, X2),
U52#(ok X1, ok X2) -> U52#(X1, X2),
U51#(mark X1, X2, X3) -> U51#(X1, X2, X3),
U51#(ok X1, ok X2, ok X3) -> U51#(X1, X2, X3),
U53# mark X -> U53# X,
U53# ok X -> U53# X,
U62#(mark X1, X2) -> U62#(X1, X2),
U62#(ok X1, ok X2) -> U62#(X1, X2),
U61#(mark X1, X2, X3) -> U61#(X1, X2, X3),
U61#(ok X1, ok X2, ok X3) -> U61#(X1, X2, X3),
U63# mark X -> U63# X,
U63# ok X -> U63# X,
s# mark X -> s# X,
s# ok X -> s# X,
length# mark X -> length# X,
length# ok X -> length# X,
U71#(mark X1, X2) -> U71#(X1, X2),
U71#(ok X1, ok X2) -> U71#(X1, X2),
U81# mark X -> U81# X,
U81# ok X -> U81# X,
take#(X1, mark X2) -> take#(X1, X2),
take#(mark X1, X2) -> take#(X1, X2),
take#(ok X1, ok X2) -> take#(X1, X2),
U91#(mark X1, X2, X3, X4) -> U91#(X1, X2, X3, X4),
U91#(ok X1, ok X2, ok X3, ok X4) -> U91#(X1, X2, X3, X4),
and#(mark X1, X2) -> and#(X1, X2),
and#(ok X1, ok X2) -> and#(X1, X2),
isNatIListKind# ok X -> isNatIListKind# X,
isNatKind# ok X -> isNatKind# X,
proper# cons(X1, X2) -> cons#(proper X1, proper X2),
proper# cons(X1, X2) -> proper# X1,
proper# cons(X1, X2) -> proper# X2,
proper# U12 X -> U12# proper X,
proper# U12 X -> proper# X,
proper# isNatList X -> isNatList# proper X,
proper# isNatList X -> proper# X,
proper# U11(X1, X2) -> U11#(proper X1, proper X2),
proper# U11(X1, X2) -> proper# X1,
proper# U11(X1, X2) -> proper# X2,
proper# U22 X -> U22# proper X,
proper# U22 X -> proper# X,
proper# isNat X -> isNat# proper X,
proper# isNat X -> proper# X,
proper# U21(X1, X2) -> U21#(proper X1, proper X2),
proper# U21(X1, X2) -> proper# X1,
proper# U21(X1, X2) -> proper# X2,
proper# U32 X -> U32# proper X,
proper# U32 X -> proper# X,
proper# U31(X1, X2) -> U31#(proper X1, proper X2),
proper# U31(X1, X2) -> proper# X1,
proper# U31(X1, X2) -> proper# X2,
proper# U42(X1, X2) -> U42#(proper X1, proper X2),
proper# U42(X1, X2) -> proper# X1,
proper# U42(X1, X2) -> proper# X2,
proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3),
proper# U41(X1, X2, X3) -> proper# X1,
proper# U41(X1, X2, X3) -> proper# X2,
proper# U41(X1, X2, X3) -> proper# X3,
proper# U43 X -> U43# proper X,
proper# U43 X -> proper# X,
proper# isNatIList X -> isNatIList# proper X,
proper# isNatIList X -> proper# X,
proper# U52(X1, X2) -> U52#(proper X1, proper X2),
proper# U52(X1, X2) -> proper# X1,
proper# U52(X1, X2) -> proper# X2,
proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3),
proper# U51(X1, X2, X3) -> proper# X1,
proper# U51(X1, X2, X3) -> proper# X2,
proper# U51(X1, X2, X3) -> proper# X3,
proper# U53 X -> U53# proper X,
proper# U53 X -> proper# X,
proper# U62(X1, X2) -> U62#(proper X1, proper X2),
proper# U62(X1, X2) -> proper# X1,
proper# U62(X1, X2) -> proper# X2,
proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3),
proper# U61(X1, X2, X3) -> proper# X1,
proper# U61(X1, X2, X3) -> proper# X2,
proper# U61(X1, X2, X3) -> proper# X3,
proper# U63 X -> U63# proper X,
proper# U63 X -> proper# X,
proper# s X -> s# proper X,
proper# s X -> proper# X,
proper# length X -> length# proper X,
proper# length X -> proper# X,
proper# U71(X1, X2) -> U71#(proper X1, proper X2),
proper# U71(X1, X2) -> proper# X1,
proper# U71(X1, X2) -> proper# X2,
proper# U81 X -> U81# proper X,
proper# U81 X -> proper# X,
proper# take(X1, X2) -> take#(proper X1, proper X2),
proper# take(X1, X2) -> proper# X1,
proper# take(X1, X2) -> proper# X2,
proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4),
proper# U91(X1, X2, X3, X4) -> proper# X1,
proper# U91(X1, X2, X3, X4) -> proper# X2,
proper# U91(X1, X2, X3, X4) -> proper# X3,
proper# U91(X1, X2, X3, X4) -> proper# X4,
proper# and(X1, X2) -> and#(proper X1, proper X2),
proper# and(X1, X2) -> proper# X1,
proper# and(X1, X2) -> proper# X2,
proper# isNatIListKind X -> isNatIListKind# proper X,
proper# isNatIListKind X -> proper# X,
proper# isNatKind X -> isNatKind# proper X,
proper# isNatKind X -> proper# X,
top# mark X -> proper# X,
top# mark X -> top# proper X,
top# ok X -> active# X,
top# ok X -> top# active X
}
TRS:
{ cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
active cons(X1, X2) -> cons(active X1, X2),
active zeros() -> mark cons(0(), zeros()),
active U12 X -> U12 active X,
active U12 tt() -> mark tt(),
active isNatList cons(V1, V2) -> mark U51(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatList nil() -> mark tt(),
active isNatList take(V1, V2) -> mark U61(and(isNatKind V1, isNatIListKind V2), V1, V2),
active U11(X1, X2) -> U11(active X1, X2),
active U11(tt(), V1) -> mark U12 isNatList V1,
active U22 X -> U22 active X,
active U22 tt() -> mark tt(),
active isNat 0() -> mark tt(),
active isNat s V1 -> mark U21(isNatKind V1, V1),
active isNat length V1 -> mark U11(isNatIListKind V1, V1),
active U21(X1, X2) -> U21(active X1, X2),
active U21(tt(), V1) -> mark U22 isNat V1,
active U32 X -> U32 active X,
active U32 tt() -> mark tt(),
active U31(X1, X2) -> U31(active X1, X2),
active U31(tt(), V) -> mark U32 isNatList V,
active U42(X1, X2) -> U42(active X1, X2),
active U42(tt(), V2) -> mark U43 isNatIList V2,
active U41(X1, X2, X3) -> U41(active X1, X2, X3),
active U41(tt(), V1, V2) -> mark U42(isNat V1, V2),
active U43 X -> U43 active X,
active U43 tt() -> mark tt(),
active isNatIList V -> mark U31(isNatIListKind V, V),
active isNatIList cons(V1, V2) -> mark U41(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatIList zeros() -> mark tt(),
active U52(X1, X2) -> U52(active X1, X2),
active U52(tt(), V2) -> mark U53 isNatList V2,
active U51(X1, X2, X3) -> U51(active X1, X2, X3),
active U51(tt(), V1, V2) -> mark U52(isNat V1, V2),
active U53 X -> U53 active X,
active U53 tt() -> mark tt(),
active U62(X1, X2) -> U62(active X1, X2),
active U62(tt(), V2) -> mark U63 isNatIList V2,
active U61(X1, X2, X3) -> U61(active X1, X2, X3),
active U61(tt(), V1, V2) -> mark U62(isNat V1, V2),
active U63 X -> U63 active X,
active U63 tt() -> mark tt(),
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark U71(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L),
active length nil() -> mark 0(),
active U71(X1, X2) -> U71(active X1, X2),
active U71(tt(), L) -> mark s length L,
active U81 X -> U81 active X,
active U81 tt() -> mark nil(),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark U81 and(isNatIList IL, isNatIListKind IL),
active take(s M, cons(N, IL)) -> mark U91(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N),
active U91(X1, X2, X3, X4) -> U91(active X1, X2, X3, X4),
active U91(tt(), IL, M, N) -> mark cons(N, take(M, IL)),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), X) -> mark X,
active isNatIListKind cons(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatIListKind zeros() -> mark tt(),
active isNatIListKind nil() -> mark tt(),
active isNatIListKind take(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatKind 0() -> mark tt(),
active isNatKind s V1 -> mark isNatKind V1,
active isNatKind length V1 -> mark isNatIListKind V1,
U12 mark X -> mark U12 X,
U12 ok X -> ok U12 X,
isNatList ok X -> ok isNatList X,
U11(mark X1, X2) -> mark U11(X1, X2),
U11(ok X1, ok X2) -> ok U11(X1, X2),
U22 mark X -> mark U22 X,
U22 ok X -> ok U22 X,
isNat ok X -> ok isNat X,
U21(mark X1, X2) -> mark U21(X1, X2),
U21(ok X1, ok X2) -> ok U21(X1, X2),
U32 mark X -> mark U32 X,
U32 ok X -> ok U32 X,
U31(mark X1, X2) -> mark U31(X1, X2),
U31(ok X1, ok X2) -> ok U31(X1, X2),
U42(mark X1, X2) -> mark U42(X1, X2),
U42(ok X1, ok X2) -> ok U42(X1, X2),
U41(mark X1, X2, X3) -> mark U41(X1, X2, X3),
U41(ok X1, ok X2, ok X3) -> ok U41(X1, X2, X3),
U43 mark X -> mark U43 X,
U43 ok X -> ok U43 X,
isNatIList ok X -> ok isNatIList X,
U52(mark X1, X2) -> mark U52(X1, X2),
U52(ok X1, ok X2) -> ok U52(X1, X2),
U51(mark X1, X2, X3) -> mark U51(X1, X2, X3),
U51(ok X1, ok X2, ok X3) -> ok U51(X1, X2, X3),
U53 mark X -> mark U53 X,
U53 ok X -> ok U53 X,
U62(mark X1, X2) -> mark U62(X1, X2),
U62(ok X1, ok X2) -> ok U62(X1, X2),
U61(mark X1, X2, X3) -> mark U61(X1, X2, X3),
U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3),
U63 mark X -> mark U63 X,
U63 ok X -> ok U63 X,
s mark X -> mark s X,
s ok X -> ok s X,
length mark X -> mark length X,
length ok X -> ok length X,
U71(mark X1, X2) -> mark U71(X1, X2),
U71(ok X1, ok X2) -> ok U71(X1, X2),
U81 mark X -> mark U81 X,
U81 ok X -> ok U81 X,
take(X1, mark X2) -> mark take(X1, X2),
take(mark X1, X2) -> mark take(X1, X2),
take(ok X1, ok X2) -> ok take(X1, X2),
U91(mark X1, X2, X3, X4) -> mark U91(X1, X2, X3, X4),
U91(ok X1, ok X2, ok X3, ok X4) -> ok U91(X1, X2, X3, X4),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatIListKind ok X -> ok isNatIListKind X,
isNatKind ok X -> ok isNatKind X,
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper 0() -> ok 0(),
proper zeros() -> ok zeros(),
proper U12 X -> U12 proper X,
proper isNatList X -> isNatList proper X,
proper U11(X1, X2) -> U11(proper X1, proper X2),
proper tt() -> ok tt(),
proper U22 X -> U22 proper X,
proper isNat X -> isNat proper X,
proper U21(X1, X2) -> U21(proper X1, proper X2),
proper U32 X -> U32 proper X,
proper U31(X1, X2) -> U31(proper X1, proper X2),
proper U42(X1, X2) -> U42(proper X1, proper X2),
proper U41(X1, X2, X3) -> U41(proper X1, proper X2, proper X3),
proper U43 X -> U43 proper X,
proper isNatIList X -> isNatIList proper X,
proper U52(X1, X2) -> U52(proper X1, proper X2),
proper U51(X1, X2, X3) -> U51(proper X1, proper X2, proper X3),
proper U53 X -> U53 proper X,
proper U62(X1, X2) -> U62(proper X1, proper X2),
proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3),
proper U63 X -> U63 proper X,
proper s X -> s proper X,
proper length X -> length proper X,
proper U71(X1, X2) -> U71(proper X1, proper X2),
proper nil() -> ok nil(),
proper U81 X -> U81 proper X,
proper take(X1, X2) -> take(proper X1, proper X2),
proper U91(X1, X2, X3, X4) -> U91(proper X1, proper X2, proper X3, proper X4),
proper and(X1, X2) -> and(proper X1, proper X2),
proper isNatIListKind X -> isNatIListKind proper X,
proper isNatKind X -> isNatKind proper X,
top mark X -> top proper X,
top ok X -> top active X}
EDG:
{
(active# isNatList take(V1, V2) -> isNatKind# V1, isNatKind# ok X -> isNatKind# X)
(active# isNat s V1 -> isNatKind# V1, isNatKind# ok X -> isNatKind# X)
(active# U21(tt(), V1) -> isNat# V1, isNat# ok X -> isNat# X)
(active# isNatIList cons(V1, V2) -> isNatKind# V1, isNatKind# ok X -> isNatKind# X)
(active# U61(tt(), V1, V2) -> isNat# V1, isNat# ok X -> isNat# X)
(active# isNatIListKind take(V1, V2) -> isNatKind# V1, isNatKind# ok X -> isNatKind# X)
(active# isNatKind length V1 -> isNatIListKind# V1, isNatIListKind# ok X -> isNatIListKind# X)
(active# take(s M, cons(N, IL)) -> isNat# M, isNat# ok X -> isNat# X)
(active# length cons(N, L) -> and#(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), and#(ok X1, ok X2) -> and#(X1, X2))
(active# length cons(N, L) -> and#(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), and#(mark X1, X2) -> and#(X1, X2))
(active# take(s M, cons(N, IL)) -> and#(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), and#(ok X1, ok X2) -> and#(X1, X2))
(active# take(s M, cons(N, IL)) -> and#(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), and#(mark X1, X2) -> and#(X1, X2))
(active# U51(X1, X2, X3) -> U51#(active X1, X2, X3), U51#(ok X1, ok X2, ok X3) -> U51#(X1, X2, X3))
(active# U51(X1, X2, X3) -> U51#(active X1, X2, X3), U51#(mark X1, X2, X3) -> U51#(X1, X2, X3))
(U41#(mark X1, X2, X3) -> U41#(X1, X2, X3), U41#(ok X1, ok X2, ok X3) -> U41#(X1, X2, X3))
(U41#(mark X1, X2, X3) -> U41#(X1, X2, X3), U41#(mark X1, X2, X3) -> U41#(X1, X2, X3))
(U51#(mark X1, X2, X3) -> U51#(X1, X2, X3), U51#(ok X1, ok X2, ok X3) -> U51#(X1, X2, X3))
(U51#(mark X1, X2, X3) -> U51#(X1, X2, X3), U51#(mark X1, X2, X3) -> U51#(X1, X2, X3))
(U61#(mark X1, X2, X3) -> U61#(X1, X2, X3), U61#(ok X1, ok X2, ok X3) -> U61#(X1, X2, X3))
(U61#(mark X1, X2, X3) -> U61#(X1, X2, X3), U61#(mark X1, X2, X3) -> U61#(X1, X2, X3))
(active# U91(tt(), IL, M, N) -> cons#(N, take(M, IL)), cons#(ok X1, ok X2) -> cons#(X1, X2))
(active# U91(tt(), IL, M, N) -> cons#(N, take(M, IL)), cons#(mark X1, X2) -> cons#(X1, X2))
(proper# U51(X1, X2, X3) -> proper# X3, proper# isNatKind X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X3, proper# isNatKind X -> isNatKind# proper X)
(proper# U51(X1, X2, X3) -> proper# X3, proper# isNatIListKind X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X3, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# U51(X1, X2, X3) -> proper# X3, proper# and(X1, X2) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X3, proper# and(X1, X2) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X3, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# U51(X1, X2, X3) -> proper# X3, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# U51(X1, X2, X3) -> proper# X3, proper# take(X1, X2) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X3, proper# take(X1, X2) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X3, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# U51(X1, X2, X3) -> proper# X3, proper# U81 X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U81 X -> U81# proper X)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U71(X1, X2) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U71(X1, X2) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# U51(X1, X2, X3) -> proper# X3, proper# length X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X3, proper# length X -> length# proper X)
(proper# U51(X1, X2, X3) -> proper# X3, proper# s X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X3, proper# s X -> s# proper X)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U63 X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U63 X -> U63# proper X)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U61(X1, X2, X3) -> proper# X3)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U61(X1, X2, X3) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U61(X1, X2, X3) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# U51(X1, X2, X3) -> proper# X3, proper# U62(X1, X2) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U62(X1, X2) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# U51(X1, X2, X3) -> proper# X3, proper# U53 X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U53 X -> U53# proper X)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U51(X1, X2, X3) -> proper# X3)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U51(X1, X2, X3) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U51(X1, X2, X3) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# U51(X1, X2, X3) -> proper# X3, proper# U52(X1, X2) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U52(X1, X2) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# U51(X1, X2, X3) -> proper# X3, proper# isNatIList X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X3, proper# isNatIList X -> isNatIList# proper X)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U43 X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U43 X -> U43# proper X)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U41(X1, X2, X3) -> proper# X3)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U41(X1, X2, X3) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U41(X1, X2, X3) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# U51(X1, X2, X3) -> proper# X3, proper# U42(X1, X2) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U42(X1, X2) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# U51(X1, X2, X3) -> proper# X3, proper# U31(X1, X2) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U31(X1, X2) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# U51(X1, X2, X3) -> proper# X3, proper# U32 X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U32 X -> U32# proper X)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U21(X1, X2) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U21(X1, X2) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# U51(X1, X2, X3) -> proper# X3, proper# isNat X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X3, proper# isNat X -> isNat# proper X)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U22 X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U22 X -> U22# proper X)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U11(X1, X2) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U11(X1, X2) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# U51(X1, X2, X3) -> proper# X3, proper# isNatList X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X3, proper# isNatList X -> isNatList# proper X)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U12 X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X3, proper# U12 X -> U12# proper X)
(proper# U51(X1, X2, X3) -> proper# X3, proper# cons(X1, X2) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X3, proper# cons(X1, X2) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X3, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# isNatKind X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# isNatKind X -> isNatKind# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# isNatIListKind X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# and(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# and(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# take(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# take(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U81 X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U81 X -> U81# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U71(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U71(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# length X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# length X -> length# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# s X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# s X -> s# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U63 X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U63 X -> U63# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U61(X1, X2, X3) -> proper# X3)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U61(X1, X2, X3) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U61(X1, X2, X3) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U62(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U62(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U53 X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U53 X -> U53# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U51(X1, X2, X3) -> proper# X3)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U51(X1, X2, X3) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U51(X1, X2, X3) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U52(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U52(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# isNatIList X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# isNatIList X -> isNatIList# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U43 X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U43 X -> U43# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U41(X1, X2, X3) -> proper# X3)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U41(X1, X2, X3) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U41(X1, X2, X3) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U42(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U42(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U31(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U31(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U32 X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U32 X -> U32# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U21(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U21(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# isNat X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# isNat X -> isNat# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U22 X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U22 X -> U22# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U11(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U11(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# isNatList X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# isNatList X -> isNatList# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U12 X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# U12 X -> U12# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# cons(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# cons(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X3, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(active# length cons(N, L) -> isNatIListKind# L, isNatIListKind# ok X -> isNatIListKind# X)
(active# cons(X1, X2) -> cons#(active X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2))
(active# cons(X1, X2) -> cons#(active X1, X2), cons#(mark X1, X2) -> cons#(X1, X2))
(active# U11(X1, X2) -> active# X1, active# isNatKind length V1 -> isNatIListKind# V1)
(active# U11(X1, X2) -> active# X1, active# isNatKind s V1 -> isNatKind# V1)
(active# U11(X1, X2) -> active# X1, active# isNatIListKind take(V1, V2) -> isNatKind# V1)
(active# U11(X1, X2) -> active# X1, active# isNatIListKind take(V1, V2) -> isNatIListKind# V2)
(active# U11(X1, X2) -> active# X1, active# isNatIListKind take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U11(X1, X2) -> active# X1, active# isNatIListKind cons(V1, V2) -> isNatKind# V1)
(active# U11(X1, X2) -> active# X1, active# isNatIListKind cons(V1, V2) -> isNatIListKind# V2)
(active# U11(X1, X2) -> active# X1, active# isNatIListKind cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U11(X1, X2) -> active# X1, active# and(X1, X2) -> and#(active X1, X2))
(active# U11(X1, X2) -> active# X1, active# and(X1, X2) -> active# X1)
(active# U11(X1, X2) -> active# X1, active# U91(tt(), IL, M, N) -> take#(M, IL))
(active# U11(X1, X2) -> active# X1, active# U91(tt(), IL, M, N) -> cons#(N, take(M, IL)))
(active# U11(X1, X2) -> active# X1, active# U91(X1, X2, X3, X4) -> U91#(active X1, X2, X3, X4))
(active# U11(X1, X2) -> active# X1, active# U91(X1, X2, X3, X4) -> active# X1)
(active# U11(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatKind# M)
(active# U11(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatKind# N)
(active# U11(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIListKind# IL)
(active# U11(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))))
(active# U11(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(and(isNat M, isNatKind M), and(isNat N, isNatKind N)))
(active# U11(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, isNatIListKind IL))
(active# U11(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat M, isNatKind M))
(active# U11(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat N, isNatKind N))
(active# U11(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> U91#(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N))
(active# U11(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIList# IL)
(active# U11(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# M)
(active# U11(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# N)
(active# U11(X1, X2) -> active# X1, active# take(0(), IL) -> isNatIListKind# IL)
(active# U11(X1, X2) -> active# X1, active# take(0(), IL) -> and#(isNatIList IL, isNatIListKind IL))
(active# U11(X1, X2) -> active# X1, active# take(0(), IL) -> U81# and(isNatIList IL, isNatIListKind IL))
(active# U11(X1, X2) -> active# X1, active# take(0(), IL) -> isNatIList# IL)
(active# U11(X1, X2) -> active# X1, active# take(X1, X2) -> take#(active X1, X2))
(active# U11(X1, X2) -> active# X1, active# take(X1, X2) -> take#(X1, active X2))
(active# U11(X1, X2) -> active# X1, active# take(X1, X2) -> active# X2)
(active# U11(X1, X2) -> active# X1, active# take(X1, X2) -> active# X1)
(active# U11(X1, X2) -> active# X1, active# U81 X -> U81# active X)
(active# U11(X1, X2) -> active# X1, active# U81 X -> active# X)
(active# U11(X1, X2) -> active# X1, active# U71(tt(), L) -> length# L)
(active# U11(X1, X2) -> active# X1, active# U71(tt(), L) -> s# length L)
(active# U11(X1, X2) -> active# X1, active# U71(X1, X2) -> U71#(active X1, X2))
(active# U11(X1, X2) -> active# X1, active# U71(X1, X2) -> active# X1)
(active# U11(X1, X2) -> active# X1, active# length cons(N, L) -> isNatKind# N)
(active# U11(X1, X2) -> active# X1, active# length cons(N, L) -> isNatIListKind# L)
(active# U11(X1, X2) -> active# X1, active# length cons(N, L) -> and#(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)))
(active# U11(X1, X2) -> active# X1, active# length cons(N, L) -> and#(isNat N, isNatKind N))
(active# U11(X1, X2) -> active# X1, active# length cons(N, L) -> and#(isNatList L, isNatIListKind L))
(active# U11(X1, X2) -> active# X1, active# length cons(N, L) -> U71#(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L))
(active# U11(X1, X2) -> active# X1, active# length cons(N, L) -> isNat# N)
(active# U11(X1, X2) -> active# X1, active# length cons(N, L) -> isNatList# L)
(active# U11(X1, X2) -> active# X1, active# length X -> length# active X)
(active# U11(X1, X2) -> active# X1, active# length X -> active# X)
(active# U11(X1, X2) -> active# X1, active# s X -> s# active X)
(active# U11(X1, X2) -> active# X1, active# s X -> active# X)
(active# U11(X1, X2) -> active# X1, active# U63 X -> U63# active X)
(active# U11(X1, X2) -> active# X1, active# U63 X -> active# X)
(active# U11(X1, X2) -> active# X1, active# U61(tt(), V1, V2) -> U62#(isNat V1, V2))
(active# U11(X1, X2) -> active# X1, active# U61(tt(), V1, V2) -> isNat# V1)
(active# U11(X1, X2) -> active# X1, active# U61(X1, X2, X3) -> U61#(active X1, X2, X3))
(active# U11(X1, X2) -> active# X1, active# U61(X1, X2, X3) -> active# X1)
(active# U11(X1, X2) -> active# X1, active# U62(tt(), V2) -> U63# isNatIList V2)
(active# U11(X1, X2) -> active# X1, active# U62(tt(), V2) -> isNatIList# V2)
(active# U11(X1, X2) -> active# X1, active# U62(X1, X2) -> U62#(active X1, X2))
(active# U11(X1, X2) -> active# X1, active# U62(X1, X2) -> active# X1)
(active# U11(X1, X2) -> active# X1, active# U53 X -> U53# active X)
(active# U11(X1, X2) -> active# X1, active# U53 X -> active# X)
(active# U11(X1, X2) -> active# X1, active# U51(tt(), V1, V2) -> U52#(isNat V1, V2))
(active# U11(X1, X2) -> active# X1, active# U51(tt(), V1, V2) -> isNat# V1)
(active# U11(X1, X2) -> active# X1, active# U51(X1, X2, X3) -> U51#(active X1, X2, X3))
(active# U11(X1, X2) -> active# X1, active# U51(X1, X2, X3) -> active# X1)
(active# U11(X1, X2) -> active# X1, active# U52(tt(), V2) -> U53# isNatList V2)
(active# U11(X1, X2) -> active# X1, active# U52(tt(), V2) -> isNatList# V2)
(active# U11(X1, X2) -> active# X1, active# U52(X1, X2) -> U52#(active X1, X2))
(active# U11(X1, X2) -> active# X1, active# U52(X1, X2) -> active# X1)
(active# U11(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNatKind# V1)
(active# U11(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNatIListKind# V2)
(active# U11(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U11(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> U41#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U11(X1, X2) -> active# X1, active# isNatIList V -> isNatIListKind# V)
(active# U11(X1, X2) -> active# X1, active# isNatIList V -> U31#(isNatIListKind V, V))
(active# U11(X1, X2) -> active# X1, active# U43 X -> U43# active X)
(active# U11(X1, X2) -> active# X1, active# U43 X -> active# X)
(active# U11(X1, X2) -> active# X1, active# U41(tt(), V1, V2) -> U42#(isNat V1, V2))
(active# U11(X1, X2) -> active# X1, active# U41(tt(), V1, V2) -> isNat# V1)
(active# U11(X1, X2) -> active# X1, active# U41(X1, X2, X3) -> U41#(active X1, X2, X3))
(active# U11(X1, X2) -> active# X1, active# U41(X1, X2, X3) -> active# X1)
(active# U11(X1, X2) -> active# X1, active# U42(tt(), V2) -> isNatIList# V2)
(active# U11(X1, X2) -> active# X1, active# U42(tt(), V2) -> U43# isNatIList V2)
(active# U11(X1, X2) -> active# X1, active# U42(X1, X2) -> U42#(active X1, X2))
(active# U11(X1, X2) -> active# X1, active# U42(X1, X2) -> active# X1)
(active# U11(X1, X2) -> active# X1, active# U31(tt(), V) -> U32# isNatList V)
(active# U11(X1, X2) -> active# X1, active# U31(tt(), V) -> isNatList# V)
(active# U11(X1, X2) -> active# X1, active# U31(X1, X2) -> U31#(active X1, X2))
(active# U11(X1, X2) -> active# X1, active# U31(X1, X2) -> active# X1)
(active# U11(X1, X2) -> active# X1, active# U32 X -> U32# active X)
(active# U11(X1, X2) -> active# X1, active# U32 X -> active# X)
(active# U11(X1, X2) -> active# X1, active# U21(tt(), V1) -> isNat# V1)
(active# U11(X1, X2) -> active# X1, active# U21(tt(), V1) -> U22# isNat V1)
(active# U11(X1, X2) -> active# X1, active# U21(X1, X2) -> U21#(active X1, X2))
(active# U11(X1, X2) -> active# X1, active# U21(X1, X2) -> active# X1)
(active# U11(X1, X2) -> active# X1, active# isNat length V1 -> isNatIListKind# V1)
(active# U11(X1, X2) -> active# X1, active# isNat length V1 -> U11#(isNatIListKind V1, V1))
(active# U11(X1, X2) -> active# X1, active# isNat s V1 -> isNatKind# V1)
(active# U11(X1, X2) -> active# X1, active# isNat s V1 -> U21#(isNatKind V1, V1))
(active# U11(X1, X2) -> active# X1, active# U22 X -> U22# active X)
(active# U11(X1, X2) -> active# X1, active# U22 X -> active# X)
(active# U11(X1, X2) -> active# X1, active# U11(tt(), V1) -> isNatList# V1)
(active# U11(X1, X2) -> active# X1, active# U11(tt(), V1) -> U12# isNatList V1)
(active# U11(X1, X2) -> active# X1, active# U11(X1, X2) -> U11#(active X1, X2))
(active# U11(X1, X2) -> active# X1, active# U11(X1, X2) -> active# X1)
(active# U11(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> isNatKind# V1)
(active# U11(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> isNatIListKind# V2)
(active# U11(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U11(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> U61#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U11(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> isNatKind# V1)
(active# U11(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> isNatIListKind# V2)
(active# U11(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U11(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> U51#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U11(X1, X2) -> active# X1, active# U12 X -> U12# active X)
(active# U11(X1, X2) -> active# X1, active# U12 X -> active# X)
(active# U11(X1, X2) -> active# X1, active# zeros() -> cons#(0(), zeros()))
(active# U11(X1, X2) -> active# X1, active# cons(X1, X2) -> active# X1)
(active# U11(X1, X2) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2))
(active# U21(X1, X2) -> active# X1, active# isNatKind length V1 -> isNatIListKind# V1)
(active# U21(X1, X2) -> active# X1, active# isNatKind s V1 -> isNatKind# V1)
(active# U21(X1, X2) -> active# X1, active# isNatIListKind take(V1, V2) -> isNatKind# V1)
(active# U21(X1, X2) -> active# X1, active# isNatIListKind take(V1, V2) -> isNatIListKind# V2)
(active# U21(X1, X2) -> active# X1, active# isNatIListKind take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U21(X1, X2) -> active# X1, active# isNatIListKind cons(V1, V2) -> isNatKind# V1)
(active# U21(X1, X2) -> active# X1, active# isNatIListKind cons(V1, V2) -> isNatIListKind# V2)
(active# U21(X1, X2) -> active# X1, active# isNatIListKind cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U21(X1, X2) -> active# X1, active# and(X1, X2) -> and#(active X1, X2))
(active# U21(X1, X2) -> active# X1, active# and(X1, X2) -> active# X1)
(active# U21(X1, X2) -> active# X1, active# U91(tt(), IL, M, N) -> take#(M, IL))
(active# U21(X1, X2) -> active# X1, active# U91(tt(), IL, M, N) -> cons#(N, take(M, IL)))
(active# U21(X1, X2) -> active# X1, active# U91(X1, X2, X3, X4) -> U91#(active X1, X2, X3, X4))
(active# U21(X1, X2) -> active# X1, active# U91(X1, X2, X3, X4) -> active# X1)
(active# U21(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatKind# M)
(active# U21(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatKind# N)
(active# U21(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIListKind# IL)
(active# U21(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))))
(active# U21(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(and(isNat M, isNatKind M), and(isNat N, isNatKind N)))
(active# U21(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, isNatIListKind IL))
(active# U21(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat M, isNatKind M))
(active# U21(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat N, isNatKind N))
(active# U21(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> U91#(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N))
(active# U21(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIList# IL)
(active# U21(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# M)
(active# U21(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# N)
(active# U21(X1, X2) -> active# X1, active# take(0(), IL) -> isNatIListKind# IL)
(active# U21(X1, X2) -> active# X1, active# take(0(), IL) -> and#(isNatIList IL, isNatIListKind IL))
(active# U21(X1, X2) -> active# X1, active# take(0(), IL) -> U81# and(isNatIList IL, isNatIListKind IL))
(active# U21(X1, X2) -> active# X1, active# take(0(), IL) -> isNatIList# IL)
(active# U21(X1, X2) -> active# X1, active# take(X1, X2) -> take#(active X1, X2))
(active# U21(X1, X2) -> active# X1, active# take(X1, X2) -> take#(X1, active X2))
(active# U21(X1, X2) -> active# X1, active# take(X1, X2) -> active# X2)
(active# U21(X1, X2) -> active# X1, active# take(X1, X2) -> active# X1)
(active# U21(X1, X2) -> active# X1, active# U81 X -> U81# active X)
(active# U21(X1, X2) -> active# X1, active# U81 X -> active# X)
(active# U21(X1, X2) -> active# X1, active# U71(tt(), L) -> length# L)
(active# U21(X1, X2) -> active# X1, active# U71(tt(), L) -> s# length L)
(active# U21(X1, X2) -> active# X1, active# U71(X1, X2) -> U71#(active X1, X2))
(active# U21(X1, X2) -> active# X1, active# U71(X1, X2) -> active# X1)
(active# U21(X1, X2) -> active# X1, active# length cons(N, L) -> isNatKind# N)
(active# U21(X1, X2) -> active# X1, active# length cons(N, L) -> isNatIListKind# L)
(active# U21(X1, X2) -> active# X1, active# length cons(N, L) -> and#(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)))
(active# U21(X1, X2) -> active# X1, active# length cons(N, L) -> and#(isNat N, isNatKind N))
(active# U21(X1, X2) -> active# X1, active# length cons(N, L) -> and#(isNatList L, isNatIListKind L))
(active# U21(X1, X2) -> active# X1, active# length cons(N, L) -> U71#(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L))
(active# U21(X1, X2) -> active# X1, active# length cons(N, L) -> isNat# N)
(active# U21(X1, X2) -> active# X1, active# length cons(N, L) -> isNatList# L)
(active# U21(X1, X2) -> active# X1, active# length X -> length# active X)
(active# U21(X1, X2) -> active# X1, active# length X -> active# X)
(active# U21(X1, X2) -> active# X1, active# s X -> s# active X)
(active# U21(X1, X2) -> active# X1, active# s X -> active# X)
(active# U21(X1, X2) -> active# X1, active# U63 X -> U63# active X)
(active# U21(X1, X2) -> active# X1, active# U63 X -> active# X)
(active# U21(X1, X2) -> active# X1, active# U61(tt(), V1, V2) -> U62#(isNat V1, V2))
(active# U21(X1, X2) -> active# X1, active# U61(tt(), V1, V2) -> isNat# V1)
(active# U21(X1, X2) -> active# X1, active# U61(X1, X2, X3) -> U61#(active X1, X2, X3))
(active# U21(X1, X2) -> active# X1, active# U61(X1, X2, X3) -> active# X1)
(active# U21(X1, X2) -> active# X1, active# U62(tt(), V2) -> U63# isNatIList V2)
(active# U21(X1, X2) -> active# X1, active# U62(tt(), V2) -> isNatIList# V2)
(active# U21(X1, X2) -> active# X1, active# U62(X1, X2) -> U62#(active X1, X2))
(active# U21(X1, X2) -> active# X1, active# U62(X1, X2) -> active# X1)
(active# U21(X1, X2) -> active# X1, active# U53 X -> U53# active X)
(active# U21(X1, X2) -> active# X1, active# U53 X -> active# X)
(active# U21(X1, X2) -> active# X1, active# U51(tt(), V1, V2) -> U52#(isNat V1, V2))
(active# U21(X1, X2) -> active# X1, active# U51(tt(), V1, V2) -> isNat# V1)
(active# U21(X1, X2) -> active# X1, active# U51(X1, X2, X3) -> U51#(active X1, X2, X3))
(active# U21(X1, X2) -> active# X1, active# U51(X1, X2, X3) -> active# X1)
(active# U21(X1, X2) -> active# X1, active# U52(tt(), V2) -> U53# isNatList V2)
(active# U21(X1, X2) -> active# X1, active# U52(tt(), V2) -> isNatList# V2)
(active# U21(X1, X2) -> active# X1, active# U52(X1, X2) -> U52#(active X1, X2))
(active# U21(X1, X2) -> active# X1, active# U52(X1, X2) -> active# X1)
(active# U21(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNatKind# V1)
(active# U21(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNatIListKind# V2)
(active# U21(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U21(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> U41#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U21(X1, X2) -> active# X1, active# isNatIList V -> isNatIListKind# V)
(active# U21(X1, X2) -> active# X1, active# isNatIList V -> U31#(isNatIListKind V, V))
(active# U21(X1, X2) -> active# X1, active# U43 X -> U43# active X)
(active# U21(X1, X2) -> active# X1, active# U43 X -> active# X)
(active# U21(X1, X2) -> active# X1, active# U41(tt(), V1, V2) -> U42#(isNat V1, V2))
(active# U21(X1, X2) -> active# X1, active# U41(tt(), V1, V2) -> isNat# V1)
(active# U21(X1, X2) -> active# X1, active# U41(X1, X2, X3) -> U41#(active X1, X2, X3))
(active# U21(X1, X2) -> active# X1, active# U41(X1, X2, X3) -> active# X1)
(active# U21(X1, X2) -> active# X1, active# U42(tt(), V2) -> isNatIList# V2)
(active# U21(X1, X2) -> active# X1, active# U42(tt(), V2) -> U43# isNatIList V2)
(active# U21(X1, X2) -> active# X1, active# U42(X1, X2) -> U42#(active X1, X2))
(active# U21(X1, X2) -> active# X1, active# U42(X1, X2) -> active# X1)
(active# U21(X1, X2) -> active# X1, active# U31(tt(), V) -> U32# isNatList V)
(active# U21(X1, X2) -> active# X1, active# U31(tt(), V) -> isNatList# V)
(active# U21(X1, X2) -> active# X1, active# U31(X1, X2) -> U31#(active X1, X2))
(active# U21(X1, X2) -> active# X1, active# U31(X1, X2) -> active# X1)
(active# U21(X1, X2) -> active# X1, active# U32 X -> U32# active X)
(active# U21(X1, X2) -> active# X1, active# U32 X -> active# X)
(active# U21(X1, X2) -> active# X1, active# U21(tt(), V1) -> isNat# V1)
(active# U21(X1, X2) -> active# X1, active# U21(tt(), V1) -> U22# isNat V1)
(active# U21(X1, X2) -> active# X1, active# U21(X1, X2) -> U21#(active X1, X2))
(active# U21(X1, X2) -> active# X1, active# U21(X1, X2) -> active# X1)
(active# U21(X1, X2) -> active# X1, active# isNat length V1 -> isNatIListKind# V1)
(active# U21(X1, X2) -> active# X1, active# isNat length V1 -> U11#(isNatIListKind V1, V1))
(active# U21(X1, X2) -> active# X1, active# isNat s V1 -> isNatKind# V1)
(active# U21(X1, X2) -> active# X1, active# isNat s V1 -> U21#(isNatKind V1, V1))
(active# U21(X1, X2) -> active# X1, active# U22 X -> U22# active X)
(active# U21(X1, X2) -> active# X1, active# U22 X -> active# X)
(active# U21(X1, X2) -> active# X1, active# U11(tt(), V1) -> isNatList# V1)
(active# U21(X1, X2) -> active# X1, active# U11(tt(), V1) -> U12# isNatList V1)
(active# U21(X1, X2) -> active# X1, active# U11(X1, X2) -> U11#(active X1, X2))
(active# U21(X1, X2) -> active# X1, active# U11(X1, X2) -> active# X1)
(active# U21(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> isNatKind# V1)
(active# U21(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> isNatIListKind# V2)
(active# U21(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U21(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> U61#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U21(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> isNatKind# V1)
(active# U21(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> isNatIListKind# V2)
(active# U21(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U21(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> U51#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U21(X1, X2) -> active# X1, active# U12 X -> U12# active X)
(active# U21(X1, X2) -> active# X1, active# U12 X -> active# X)
(active# U21(X1, X2) -> active# X1, active# zeros() -> cons#(0(), zeros()))
(active# U21(X1, X2) -> active# X1, active# cons(X1, X2) -> active# X1)
(active# U21(X1, X2) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2))
(active# U31(X1, X2) -> active# X1, active# isNatKind length V1 -> isNatIListKind# V1)
(active# U31(X1, X2) -> active# X1, active# isNatKind s V1 -> isNatKind# V1)
(active# U31(X1, X2) -> active# X1, active# isNatIListKind take(V1, V2) -> isNatKind# V1)
(active# U31(X1, X2) -> active# X1, active# isNatIListKind take(V1, V2) -> isNatIListKind# V2)
(active# U31(X1, X2) -> active# X1, active# isNatIListKind take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U31(X1, X2) -> active# X1, active# isNatIListKind cons(V1, V2) -> isNatKind# V1)
(active# U31(X1, X2) -> active# X1, active# isNatIListKind cons(V1, V2) -> isNatIListKind# V2)
(active# U31(X1, X2) -> active# X1, active# isNatIListKind cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U31(X1, X2) -> active# X1, active# and(X1, X2) -> and#(active X1, X2))
(active# U31(X1, X2) -> active# X1, active# and(X1, X2) -> active# X1)
(active# U31(X1, X2) -> active# X1, active# U91(tt(), IL, M, N) -> take#(M, IL))
(active# U31(X1, X2) -> active# X1, active# U91(tt(), IL, M, N) -> cons#(N, take(M, IL)))
(active# U31(X1, X2) -> active# X1, active# U91(X1, X2, X3, X4) -> U91#(active X1, X2, X3, X4))
(active# U31(X1, X2) -> active# X1, active# U91(X1, X2, X3, X4) -> active# X1)
(active# U31(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatKind# M)
(active# U31(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatKind# N)
(active# U31(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIListKind# IL)
(active# U31(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))))
(active# U31(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(and(isNat M, isNatKind M), and(isNat N, isNatKind N)))
(active# U31(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, isNatIListKind IL))
(active# U31(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat M, isNatKind M))
(active# U31(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat N, isNatKind N))
(active# U31(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> U91#(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N))
(active# U31(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIList# IL)
(active# U31(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# M)
(active# U31(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# N)
(active# U31(X1, X2) -> active# X1, active# take(0(), IL) -> isNatIListKind# IL)
(active# U31(X1, X2) -> active# X1, active# take(0(), IL) -> and#(isNatIList IL, isNatIListKind IL))
(active# U31(X1, X2) -> active# X1, active# take(0(), IL) -> U81# and(isNatIList IL, isNatIListKind IL))
(active# U31(X1, X2) -> active# X1, active# take(0(), IL) -> isNatIList# IL)
(active# U31(X1, X2) -> active# X1, active# take(X1, X2) -> take#(active X1, X2))
(active# U31(X1, X2) -> active# X1, active# take(X1, X2) -> take#(X1, active X2))
(active# U31(X1, X2) -> active# X1, active# take(X1, X2) -> active# X2)
(active# U31(X1, X2) -> active# X1, active# take(X1, X2) -> active# X1)
(active# U31(X1, X2) -> active# X1, active# U81 X -> U81# active X)
(active# U31(X1, X2) -> active# X1, active# U81 X -> active# X)
(active# U31(X1, X2) -> active# X1, active# U71(tt(), L) -> length# L)
(active# U31(X1, X2) -> active# X1, active# U71(tt(), L) -> s# length L)
(active# U31(X1, X2) -> active# X1, active# U71(X1, X2) -> U71#(active X1, X2))
(active# U31(X1, X2) -> active# X1, active# U71(X1, X2) -> active# X1)
(active# U31(X1, X2) -> active# X1, active# length cons(N, L) -> isNatKind# N)
(active# U31(X1, X2) -> active# X1, active# length cons(N, L) -> isNatIListKind# L)
(active# U31(X1, X2) -> active# X1, active# length cons(N, L) -> and#(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)))
(active# U31(X1, X2) -> active# X1, active# length cons(N, L) -> and#(isNat N, isNatKind N))
(active# U31(X1, X2) -> active# X1, active# length cons(N, L) -> and#(isNatList L, isNatIListKind L))
(active# U31(X1, X2) -> active# X1, active# length cons(N, L) -> U71#(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L))
(active# U31(X1, X2) -> active# X1, active# length cons(N, L) -> isNat# N)
(active# U31(X1, X2) -> active# X1, active# length cons(N, L) -> isNatList# L)
(active# U31(X1, X2) -> active# X1, active# length X -> length# active X)
(active# U31(X1, X2) -> active# X1, active# length X -> active# X)
(active# U31(X1, X2) -> active# X1, active# s X -> s# active X)
(active# U31(X1, X2) -> active# X1, active# s X -> active# X)
(active# U31(X1, X2) -> active# X1, active# U63 X -> U63# active X)
(active# U31(X1, X2) -> active# X1, active# U63 X -> active# X)
(active# U31(X1, X2) -> active# X1, active# U61(tt(), V1, V2) -> U62#(isNat V1, V2))
(active# U31(X1, X2) -> active# X1, active# U61(tt(), V1, V2) -> isNat# V1)
(active# U31(X1, X2) -> active# X1, active# U61(X1, X2, X3) -> U61#(active X1, X2, X3))
(active# U31(X1, X2) -> active# X1, active# U61(X1, X2, X3) -> active# X1)
(active# U31(X1, X2) -> active# X1, active# U62(tt(), V2) -> U63# isNatIList V2)
(active# U31(X1, X2) -> active# X1, active# U62(tt(), V2) -> isNatIList# V2)
(active# U31(X1, X2) -> active# X1, active# U62(X1, X2) -> U62#(active X1, X2))
(active# U31(X1, X2) -> active# X1, active# U62(X1, X2) -> active# X1)
(active# U31(X1, X2) -> active# X1, active# U53 X -> U53# active X)
(active# U31(X1, X2) -> active# X1, active# U53 X -> active# X)
(active# U31(X1, X2) -> active# X1, active# U51(tt(), V1, V2) -> U52#(isNat V1, V2))
(active# U31(X1, X2) -> active# X1, active# U51(tt(), V1, V2) -> isNat# V1)
(active# U31(X1, X2) -> active# X1, active# U51(X1, X2, X3) -> U51#(active X1, X2, X3))
(active# U31(X1, X2) -> active# X1, active# U51(X1, X2, X3) -> active# X1)
(active# U31(X1, X2) -> active# X1, active# U52(tt(), V2) -> U53# isNatList V2)
(active# U31(X1, X2) -> active# X1, active# U52(tt(), V2) -> isNatList# V2)
(active# U31(X1, X2) -> active# X1, active# U52(X1, X2) -> U52#(active X1, X2))
(active# U31(X1, X2) -> active# X1, active# U52(X1, X2) -> active# X1)
(active# U31(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNatKind# V1)
(active# U31(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNatIListKind# V2)
(active# U31(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U31(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> U41#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U31(X1, X2) -> active# X1, active# isNatIList V -> isNatIListKind# V)
(active# U31(X1, X2) -> active# X1, active# isNatIList V -> U31#(isNatIListKind V, V))
(active# U31(X1, X2) -> active# X1, active# U43 X -> U43# active X)
(active# U31(X1, X2) -> active# X1, active# U43 X -> active# X)
(active# U31(X1, X2) -> active# X1, active# U41(tt(), V1, V2) -> U42#(isNat V1, V2))
(active# U31(X1, X2) -> active# X1, active# U41(tt(), V1, V2) -> isNat# V1)
(active# U31(X1, X2) -> active# X1, active# U41(X1, X2, X3) -> U41#(active X1, X2, X3))
(active# U31(X1, X2) -> active# X1, active# U41(X1, X2, X3) -> active# X1)
(active# U31(X1, X2) -> active# X1, active# U42(tt(), V2) -> isNatIList# V2)
(active# U31(X1, X2) -> active# X1, active# U42(tt(), V2) -> U43# isNatIList V2)
(active# U31(X1, X2) -> active# X1, active# U42(X1, X2) -> U42#(active X1, X2))
(active# U31(X1, X2) -> active# X1, active# U42(X1, X2) -> active# X1)
(active# U31(X1, X2) -> active# X1, active# U31(tt(), V) -> U32# isNatList V)
(active# U31(X1, X2) -> active# X1, active# U31(tt(), V) -> isNatList# V)
(active# U31(X1, X2) -> active# X1, active# U31(X1, X2) -> U31#(active X1, X2))
(active# U31(X1, X2) -> active# X1, active# U31(X1, X2) -> active# X1)
(active# U31(X1, X2) -> active# X1, active# U32 X -> U32# active X)
(active# U31(X1, X2) -> active# X1, active# U32 X -> active# X)
(active# U31(X1, X2) -> active# X1, active# U21(tt(), V1) -> isNat# V1)
(active# U31(X1, X2) -> active# X1, active# U21(tt(), V1) -> U22# isNat V1)
(active# U31(X1, X2) -> active# X1, active# U21(X1, X2) -> U21#(active X1, X2))
(active# U31(X1, X2) -> active# X1, active# U21(X1, X2) -> active# X1)
(active# U31(X1, X2) -> active# X1, active# isNat length V1 -> isNatIListKind# V1)
(active# U31(X1, X2) -> active# X1, active# isNat length V1 -> U11#(isNatIListKind V1, V1))
(active# U31(X1, X2) -> active# X1, active# isNat s V1 -> isNatKind# V1)
(active# U31(X1, X2) -> active# X1, active# isNat s V1 -> U21#(isNatKind V1, V1))
(active# U31(X1, X2) -> active# X1, active# U22 X -> U22# active X)
(active# U31(X1, X2) -> active# X1, active# U22 X -> active# X)
(active# U31(X1, X2) -> active# X1, active# U11(tt(), V1) -> isNatList# V1)
(active# U31(X1, X2) -> active# X1, active# U11(tt(), V1) -> U12# isNatList V1)
(active# U31(X1, X2) -> active# X1, active# U11(X1, X2) -> U11#(active X1, X2))
(active# U31(X1, X2) -> active# X1, active# U11(X1, X2) -> active# X1)
(active# U31(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> isNatKind# V1)
(active# U31(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> isNatIListKind# V2)
(active# U31(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U31(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> U61#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U31(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> isNatKind# V1)
(active# U31(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> isNatIListKind# V2)
(active# U31(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U31(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> U51#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U31(X1, X2) -> active# X1, active# U12 X -> U12# active X)
(active# U31(X1, X2) -> active# X1, active# U12 X -> active# X)
(active# U31(X1, X2) -> active# X1, active# zeros() -> cons#(0(), zeros()))
(active# U31(X1, X2) -> active# X1, active# cons(X1, X2) -> active# X1)
(active# U31(X1, X2) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2))
(active# U42(X1, X2) -> active# X1, active# isNatKind length V1 -> isNatIListKind# V1)
(active# U42(X1, X2) -> active# X1, active# isNatKind s V1 -> isNatKind# V1)
(active# U42(X1, X2) -> active# X1, active# isNatIListKind take(V1, V2) -> isNatKind# V1)
(active# U42(X1, X2) -> active# X1, active# isNatIListKind take(V1, V2) -> isNatIListKind# V2)
(active# U42(X1, X2) -> active# X1, active# isNatIListKind take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U42(X1, X2) -> active# X1, active# isNatIListKind cons(V1, V2) -> isNatKind# V1)
(active# U42(X1, X2) -> active# X1, active# isNatIListKind cons(V1, V2) -> isNatIListKind# V2)
(active# U42(X1, X2) -> active# X1, active# isNatIListKind cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U42(X1, X2) -> active# X1, active# and(X1, X2) -> and#(active X1, X2))
(active# U42(X1, X2) -> active# X1, active# and(X1, X2) -> active# X1)
(active# U42(X1, X2) -> active# X1, active# U91(tt(), IL, M, N) -> take#(M, IL))
(active# U42(X1, X2) -> active# X1, active# U91(tt(), IL, M, N) -> cons#(N, take(M, IL)))
(active# U42(X1, X2) -> active# X1, active# U91(X1, X2, X3, X4) -> U91#(active X1, X2, X3, X4))
(active# U42(X1, X2) -> active# X1, active# U91(X1, X2, X3, X4) -> active# X1)
(active# U42(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatKind# M)
(active# U42(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatKind# N)
(active# U42(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIListKind# IL)
(active# U42(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))))
(active# U42(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(and(isNat M, isNatKind M), and(isNat N, isNatKind N)))
(active# U42(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, isNatIListKind IL))
(active# U42(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat M, isNatKind M))
(active# U42(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat N, isNatKind N))
(active# U42(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> U91#(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N))
(active# U42(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIList# IL)
(active# U42(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# M)
(active# U42(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# N)
(active# U42(X1, X2) -> active# X1, active# take(0(), IL) -> isNatIListKind# IL)
(active# U42(X1, X2) -> active# X1, active# take(0(), IL) -> and#(isNatIList IL, isNatIListKind IL))
(active# U42(X1, X2) -> active# X1, active# take(0(), IL) -> U81# and(isNatIList IL, isNatIListKind IL))
(active# U42(X1, X2) -> active# X1, active# take(0(), IL) -> isNatIList# IL)
(active# U42(X1, X2) -> active# X1, active# take(X1, X2) -> take#(active X1, X2))
(active# U42(X1, X2) -> active# X1, active# take(X1, X2) -> take#(X1, active X2))
(active# U42(X1, X2) -> active# X1, active# take(X1, X2) -> active# X2)
(active# U42(X1, X2) -> active# X1, active# take(X1, X2) -> active# X1)
(active# U42(X1, X2) -> active# X1, active# U81 X -> U81# active X)
(active# U42(X1, X2) -> active# X1, active# U81 X -> active# X)
(active# U42(X1, X2) -> active# X1, active# U71(tt(), L) -> length# L)
(active# U42(X1, X2) -> active# X1, active# U71(tt(), L) -> s# length L)
(active# U42(X1, X2) -> active# X1, active# U71(X1, X2) -> U71#(active X1, X2))
(active# U42(X1, X2) -> active# X1, active# U71(X1, X2) -> active# X1)
(active# U42(X1, X2) -> active# X1, active# length cons(N, L) -> isNatKind# N)
(active# U42(X1, X2) -> active# X1, active# length cons(N, L) -> isNatIListKind# L)
(active# U42(X1, X2) -> active# X1, active# length cons(N, L) -> and#(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)))
(active# U42(X1, X2) -> active# X1, active# length cons(N, L) -> and#(isNat N, isNatKind N))
(active# U42(X1, X2) -> active# X1, active# length cons(N, L) -> and#(isNatList L, isNatIListKind L))
(active# U42(X1, X2) -> active# X1, active# length cons(N, L) -> U71#(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L))
(active# U42(X1, X2) -> active# X1, active# length cons(N, L) -> isNat# N)
(active# U42(X1, X2) -> active# X1, active# length cons(N, L) -> isNatList# L)
(active# U42(X1, X2) -> active# X1, active# length X -> length# active X)
(active# U42(X1, X2) -> active# X1, active# length X -> active# X)
(active# U42(X1, X2) -> active# X1, active# s X -> s# active X)
(active# U42(X1, X2) -> active# X1, active# s X -> active# X)
(active# U42(X1, X2) -> active# X1, active# U63 X -> U63# active X)
(active# U42(X1, X2) -> active# X1, active# U63 X -> active# X)
(active# U42(X1, X2) -> active# X1, active# U61(tt(), V1, V2) -> U62#(isNat V1, V2))
(active# U42(X1, X2) -> active# X1, active# U61(tt(), V1, V2) -> isNat# V1)
(active# U42(X1, X2) -> active# X1, active# U61(X1, X2, X3) -> U61#(active X1, X2, X3))
(active# U42(X1, X2) -> active# X1, active# U61(X1, X2, X3) -> active# X1)
(active# U42(X1, X2) -> active# X1, active# U62(tt(), V2) -> U63# isNatIList V2)
(active# U42(X1, X2) -> active# X1, active# U62(tt(), V2) -> isNatIList# V2)
(active# U42(X1, X2) -> active# X1, active# U62(X1, X2) -> U62#(active X1, X2))
(active# U42(X1, X2) -> active# X1, active# U62(X1, X2) -> active# X1)
(active# U42(X1, X2) -> active# X1, active# U53 X -> U53# active X)
(active# U42(X1, X2) -> active# X1, active# U53 X -> active# X)
(active# U42(X1, X2) -> active# X1, active# U51(tt(), V1, V2) -> U52#(isNat V1, V2))
(active# U42(X1, X2) -> active# X1, active# U51(tt(), V1, V2) -> isNat# V1)
(active# U42(X1, X2) -> active# X1, active# U51(X1, X2, X3) -> U51#(active X1, X2, X3))
(active# U42(X1, X2) -> active# X1, active# U51(X1, X2, X3) -> active# X1)
(active# U42(X1, X2) -> active# X1, active# U52(tt(), V2) -> U53# isNatList V2)
(active# U42(X1, X2) -> active# X1, active# U52(tt(), V2) -> isNatList# V2)
(active# U42(X1, X2) -> active# X1, active# U52(X1, X2) -> U52#(active X1, X2))
(active# U42(X1, X2) -> active# X1, active# U52(X1, X2) -> active# X1)
(active# U42(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNatKind# V1)
(active# U42(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNatIListKind# V2)
(active# U42(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U42(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> U41#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U42(X1, X2) -> active# X1, active# isNatIList V -> isNatIListKind# V)
(active# U42(X1, X2) -> active# X1, active# isNatIList V -> U31#(isNatIListKind V, V))
(active# U42(X1, X2) -> active# X1, active# U43 X -> U43# active X)
(active# U42(X1, X2) -> active# X1, active# U43 X -> active# X)
(active# U42(X1, X2) -> active# X1, active# U41(tt(), V1, V2) -> U42#(isNat V1, V2))
(active# U42(X1, X2) -> active# X1, active# U41(tt(), V1, V2) -> isNat# V1)
(active# U42(X1, X2) -> active# X1, active# U41(X1, X2, X3) -> U41#(active X1, X2, X3))
(active# U42(X1, X2) -> active# X1, active# U41(X1, X2, X3) -> active# X1)
(active# U42(X1, X2) -> active# X1, active# U42(tt(), V2) -> isNatIList# V2)
(active# U42(X1, X2) -> active# X1, active# U42(tt(), V2) -> U43# isNatIList V2)
(active# U42(X1, X2) -> active# X1, active# U42(X1, X2) -> U42#(active X1, X2))
(active# U42(X1, X2) -> active# X1, active# U42(X1, X2) -> active# X1)
(active# U42(X1, X2) -> active# X1, active# U31(tt(), V) -> U32# isNatList V)
(active# U42(X1, X2) -> active# X1, active# U31(tt(), V) -> isNatList# V)
(active# U42(X1, X2) -> active# X1, active# U31(X1, X2) -> U31#(active X1, X2))
(active# U42(X1, X2) -> active# X1, active# U31(X1, X2) -> active# X1)
(active# U42(X1, X2) -> active# X1, active# U32 X -> U32# active X)
(active# U42(X1, X2) -> active# X1, active# U32 X -> active# X)
(active# U42(X1, X2) -> active# X1, active# U21(tt(), V1) -> isNat# V1)
(active# U42(X1, X2) -> active# X1, active# U21(tt(), V1) -> U22# isNat V1)
(active# U42(X1, X2) -> active# X1, active# U21(X1, X2) -> U21#(active X1, X2))
(active# U42(X1, X2) -> active# X1, active# U21(X1, X2) -> active# X1)
(active# U42(X1, X2) -> active# X1, active# isNat length V1 -> isNatIListKind# V1)
(active# U42(X1, X2) -> active# X1, active# isNat length V1 -> U11#(isNatIListKind V1, V1))
(active# U42(X1, X2) -> active# X1, active# isNat s V1 -> isNatKind# V1)
(active# U42(X1, X2) -> active# X1, active# isNat s V1 -> U21#(isNatKind V1, V1))
(active# U42(X1, X2) -> active# X1, active# U22 X -> U22# active X)
(active# U42(X1, X2) -> active# X1, active# U22 X -> active# X)
(active# U42(X1, X2) -> active# X1, active# U11(tt(), V1) -> isNatList# V1)
(active# U42(X1, X2) -> active# X1, active# U11(tt(), V1) -> U12# isNatList V1)
(active# U42(X1, X2) -> active# X1, active# U11(X1, X2) -> U11#(active X1, X2))
(active# U42(X1, X2) -> active# X1, active# U11(X1, X2) -> active# X1)
(active# U42(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> isNatKind# V1)
(active# U42(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> isNatIListKind# V2)
(active# U42(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U42(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> U61#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U42(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> isNatKind# V1)
(active# U42(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> isNatIListKind# V2)
(active# U42(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U42(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> U51#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U42(X1, X2) -> active# X1, active# U12 X -> U12# active X)
(active# U42(X1, X2) -> active# X1, active# U12 X -> active# X)
(active# U42(X1, X2) -> active# X1, active# zeros() -> cons#(0(), zeros()))
(active# U42(X1, X2) -> active# X1, active# cons(X1, X2) -> active# X1)
(active# U42(X1, X2) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2))
(active# U41(X1, X2, X3) -> active# X1, active# isNatKind length V1 -> isNatIListKind# V1)
(active# U41(X1, X2, X3) -> active# X1, active# isNatKind s V1 -> isNatKind# V1)
(active# U41(X1, X2, X3) -> active# X1, active# isNatIListKind take(V1, V2) -> isNatKind# V1)
(active# U41(X1, X2, X3) -> active# X1, active# isNatIListKind take(V1, V2) -> isNatIListKind# V2)
(active# U41(X1, X2, X3) -> active# X1, active# isNatIListKind take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U41(X1, X2, X3) -> active# X1, active# isNatIListKind cons(V1, V2) -> isNatKind# V1)
(active# U41(X1, X2, X3) -> active# X1, active# isNatIListKind cons(V1, V2) -> isNatIListKind# V2)
(active# U41(X1, X2, X3) -> active# X1, active# isNatIListKind cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U41(X1, X2, X3) -> active# X1, active# and(X1, X2) -> and#(active X1, X2))
(active# U41(X1, X2, X3) -> active# X1, active# and(X1, X2) -> active# X1)
(active# U41(X1, X2, X3) -> active# X1, active# U91(tt(), IL, M, N) -> take#(M, IL))
(active# U41(X1, X2, X3) -> active# X1, active# U91(tt(), IL, M, N) -> cons#(N, take(M, IL)))
(active# U41(X1, X2, X3) -> active# X1, active# U91(X1, X2, X3, X4) -> U91#(active X1, X2, X3, X4))
(active# U41(X1, X2, X3) -> active# X1, active# U91(X1, X2, X3, X4) -> active# X1)
(active# U41(X1, X2, X3) -> active# X1, active# take(s M, cons(N, IL)) -> isNatKind# M)
(active# U41(X1, X2, X3) -> active# X1, active# take(s M, cons(N, IL)) -> isNatKind# N)
(active# U41(X1, X2, X3) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIListKind# IL)
(active# U41(X1, X2, X3) -> active# X1, active# take(s M, cons(N, IL)) -> and#(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))))
(active# U41(X1, X2, X3) -> active# X1, active# take(s M, cons(N, IL)) -> and#(and(isNat M, isNatKind M), and(isNat N, isNatKind N)))
(active# U41(X1, X2, X3) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, isNatIListKind IL))
(active# U41(X1, X2, X3) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat M, isNatKind M))
(active# U41(X1, X2, X3) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat N, isNatKind N))
(active# U41(X1, X2, X3) -> active# X1, active# take(s M, cons(N, IL)) -> U91#(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N))
(active# U41(X1, X2, X3) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIList# IL)
(active# U41(X1, X2, X3) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# M)
(active# U41(X1, X2, X3) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# N)
(active# U41(X1, X2, X3) -> active# X1, active# take(0(), IL) -> isNatIListKind# IL)
(active# U41(X1, X2, X3) -> active# X1, active# take(0(), IL) -> and#(isNatIList IL, isNatIListKind IL))
(active# U41(X1, X2, X3) -> active# X1, active# take(0(), IL) -> U81# and(isNatIList IL, isNatIListKind IL))
(active# U41(X1, X2, X3) -> active# X1, active# take(0(), IL) -> isNatIList# IL)
(active# U41(X1, X2, X3) -> active# X1, active# take(X1, X2) -> take#(active X1, X2))
(active# U41(X1, X2, X3) -> active# X1, active# take(X1, X2) -> take#(X1, active X2))
(active# U41(X1, X2, X3) -> active# X1, active# take(X1, X2) -> active# X2)
(active# U41(X1, X2, X3) -> active# X1, active# take(X1, X2) -> active# X1)
(active# U41(X1, X2, X3) -> active# X1, active# U81 X -> U81# active X)
(active# U41(X1, X2, X3) -> active# X1, active# U81 X -> active# X)
(active# U41(X1, X2, X3) -> active# X1, active# U71(tt(), L) -> length# L)
(active# U41(X1, X2, X3) -> active# X1, active# U71(tt(), L) -> s# length L)
(active# U41(X1, X2, X3) -> active# X1, active# U71(X1, X2) -> U71#(active X1, X2))
(active# U41(X1, X2, X3) -> active# X1, active# U71(X1, X2) -> active# X1)
(active# U41(X1, X2, X3) -> active# X1, active# length cons(N, L) -> isNatKind# N)
(active# U41(X1, X2, X3) -> active# X1, active# length cons(N, L) -> isNatIListKind# L)
(active# U41(X1, X2, X3) -> active# X1, active# length cons(N, L) -> and#(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)))
(active# U41(X1, X2, X3) -> active# X1, active# length cons(N, L) -> and#(isNat N, isNatKind N))
(active# U41(X1, X2, X3) -> active# X1, active# length cons(N, L) -> and#(isNatList L, isNatIListKind L))
(active# U41(X1, X2, X3) -> active# X1, active# length cons(N, L) -> U71#(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L))
(active# U41(X1, X2, X3) -> active# X1, active# length cons(N, L) -> isNat# N)
(active# U41(X1, X2, X3) -> active# X1, active# length cons(N, L) -> isNatList# L)
(active# U41(X1, X2, X3) -> active# X1, active# length X -> length# active X)
(active# U41(X1, X2, X3) -> active# X1, active# length X -> active# X)
(active# U41(X1, X2, X3) -> active# X1, active# s X -> s# active X)
(active# U41(X1, X2, X3) -> active# X1, active# s X -> active# X)
(active# U41(X1, X2, X3) -> active# X1, active# U63 X -> U63# active X)
(active# U41(X1, X2, X3) -> active# X1, active# U63 X -> active# X)
(active# U41(X1, X2, X3) -> active# X1, active# U61(tt(), V1, V2) -> U62#(isNat V1, V2))
(active# U41(X1, X2, X3) -> active# X1, active# U61(tt(), V1, V2) -> isNat# V1)
(active# U41(X1, X2, X3) -> active# X1, active# U61(X1, X2, X3) -> U61#(active X1, X2, X3))
(active# U41(X1, X2, X3) -> active# X1, active# U61(X1, X2, X3) -> active# X1)
(active# U41(X1, X2, X3) -> active# X1, active# U62(tt(), V2) -> U63# isNatIList V2)
(active# U41(X1, X2, X3) -> active# X1, active# U62(tt(), V2) -> isNatIList# V2)
(active# U41(X1, X2, X3) -> active# X1, active# U62(X1, X2) -> U62#(active X1, X2))
(active# U41(X1, X2, X3) -> active# X1, active# U62(X1, X2) -> active# X1)
(active# U41(X1, X2, X3) -> active# X1, active# U53 X -> U53# active X)
(active# U41(X1, X2, X3) -> active# X1, active# U53 X -> active# X)
(active# U41(X1, X2, X3) -> active# X1, active# U51(tt(), V1, V2) -> U52#(isNat V1, V2))
(active# U41(X1, X2, X3) -> active# X1, active# U51(tt(), V1, V2) -> isNat# V1)
(active# U41(X1, X2, X3) -> active# X1, active# U51(X1, X2, X3) -> U51#(active X1, X2, X3))
(active# U41(X1, X2, X3) -> active# X1, active# U51(X1, X2, X3) -> active# X1)
(active# U41(X1, X2, X3) -> active# X1, active# U52(tt(), V2) -> U53# isNatList V2)
(active# U41(X1, X2, X3) -> active# X1, active# U52(tt(), V2) -> isNatList# V2)
(active# U41(X1, X2, X3) -> active# X1, active# U52(X1, X2) -> U52#(active X1, X2))
(active# U41(X1, X2, X3) -> active# X1, active# U52(X1, X2) -> active# X1)
(active# U41(X1, X2, X3) -> active# X1, active# isNatIList cons(V1, V2) -> isNatKind# V1)
(active# U41(X1, X2, X3) -> active# X1, active# isNatIList cons(V1, V2) -> isNatIListKind# V2)
(active# U41(X1, X2, X3) -> active# X1, active# isNatIList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U41(X1, X2, X3) -> active# X1, active# isNatIList cons(V1, V2) -> U41#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U41(X1, X2, X3) -> active# X1, active# isNatIList V -> isNatIListKind# V)
(active# U41(X1, X2, X3) -> active# X1, active# isNatIList V -> U31#(isNatIListKind V, V))
(active# U41(X1, X2, X3) -> active# X1, active# U43 X -> U43# active X)
(active# U41(X1, X2, X3) -> active# X1, active# U43 X -> active# X)
(active# U41(X1, X2, X3) -> active# X1, active# U41(tt(), V1, V2) -> U42#(isNat V1, V2))
(active# U41(X1, X2, X3) -> active# X1, active# U41(tt(), V1, V2) -> isNat# V1)
(active# U41(X1, X2, X3) -> active# X1, active# U41(X1, X2, X3) -> U41#(active X1, X2, X3))
(active# U41(X1, X2, X3) -> active# X1, active# U41(X1, X2, X3) -> active# X1)
(active# U41(X1, X2, X3) -> active# X1, active# U42(tt(), V2) -> isNatIList# V2)
(active# U41(X1, X2, X3) -> active# X1, active# U42(tt(), V2) -> U43# isNatIList V2)
(active# U41(X1, X2, X3) -> active# X1, active# U42(X1, X2) -> U42#(active X1, X2))
(active# U41(X1, X2, X3) -> active# X1, active# U42(X1, X2) -> active# X1)
(active# U41(X1, X2, X3) -> active# X1, active# U31(tt(), V) -> U32# isNatList V)
(active# U41(X1, X2, X3) -> active# X1, active# U31(tt(), V) -> isNatList# V)
(active# U41(X1, X2, X3) -> active# X1, active# U31(X1, X2) -> U31#(active X1, X2))
(active# U41(X1, X2, X3) -> active# X1, active# U31(X1, X2) -> active# X1)
(active# U41(X1, X2, X3) -> active# X1, active# U32 X -> U32# active X)
(active# U41(X1, X2, X3) -> active# X1, active# U32 X -> active# X)
(active# U41(X1, X2, X3) -> active# X1, active# U21(tt(), V1) -> isNat# V1)
(active# U41(X1, X2, X3) -> active# X1, active# U21(tt(), V1) -> U22# isNat V1)
(active# U41(X1, X2, X3) -> active# X1, active# U21(X1, X2) -> U21#(active X1, X2))
(active# U41(X1, X2, X3) -> active# X1, active# U21(X1, X2) -> active# X1)
(active# U41(X1, X2, X3) -> active# X1, active# isNat length V1 -> isNatIListKind# V1)
(active# U41(X1, X2, X3) -> active# X1, active# isNat length V1 -> U11#(isNatIListKind V1, V1))
(active# U41(X1, X2, X3) -> active# X1, active# isNat s V1 -> isNatKind# V1)
(active# U41(X1, X2, X3) -> active# X1, active# isNat s V1 -> U21#(isNatKind V1, V1))
(active# U41(X1, X2, X3) -> active# X1, active# U22 X -> U22# active X)
(active# U41(X1, X2, X3) -> active# X1, active# U22 X -> active# X)
(active# U41(X1, X2, X3) -> active# X1, active# U11(tt(), V1) -> isNatList# V1)
(active# U41(X1, X2, X3) -> active# X1, active# U11(tt(), V1) -> U12# isNatList V1)
(active# U41(X1, X2, X3) -> active# X1, active# U11(X1, X2) -> U11#(active X1, X2))
(active# U41(X1, X2, X3) -> active# X1, active# U11(X1, X2) -> active# X1)
(active# U41(X1, X2, X3) -> active# X1, active# isNatList take(V1, V2) -> isNatKind# V1)
(active# U41(X1, X2, X3) -> active# X1, active# isNatList take(V1, V2) -> isNatIListKind# V2)
(active# U41(X1, X2, X3) -> active# X1, active# isNatList take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U41(X1, X2, X3) -> active# X1, active# isNatList take(V1, V2) -> U61#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U41(X1, X2, X3) -> active# X1, active# isNatList cons(V1, V2) -> isNatKind# V1)
(active# U41(X1, X2, X3) -> active# X1, active# isNatList cons(V1, V2) -> isNatIListKind# V2)
(active# U41(X1, X2, X3) -> active# X1, active# isNatList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U41(X1, X2, X3) -> active# X1, active# isNatList cons(V1, V2) -> U51#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U41(X1, X2, X3) -> active# X1, active# U12 X -> U12# active X)
(active# U41(X1, X2, X3) -> active# X1, active# U12 X -> active# X)
(active# U41(X1, X2, X3) -> active# X1, active# zeros() -> cons#(0(), zeros()))
(active# U41(X1, X2, X3) -> active# X1, active# cons(X1, X2) -> active# X1)
(active# U41(X1, X2, X3) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2))
(active# U52(X1, X2) -> U52#(active X1, X2), U52#(ok X1, ok X2) -> U52#(X1, X2))
(active# U52(X1, X2) -> U52#(active X1, X2), U52#(mark X1, X2) -> U52#(X1, X2))
(active# U62(X1, X2) -> active# X1, active# isNatKind length V1 -> isNatIListKind# V1)
(active# U62(X1, X2) -> active# X1, active# isNatKind s V1 -> isNatKind# V1)
(active# U62(X1, X2) -> active# X1, active# isNatIListKind take(V1, V2) -> isNatKind# V1)
(active# U62(X1, X2) -> active# X1, active# isNatIListKind take(V1, V2) -> isNatIListKind# V2)
(active# U62(X1, X2) -> active# X1, active# isNatIListKind take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U62(X1, X2) -> active# X1, active# isNatIListKind cons(V1, V2) -> isNatKind# V1)
(active# U62(X1, X2) -> active# X1, active# isNatIListKind cons(V1, V2) -> isNatIListKind# V2)
(active# U62(X1, X2) -> active# X1, active# isNatIListKind cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U62(X1, X2) -> active# X1, active# and(X1, X2) -> and#(active X1, X2))
(active# U62(X1, X2) -> active# X1, active# and(X1, X2) -> active# X1)
(active# U62(X1, X2) -> active# X1, active# U91(tt(), IL, M, N) -> take#(M, IL))
(active# U62(X1, X2) -> active# X1, active# U91(tt(), IL, M, N) -> cons#(N, take(M, IL)))
(active# U62(X1, X2) -> active# X1, active# U91(X1, X2, X3, X4) -> U91#(active X1, X2, X3, X4))
(active# U62(X1, X2) -> active# X1, active# U91(X1, X2, X3, X4) -> active# X1)
(active# U62(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatKind# M)
(active# U62(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatKind# N)
(active# U62(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIListKind# IL)
(active# U62(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))))
(active# U62(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(and(isNat M, isNatKind M), and(isNat N, isNatKind N)))
(active# U62(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, isNatIListKind IL))
(active# U62(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat M, isNatKind M))
(active# U62(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat N, isNatKind N))
(active# U62(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> U91#(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N))
(active# U62(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIList# IL)
(active# U62(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# M)
(active# U62(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# N)
(active# U62(X1, X2) -> active# X1, active# take(0(), IL) -> isNatIListKind# IL)
(active# U62(X1, X2) -> active# X1, active# take(0(), IL) -> and#(isNatIList IL, isNatIListKind IL))
(active# U62(X1, X2) -> active# X1, active# take(0(), IL) -> U81# and(isNatIList IL, isNatIListKind IL))
(active# U62(X1, X2) -> active# X1, active# take(0(), IL) -> isNatIList# IL)
(active# U62(X1, X2) -> active# X1, active# take(X1, X2) -> take#(active X1, X2))
(active# U62(X1, X2) -> active# X1, active# take(X1, X2) -> take#(X1, active X2))
(active# U62(X1, X2) -> active# X1, active# take(X1, X2) -> active# X2)
(active# U62(X1, X2) -> active# X1, active# take(X1, X2) -> active# X1)
(active# U62(X1, X2) -> active# X1, active# U81 X -> U81# active X)
(active# U62(X1, X2) -> active# X1, active# U81 X -> active# X)
(active# U62(X1, X2) -> active# X1, active# U71(tt(), L) -> length# L)
(active# U62(X1, X2) -> active# X1, active# U71(tt(), L) -> s# length L)
(active# U62(X1, X2) -> active# X1, active# U71(X1, X2) -> U71#(active X1, X2))
(active# U62(X1, X2) -> active# X1, active# U71(X1, X2) -> active# X1)
(active# U62(X1, X2) -> active# X1, active# length cons(N, L) -> isNatKind# N)
(active# U62(X1, X2) -> active# X1, active# length cons(N, L) -> isNatIListKind# L)
(active# U62(X1, X2) -> active# X1, active# length cons(N, L) -> and#(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)))
(active# U62(X1, X2) -> active# X1, active# length cons(N, L) -> and#(isNat N, isNatKind N))
(active# U62(X1, X2) -> active# X1, active# length cons(N, L) -> and#(isNatList L, isNatIListKind L))
(active# U62(X1, X2) -> active# X1, active# length cons(N, L) -> U71#(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L))
(active# U62(X1, X2) -> active# X1, active# length cons(N, L) -> isNat# N)
(active# U62(X1, X2) -> active# X1, active# length cons(N, L) -> isNatList# L)
(active# U62(X1, X2) -> active# X1, active# length X -> length# active X)
(active# U62(X1, X2) -> active# X1, active# length X -> active# X)
(active# U62(X1, X2) -> active# X1, active# s X -> s# active X)
(active# U62(X1, X2) -> active# X1, active# s X -> active# X)
(active# U62(X1, X2) -> active# X1, active# U63 X -> U63# active X)
(active# U62(X1, X2) -> active# X1, active# U63 X -> active# X)
(active# U62(X1, X2) -> active# X1, active# U61(tt(), V1, V2) -> U62#(isNat V1, V2))
(active# U62(X1, X2) -> active# X1, active# U61(tt(), V1, V2) -> isNat# V1)
(active# U62(X1, X2) -> active# X1, active# U61(X1, X2, X3) -> U61#(active X1, X2, X3))
(active# U62(X1, X2) -> active# X1, active# U61(X1, X2, X3) -> active# X1)
(active# U62(X1, X2) -> active# X1, active# U62(tt(), V2) -> U63# isNatIList V2)
(active# U62(X1, X2) -> active# X1, active# U62(tt(), V2) -> isNatIList# V2)
(active# U62(X1, X2) -> active# X1, active# U62(X1, X2) -> U62#(active X1, X2))
(active# U62(X1, X2) -> active# X1, active# U62(X1, X2) -> active# X1)
(active# U62(X1, X2) -> active# X1, active# U53 X -> U53# active X)
(active# U62(X1, X2) -> active# X1, active# U53 X -> active# X)
(active# U62(X1, X2) -> active# X1, active# U51(tt(), V1, V2) -> U52#(isNat V1, V2))
(active# U62(X1, X2) -> active# X1, active# U51(tt(), V1, V2) -> isNat# V1)
(active# U62(X1, X2) -> active# X1, active# U51(X1, X2, X3) -> U51#(active X1, X2, X3))
(active# U62(X1, X2) -> active# X1, active# U51(X1, X2, X3) -> active# X1)
(active# U62(X1, X2) -> active# X1, active# U52(tt(), V2) -> U53# isNatList V2)
(active# U62(X1, X2) -> active# X1, active# U52(tt(), V2) -> isNatList# V2)
(active# U62(X1, X2) -> active# X1, active# U52(X1, X2) -> U52#(active X1, X2))
(active# U62(X1, X2) -> active# X1, active# U52(X1, X2) -> active# X1)
(active# U62(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNatKind# V1)
(active# U62(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNatIListKind# V2)
(active# U62(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U62(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> U41#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U62(X1, X2) -> active# X1, active# isNatIList V -> isNatIListKind# V)
(active# U62(X1, X2) -> active# X1, active# isNatIList V -> U31#(isNatIListKind V, V))
(active# U62(X1, X2) -> active# X1, active# U43 X -> U43# active X)
(active# U62(X1, X2) -> active# X1, active# U43 X -> active# X)
(active# U62(X1, X2) -> active# X1, active# U41(tt(), V1, V2) -> U42#(isNat V1, V2))
(active# U62(X1, X2) -> active# X1, active# U41(tt(), V1, V2) -> isNat# V1)
(active# U62(X1, X2) -> active# X1, active# U41(X1, X2, X3) -> U41#(active X1, X2, X3))
(active# U62(X1, X2) -> active# X1, active# U41(X1, X2, X3) -> active# X1)
(active# U62(X1, X2) -> active# X1, active# U42(tt(), V2) -> isNatIList# V2)
(active# U62(X1, X2) -> active# X1, active# U42(tt(), V2) -> U43# isNatIList V2)
(active# U62(X1, X2) -> active# X1, active# U42(X1, X2) -> U42#(active X1, X2))
(active# U62(X1, X2) -> active# X1, active# U42(X1, X2) -> active# X1)
(active# U62(X1, X2) -> active# X1, active# U31(tt(), V) -> U32# isNatList V)
(active# U62(X1, X2) -> active# X1, active# U31(tt(), V) -> isNatList# V)
(active# U62(X1, X2) -> active# X1, active# U31(X1, X2) -> U31#(active X1, X2))
(active# U62(X1, X2) -> active# X1, active# U31(X1, X2) -> active# X1)
(active# U62(X1, X2) -> active# X1, active# U32 X -> U32# active X)
(active# U62(X1, X2) -> active# X1, active# U32 X -> active# X)
(active# U62(X1, X2) -> active# X1, active# U21(tt(), V1) -> isNat# V1)
(active# U62(X1, X2) -> active# X1, active# U21(tt(), V1) -> U22# isNat V1)
(active# U62(X1, X2) -> active# X1, active# U21(X1, X2) -> U21#(active X1, X2))
(active# U62(X1, X2) -> active# X1, active# U21(X1, X2) -> active# X1)
(active# U62(X1, X2) -> active# X1, active# isNat length V1 -> isNatIListKind# V1)
(active# U62(X1, X2) -> active# X1, active# isNat length V1 -> U11#(isNatIListKind V1, V1))
(active# U62(X1, X2) -> active# X1, active# isNat s V1 -> isNatKind# V1)
(active# U62(X1, X2) -> active# X1, active# isNat s V1 -> U21#(isNatKind V1, V1))
(active# U62(X1, X2) -> active# X1, active# U22 X -> U22# active X)
(active# U62(X1, X2) -> active# X1, active# U22 X -> active# X)
(active# U62(X1, X2) -> active# X1, active# U11(tt(), V1) -> isNatList# V1)
(active# U62(X1, X2) -> active# X1, active# U11(tt(), V1) -> U12# isNatList V1)
(active# U62(X1, X2) -> active# X1, active# U11(X1, X2) -> U11#(active X1, X2))
(active# U62(X1, X2) -> active# X1, active# U11(X1, X2) -> active# X1)
(active# U62(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> isNatKind# V1)
(active# U62(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> isNatIListKind# V2)
(active# U62(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U62(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> U61#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U62(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> isNatKind# V1)
(active# U62(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> isNatIListKind# V2)
(active# U62(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U62(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> U51#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U62(X1, X2) -> active# X1, active# U12 X -> U12# active X)
(active# U62(X1, X2) -> active# X1, active# U12 X -> active# X)
(active# U62(X1, X2) -> active# X1, active# zeros() -> cons#(0(), zeros()))
(active# U62(X1, X2) -> active# X1, active# cons(X1, X2) -> active# X1)
(active# U62(X1, X2) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2))
(active# U61(X1, X2, X3) -> active# X1, active# isNatKind length V1 -> isNatIListKind# V1)
(active# U61(X1, X2, X3) -> active# X1, active# isNatKind s V1 -> isNatKind# V1)
(active# U61(X1, X2, X3) -> active# X1, active# isNatIListKind take(V1, V2) -> isNatKind# V1)
(active# U61(X1, X2, X3) -> active# X1, active# isNatIListKind take(V1, V2) -> isNatIListKind# V2)
(active# U61(X1, X2, X3) -> active# X1, active# isNatIListKind take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U61(X1, X2, X3) -> active# X1, active# isNatIListKind cons(V1, V2) -> isNatKind# V1)
(active# U61(X1, X2, X3) -> active# X1, active# isNatIListKind cons(V1, V2) -> isNatIListKind# V2)
(active# U61(X1, X2, X3) -> active# X1, active# isNatIListKind cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U61(X1, X2, X3) -> active# X1, active# and(X1, X2) -> and#(active X1, X2))
(active# U61(X1, X2, X3) -> active# X1, active# and(X1, X2) -> active# X1)
(active# U61(X1, X2, X3) -> active# X1, active# U91(tt(), IL, M, N) -> take#(M, IL))
(active# U61(X1, X2, X3) -> active# X1, active# U91(tt(), IL, M, N) -> cons#(N, take(M, IL)))
(active# U61(X1, X2, X3) -> active# X1, active# U91(X1, X2, X3, X4) -> U91#(active X1, X2, X3, X4))
(active# U61(X1, X2, X3) -> active# X1, active# U91(X1, X2, X3, X4) -> active# X1)
(active# U61(X1, X2, X3) -> active# X1, active# take(s M, cons(N, IL)) -> isNatKind# M)
(active# U61(X1, X2, X3) -> active# X1, active# take(s M, cons(N, IL)) -> isNatKind# N)
(active# U61(X1, X2, X3) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIListKind# IL)
(active# U61(X1, X2, X3) -> active# X1, active# take(s M, cons(N, IL)) -> and#(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))))
(active# U61(X1, X2, X3) -> active# X1, active# take(s M, cons(N, IL)) -> and#(and(isNat M, isNatKind M), and(isNat N, isNatKind N)))
(active# U61(X1, X2, X3) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, isNatIListKind IL))
(active# U61(X1, X2, X3) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat M, isNatKind M))
(active# U61(X1, X2, X3) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat N, isNatKind N))
(active# U61(X1, X2, X3) -> active# X1, active# take(s M, cons(N, IL)) -> U91#(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N))
(active# U61(X1, X2, X3) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIList# IL)
(active# U61(X1, X2, X3) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# M)
(active# U61(X1, X2, X3) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# N)
(active# U61(X1, X2, X3) -> active# X1, active# take(0(), IL) -> isNatIListKind# IL)
(active# U61(X1, X2, X3) -> active# X1, active# take(0(), IL) -> and#(isNatIList IL, isNatIListKind IL))
(active# U61(X1, X2, X3) -> active# X1, active# take(0(), IL) -> U81# and(isNatIList IL, isNatIListKind IL))
(active# U61(X1, X2, X3) -> active# X1, active# take(0(), IL) -> isNatIList# IL)
(active# U61(X1, X2, X3) -> active# X1, active# take(X1, X2) -> take#(active X1, X2))
(active# U61(X1, X2, X3) -> active# X1, active# take(X1, X2) -> take#(X1, active X2))
(active# U61(X1, X2, X3) -> active# X1, active# take(X1, X2) -> active# X2)
(active# U61(X1, X2, X3) -> active# X1, active# take(X1, X2) -> active# X1)
(active# U61(X1, X2, X3) -> active# X1, active# U81 X -> U81# active X)
(active# U61(X1, X2, X3) -> active# X1, active# U81 X -> active# X)
(active# U61(X1, X2, X3) -> active# X1, active# U71(tt(), L) -> length# L)
(active# U61(X1, X2, X3) -> active# X1, active# U71(tt(), L) -> s# length L)
(active# U61(X1, X2, X3) -> active# X1, active# U71(X1, X2) -> U71#(active X1, X2))
(active# U61(X1, X2, X3) -> active# X1, active# U71(X1, X2) -> active# X1)
(active# U61(X1, X2, X3) -> active# X1, active# length cons(N, L) -> isNatKind# N)
(active# U61(X1, X2, X3) -> active# X1, active# length cons(N, L) -> isNatIListKind# L)
(active# U61(X1, X2, X3) -> active# X1, active# length cons(N, L) -> and#(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)))
(active# U61(X1, X2, X3) -> active# X1, active# length cons(N, L) -> and#(isNat N, isNatKind N))
(active# U61(X1, X2, X3) -> active# X1, active# length cons(N, L) -> and#(isNatList L, isNatIListKind L))
(active# U61(X1, X2, X3) -> active# X1, active# length cons(N, L) -> U71#(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L))
(active# U61(X1, X2, X3) -> active# X1, active# length cons(N, L) -> isNat# N)
(active# U61(X1, X2, X3) -> active# X1, active# length cons(N, L) -> isNatList# L)
(active# U61(X1, X2, X3) -> active# X1, active# length X -> length# active X)
(active# U61(X1, X2, X3) -> active# X1, active# length X -> active# X)
(active# U61(X1, X2, X3) -> active# X1, active# s X -> s# active X)
(active# U61(X1, X2, X3) -> active# X1, active# s X -> active# X)
(active# U61(X1, X2, X3) -> active# X1, active# U63 X -> U63# active X)
(active# U61(X1, X2, X3) -> active# X1, active# U63 X -> active# X)
(active# U61(X1, X2, X3) -> active# X1, active# U61(tt(), V1, V2) -> U62#(isNat V1, V2))
(active# U61(X1, X2, X3) -> active# X1, active# U61(tt(), V1, V2) -> isNat# V1)
(active# U61(X1, X2, X3) -> active# X1, active# U61(X1, X2, X3) -> U61#(active X1, X2, X3))
(active# U61(X1, X2, X3) -> active# X1, active# U61(X1, X2, X3) -> active# X1)
(active# U61(X1, X2, X3) -> active# X1, active# U62(tt(), V2) -> U63# isNatIList V2)
(active# U61(X1, X2, X3) -> active# X1, active# U62(tt(), V2) -> isNatIList# V2)
(active# U61(X1, X2, X3) -> active# X1, active# U62(X1, X2) -> U62#(active X1, X2))
(active# U61(X1, X2, X3) -> active# X1, active# U62(X1, X2) -> active# X1)
(active# U61(X1, X2, X3) -> active# X1, active# U53 X -> U53# active X)
(active# U61(X1, X2, X3) -> active# X1, active# U53 X -> active# X)
(active# U61(X1, X2, X3) -> active# X1, active# U51(tt(), V1, V2) -> U52#(isNat V1, V2))
(active# U61(X1, X2, X3) -> active# X1, active# U51(tt(), V1, V2) -> isNat# V1)
(active# U61(X1, X2, X3) -> active# X1, active# U51(X1, X2, X3) -> U51#(active X1, X2, X3))
(active# U61(X1, X2, X3) -> active# X1, active# U51(X1, X2, X3) -> active# X1)
(active# U61(X1, X2, X3) -> active# X1, active# U52(tt(), V2) -> U53# isNatList V2)
(active# U61(X1, X2, X3) -> active# X1, active# U52(tt(), V2) -> isNatList# V2)
(active# U61(X1, X2, X3) -> active# X1, active# U52(X1, X2) -> U52#(active X1, X2))
(active# U61(X1, X2, X3) -> active# X1, active# U52(X1, X2) -> active# X1)
(active# U61(X1, X2, X3) -> active# X1, active# isNatIList cons(V1, V2) -> isNatKind# V1)
(active# U61(X1, X2, X3) -> active# X1, active# isNatIList cons(V1, V2) -> isNatIListKind# V2)
(active# U61(X1, X2, X3) -> active# X1, active# isNatIList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U61(X1, X2, X3) -> active# X1, active# isNatIList cons(V1, V2) -> U41#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U61(X1, X2, X3) -> active# X1, active# isNatIList V -> isNatIListKind# V)
(active# U61(X1, X2, X3) -> active# X1, active# isNatIList V -> U31#(isNatIListKind V, V))
(active# U61(X1, X2, X3) -> active# X1, active# U43 X -> U43# active X)
(active# U61(X1, X2, X3) -> active# X1, active# U43 X -> active# X)
(active# U61(X1, X2, X3) -> active# X1, active# U41(tt(), V1, V2) -> U42#(isNat V1, V2))
(active# U61(X1, X2, X3) -> active# X1, active# U41(tt(), V1, V2) -> isNat# V1)
(active# U61(X1, X2, X3) -> active# X1, active# U41(X1, X2, X3) -> U41#(active X1, X2, X3))
(active# U61(X1, X2, X3) -> active# X1, active# U41(X1, X2, X3) -> active# X1)
(active# U61(X1, X2, X3) -> active# X1, active# U42(tt(), V2) -> isNatIList# V2)
(active# U61(X1, X2, X3) -> active# X1, active# U42(tt(), V2) -> U43# isNatIList V2)
(active# U61(X1, X2, X3) -> active# X1, active# U42(X1, X2) -> U42#(active X1, X2))
(active# U61(X1, X2, X3) -> active# X1, active# U42(X1, X2) -> active# X1)
(active# U61(X1, X2, X3) -> active# X1, active# U31(tt(), V) -> U32# isNatList V)
(active# U61(X1, X2, X3) -> active# X1, active# U31(tt(), V) -> isNatList# V)
(active# U61(X1, X2, X3) -> active# X1, active# U31(X1, X2) -> U31#(active X1, X2))
(active# U61(X1, X2, X3) -> active# X1, active# U31(X1, X2) -> active# X1)
(active# U61(X1, X2, X3) -> active# X1, active# U32 X -> U32# active X)
(active# U61(X1, X2, X3) -> active# X1, active# U32 X -> active# X)
(active# U61(X1, X2, X3) -> active# X1, active# U21(tt(), V1) -> isNat# V1)
(active# U61(X1, X2, X3) -> active# X1, active# U21(tt(), V1) -> U22# isNat V1)
(active# U61(X1, X2, X3) -> active# X1, active# U21(X1, X2) -> U21#(active X1, X2))
(active# U61(X1, X2, X3) -> active# X1, active# U21(X1, X2) -> active# X1)
(active# U61(X1, X2, X3) -> active# X1, active# isNat length V1 -> isNatIListKind# V1)
(active# U61(X1, X2, X3) -> active# X1, active# isNat length V1 -> U11#(isNatIListKind V1, V1))
(active# U61(X1, X2, X3) -> active# X1, active# isNat s V1 -> isNatKind# V1)
(active# U61(X1, X2, X3) -> active# X1, active# isNat s V1 -> U21#(isNatKind V1, V1))
(active# U61(X1, X2, X3) -> active# X1, active# U22 X -> U22# active X)
(active# U61(X1, X2, X3) -> active# X1, active# U22 X -> active# X)
(active# U61(X1, X2, X3) -> active# X1, active# U11(tt(), V1) -> isNatList# V1)
(active# U61(X1, X2, X3) -> active# X1, active# U11(tt(), V1) -> U12# isNatList V1)
(active# U61(X1, X2, X3) -> active# X1, active# U11(X1, X2) -> U11#(active X1, X2))
(active# U61(X1, X2, X3) -> active# X1, active# U11(X1, X2) -> active# X1)
(active# U61(X1, X2, X3) -> active# X1, active# isNatList take(V1, V2) -> isNatKind# V1)
(active# U61(X1, X2, X3) -> active# X1, active# isNatList take(V1, V2) -> isNatIListKind# V2)
(active# U61(X1, X2, X3) -> active# X1, active# isNatList take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U61(X1, X2, X3) -> active# X1, active# isNatList take(V1, V2) -> U61#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U61(X1, X2, X3) -> active# X1, active# isNatList cons(V1, V2) -> isNatKind# V1)
(active# U61(X1, X2, X3) -> active# X1, active# isNatList cons(V1, V2) -> isNatIListKind# V2)
(active# U61(X1, X2, X3) -> active# X1, active# isNatList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U61(X1, X2, X3) -> active# X1, active# isNatList cons(V1, V2) -> U51#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U61(X1, X2, X3) -> active# X1, active# U12 X -> U12# active X)
(active# U61(X1, X2, X3) -> active# X1, active# U12 X -> active# X)
(active# U61(X1, X2, X3) -> active# X1, active# zeros() -> cons#(0(), zeros()))
(active# U61(X1, X2, X3) -> active# X1, active# cons(X1, X2) -> active# X1)
(active# U61(X1, X2, X3) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2))
(active# U71(X1, X2) -> U71#(active X1, X2), U71#(ok X1, ok X2) -> U71#(X1, X2))
(active# U71(X1, X2) -> U71#(active X1, X2), U71#(mark X1, X2) -> U71#(X1, X2))
(active# take(X1, X2) -> take#(active X1, X2), take#(ok X1, ok X2) -> take#(X1, X2))
(active# take(X1, X2) -> take#(active X1, X2), take#(mark X1, X2) -> take#(X1, X2))
(active# take(X1, X2) -> take#(active X1, X2), take#(X1, mark X2) -> take#(X1, X2))
(active# and(X1, X2) -> active# X1, active# isNatKind length V1 -> isNatIListKind# V1)
(active# and(X1, X2) -> active# X1, active# isNatKind s V1 -> isNatKind# V1)
(active# and(X1, X2) -> active# X1, active# isNatIListKind take(V1, V2) -> isNatKind# V1)
(active# and(X1, X2) -> active# X1, active# isNatIListKind take(V1, V2) -> isNatIListKind# V2)
(active# and(X1, X2) -> active# X1, active# isNatIListKind take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# and(X1, X2) -> active# X1, active# isNatIListKind cons(V1, V2) -> isNatKind# V1)
(active# and(X1, X2) -> active# X1, active# isNatIListKind cons(V1, V2) -> isNatIListKind# V2)
(active# and(X1, X2) -> active# X1, active# isNatIListKind cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# and(X1, X2) -> active# X1, active# and(X1, X2) -> and#(active X1, X2))
(active# and(X1, X2) -> active# X1, active# and(X1, X2) -> active# X1)
(active# and(X1, X2) -> active# X1, active# U91(tt(), IL, M, N) -> take#(M, IL))
(active# and(X1, X2) -> active# X1, active# U91(tt(), IL, M, N) -> cons#(N, take(M, IL)))
(active# and(X1, X2) -> active# X1, active# U91(X1, X2, X3, X4) -> U91#(active X1, X2, X3, X4))
(active# and(X1, X2) -> active# X1, active# U91(X1, X2, X3, X4) -> active# X1)
(active# and(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatKind# M)
(active# and(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatKind# N)
(active# and(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIListKind# IL)
(active# and(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))))
(active# and(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(and(isNat M, isNatKind M), and(isNat N, isNatKind N)))
(active# and(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, isNatIListKind IL))
(active# and(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat M, isNatKind M))
(active# and(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat N, isNatKind N))
(active# and(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> U91#(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N))
(active# and(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIList# IL)
(active# and(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# M)
(active# and(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# N)
(active# and(X1, X2) -> active# X1, active# take(0(), IL) -> isNatIListKind# IL)
(active# and(X1, X2) -> active# X1, active# take(0(), IL) -> and#(isNatIList IL, isNatIListKind IL))
(active# and(X1, X2) -> active# X1, active# take(0(), IL) -> U81# and(isNatIList IL, isNatIListKind IL))
(active# and(X1, X2) -> active# X1, active# take(0(), IL) -> isNatIList# IL)
(active# and(X1, X2) -> active# X1, active# take(X1, X2) -> take#(active X1, X2))
(active# and(X1, X2) -> active# X1, active# take(X1, X2) -> take#(X1, active X2))
(active# and(X1, X2) -> active# X1, active# take(X1, X2) -> active# X2)
(active# and(X1, X2) -> active# X1, active# take(X1, X2) -> active# X1)
(active# and(X1, X2) -> active# X1, active# U81 X -> U81# active X)
(active# and(X1, X2) -> active# X1, active# U81 X -> active# X)
(active# and(X1, X2) -> active# X1, active# U71(tt(), L) -> length# L)
(active# and(X1, X2) -> active# X1, active# U71(tt(), L) -> s# length L)
(active# and(X1, X2) -> active# X1, active# U71(X1, X2) -> U71#(active X1, X2))
(active# and(X1, X2) -> active# X1, active# U71(X1, X2) -> active# X1)
(active# and(X1, X2) -> active# X1, active# length cons(N, L) -> isNatKind# N)
(active# and(X1, X2) -> active# X1, active# length cons(N, L) -> isNatIListKind# L)
(active# and(X1, X2) -> active# X1, active# length cons(N, L) -> and#(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)))
(active# and(X1, X2) -> active# X1, active# length cons(N, L) -> and#(isNat N, isNatKind N))
(active# and(X1, X2) -> active# X1, active# length cons(N, L) -> and#(isNatList L, isNatIListKind L))
(active# and(X1, X2) -> active# X1, active# length cons(N, L) -> U71#(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L))
(active# and(X1, X2) -> active# X1, active# length cons(N, L) -> isNat# N)
(active# and(X1, X2) -> active# X1, active# length cons(N, L) -> isNatList# L)
(active# and(X1, X2) -> active# X1, active# length X -> length# active X)
(active# and(X1, X2) -> active# X1, active# length X -> active# X)
(active# and(X1, X2) -> active# X1, active# s X -> s# active X)
(active# and(X1, X2) -> active# X1, active# s X -> active# X)
(active# and(X1, X2) -> active# X1, active# U63 X -> U63# active X)
(active# and(X1, X2) -> active# X1, active# U63 X -> active# X)
(active# and(X1, X2) -> active# X1, active# U61(tt(), V1, V2) -> U62#(isNat V1, V2))
(active# and(X1, X2) -> active# X1, active# U61(tt(), V1, V2) -> isNat# V1)
(active# and(X1, X2) -> active# X1, active# U61(X1, X2, X3) -> U61#(active X1, X2, X3))
(active# and(X1, X2) -> active# X1, active# U61(X1, X2, X3) -> active# X1)
(active# and(X1, X2) -> active# X1, active# U62(tt(), V2) -> U63# isNatIList V2)
(active# and(X1, X2) -> active# X1, active# U62(tt(), V2) -> isNatIList# V2)
(active# and(X1, X2) -> active# X1, active# U62(X1, X2) -> U62#(active X1, X2))
(active# and(X1, X2) -> active# X1, active# U62(X1, X2) -> active# X1)
(active# and(X1, X2) -> active# X1, active# U53 X -> U53# active X)
(active# and(X1, X2) -> active# X1, active# U53 X -> active# X)
(active# and(X1, X2) -> active# X1, active# U51(tt(), V1, V2) -> U52#(isNat V1, V2))
(active# and(X1, X2) -> active# X1, active# U51(tt(), V1, V2) -> isNat# V1)
(active# and(X1, X2) -> active# X1, active# U51(X1, X2, X3) -> U51#(active X1, X2, X3))
(active# and(X1, X2) -> active# X1, active# U51(X1, X2, X3) -> active# X1)
(active# and(X1, X2) -> active# X1, active# U52(tt(), V2) -> U53# isNatList V2)
(active# and(X1, X2) -> active# X1, active# U52(tt(), V2) -> isNatList# V2)
(active# and(X1, X2) -> active# X1, active# U52(X1, X2) -> U52#(active X1, X2))
(active# and(X1, X2) -> active# X1, active# U52(X1, X2) -> active# X1)
(active# and(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNatKind# V1)
(active# and(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNatIListKind# V2)
(active# and(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# and(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> U41#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# and(X1, X2) -> active# X1, active# isNatIList V -> isNatIListKind# V)
(active# and(X1, X2) -> active# X1, active# isNatIList V -> U31#(isNatIListKind V, V))
(active# and(X1, X2) -> active# X1, active# U43 X -> U43# active X)
(active# and(X1, X2) -> active# X1, active# U43 X -> active# X)
(active# and(X1, X2) -> active# X1, active# U41(tt(), V1, V2) -> U42#(isNat V1, V2))
(active# and(X1, X2) -> active# X1, active# U41(tt(), V1, V2) -> isNat# V1)
(active# and(X1, X2) -> active# X1, active# U41(X1, X2, X3) -> U41#(active X1, X2, X3))
(active# and(X1, X2) -> active# X1, active# U41(X1, X2, X3) -> active# X1)
(active# and(X1, X2) -> active# X1, active# U42(tt(), V2) -> isNatIList# V2)
(active# and(X1, X2) -> active# X1, active# U42(tt(), V2) -> U43# isNatIList V2)
(active# and(X1, X2) -> active# X1, active# U42(X1, X2) -> U42#(active X1, X2))
(active# and(X1, X2) -> active# X1, active# U42(X1, X2) -> active# X1)
(active# and(X1, X2) -> active# X1, active# U31(tt(), V) -> U32# isNatList V)
(active# and(X1, X2) -> active# X1, active# U31(tt(), V) -> isNatList# V)
(active# and(X1, X2) -> active# X1, active# U31(X1, X2) -> U31#(active X1, X2))
(active# and(X1, X2) -> active# X1, active# U31(X1, X2) -> active# X1)
(active# and(X1, X2) -> active# X1, active# U32 X -> U32# active X)
(active# and(X1, X2) -> active# X1, active# U32 X -> active# X)
(active# and(X1, X2) -> active# X1, active# U21(tt(), V1) -> isNat# V1)
(active# and(X1, X2) -> active# X1, active# U21(tt(), V1) -> U22# isNat V1)
(active# and(X1, X2) -> active# X1, active# U21(X1, X2) -> U21#(active X1, X2))
(active# and(X1, X2) -> active# X1, active# U21(X1, X2) -> active# X1)
(active# and(X1, X2) -> active# X1, active# isNat length V1 -> isNatIListKind# V1)
(active# and(X1, X2) -> active# X1, active# isNat length V1 -> U11#(isNatIListKind V1, V1))
(active# and(X1, X2) -> active# X1, active# isNat s V1 -> isNatKind# V1)
(active# and(X1, X2) -> active# X1, active# isNat s V1 -> U21#(isNatKind V1, V1))
(active# and(X1, X2) -> active# X1, active# U22 X -> U22# active X)
(active# and(X1, X2) -> active# X1, active# U22 X -> active# X)
(active# and(X1, X2) -> active# X1, active# U11(tt(), V1) -> isNatList# V1)
(active# and(X1, X2) -> active# X1, active# U11(tt(), V1) -> U12# isNatList V1)
(active# and(X1, X2) -> active# X1, active# U11(X1, X2) -> U11#(active X1, X2))
(active# and(X1, X2) -> active# X1, active# U11(X1, X2) -> active# X1)
(active# and(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> isNatKind# V1)
(active# and(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> isNatIListKind# V2)
(active# and(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# and(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> U61#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# and(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> isNatKind# V1)
(active# and(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> isNatIListKind# V2)
(active# and(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# and(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> U51#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# and(X1, X2) -> active# X1, active# U12 X -> U12# active X)
(active# and(X1, X2) -> active# X1, active# U12 X -> active# X)
(active# and(X1, X2) -> active# X1, active# zeros() -> cons#(0(), zeros()))
(active# and(X1, X2) -> active# X1, active# cons(X1, X2) -> active# X1)
(active# and(X1, X2) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2))
(proper# cons(X1, X2) -> proper# X1, proper# isNatKind X -> proper# X)
(proper# cons(X1, X2) -> proper# X1, proper# isNatKind X -> isNatKind# proper X)
(proper# cons(X1, X2) -> proper# X1, proper# isNatIListKind X -> proper# X)
(proper# cons(X1, X2) -> proper# X1, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# cons(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2)
(proper# cons(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X1)
(proper# cons(X1, X2) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# cons(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# cons(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# cons(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# cons(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# cons(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# cons(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X2)
(proper# cons(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X1)
(proper# cons(X1, X2) -> proper# X1, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# cons(X1, X2) -> proper# X1, proper# U81 X -> proper# X)
(proper# cons(X1, X2) -> proper# X1, proper# U81 X -> U81# proper X)
(proper# cons(X1, X2) -> proper# X1, proper# U71(X1, X2) -> proper# X2)
(proper# cons(X1, X2) -> proper# X1, proper# U71(X1, X2) -> proper# X1)
(proper# cons(X1, X2) -> proper# X1, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# cons(X1, X2) -> proper# X1, proper# length X -> proper# X)
(proper# cons(X1, X2) -> proper# X1, proper# length X -> length# proper X)
(proper# cons(X1, X2) -> proper# X1, proper# s X -> proper# X)
(proper# cons(X1, X2) -> proper# X1, proper# s X -> s# proper X)
(proper# cons(X1, X2) -> proper# X1, proper# U63 X -> proper# X)
(proper# cons(X1, X2) -> proper# X1, proper# U63 X -> U63# proper X)
(proper# cons(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X3)
(proper# cons(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X2)
(proper# cons(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X1)
(proper# cons(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# cons(X1, X2) -> proper# X1, proper# U62(X1, X2) -> proper# X2)
(proper# cons(X1, X2) -> proper# X1, proper# U62(X1, X2) -> proper# X1)
(proper# cons(X1, X2) -> proper# X1, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# cons(X1, X2) -> proper# X1, proper# U53 X -> proper# X)
(proper# cons(X1, X2) -> proper# X1, proper# U53 X -> U53# proper X)
(proper# cons(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X3)
(proper# cons(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X2)
(proper# cons(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X1)
(proper# cons(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# cons(X1, X2) -> proper# X1, proper# U52(X1, X2) -> proper# X2)
(proper# cons(X1, X2) -> proper# X1, proper# U52(X1, X2) -> proper# X1)
(proper# cons(X1, X2) -> proper# X1, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# cons(X1, X2) -> proper# X1, proper# isNatIList X -> proper# X)
(proper# cons(X1, X2) -> proper# X1, proper# isNatIList X -> isNatIList# proper X)
(proper# cons(X1, X2) -> proper# X1, proper# U43 X -> proper# X)
(proper# cons(X1, X2) -> proper# X1, proper# U43 X -> U43# proper X)
(proper# cons(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X3)
(proper# cons(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X2)
(proper# cons(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X1)
(proper# cons(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# cons(X1, X2) -> proper# X1, proper# U42(X1, X2) -> proper# X2)
(proper# cons(X1, X2) -> proper# X1, proper# U42(X1, X2) -> proper# X1)
(proper# cons(X1, X2) -> proper# X1, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# cons(X1, X2) -> proper# X1, proper# U31(X1, X2) -> proper# X2)
(proper# cons(X1, X2) -> proper# X1, proper# U31(X1, X2) -> proper# X1)
(proper# cons(X1, X2) -> proper# X1, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# cons(X1, X2) -> proper# X1, proper# U32 X -> proper# X)
(proper# cons(X1, X2) -> proper# X1, proper# U32 X -> U32# proper X)
(proper# cons(X1, X2) -> proper# X1, proper# U21(X1, X2) -> proper# X2)
(proper# cons(X1, X2) -> proper# X1, proper# U21(X1, X2) -> proper# X1)
(proper# cons(X1, X2) -> proper# X1, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# cons(X1, X2) -> proper# X1, proper# isNat X -> proper# X)
(proper# cons(X1, X2) -> proper# X1, proper# isNat X -> isNat# proper X)
(proper# cons(X1, X2) -> proper# X1, proper# U22 X -> proper# X)
(proper# cons(X1, X2) -> proper# X1, proper# U22 X -> U22# proper X)
(proper# cons(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X2)
(proper# cons(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X1)
(proper# cons(X1, X2) -> proper# X1, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# cons(X1, X2) -> proper# X1, proper# isNatList X -> proper# X)
(proper# cons(X1, X2) -> proper# X1, proper# isNatList X -> isNatList# proper X)
(proper# cons(X1, X2) -> proper# X1, proper# U12 X -> proper# X)
(proper# cons(X1, X2) -> proper# X1, proper# U12 X -> U12# proper X)
(proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2)
(proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1)
(proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# U21(X1, X2) -> proper# X1, proper# isNatKind X -> proper# X)
(proper# U21(X1, X2) -> proper# X1, proper# isNatKind X -> isNatKind# proper X)
(proper# U21(X1, X2) -> proper# X1, proper# isNatIListKind X -> proper# X)
(proper# U21(X1, X2) -> proper# X1, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# U21(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2)
(proper# U21(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X1)
(proper# U21(X1, X2) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# U21(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# U21(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# U21(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# U21(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# U21(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# U21(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X2)
(proper# U21(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X1)
(proper# U21(X1, X2) -> proper# X1, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# U21(X1, X2) -> proper# X1, proper# U81 X -> proper# X)
(proper# U21(X1, X2) -> proper# X1, proper# U81 X -> U81# proper X)
(proper# U21(X1, X2) -> proper# X1, proper# U71(X1, X2) -> proper# X2)
(proper# U21(X1, X2) -> proper# X1, proper# U71(X1, X2) -> proper# X1)
(proper# U21(X1, X2) -> proper# X1, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# U21(X1, X2) -> proper# X1, proper# length X -> proper# X)
(proper# U21(X1, X2) -> proper# X1, proper# length X -> length# proper X)
(proper# U21(X1, X2) -> proper# X1, proper# s X -> proper# X)
(proper# U21(X1, X2) -> proper# X1, proper# s X -> s# proper X)
(proper# U21(X1, X2) -> proper# X1, proper# U63 X -> proper# X)
(proper# U21(X1, X2) -> proper# X1, proper# U63 X -> U63# proper X)
(proper# U21(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X3)
(proper# U21(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X2)
(proper# U21(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X1)
(proper# U21(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# U21(X1, X2) -> proper# X1, proper# U62(X1, X2) -> proper# X2)
(proper# U21(X1, X2) -> proper# X1, proper# U62(X1, X2) -> proper# X1)
(proper# U21(X1, X2) -> proper# X1, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# U21(X1, X2) -> proper# X1, proper# U53 X -> proper# X)
(proper# U21(X1, X2) -> proper# X1, proper# U53 X -> U53# proper X)
(proper# U21(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X3)
(proper# U21(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X2)
(proper# U21(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X1)
(proper# U21(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# U21(X1, X2) -> proper# X1, proper# U52(X1, X2) -> proper# X2)
(proper# U21(X1, X2) -> proper# X1, proper# U52(X1, X2) -> proper# X1)
(proper# U21(X1, X2) -> proper# X1, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# U21(X1, X2) -> proper# X1, proper# isNatIList X -> proper# X)
(proper# U21(X1, X2) -> proper# X1, proper# isNatIList X -> isNatIList# proper X)
(proper# U21(X1, X2) -> proper# X1, proper# U43 X -> proper# X)
(proper# U21(X1, X2) -> proper# X1, proper# U43 X -> U43# proper X)
(proper# U21(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X3)
(proper# U21(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X2)
(proper# U21(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X1)
(proper# U21(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# U21(X1, X2) -> proper# X1, proper# U42(X1, X2) -> proper# X2)
(proper# U21(X1, X2) -> proper# X1, proper# U42(X1, X2) -> proper# X1)
(proper# U21(X1, X2) -> proper# X1, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# U21(X1, X2) -> proper# X1, proper# U31(X1, X2) -> proper# X2)
(proper# U21(X1, X2) -> proper# X1, proper# U31(X1, X2) -> proper# X1)
(proper# U21(X1, X2) -> proper# X1, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# U21(X1, X2) -> proper# X1, proper# U32 X -> proper# X)
(proper# U21(X1, X2) -> proper# X1, proper# U32 X -> U32# proper X)
(proper# U21(X1, X2) -> proper# X1, proper# U21(X1, X2) -> proper# X2)
(proper# U21(X1, X2) -> proper# X1, proper# U21(X1, X2) -> proper# X1)
(proper# U21(X1, X2) -> proper# X1, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# U21(X1, X2) -> proper# X1, proper# isNat X -> proper# X)
(proper# U21(X1, X2) -> proper# X1, proper# isNat X -> isNat# proper X)
(proper# U21(X1, X2) -> proper# X1, proper# U22 X -> proper# X)
(proper# U21(X1, X2) -> proper# X1, proper# U22 X -> U22# proper X)
(proper# U21(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X2)
(proper# U21(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X1)
(proper# U21(X1, X2) -> proper# X1, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# U21(X1, X2) -> proper# X1, proper# isNatList X -> proper# X)
(proper# U21(X1, X2) -> proper# X1, proper# isNatList X -> isNatList# proper X)
(proper# U21(X1, X2) -> proper# X1, proper# U12 X -> proper# X)
(proper# U21(X1, X2) -> proper# X1, proper# U12 X -> U12# proper X)
(proper# U21(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2)
(proper# U21(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1)
(proper# U21(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# U42(X1, X2) -> proper# X1, proper# isNatKind X -> proper# X)
(proper# U42(X1, X2) -> proper# X1, proper# isNatKind X -> isNatKind# proper X)
(proper# U42(X1, X2) -> proper# X1, proper# isNatIListKind X -> proper# X)
(proper# U42(X1, X2) -> proper# X1, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# U42(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2)
(proper# U42(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X1)
(proper# U42(X1, X2) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# U42(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# U42(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# U42(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# U42(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# U42(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# U42(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X2)
(proper# U42(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X1)
(proper# U42(X1, X2) -> proper# X1, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# U42(X1, X2) -> proper# X1, proper# U81 X -> proper# X)
(proper# U42(X1, X2) -> proper# X1, proper# U81 X -> U81# proper X)
(proper# U42(X1, X2) -> proper# X1, proper# U71(X1, X2) -> proper# X2)
(proper# U42(X1, X2) -> proper# X1, proper# U71(X1, X2) -> proper# X1)
(proper# U42(X1, X2) -> proper# X1, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# U42(X1, X2) -> proper# X1, proper# length X -> proper# X)
(proper# U42(X1, X2) -> proper# X1, proper# length X -> length# proper X)
(proper# U42(X1, X2) -> proper# X1, proper# s X -> proper# X)
(proper# U42(X1, X2) -> proper# X1, proper# s X -> s# proper X)
(proper# U42(X1, X2) -> proper# X1, proper# U63 X -> proper# X)
(proper# U42(X1, X2) -> proper# X1, proper# U63 X -> U63# proper X)
(proper# U42(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X3)
(proper# U42(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X2)
(proper# U42(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X1)
(proper# U42(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# U42(X1, X2) -> proper# X1, proper# U62(X1, X2) -> proper# X2)
(proper# U42(X1, X2) -> proper# X1, proper# U62(X1, X2) -> proper# X1)
(proper# U42(X1, X2) -> proper# X1, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# U42(X1, X2) -> proper# X1, proper# U53 X -> proper# X)
(proper# U42(X1, X2) -> proper# X1, proper# U53 X -> U53# proper X)
(proper# U42(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X3)
(proper# U42(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X2)
(proper# U42(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X1)
(proper# U42(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# U42(X1, X2) -> proper# X1, proper# U52(X1, X2) -> proper# X2)
(proper# U42(X1, X2) -> proper# X1, proper# U52(X1, X2) -> proper# X1)
(proper# U42(X1, X2) -> proper# X1, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# U42(X1, X2) -> proper# X1, proper# isNatIList X -> proper# X)
(proper# U42(X1, X2) -> proper# X1, proper# isNatIList X -> isNatIList# proper X)
(proper# U42(X1, X2) -> proper# X1, proper# U43 X -> proper# X)
(proper# U42(X1, X2) -> proper# X1, proper# U43 X -> U43# proper X)
(proper# U42(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X3)
(proper# U42(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X2)
(proper# U42(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X1)
(proper# U42(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# U42(X1, X2) -> proper# X1, proper# U42(X1, X2) -> proper# X2)
(proper# U42(X1, X2) -> proper# X1, proper# U42(X1, X2) -> proper# X1)
(proper# U42(X1, X2) -> proper# X1, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# U42(X1, X2) -> proper# X1, proper# U31(X1, X2) -> proper# X2)
(proper# U42(X1, X2) -> proper# X1, proper# U31(X1, X2) -> proper# X1)
(proper# U42(X1, X2) -> proper# X1, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# U42(X1, X2) -> proper# X1, proper# U32 X -> proper# X)
(proper# U42(X1, X2) -> proper# X1, proper# U32 X -> U32# proper X)
(proper# U42(X1, X2) -> proper# X1, proper# U21(X1, X2) -> proper# X2)
(proper# U42(X1, X2) -> proper# X1, proper# U21(X1, X2) -> proper# X1)
(proper# U42(X1, X2) -> proper# X1, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# U42(X1, X2) -> proper# X1, proper# isNat X -> proper# X)
(proper# U42(X1, X2) -> proper# X1, proper# isNat X -> isNat# proper X)
(proper# U42(X1, X2) -> proper# X1, proper# U22 X -> proper# X)
(proper# U42(X1, X2) -> proper# X1, proper# U22 X -> U22# proper X)
(proper# U42(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X2)
(proper# U42(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X1)
(proper# U42(X1, X2) -> proper# X1, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# U42(X1, X2) -> proper# X1, proper# isNatList X -> proper# X)
(proper# U42(X1, X2) -> proper# X1, proper# isNatList X -> isNatList# proper X)
(proper# U42(X1, X2) -> proper# X1, proper# U12 X -> proper# X)
(proper# U42(X1, X2) -> proper# X1, proper# U12 X -> U12# proper X)
(proper# U42(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2)
(proper# U42(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1)
(proper# U42(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# U52(X1, X2) -> proper# X1, proper# isNatKind X -> proper# X)
(proper# U52(X1, X2) -> proper# X1, proper# isNatKind X -> isNatKind# proper X)
(proper# U52(X1, X2) -> proper# X1, proper# isNatIListKind X -> proper# X)
(proper# U52(X1, X2) -> proper# X1, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# U52(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2)
(proper# U52(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X1)
(proper# U52(X1, X2) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# U52(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# U52(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# U52(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# U52(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# U52(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# U52(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X2)
(proper# U52(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X1)
(proper# U52(X1, X2) -> proper# X1, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# U52(X1, X2) -> proper# X1, proper# U81 X -> proper# X)
(proper# U52(X1, X2) -> proper# X1, proper# U81 X -> U81# proper X)
(proper# U52(X1, X2) -> proper# X1, proper# U71(X1, X2) -> proper# X2)
(proper# U52(X1, X2) -> proper# X1, proper# U71(X1, X2) -> proper# X1)
(proper# U52(X1, X2) -> proper# X1, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# U52(X1, X2) -> proper# X1, proper# length X -> proper# X)
(proper# U52(X1, X2) -> proper# X1, proper# length X -> length# proper X)
(proper# U52(X1, X2) -> proper# X1, proper# s X -> proper# X)
(proper# U52(X1, X2) -> proper# X1, proper# s X -> s# proper X)
(proper# U52(X1, X2) -> proper# X1, proper# U63 X -> proper# X)
(proper# U52(X1, X2) -> proper# X1, proper# U63 X -> U63# proper X)
(proper# U52(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X3)
(proper# U52(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X2)
(proper# U52(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X1)
(proper# U52(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# U52(X1, X2) -> proper# X1, proper# U62(X1, X2) -> proper# X2)
(proper# U52(X1, X2) -> proper# X1, proper# U62(X1, X2) -> proper# X1)
(proper# U52(X1, X2) -> proper# X1, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# U52(X1, X2) -> proper# X1, proper# U53 X -> proper# X)
(proper# U52(X1, X2) -> proper# X1, proper# U53 X -> U53# proper X)
(proper# U52(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X3)
(proper# U52(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X2)
(proper# U52(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X1)
(proper# U52(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# U52(X1, X2) -> proper# X1, proper# U52(X1, X2) -> proper# X2)
(proper# U52(X1, X2) -> proper# X1, proper# U52(X1, X2) -> proper# X1)
(proper# U52(X1, X2) -> proper# X1, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# U52(X1, X2) -> proper# X1, proper# isNatIList X -> proper# X)
(proper# U52(X1, X2) -> proper# X1, proper# isNatIList X -> isNatIList# proper X)
(proper# U52(X1, X2) -> proper# X1, proper# U43 X -> proper# X)
(proper# U52(X1, X2) -> proper# X1, proper# U43 X -> U43# proper X)
(proper# U52(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X3)
(proper# U52(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X2)
(proper# U52(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X1)
(proper# U52(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# U52(X1, X2) -> proper# X1, proper# U42(X1, X2) -> proper# X2)
(proper# U52(X1, X2) -> proper# X1, proper# U42(X1, X2) -> proper# X1)
(proper# U52(X1, X2) -> proper# X1, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# U52(X1, X2) -> proper# X1, proper# U31(X1, X2) -> proper# X2)
(proper# U52(X1, X2) -> proper# X1, proper# U31(X1, X2) -> proper# X1)
(proper# U52(X1, X2) -> proper# X1, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# U52(X1, X2) -> proper# X1, proper# U32 X -> proper# X)
(proper# U52(X1, X2) -> proper# X1, proper# U32 X -> U32# proper X)
(proper# U52(X1, X2) -> proper# X1, proper# U21(X1, X2) -> proper# X2)
(proper# U52(X1, X2) -> proper# X1, proper# U21(X1, X2) -> proper# X1)
(proper# U52(X1, X2) -> proper# X1, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# U52(X1, X2) -> proper# X1, proper# isNat X -> proper# X)
(proper# U52(X1, X2) -> proper# X1, proper# isNat X -> isNat# proper X)
(proper# U52(X1, X2) -> proper# X1, proper# U22 X -> proper# X)
(proper# U52(X1, X2) -> proper# X1, proper# U22 X -> U22# proper X)
(proper# U52(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X2)
(proper# U52(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X1)
(proper# U52(X1, X2) -> proper# X1, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# U52(X1, X2) -> proper# X1, proper# isNatList X -> proper# X)
(proper# U52(X1, X2) -> proper# X1, proper# isNatList X -> isNatList# proper X)
(proper# U52(X1, X2) -> proper# X1, proper# U12 X -> proper# X)
(proper# U52(X1, X2) -> proper# X1, proper# U12 X -> U12# proper X)
(proper# U52(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2)
(proper# U52(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1)
(proper# U52(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# U62(X1, X2) -> proper# X1, proper# isNatKind X -> proper# X)
(proper# U62(X1, X2) -> proper# X1, proper# isNatKind X -> isNatKind# proper X)
(proper# U62(X1, X2) -> proper# X1, proper# isNatIListKind X -> proper# X)
(proper# U62(X1, X2) -> proper# X1, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# U62(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2)
(proper# U62(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X1)
(proper# U62(X1, X2) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# U62(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# U62(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# U62(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# U62(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# U62(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# U62(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X2)
(proper# U62(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X1)
(proper# U62(X1, X2) -> proper# X1, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# U62(X1, X2) -> proper# X1, proper# U81 X -> proper# X)
(proper# U62(X1, X2) -> proper# X1, proper# U81 X -> U81# proper X)
(proper# U62(X1, X2) -> proper# X1, proper# U71(X1, X2) -> proper# X2)
(proper# U62(X1, X2) -> proper# X1, proper# U71(X1, X2) -> proper# X1)
(proper# U62(X1, X2) -> proper# X1, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# U62(X1, X2) -> proper# X1, proper# length X -> proper# X)
(proper# U62(X1, X2) -> proper# X1, proper# length X -> length# proper X)
(proper# U62(X1, X2) -> proper# X1, proper# s X -> proper# X)
(proper# U62(X1, X2) -> proper# X1, proper# s X -> s# proper X)
(proper# U62(X1, X2) -> proper# X1, proper# U63 X -> proper# X)
(proper# U62(X1, X2) -> proper# X1, proper# U63 X -> U63# proper X)
(proper# U62(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X3)
(proper# U62(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X2)
(proper# U62(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X1)
(proper# U62(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# U62(X1, X2) -> proper# X1, proper# U62(X1, X2) -> proper# X2)
(proper# U62(X1, X2) -> proper# X1, proper# U62(X1, X2) -> proper# X1)
(proper# U62(X1, X2) -> proper# X1, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# U62(X1, X2) -> proper# X1, proper# U53 X -> proper# X)
(proper# U62(X1, X2) -> proper# X1, proper# U53 X -> U53# proper X)
(proper# U62(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X3)
(proper# U62(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X2)
(proper# U62(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X1)
(proper# U62(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# U62(X1, X2) -> proper# X1, proper# U52(X1, X2) -> proper# X2)
(proper# U62(X1, X2) -> proper# X1, proper# U52(X1, X2) -> proper# X1)
(proper# U62(X1, X2) -> proper# X1, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# U62(X1, X2) -> proper# X1, proper# isNatIList X -> proper# X)
(proper# U62(X1, X2) -> proper# X1, proper# isNatIList X -> isNatIList# proper X)
(proper# U62(X1, X2) -> proper# X1, proper# U43 X -> proper# X)
(proper# U62(X1, X2) -> proper# X1, proper# U43 X -> U43# proper X)
(proper# U62(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X3)
(proper# U62(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X2)
(proper# U62(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X1)
(proper# U62(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# U62(X1, X2) -> proper# X1, proper# U42(X1, X2) -> proper# X2)
(proper# U62(X1, X2) -> proper# X1, proper# U42(X1, X2) -> proper# X1)
(proper# U62(X1, X2) -> proper# X1, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# U62(X1, X2) -> proper# X1, proper# U31(X1, X2) -> proper# X2)
(proper# U62(X1, X2) -> proper# X1, proper# U31(X1, X2) -> proper# X1)
(proper# U62(X1, X2) -> proper# X1, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# U62(X1, X2) -> proper# X1, proper# U32 X -> proper# X)
(proper# U62(X1, X2) -> proper# X1, proper# U32 X -> U32# proper X)
(proper# U62(X1, X2) -> proper# X1, proper# U21(X1, X2) -> proper# X2)
(proper# U62(X1, X2) -> proper# X1, proper# U21(X1, X2) -> proper# X1)
(proper# U62(X1, X2) -> proper# X1, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# U62(X1, X2) -> proper# X1, proper# isNat X -> proper# X)
(proper# U62(X1, X2) -> proper# X1, proper# isNat X -> isNat# proper X)
(proper# U62(X1, X2) -> proper# X1, proper# U22 X -> proper# X)
(proper# U62(X1, X2) -> proper# X1, proper# U22 X -> U22# proper X)
(proper# U62(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X2)
(proper# U62(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X1)
(proper# U62(X1, X2) -> proper# X1, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# U62(X1, X2) -> proper# X1, proper# isNatList X -> proper# X)
(proper# U62(X1, X2) -> proper# X1, proper# isNatList X -> isNatList# proper X)
(proper# U62(X1, X2) -> proper# X1, proper# U12 X -> proper# X)
(proper# U62(X1, X2) -> proper# X1, proper# U12 X -> U12# proper X)
(proper# U62(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2)
(proper# U62(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1)
(proper# U62(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# U71(X1, X2) -> proper# X1, proper# isNatKind X -> proper# X)
(proper# U71(X1, X2) -> proper# X1, proper# isNatKind X -> isNatKind# proper X)
(proper# U71(X1, X2) -> proper# X1, proper# isNatIListKind X -> proper# X)
(proper# U71(X1, X2) -> proper# X1, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# U71(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2)
(proper# U71(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X1)
(proper# U71(X1, X2) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# U71(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# U71(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# U71(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# U71(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# U71(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# U71(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X2)
(proper# U71(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X1)
(proper# U71(X1, X2) -> proper# X1, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# U71(X1, X2) -> proper# X1, proper# U81 X -> proper# X)
(proper# U71(X1, X2) -> proper# X1, proper# U81 X -> U81# proper X)
(proper# U71(X1, X2) -> proper# X1, proper# U71(X1, X2) -> proper# X2)
(proper# U71(X1, X2) -> proper# X1, proper# U71(X1, X2) -> proper# X1)
(proper# U71(X1, X2) -> proper# X1, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# U71(X1, X2) -> proper# X1, proper# length X -> proper# X)
(proper# U71(X1, X2) -> proper# X1, proper# length X -> length# proper X)
(proper# U71(X1, X2) -> proper# X1, proper# s X -> proper# X)
(proper# U71(X1, X2) -> proper# X1, proper# s X -> s# proper X)
(proper# U71(X1, X2) -> proper# X1, proper# U63 X -> proper# X)
(proper# U71(X1, X2) -> proper# X1, proper# U63 X -> U63# proper X)
(proper# U71(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X3)
(proper# U71(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X2)
(proper# U71(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X1)
(proper# U71(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# U71(X1, X2) -> proper# X1, proper# U62(X1, X2) -> proper# X2)
(proper# U71(X1, X2) -> proper# X1, proper# U62(X1, X2) -> proper# X1)
(proper# U71(X1, X2) -> proper# X1, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# U71(X1, X2) -> proper# X1, proper# U53 X -> proper# X)
(proper# U71(X1, X2) -> proper# X1, proper# U53 X -> U53# proper X)
(proper# U71(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X3)
(proper# U71(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X2)
(proper# U71(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X1)
(proper# U71(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# U71(X1, X2) -> proper# X1, proper# U52(X1, X2) -> proper# X2)
(proper# U71(X1, X2) -> proper# X1, proper# U52(X1, X2) -> proper# X1)
(proper# U71(X1, X2) -> proper# X1, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# U71(X1, X2) -> proper# X1, proper# isNatIList X -> proper# X)
(proper# U71(X1, X2) -> proper# X1, proper# isNatIList X -> isNatIList# proper X)
(proper# U71(X1, X2) -> proper# X1, proper# U43 X -> proper# X)
(proper# U71(X1, X2) -> proper# X1, proper# U43 X -> U43# proper X)
(proper# U71(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X3)
(proper# U71(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X2)
(proper# U71(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X1)
(proper# U71(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# U71(X1, X2) -> proper# X1, proper# U42(X1, X2) -> proper# X2)
(proper# U71(X1, X2) -> proper# X1, proper# U42(X1, X2) -> proper# X1)
(proper# U71(X1, X2) -> proper# X1, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# U71(X1, X2) -> proper# X1, proper# U31(X1, X2) -> proper# X2)
(proper# U71(X1, X2) -> proper# X1, proper# U31(X1, X2) -> proper# X1)
(proper# U71(X1, X2) -> proper# X1, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# U71(X1, X2) -> proper# X1, proper# U32 X -> proper# X)
(proper# U71(X1, X2) -> proper# X1, proper# U32 X -> U32# proper X)
(proper# U71(X1, X2) -> proper# X1, proper# U21(X1, X2) -> proper# X2)
(proper# U71(X1, X2) -> proper# X1, proper# U21(X1, X2) -> proper# X1)
(proper# U71(X1, X2) -> proper# X1, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# U71(X1, X2) -> proper# X1, proper# isNat X -> proper# X)
(proper# U71(X1, X2) -> proper# X1, proper# isNat X -> isNat# proper X)
(proper# U71(X1, X2) -> proper# X1, proper# U22 X -> proper# X)
(proper# U71(X1, X2) -> proper# X1, proper# U22 X -> U22# proper X)
(proper# U71(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X2)
(proper# U71(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X1)
(proper# U71(X1, X2) -> proper# X1, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# U71(X1, X2) -> proper# X1, proper# isNatList X -> proper# X)
(proper# U71(X1, X2) -> proper# X1, proper# isNatList X -> isNatList# proper X)
(proper# U71(X1, X2) -> proper# X1, proper# U12 X -> proper# X)
(proper# U71(X1, X2) -> proper# X1, proper# U12 X -> U12# proper X)
(proper# U71(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2)
(proper# U71(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1)
(proper# U71(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# isNatKind X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# isNatKind X -> isNatKind# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# isNatIListKind X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# and(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# and(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# take(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# take(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U81 X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U81 X -> U81# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U71(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U71(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# length X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# length X -> length# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# s X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# s X -> s# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U63 X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U63 X -> U63# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X3)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U62(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U62(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U53 X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U53 X -> U53# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X3)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U52(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U52(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# isNatIList X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# isNatIList X -> isNatIList# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U43 X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U43 X -> U43# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X3)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U42(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U42(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U31(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U31(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U32 X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U32 X -> U32# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U21(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U21(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# isNat X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# isNat X -> isNat# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U22 X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U22 X -> U22# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U11(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U11(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# isNatList X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# isNatList X -> isNatList# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U12 X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# U12 X -> U12# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# cons(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# cons(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(active# U41(tt(), V1, V2) -> U42#(isNat V1, V2), U42#(ok X1, ok X2) -> U42#(X1, X2))
(active# U41(tt(), V1, V2) -> U42#(isNat V1, V2), U42#(mark X1, X2) -> U42#(X1, X2))
(active# U61(tt(), V1, V2) -> U62#(isNat V1, V2), U62#(ok X1, ok X2) -> U62#(X1, X2))
(active# U61(tt(), V1, V2) -> U62#(isNat V1, V2), U62#(mark X1, X2) -> U62#(X1, X2))
(cons#(ok X1, ok X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2))
(cons#(ok X1, ok X2) -> cons#(X1, X2), cons#(mark X1, X2) -> cons#(X1, X2))
(U11#(ok X1, ok X2) -> U11#(X1, X2), U11#(ok X1, ok X2) -> U11#(X1, X2))
(U11#(ok X1, ok X2) -> U11#(X1, X2), U11#(mark X1, X2) -> U11#(X1, X2))
(U21#(ok X1, ok X2) -> U21#(X1, X2), U21#(ok X1, ok X2) -> U21#(X1, X2))
(U21#(ok X1, ok X2) -> U21#(X1, X2), U21#(mark X1, X2) -> U21#(X1, X2))
(U31#(ok X1, ok X2) -> U31#(X1, X2), U31#(ok X1, ok X2) -> U31#(X1, X2))
(U31#(ok X1, ok X2) -> U31#(X1, X2), U31#(mark X1, X2) -> U31#(X1, X2))
(U42#(ok X1, ok X2) -> U42#(X1, X2), U42#(ok X1, ok X2) -> U42#(X1, X2))
(U42#(ok X1, ok X2) -> U42#(X1, X2), U42#(mark X1, X2) -> U42#(X1, X2))
(U52#(ok X1, ok X2) -> U52#(X1, X2), U52#(ok X1, ok X2) -> U52#(X1, X2))
(U52#(ok X1, ok X2) -> U52#(X1, X2), U52#(mark X1, X2) -> U52#(X1, X2))
(U62#(ok X1, ok X2) -> U62#(X1, X2), U62#(ok X1, ok X2) -> U62#(X1, X2))
(U62#(ok X1, ok X2) -> U62#(X1, X2), U62#(mark X1, X2) -> U62#(X1, X2))
(U71#(ok X1, ok X2) -> U71#(X1, X2), U71#(ok X1, ok X2) -> U71#(X1, X2))
(U71#(ok X1, ok X2) -> U71#(X1, X2), U71#(mark X1, X2) -> U71#(X1, X2))
(take#(mark X1, X2) -> take#(X1, X2), take#(ok X1, ok X2) -> take#(X1, X2))
(take#(mark X1, X2) -> take#(X1, X2), take#(mark X1, X2) -> take#(X1, X2))
(take#(mark X1, X2) -> take#(X1, X2), take#(X1, mark X2) -> take#(X1, X2))
(and#(mark X1, X2) -> and#(X1, X2), and#(ok X1, ok X2) -> and#(X1, X2))
(and#(mark X1, X2) -> and#(X1, X2), and#(mark X1, X2) -> and#(X1, X2))
(active# isNatList cons(V1, V2) -> U51#(and(isNatKind V1, isNatIListKind V2), V1, V2), U51#(ok X1, ok X2, ok X3) -> U51#(X1, X2, X3))
(active# isNatList cons(V1, V2) -> U51#(and(isNatKind V1, isNatIListKind V2), V1, V2), U51#(mark X1, X2, X3) -> U51#(X1, X2, X3))
(active# isNatIList cons(V1, V2) -> U41#(and(isNatKind V1, isNatIListKind V2), V1, V2), U41#(ok X1, ok X2, ok X3) -> U41#(X1, X2, X3))
(active# isNatIList cons(V1, V2) -> U41#(and(isNatKind V1, isNatIListKind V2), V1, V2), U41#(mark X1, X2, X3) -> U41#(X1, X2, X3))
(active# isNatIList V -> isNatIListKind# V, isNatIListKind# ok X -> isNatIListKind# X)
(proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3), U51#(ok X1, ok X2, ok X3) -> U51#(X1, X2, X3))
(proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3), U51#(mark X1, X2, X3) -> U51#(X1, X2, X3))
(active# U12 X -> U12# active X, U12# ok X -> U12# X)
(active# U12 X -> U12# active X, U12# mark X -> U12# X)
(active# U32 X -> U32# active X, U32# ok X -> U32# X)
(active# U32 X -> U32# active X, U32# mark X -> U32# X)
(active# U53 X -> U53# active X, U53# ok X -> U53# X)
(active# U53 X -> U53# active X, U53# mark X -> U53# X)
(active# s X -> s# active X, s# ok X -> s# X)
(active# s X -> s# active X, s# mark X -> s# X)
(active# U81 X -> U81# active X, U81# ok X -> U81# X)
(active# U81 X -> U81# active X, U81# mark X -> U81# X)
(proper# isNatList X -> isNatList# proper X, isNatList# ok X -> isNatList# X)
(proper# isNat X -> isNat# proper X, isNat# ok X -> isNat# X)
(proper# U43 X -> U43# proper X, U43# ok X -> U43# X)
(proper# U43 X -> U43# proper X, U43# mark X -> U43# X)
(proper# U53 X -> U53# proper X, U53# ok X -> U53# X)
(proper# U53 X -> U53# proper X, U53# mark X -> U53# X)
(proper# s X -> s# proper X, s# ok X -> s# X)
(proper# s X -> s# proper X, s# mark X -> s# X)
(proper# U81 X -> U81# proper X, U81# ok X -> U81# X)
(proper# U81 X -> U81# proper X, U81# mark X -> U81# X)
(proper# isNatKind X -> isNatKind# proper X, isNatKind# ok X -> isNatKind# X)
(top# ok X -> top# active X, top# ok X -> top# active X)
(top# ok X -> top# active X, top# ok X -> active# X)
(top# ok X -> top# active X, top# mark X -> top# proper X)
(top# ok X -> top# active X, top# mark X -> proper# X)
(active# U42(tt(), V2) -> U43# isNatIList V2, U43# ok X -> U43# X)
(active# U42(tt(), V2) -> U43# isNatIList V2, U43# mark X -> U43# X)
(active# U62(tt(), V2) -> U63# isNatIList V2, U63# ok X -> U63# X)
(active# U62(tt(), V2) -> U63# isNatIList V2, U63# mark X -> U63# X)
(active# U11(tt(), V1) -> U12# isNatList V1, U12# ok X -> U12# X)
(active# U11(tt(), V1) -> U12# isNatList V1, U12# mark X -> U12# X)
(active# take(0(), IL) -> isNatIList# IL, isNatIList# ok X -> isNatIList# X)
(active# take(s M, cons(N, IL)) -> isNatIList# IL, isNatIList# ok X -> isNatIList# X)
(active# U91(X1, X2, X3, X4) -> U91#(active X1, X2, X3, X4), U91#(ok X1, ok X2, ok X3, ok X4) -> U91#(X1, X2, X3, X4))
(active# U91(X1, X2, X3, X4) -> U91#(active X1, X2, X3, X4), U91#(mark X1, X2, X3, X4) -> U91#(X1, X2, X3, X4))
(U91#(ok X1, ok X2, ok X3, ok X4) -> U91#(X1, X2, X3, X4), U91#(ok X1, ok X2, ok X3, ok X4) -> U91#(X1, X2, X3, X4))
(U91#(ok X1, ok X2, ok X3, ok X4) -> U91#(X1, X2, X3, X4), U91#(mark X1, X2, X3, X4) -> U91#(X1, X2, X3, X4))
(active# isNatList take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2), and#(ok X1, ok X2) -> and#(X1, X2))
(active# isNatList take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2), and#(mark X1, X2) -> and#(X1, X2))
(active# length cons(N, L) -> and#(isNatList L, isNatIListKind L), and#(ok X1, ok X2) -> and#(X1, X2))
(active# length cons(N, L) -> and#(isNatList L, isNatIListKind L), and#(mark X1, X2) -> and#(X1, X2))
(active# take(X1, X2) -> take#(X1, active X2), take#(ok X1, ok X2) -> take#(X1, X2))
(active# take(X1, X2) -> take#(X1, active X2), take#(mark X1, X2) -> take#(X1, X2))
(active# take(X1, X2) -> take#(X1, active X2), take#(X1, mark X2) -> take#(X1, X2))
(active# take(s M, cons(N, IL)) -> and#(isNat N, isNatKind N), and#(ok X1, ok X2) -> and#(X1, X2))
(active# take(s M, cons(N, IL)) -> and#(isNat N, isNatKind N), and#(mark X1, X2) -> and#(X1, X2))
(active# take(s M, cons(N, IL)) -> and#(isNatIList IL, isNatIListKind IL), and#(ok X1, ok X2) -> and#(X1, X2))
(active# take(s M, cons(N, IL)) -> and#(isNatIList IL, isNatIListKind IL), and#(mark X1, X2) -> and#(X1, X2))
(active# isNatIListKind take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2), and#(ok X1, ok X2) -> and#(X1, X2))
(active# isNatIListKind take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2), and#(mark X1, X2) -> and#(X1, X2))
(proper# U11(X1, X2) -> U11#(proper X1, proper X2), U11#(ok X1, ok X2) -> U11#(X1, X2))
(proper# U11(X1, X2) -> U11#(proper X1, proper X2), U11#(mark X1, X2) -> U11#(X1, X2))
(proper# U31(X1, X2) -> U31#(proper X1, proper X2), U31#(ok X1, ok X2) -> U31#(X1, X2))
(proper# U31(X1, X2) -> U31#(proper X1, proper X2), U31#(mark X1, X2) -> U31#(X1, X2))
(proper# U52(X1, X2) -> U52#(proper X1, proper X2), U52#(ok X1, ok X2) -> U52#(X1, X2))
(proper# U52(X1, X2) -> U52#(proper X1, proper X2), U52#(mark X1, X2) -> U52#(X1, X2))
(proper# U71(X1, X2) -> U71#(proper X1, proper X2), U71#(ok X1, ok X2) -> U71#(X1, X2))
(proper# U71(X1, X2) -> U71#(proper X1, proper X2), U71#(mark X1, X2) -> U71#(X1, X2))
(proper# and(X1, X2) -> and#(proper X1, proper X2), and#(ok X1, ok X2) -> and#(X1, X2))
(proper# and(X1, X2) -> and#(proper X1, proper X2), and#(mark X1, X2) -> and#(X1, X2))
(active# take(s M, cons(N, IL)) -> U91#(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N), U91#(ok X1, ok X2, ok X3, ok X4) -> U91#(X1, X2, X3, X4))
(active# take(s M, cons(N, IL)) -> U91#(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N), U91#(mark X1, X2, X3, X4) -> U91#(X1, X2, X3, X4))
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# isNatKind X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# isNatKind X -> isNatKind# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# isNatIListKind X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# and(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# and(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# take(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# take(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U81 X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U81 X -> U81# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U71(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U71(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# length X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# length X -> length# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# s X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# s X -> s# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U63 X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U63 X -> U63# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U61(X1, X2, X3) -> proper# X3)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U61(X1, X2, X3) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U61(X1, X2, X3) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U62(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U62(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U53 X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U53 X -> U53# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U51(X1, X2, X3) -> proper# X3)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U51(X1, X2, X3) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U51(X1, X2, X3) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U52(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U52(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# isNatIList X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# isNatIList X -> isNatIList# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U43 X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U43 X -> U43# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U41(X1, X2, X3) -> proper# X3)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U41(X1, X2, X3) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U41(X1, X2, X3) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U42(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U42(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U31(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U31(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U32 X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U32 X -> U32# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U21(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U21(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# isNat X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# isNat X -> isNat# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U22 X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U22 X -> U22# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U11(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U11(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# isNatList X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# isNatList X -> isNatList# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U12 X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# U12 X -> U12# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# cons(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# cons(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X4, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(active# length cons(N, L) -> isNat# N, isNat# ok X -> isNat# X)
(active# take(s M, cons(N, IL)) -> isNat# N, isNat# ok X -> isNat# X)
(active# take(X1, X2) -> active# X2, active# isNatKind length V1 -> isNatIListKind# V1)
(active# take(X1, X2) -> active# X2, active# isNatKind s V1 -> isNatKind# V1)
(active# take(X1, X2) -> active# X2, active# isNatIListKind take(V1, V2) -> isNatKind# V1)
(active# take(X1, X2) -> active# X2, active# isNatIListKind take(V1, V2) -> isNatIListKind# V2)
(active# take(X1, X2) -> active# X2, active# isNatIListKind take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# take(X1, X2) -> active# X2, active# isNatIListKind cons(V1, V2) -> isNatKind# V1)
(active# take(X1, X2) -> active# X2, active# isNatIListKind cons(V1, V2) -> isNatIListKind# V2)
(active# take(X1, X2) -> active# X2, active# isNatIListKind cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# take(X1, X2) -> active# X2, active# and(X1, X2) -> and#(active X1, X2))
(active# take(X1, X2) -> active# X2, active# and(X1, X2) -> active# X1)
(active# take(X1, X2) -> active# X2, active# U91(tt(), IL, M, N) -> take#(M, IL))
(active# take(X1, X2) -> active# X2, active# U91(tt(), IL, M, N) -> cons#(N, take(M, IL)))
(active# take(X1, X2) -> active# X2, active# U91(X1, X2, X3, X4) -> U91#(active X1, X2, X3, X4))
(active# take(X1, X2) -> active# X2, active# U91(X1, X2, X3, X4) -> active# X1)
(active# take(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> isNatKind# M)
(active# take(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> isNatKind# N)
(active# take(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> isNatIListKind# IL)
(active# take(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> and#(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))))
(active# take(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> and#(and(isNat M, isNatKind M), and(isNat N, isNatKind N)))
(active# take(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, isNatIListKind IL))
(active# take(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> and#(isNat M, isNatKind M))
(active# take(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> and#(isNat N, isNatKind N))
(active# take(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> U91#(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N))
(active# take(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> isNatIList# IL)
(active# take(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> isNat# M)
(active# take(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> isNat# N)
(active# take(X1, X2) -> active# X2, active# take(0(), IL) -> isNatIListKind# IL)
(active# take(X1, X2) -> active# X2, active# take(0(), IL) -> and#(isNatIList IL, isNatIListKind IL))
(active# take(X1, X2) -> active# X2, active# take(0(), IL) -> U81# and(isNatIList IL, isNatIListKind IL))
(active# take(X1, X2) -> active# X2, active# take(0(), IL) -> isNatIList# IL)
(active# take(X1, X2) -> active# X2, active# take(X1, X2) -> take#(active X1, X2))
(active# take(X1, X2) -> active# X2, active# take(X1, X2) -> take#(X1, active X2))
(active# take(X1, X2) -> active# X2, active# take(X1, X2) -> active# X2)
(active# take(X1, X2) -> active# X2, active# take(X1, X2) -> active# X1)
(active# take(X1, X2) -> active# X2, active# U81 X -> U81# active X)
(active# take(X1, X2) -> active# X2, active# U81 X -> active# X)
(active# take(X1, X2) -> active# X2, active# U71(tt(), L) -> length# L)
(active# take(X1, X2) -> active# X2, active# U71(tt(), L) -> s# length L)
(active# take(X1, X2) -> active# X2, active# U71(X1, X2) -> U71#(active X1, X2))
(active# take(X1, X2) -> active# X2, active# U71(X1, X2) -> active# X1)
(active# take(X1, X2) -> active# X2, active# length cons(N, L) -> isNatKind# N)
(active# take(X1, X2) -> active# X2, active# length cons(N, L) -> isNatIListKind# L)
(active# take(X1, X2) -> active# X2, active# length cons(N, L) -> and#(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)))
(active# take(X1, X2) -> active# X2, active# length cons(N, L) -> and#(isNat N, isNatKind N))
(active# take(X1, X2) -> active# X2, active# length cons(N, L) -> and#(isNatList L, isNatIListKind L))
(active# take(X1, X2) -> active# X2, active# length cons(N, L) -> U71#(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L))
(active# take(X1, X2) -> active# X2, active# length cons(N, L) -> isNat# N)
(active# take(X1, X2) -> active# X2, active# length cons(N, L) -> isNatList# L)
(active# take(X1, X2) -> active# X2, active# length X -> length# active X)
(active# take(X1, X2) -> active# X2, active# length X -> active# X)
(active# take(X1, X2) -> active# X2, active# s X -> s# active X)
(active# take(X1, X2) -> active# X2, active# s X -> active# X)
(active# take(X1, X2) -> active# X2, active# U63 X -> U63# active X)
(active# take(X1, X2) -> active# X2, active# U63 X -> active# X)
(active# take(X1, X2) -> active# X2, active# U61(tt(), V1, V2) -> U62#(isNat V1, V2))
(active# take(X1, X2) -> active# X2, active# U61(tt(), V1, V2) -> isNat# V1)
(active# take(X1, X2) -> active# X2, active# U61(X1, X2, X3) -> U61#(active X1, X2, X3))
(active# take(X1, X2) -> active# X2, active# U61(X1, X2, X3) -> active# X1)
(active# take(X1, X2) -> active# X2, active# U62(tt(), V2) -> U63# isNatIList V2)
(active# take(X1, X2) -> active# X2, active# U62(tt(), V2) -> isNatIList# V2)
(active# take(X1, X2) -> active# X2, active# U62(X1, X2) -> U62#(active X1, X2))
(active# take(X1, X2) -> active# X2, active# U62(X1, X2) -> active# X1)
(active# take(X1, X2) -> active# X2, active# U53 X -> U53# active X)
(active# take(X1, X2) -> active# X2, active# U53 X -> active# X)
(active# take(X1, X2) -> active# X2, active# U51(tt(), V1, V2) -> U52#(isNat V1, V2))
(active# take(X1, X2) -> active# X2, active# U51(tt(), V1, V2) -> isNat# V1)
(active# take(X1, X2) -> active# X2, active# U51(X1, X2, X3) -> U51#(active X1, X2, X3))
(active# take(X1, X2) -> active# X2, active# U51(X1, X2, X3) -> active# X1)
(active# take(X1, X2) -> active# X2, active# U52(tt(), V2) -> U53# isNatList V2)
(active# take(X1, X2) -> active# X2, active# U52(tt(), V2) -> isNatList# V2)
(active# take(X1, X2) -> active# X2, active# U52(X1, X2) -> U52#(active X1, X2))
(active# take(X1, X2) -> active# X2, active# U52(X1, X2) -> active# X1)
(active# take(X1, X2) -> active# X2, active# isNatIList cons(V1, V2) -> isNatKind# V1)
(active# take(X1, X2) -> active# X2, active# isNatIList cons(V1, V2) -> isNatIListKind# V2)
(active# take(X1, X2) -> active# X2, active# isNatIList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# take(X1, X2) -> active# X2, active# isNatIList cons(V1, V2) -> U41#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# take(X1, X2) -> active# X2, active# isNatIList V -> isNatIListKind# V)
(active# take(X1, X2) -> active# X2, active# isNatIList V -> U31#(isNatIListKind V, V))
(active# take(X1, X2) -> active# X2, active# U43 X -> U43# active X)
(active# take(X1, X2) -> active# X2, active# U43 X -> active# X)
(active# take(X1, X2) -> active# X2, active# U41(tt(), V1, V2) -> U42#(isNat V1, V2))
(active# take(X1, X2) -> active# X2, active# U41(tt(), V1, V2) -> isNat# V1)
(active# take(X1, X2) -> active# X2, active# U41(X1, X2, X3) -> U41#(active X1, X2, X3))
(active# take(X1, X2) -> active# X2, active# U41(X1, X2, X3) -> active# X1)
(active# take(X1, X2) -> active# X2, active# U42(tt(), V2) -> isNatIList# V2)
(active# take(X1, X2) -> active# X2, active# U42(tt(), V2) -> U43# isNatIList V2)
(active# take(X1, X2) -> active# X2, active# U42(X1, X2) -> U42#(active X1, X2))
(active# take(X1, X2) -> active# X2, active# U42(X1, X2) -> active# X1)
(active# take(X1, X2) -> active# X2, active# U31(tt(), V) -> U32# isNatList V)
(active# take(X1, X2) -> active# X2, active# U31(tt(), V) -> isNatList# V)
(active# take(X1, X2) -> active# X2, active# U31(X1, X2) -> U31#(active X1, X2))
(active# take(X1, X2) -> active# X2, active# U31(X1, X2) -> active# X1)
(active# take(X1, X2) -> active# X2, active# U32 X -> U32# active X)
(active# take(X1, X2) -> active# X2, active# U32 X -> active# X)
(active# take(X1, X2) -> active# X2, active# U21(tt(), V1) -> isNat# V1)
(active# take(X1, X2) -> active# X2, active# U21(tt(), V1) -> U22# isNat V1)
(active# take(X1, X2) -> active# X2, active# U21(X1, X2) -> U21#(active X1, X2))
(active# take(X1, X2) -> active# X2, active# U21(X1, X2) -> active# X1)
(active# take(X1, X2) -> active# X2, active# isNat length V1 -> isNatIListKind# V1)
(active# take(X1, X2) -> active# X2, active# isNat length V1 -> U11#(isNatIListKind V1, V1))
(active# take(X1, X2) -> active# X2, active# isNat s V1 -> isNatKind# V1)
(active# take(X1, X2) -> active# X2, active# isNat s V1 -> U21#(isNatKind V1, V1))
(active# take(X1, X2) -> active# X2, active# U22 X -> U22# active X)
(active# take(X1, X2) -> active# X2, active# U22 X -> active# X)
(active# take(X1, X2) -> active# X2, active# U11(tt(), V1) -> isNatList# V1)
(active# take(X1, X2) -> active# X2, active# U11(tt(), V1) -> U12# isNatList V1)
(active# take(X1, X2) -> active# X2, active# U11(X1, X2) -> U11#(active X1, X2))
(active# take(X1, X2) -> active# X2, active# U11(X1, X2) -> active# X1)
(active# take(X1, X2) -> active# X2, active# isNatList take(V1, V2) -> isNatKind# V1)
(active# take(X1, X2) -> active# X2, active# isNatList take(V1, V2) -> isNatIListKind# V2)
(active# take(X1, X2) -> active# X2, active# isNatList take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# take(X1, X2) -> active# X2, active# isNatList take(V1, V2) -> U61#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# take(X1, X2) -> active# X2, active# isNatList cons(V1, V2) -> isNatKind# V1)
(active# take(X1, X2) -> active# X2, active# isNatList cons(V1, V2) -> isNatIListKind# V2)
(active# take(X1, X2) -> active# X2, active# isNatList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# take(X1, X2) -> active# X2, active# isNatList cons(V1, V2) -> U51#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# take(X1, X2) -> active# X2, active# U12 X -> U12# active X)
(active# take(X1, X2) -> active# X2, active# U12 X -> active# X)
(active# take(X1, X2) -> active# X2, active# zeros() -> cons#(0(), zeros()))
(active# take(X1, X2) -> active# X2, active# cons(X1, X2) -> active# X1)
(active# take(X1, X2) -> active# X2, active# cons(X1, X2) -> cons#(active X1, X2))
(proper# U11(X1, X2) -> proper# X2, proper# isNatKind X -> proper# X)
(proper# U11(X1, X2) -> proper# X2, proper# isNatKind X -> isNatKind# proper X)
(proper# U11(X1, X2) -> proper# X2, proper# isNatIListKind X -> proper# X)
(proper# U11(X1, X2) -> proper# X2, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# U11(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X2)
(proper# U11(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X1)
(proper# U11(X1, X2) -> proper# X2, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# U11(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# U11(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# U11(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# U11(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# U11(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# U11(X1, X2) -> proper# X2, proper# take(X1, X2) -> proper# X2)
(proper# U11(X1, X2) -> proper# X2, proper# take(X1, X2) -> proper# X1)
(proper# U11(X1, X2) -> proper# X2, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# U11(X1, X2) -> proper# X2, proper# U81 X -> proper# X)
(proper# U11(X1, X2) -> proper# X2, proper# U81 X -> U81# proper X)
(proper# U11(X1, X2) -> proper# X2, proper# U71(X1, X2) -> proper# X2)
(proper# U11(X1, X2) -> proper# X2, proper# U71(X1, X2) -> proper# X1)
(proper# U11(X1, X2) -> proper# X2, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# U11(X1, X2) -> proper# X2, proper# length X -> proper# X)
(proper# U11(X1, X2) -> proper# X2, proper# length X -> length# proper X)
(proper# U11(X1, X2) -> proper# X2, proper# s X -> proper# X)
(proper# U11(X1, X2) -> proper# X2, proper# s X -> s# proper X)
(proper# U11(X1, X2) -> proper# X2, proper# U63 X -> proper# X)
(proper# U11(X1, X2) -> proper# X2, proper# U63 X -> U63# proper X)
(proper# U11(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X3)
(proper# U11(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X2)
(proper# U11(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X1)
(proper# U11(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# U11(X1, X2) -> proper# X2, proper# U62(X1, X2) -> proper# X2)
(proper# U11(X1, X2) -> proper# X2, proper# U62(X1, X2) -> proper# X1)
(proper# U11(X1, X2) -> proper# X2, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# U11(X1, X2) -> proper# X2, proper# U53 X -> proper# X)
(proper# U11(X1, X2) -> proper# X2, proper# U53 X -> U53# proper X)
(proper# U11(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X3)
(proper# U11(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X2)
(proper# U11(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X1)
(proper# U11(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# U11(X1, X2) -> proper# X2, proper# U52(X1, X2) -> proper# X2)
(proper# U11(X1, X2) -> proper# X2, proper# U52(X1, X2) -> proper# X1)
(proper# U11(X1, X2) -> proper# X2, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# U11(X1, X2) -> proper# X2, proper# isNatIList X -> proper# X)
(proper# U11(X1, X2) -> proper# X2, proper# isNatIList X -> isNatIList# proper X)
(proper# U11(X1, X2) -> proper# X2, proper# U43 X -> proper# X)
(proper# U11(X1, X2) -> proper# X2, proper# U43 X -> U43# proper X)
(proper# U11(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X3)
(proper# U11(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X2)
(proper# U11(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X1)
(proper# U11(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# U11(X1, X2) -> proper# X2, proper# U42(X1, X2) -> proper# X2)
(proper# U11(X1, X2) -> proper# X2, proper# U42(X1, X2) -> proper# X1)
(proper# U11(X1, X2) -> proper# X2, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# U11(X1, X2) -> proper# X2, proper# U31(X1, X2) -> proper# X2)
(proper# U11(X1, X2) -> proper# X2, proper# U31(X1, X2) -> proper# X1)
(proper# U11(X1, X2) -> proper# X2, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# U11(X1, X2) -> proper# X2, proper# U32 X -> proper# X)
(proper# U11(X1, X2) -> proper# X2, proper# U32 X -> U32# proper X)
(proper# U11(X1, X2) -> proper# X2, proper# U21(X1, X2) -> proper# X2)
(proper# U11(X1, X2) -> proper# X2, proper# U21(X1, X2) -> proper# X1)
(proper# U11(X1, X2) -> proper# X2, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# U11(X1, X2) -> proper# X2, proper# isNat X -> proper# X)
(proper# U11(X1, X2) -> proper# X2, proper# isNat X -> isNat# proper X)
(proper# U11(X1, X2) -> proper# X2, proper# U22 X -> proper# X)
(proper# U11(X1, X2) -> proper# X2, proper# U22 X -> U22# proper X)
(proper# U11(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X2)
(proper# U11(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X1)
(proper# U11(X1, X2) -> proper# X2, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# U11(X1, X2) -> proper# X2, proper# isNatList X -> proper# X)
(proper# U11(X1, X2) -> proper# X2, proper# isNatList X -> isNatList# proper X)
(proper# U11(X1, X2) -> proper# X2, proper# U12 X -> proper# X)
(proper# U11(X1, X2) -> proper# X2, proper# U12 X -> U12# proper X)
(proper# U11(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X2)
(proper# U11(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1)
(proper# U11(X1, X2) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# U31(X1, X2) -> proper# X2, proper# isNatKind X -> proper# X)
(proper# U31(X1, X2) -> proper# X2, proper# isNatKind X -> isNatKind# proper X)
(proper# U31(X1, X2) -> proper# X2, proper# isNatIListKind X -> proper# X)
(proper# U31(X1, X2) -> proper# X2, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# U31(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X2)
(proper# U31(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X1)
(proper# U31(X1, X2) -> proper# X2, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# U31(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# U31(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# U31(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# U31(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# U31(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# U31(X1, X2) -> proper# X2, proper# take(X1, X2) -> proper# X2)
(proper# U31(X1, X2) -> proper# X2, proper# take(X1, X2) -> proper# X1)
(proper# U31(X1, X2) -> proper# X2, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# U31(X1, X2) -> proper# X2, proper# U81 X -> proper# X)
(proper# U31(X1, X2) -> proper# X2, proper# U81 X -> U81# proper X)
(proper# U31(X1, X2) -> proper# X2, proper# U71(X1, X2) -> proper# X2)
(proper# U31(X1, X2) -> proper# X2, proper# U71(X1, X2) -> proper# X1)
(proper# U31(X1, X2) -> proper# X2, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# U31(X1, X2) -> proper# X2, proper# length X -> proper# X)
(proper# U31(X1, X2) -> proper# X2, proper# length X -> length# proper X)
(proper# U31(X1, X2) -> proper# X2, proper# s X -> proper# X)
(proper# U31(X1, X2) -> proper# X2, proper# s X -> s# proper X)
(proper# U31(X1, X2) -> proper# X2, proper# U63 X -> proper# X)
(proper# U31(X1, X2) -> proper# X2, proper# U63 X -> U63# proper X)
(proper# U31(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X3)
(proper# U31(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X2)
(proper# U31(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X1)
(proper# U31(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# U31(X1, X2) -> proper# X2, proper# U62(X1, X2) -> proper# X2)
(proper# U31(X1, X2) -> proper# X2, proper# U62(X1, X2) -> proper# X1)
(proper# U31(X1, X2) -> proper# X2, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# U31(X1, X2) -> proper# X2, proper# U53 X -> proper# X)
(proper# U31(X1, X2) -> proper# X2, proper# U53 X -> U53# proper X)
(proper# U31(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X3)
(proper# U31(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X2)
(proper# U31(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X1)
(proper# U31(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# U31(X1, X2) -> proper# X2, proper# U52(X1, X2) -> proper# X2)
(proper# U31(X1, X2) -> proper# X2, proper# U52(X1, X2) -> proper# X1)
(proper# U31(X1, X2) -> proper# X2, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# U31(X1, X2) -> proper# X2, proper# isNatIList X -> proper# X)
(proper# U31(X1, X2) -> proper# X2, proper# isNatIList X -> isNatIList# proper X)
(proper# U31(X1, X2) -> proper# X2, proper# U43 X -> proper# X)
(proper# U31(X1, X2) -> proper# X2, proper# U43 X -> U43# proper X)
(proper# U31(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X3)
(proper# U31(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X2)
(proper# U31(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X1)
(proper# U31(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# U31(X1, X2) -> proper# X2, proper# U42(X1, X2) -> proper# X2)
(proper# U31(X1, X2) -> proper# X2, proper# U42(X1, X2) -> proper# X1)
(proper# U31(X1, X2) -> proper# X2, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# U31(X1, X2) -> proper# X2, proper# U31(X1, X2) -> proper# X2)
(proper# U31(X1, X2) -> proper# X2, proper# U31(X1, X2) -> proper# X1)
(proper# U31(X1, X2) -> proper# X2, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# U31(X1, X2) -> proper# X2, proper# U32 X -> proper# X)
(proper# U31(X1, X2) -> proper# X2, proper# U32 X -> U32# proper X)
(proper# U31(X1, X2) -> proper# X2, proper# U21(X1, X2) -> proper# X2)
(proper# U31(X1, X2) -> proper# X2, proper# U21(X1, X2) -> proper# X1)
(proper# U31(X1, X2) -> proper# X2, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# U31(X1, X2) -> proper# X2, proper# isNat X -> proper# X)
(proper# U31(X1, X2) -> proper# X2, proper# isNat X -> isNat# proper X)
(proper# U31(X1, X2) -> proper# X2, proper# U22 X -> proper# X)
(proper# U31(X1, X2) -> proper# X2, proper# U22 X -> U22# proper X)
(proper# U31(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X2)
(proper# U31(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X1)
(proper# U31(X1, X2) -> proper# X2, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# U31(X1, X2) -> proper# X2, proper# isNatList X -> proper# X)
(proper# U31(X1, X2) -> proper# X2, proper# isNatList X -> isNatList# proper X)
(proper# U31(X1, X2) -> proper# X2, proper# U12 X -> proper# X)
(proper# U31(X1, X2) -> proper# X2, proper# U12 X -> U12# proper X)
(proper# U31(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X2)
(proper# U31(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1)
(proper# U31(X1, X2) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# U41(X1, X2, X3) -> proper# X2, proper# isNatKind X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X2, proper# isNatKind X -> isNatKind# proper X)
(proper# U41(X1, X2, X3) -> proper# X2, proper# isNatIListKind X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X2, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# U41(X1, X2, X3) -> proper# X2, proper# and(X1, X2) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X2, proper# and(X1, X2) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X2, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# U41(X1, X2, X3) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# U41(X1, X2, X3) -> proper# X2, proper# take(X1, X2) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X2, proper# take(X1, X2) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X2, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# U41(X1, X2, X3) -> proper# X2, proper# U81 X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U81 X -> U81# proper X)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U71(X1, X2) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U71(X1, X2) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# U41(X1, X2, X3) -> proper# X2, proper# length X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X2, proper# length X -> length# proper X)
(proper# U41(X1, X2, X3) -> proper# X2, proper# s X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X2, proper# s X -> s# proper X)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U63 X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U63 X -> U63# proper X)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X3)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# U41(X1, X2, X3) -> proper# X2, proper# U62(X1, X2) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U62(X1, X2) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# U41(X1, X2, X3) -> proper# X2, proper# U53 X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U53 X -> U53# proper X)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X3)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# U41(X1, X2, X3) -> proper# X2, proper# U52(X1, X2) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U52(X1, X2) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# U41(X1, X2, X3) -> proper# X2, proper# isNatIList X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X2, proper# isNatIList X -> isNatIList# proper X)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U43 X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U43 X -> U43# proper X)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X3)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# U41(X1, X2, X3) -> proper# X2, proper# U42(X1, X2) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U42(X1, X2) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# U41(X1, X2, X3) -> proper# X2, proper# U31(X1, X2) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U31(X1, X2) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# U41(X1, X2, X3) -> proper# X2, proper# U32 X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U32 X -> U32# proper X)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U21(X1, X2) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U21(X1, X2) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# U41(X1, X2, X3) -> proper# X2, proper# isNat X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X2, proper# isNat X -> isNat# proper X)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U22 X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U22 X -> U22# proper X)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U11(X1, X2) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U11(X1, X2) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# U41(X1, X2, X3) -> proper# X2, proper# isNatList X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X2, proper# isNatList X -> isNatList# proper X)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U12 X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X2, proper# U12 X -> U12# proper X)
(proper# U41(X1, X2, X3) -> proper# X2, proper# cons(X1, X2) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X2, proper# cons(X1, X2) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# U51(X1, X2, X3) -> proper# X2, proper# isNatKind X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X2, proper# isNatKind X -> isNatKind# proper X)
(proper# U51(X1, X2, X3) -> proper# X2, proper# isNatIListKind X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X2, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# U51(X1, X2, X3) -> proper# X2, proper# and(X1, X2) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X2, proper# and(X1, X2) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X2, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# U51(X1, X2, X3) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# U51(X1, X2, X3) -> proper# X2, proper# take(X1, X2) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X2, proper# take(X1, X2) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X2, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# U51(X1, X2, X3) -> proper# X2, proper# U81 X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U81 X -> U81# proper X)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U71(X1, X2) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U71(X1, X2) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# U51(X1, X2, X3) -> proper# X2, proper# length X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X2, proper# length X -> length# proper X)
(proper# U51(X1, X2, X3) -> proper# X2, proper# s X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X2, proper# s X -> s# proper X)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U63 X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U63 X -> U63# proper X)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X3)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# U51(X1, X2, X3) -> proper# X2, proper# U62(X1, X2) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U62(X1, X2) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# U51(X1, X2, X3) -> proper# X2, proper# U53 X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U53 X -> U53# proper X)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X3)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# U51(X1, X2, X3) -> proper# X2, proper# U52(X1, X2) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U52(X1, X2) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# U51(X1, X2, X3) -> proper# X2, proper# isNatIList X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X2, proper# isNatIList X -> isNatIList# proper X)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U43 X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U43 X -> U43# proper X)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X3)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# U51(X1, X2, X3) -> proper# X2, proper# U42(X1, X2) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U42(X1, X2) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# U51(X1, X2, X3) -> proper# X2, proper# U31(X1, X2) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U31(X1, X2) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# U51(X1, X2, X3) -> proper# X2, proper# U32 X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U32 X -> U32# proper X)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U21(X1, X2) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U21(X1, X2) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# U51(X1, X2, X3) -> proper# X2, proper# isNat X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X2, proper# isNat X -> isNat# proper X)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U22 X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U22 X -> U22# proper X)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U11(X1, X2) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U11(X1, X2) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# U51(X1, X2, X3) -> proper# X2, proper# isNatList X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X2, proper# isNatList X -> isNatList# proper X)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U12 X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X2, proper# U12 X -> U12# proper X)
(proper# U51(X1, X2, X3) -> proper# X2, proper# cons(X1, X2) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X2, proper# cons(X1, X2) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# U61(X1, X2, X3) -> proper# X2, proper# isNatKind X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X2, proper# isNatKind X -> isNatKind# proper X)
(proper# U61(X1, X2, X3) -> proper# X2, proper# isNatIListKind X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X2, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# U61(X1, X2, X3) -> proper# X2, proper# and(X1, X2) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X2, proper# and(X1, X2) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X2, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# U61(X1, X2, X3) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# U61(X1, X2, X3) -> proper# X2, proper# take(X1, X2) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X2, proper# take(X1, X2) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X2, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# U61(X1, X2, X3) -> proper# X2, proper# U81 X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U81 X -> U81# proper X)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U71(X1, X2) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U71(X1, X2) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# U61(X1, X2, X3) -> proper# X2, proper# length X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X2, proper# length X -> length# proper X)
(proper# U61(X1, X2, X3) -> proper# X2, proper# s X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X2, proper# s X -> s# proper X)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U63 X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U63 X -> U63# proper X)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X3)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# U61(X1, X2, X3) -> proper# X2, proper# U62(X1, X2) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U62(X1, X2) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# U61(X1, X2, X3) -> proper# X2, proper# U53 X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U53 X -> U53# proper X)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X3)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# U61(X1, X2, X3) -> proper# X2, proper# U52(X1, X2) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U52(X1, X2) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# U61(X1, X2, X3) -> proper# X2, proper# isNatIList X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X2, proper# isNatIList X -> isNatIList# proper X)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U43 X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U43 X -> U43# proper X)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X3)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# U61(X1, X2, X3) -> proper# X2, proper# U42(X1, X2) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U42(X1, X2) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# U61(X1, X2, X3) -> proper# X2, proper# U31(X1, X2) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U31(X1, X2) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# U61(X1, X2, X3) -> proper# X2, proper# U32 X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U32 X -> U32# proper X)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U21(X1, X2) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U21(X1, X2) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# U61(X1, X2, X3) -> proper# X2, proper# isNat X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X2, proper# isNat X -> isNat# proper X)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U22 X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U22 X -> U22# proper X)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U11(X1, X2) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U11(X1, X2) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# U61(X1, X2, X3) -> proper# X2, proper# isNatList X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X2, proper# isNatList X -> isNatList# proper X)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U12 X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X2, proper# U12 X -> U12# proper X)
(proper# U61(X1, X2, X3) -> proper# X2, proper# cons(X1, X2) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X2, proper# cons(X1, X2) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# take(X1, X2) -> proper# X2, proper# isNatKind X -> proper# X)
(proper# take(X1, X2) -> proper# X2, proper# isNatKind X -> isNatKind# proper X)
(proper# take(X1, X2) -> proper# X2, proper# isNatIListKind X -> proper# X)
(proper# take(X1, X2) -> proper# X2, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# take(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X2)
(proper# take(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X1)
(proper# take(X1, X2) -> proper# X2, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# take(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# take(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# take(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# take(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# take(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# take(X1, X2) -> proper# X2, proper# take(X1, X2) -> proper# X2)
(proper# take(X1, X2) -> proper# X2, proper# take(X1, X2) -> proper# X1)
(proper# take(X1, X2) -> proper# X2, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# take(X1, X2) -> proper# X2, proper# U81 X -> proper# X)
(proper# take(X1, X2) -> proper# X2, proper# U81 X -> U81# proper X)
(proper# take(X1, X2) -> proper# X2, proper# U71(X1, X2) -> proper# X2)
(proper# take(X1, X2) -> proper# X2, proper# U71(X1, X2) -> proper# X1)
(proper# take(X1, X2) -> proper# X2, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# take(X1, X2) -> proper# X2, proper# length X -> proper# X)
(proper# take(X1, X2) -> proper# X2, proper# length X -> length# proper X)
(proper# take(X1, X2) -> proper# X2, proper# s X -> proper# X)
(proper# take(X1, X2) -> proper# X2, proper# s X -> s# proper X)
(proper# take(X1, X2) -> proper# X2, proper# U63 X -> proper# X)
(proper# take(X1, X2) -> proper# X2, proper# U63 X -> U63# proper X)
(proper# take(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X3)
(proper# take(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X2)
(proper# take(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X1)
(proper# take(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# take(X1, X2) -> proper# X2, proper# U62(X1, X2) -> proper# X2)
(proper# take(X1, X2) -> proper# X2, proper# U62(X1, X2) -> proper# X1)
(proper# take(X1, X2) -> proper# X2, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# take(X1, X2) -> proper# X2, proper# U53 X -> proper# X)
(proper# take(X1, X2) -> proper# X2, proper# U53 X -> U53# proper X)
(proper# take(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X3)
(proper# take(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X2)
(proper# take(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X1)
(proper# take(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# take(X1, X2) -> proper# X2, proper# U52(X1, X2) -> proper# X2)
(proper# take(X1, X2) -> proper# X2, proper# U52(X1, X2) -> proper# X1)
(proper# take(X1, X2) -> proper# X2, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# take(X1, X2) -> proper# X2, proper# isNatIList X -> proper# X)
(proper# take(X1, X2) -> proper# X2, proper# isNatIList X -> isNatIList# proper X)
(proper# take(X1, X2) -> proper# X2, proper# U43 X -> proper# X)
(proper# take(X1, X2) -> proper# X2, proper# U43 X -> U43# proper X)
(proper# take(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X3)
(proper# take(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X2)
(proper# take(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X1)
(proper# take(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# take(X1, X2) -> proper# X2, proper# U42(X1, X2) -> proper# X2)
(proper# take(X1, X2) -> proper# X2, proper# U42(X1, X2) -> proper# X1)
(proper# take(X1, X2) -> proper# X2, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# take(X1, X2) -> proper# X2, proper# U31(X1, X2) -> proper# X2)
(proper# take(X1, X2) -> proper# X2, proper# U31(X1, X2) -> proper# X1)
(proper# take(X1, X2) -> proper# X2, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# take(X1, X2) -> proper# X2, proper# U32 X -> proper# X)
(proper# take(X1, X2) -> proper# X2, proper# U32 X -> U32# proper X)
(proper# take(X1, X2) -> proper# X2, proper# U21(X1, X2) -> proper# X2)
(proper# take(X1, X2) -> proper# X2, proper# U21(X1, X2) -> proper# X1)
(proper# take(X1, X2) -> proper# X2, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# take(X1, X2) -> proper# X2, proper# isNat X -> proper# X)
(proper# take(X1, X2) -> proper# X2, proper# isNat X -> isNat# proper X)
(proper# take(X1, X2) -> proper# X2, proper# U22 X -> proper# X)
(proper# take(X1, X2) -> proper# X2, proper# U22 X -> U22# proper X)
(proper# take(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X2)
(proper# take(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X1)
(proper# take(X1, X2) -> proper# X2, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# take(X1, X2) -> proper# X2, proper# isNatList X -> proper# X)
(proper# take(X1, X2) -> proper# X2, proper# isNatList X -> isNatList# proper X)
(proper# take(X1, X2) -> proper# X2, proper# U12 X -> proper# X)
(proper# take(X1, X2) -> proper# X2, proper# U12 X -> U12# proper X)
(proper# take(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X2)
(proper# take(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1)
(proper# take(X1, X2) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# and(X1, X2) -> proper# X2, proper# isNatKind X -> proper# X)
(proper# and(X1, X2) -> proper# X2, proper# isNatKind X -> isNatKind# proper X)
(proper# and(X1, X2) -> proper# X2, proper# isNatIListKind X -> proper# X)
(proper# and(X1, X2) -> proper# X2, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# and(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X2)
(proper# and(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X1)
(proper# and(X1, X2) -> proper# X2, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# and(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# and(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# and(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# and(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# and(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# and(X1, X2) -> proper# X2, proper# take(X1, X2) -> proper# X2)
(proper# and(X1, X2) -> proper# X2, proper# take(X1, X2) -> proper# X1)
(proper# and(X1, X2) -> proper# X2, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# and(X1, X2) -> proper# X2, proper# U81 X -> proper# X)
(proper# and(X1, X2) -> proper# X2, proper# U81 X -> U81# proper X)
(proper# and(X1, X2) -> proper# X2, proper# U71(X1, X2) -> proper# X2)
(proper# and(X1, X2) -> proper# X2, proper# U71(X1, X2) -> proper# X1)
(proper# and(X1, X2) -> proper# X2, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# and(X1, X2) -> proper# X2, proper# length X -> proper# X)
(proper# and(X1, X2) -> proper# X2, proper# length X -> length# proper X)
(proper# and(X1, X2) -> proper# X2, proper# s X -> proper# X)
(proper# and(X1, X2) -> proper# X2, proper# s X -> s# proper X)
(proper# and(X1, X2) -> proper# X2, proper# U63 X -> proper# X)
(proper# and(X1, X2) -> proper# X2, proper# U63 X -> U63# proper X)
(proper# and(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X3)
(proper# and(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X2)
(proper# and(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X1)
(proper# and(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# and(X1, X2) -> proper# X2, proper# U62(X1, X2) -> proper# X2)
(proper# and(X1, X2) -> proper# X2, proper# U62(X1, X2) -> proper# X1)
(proper# and(X1, X2) -> proper# X2, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# and(X1, X2) -> proper# X2, proper# U53 X -> proper# X)
(proper# and(X1, X2) -> proper# X2, proper# U53 X -> U53# proper X)
(proper# and(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X3)
(proper# and(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X2)
(proper# and(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X1)
(proper# and(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# and(X1, X2) -> proper# X2, proper# U52(X1, X2) -> proper# X2)
(proper# and(X1, X2) -> proper# X2, proper# U52(X1, X2) -> proper# X1)
(proper# and(X1, X2) -> proper# X2, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# and(X1, X2) -> proper# X2, proper# isNatIList X -> proper# X)
(proper# and(X1, X2) -> proper# X2, proper# isNatIList X -> isNatIList# proper X)
(proper# and(X1, X2) -> proper# X2, proper# U43 X -> proper# X)
(proper# and(X1, X2) -> proper# X2, proper# U43 X -> U43# proper X)
(proper# and(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X3)
(proper# and(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X2)
(proper# and(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X1)
(proper# and(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# and(X1, X2) -> proper# X2, proper# U42(X1, X2) -> proper# X2)
(proper# and(X1, X2) -> proper# X2, proper# U42(X1, X2) -> proper# X1)
(proper# and(X1, X2) -> proper# X2, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# and(X1, X2) -> proper# X2, proper# U31(X1, X2) -> proper# X2)
(proper# and(X1, X2) -> proper# X2, proper# U31(X1, X2) -> proper# X1)
(proper# and(X1, X2) -> proper# X2, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# and(X1, X2) -> proper# X2, proper# U32 X -> proper# X)
(proper# and(X1, X2) -> proper# X2, proper# U32 X -> U32# proper X)
(proper# and(X1, X2) -> proper# X2, proper# U21(X1, X2) -> proper# X2)
(proper# and(X1, X2) -> proper# X2, proper# U21(X1, X2) -> proper# X1)
(proper# and(X1, X2) -> proper# X2, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# and(X1, X2) -> proper# X2, proper# isNat X -> proper# X)
(proper# and(X1, X2) -> proper# X2, proper# isNat X -> isNat# proper X)
(proper# and(X1, X2) -> proper# X2, proper# U22 X -> proper# X)
(proper# and(X1, X2) -> proper# X2, proper# U22 X -> U22# proper X)
(proper# and(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X2)
(proper# and(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X1)
(proper# and(X1, X2) -> proper# X2, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# and(X1, X2) -> proper# X2, proper# isNatList X -> proper# X)
(proper# and(X1, X2) -> proper# X2, proper# isNatList X -> isNatList# proper X)
(proper# and(X1, X2) -> proper# X2, proper# U12 X -> proper# X)
(proper# and(X1, X2) -> proper# X2, proper# U12 X -> U12# proper X)
(proper# and(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X2)
(proper# and(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1)
(proper# and(X1, X2) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(active# isNat length V1 -> U11#(isNatIListKind V1, V1), U11#(ok X1, ok X2) -> U11#(X1, X2))
(active# isNat length V1 -> U11#(isNatIListKind V1, V1), U11#(mark X1, X2) -> U11#(X1, X2))
(active# isNatList take(V1, V2) -> isNatIListKind# V2, isNatIListKind# ok X -> isNatIListKind# X)
(active# isNatIList cons(V1, V2) -> isNatIListKind# V2, isNatIListKind# ok X -> isNatIListKind# X)
(active# U62(tt(), V2) -> isNatIList# V2, isNatIList# ok X -> isNatIList# X)
(active# isNatIListKind take(V1, V2) -> isNatIListKind# V2, isNatIListKind# ok X -> isNatIListKind# X)
(active# U12 X -> active# X, active# isNatKind length V1 -> isNatIListKind# V1)
(active# U12 X -> active# X, active# isNatKind s V1 -> isNatKind# V1)
(active# U12 X -> active# X, active# isNatIListKind take(V1, V2) -> isNatKind# V1)
(active# U12 X -> active# X, active# isNatIListKind take(V1, V2) -> isNatIListKind# V2)
(active# U12 X -> active# X, active# isNatIListKind take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U12 X -> active# X, active# isNatIListKind cons(V1, V2) -> isNatKind# V1)
(active# U12 X -> active# X, active# isNatIListKind cons(V1, V2) -> isNatIListKind# V2)
(active# U12 X -> active# X, active# isNatIListKind cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U12 X -> active# X, active# and(X1, X2) -> and#(active X1, X2))
(active# U12 X -> active# X, active# and(X1, X2) -> active# X1)
(active# U12 X -> active# X, active# U91(tt(), IL, M, N) -> take#(M, IL))
(active# U12 X -> active# X, active# U91(tt(), IL, M, N) -> cons#(N, take(M, IL)))
(active# U12 X -> active# X, active# U91(X1, X2, X3, X4) -> U91#(active X1, X2, X3, X4))
(active# U12 X -> active# X, active# U91(X1, X2, X3, X4) -> active# X1)
(active# U12 X -> active# X, active# take(s M, cons(N, IL)) -> isNatKind# M)
(active# U12 X -> active# X, active# take(s M, cons(N, IL)) -> isNatKind# N)
(active# U12 X -> active# X, active# take(s M, cons(N, IL)) -> isNatIListKind# IL)
(active# U12 X -> active# X, active# take(s M, cons(N, IL)) -> and#(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))))
(active# U12 X -> active# X, active# take(s M, cons(N, IL)) -> and#(and(isNat M, isNatKind M), and(isNat N, isNatKind N)))
(active# U12 X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, isNatIListKind IL))
(active# U12 X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNat M, isNatKind M))
(active# U12 X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNat N, isNatKind N))
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(active# U12 X -> active# X, active# take(0(), IL) -> isNatIList# IL)
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(active# U12 X -> active# X, active# take(X1, X2) -> take#(X1, active X2))
(active# U12 X -> active# X, active# take(X1, X2) -> active# X2)
(active# U12 X -> active# X, active# take(X1, X2) -> active# X1)
(active# U12 X -> active# X, active# U81 X -> U81# active X)
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(active# U12 X -> active# X, active# U71(X1, X2) -> active# X1)
(active# U12 X -> active# X, active# length cons(N, L) -> isNatKind# N)
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(active# U12 X -> active# X, active# U63 X -> U63# active X)
(active# U12 X -> active# X, active# U63 X -> active# X)
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(active# U12 X -> active# X, active# U53 X -> active# X)
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(active# U12 X -> active# X, active# U52(X1, X2) -> active# X1)
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(active# U12 X -> active# X, active# isNatIList V -> isNatIListKind# V)
(active# U12 X -> active# X, active# isNatIList V -> U31#(isNatIListKind V, V))
(active# U12 X -> active# X, active# U43 X -> U43# active X)
(active# U12 X -> active# X, active# U43 X -> active# X)
(active# U12 X -> active# X, active# U41(tt(), V1, V2) -> U42#(isNat V1, V2))
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(active# U12 X -> active# X, active# U41(X1, X2, X3) -> U41#(active X1, X2, X3))
(active# U12 X -> active# X, active# U41(X1, X2, X3) -> active# X1)
(active# U12 X -> active# X, active# U42(tt(), V2) -> isNatIList# V2)
(active# U12 X -> active# X, active# U42(tt(), V2) -> U43# isNatIList V2)
(active# U12 X -> active# X, active# U42(X1, X2) -> U42#(active X1, X2))
(active# U12 X -> active# X, active# U42(X1, X2) -> active# X1)
(active# U12 X -> active# X, active# U31(tt(), V) -> U32# isNatList V)
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(active# U12 X -> active# X, active# U31(X1, X2) -> U31#(active X1, X2))
(active# U12 X -> active# X, active# U31(X1, X2) -> active# X1)
(active# U12 X -> active# X, active# U32 X -> U32# active X)
(active# U12 X -> active# X, active# U32 X -> active# X)
(active# U12 X -> active# X, active# U21(tt(), V1) -> isNat# V1)
(active# U12 X -> active# X, active# U21(tt(), V1) -> U22# isNat V1)
(active# U12 X -> active# X, active# U21(X1, X2) -> U21#(active X1, X2))
(active# U12 X -> active# X, active# U21(X1, X2) -> active# X1)
(active# U12 X -> active# X, active# isNat length V1 -> isNatIListKind# V1)
(active# U12 X -> active# X, active# isNat length V1 -> U11#(isNatIListKind V1, V1))
(active# U12 X -> active# X, active# isNat s V1 -> isNatKind# V1)
(active# U12 X -> active# X, active# isNat s V1 -> U21#(isNatKind V1, V1))
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(active# U12 X -> active# X, active# U22 X -> active# X)
(active# U12 X -> active# X, active# U11(tt(), V1) -> isNatList# V1)
(active# U12 X -> active# X, active# U11(tt(), V1) -> U12# isNatList V1)
(active# U12 X -> active# X, active# U11(X1, X2) -> U11#(active X1, X2))
(active# U12 X -> active# X, active# U11(X1, X2) -> active# X1)
(active# U12 X -> active# X, active# isNatList take(V1, V2) -> isNatKind# V1)
(active# U12 X -> active# X, active# isNatList take(V1, V2) -> isNatIListKind# V2)
(active# U12 X -> active# X, active# isNatList take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U12 X -> active# X, active# isNatList take(V1, V2) -> U61#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U12 X -> active# X, active# isNatList cons(V1, V2) -> isNatKind# V1)
(active# U12 X -> active# X, active# isNatList cons(V1, V2) -> isNatIListKind# V2)
(active# U12 X -> active# X, active# isNatList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U12 X -> active# X, active# isNatList cons(V1, V2) -> U51#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U12 X -> active# X, active# U12 X -> U12# active X)
(active# U12 X -> active# X, active# U12 X -> active# X)
(active# U12 X -> active# X, active# zeros() -> cons#(0(), zeros()))
(active# U12 X -> active# X, active# cons(X1, X2) -> active# X1)
(active# U12 X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2))
(active# U32 X -> active# X, active# isNatKind length V1 -> isNatIListKind# V1)
(active# U32 X -> active# X, active# isNatKind s V1 -> isNatKind# V1)
(active# U32 X -> active# X, active# isNatIListKind take(V1, V2) -> isNatKind# V1)
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(active# U32 X -> active# X, active# isNatIListKind cons(V1, V2) -> isNatKind# V1)
(active# U32 X -> active# X, active# isNatIListKind cons(V1, V2) -> isNatIListKind# V2)
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(active# U32 X -> active# X, active# and(X1, X2) -> active# X1)
(active# U32 X -> active# X, active# U91(tt(), IL, M, N) -> take#(M, IL))
(active# U32 X -> active# X, active# U91(tt(), IL, M, N) -> cons#(N, take(M, IL)))
(active# U32 X -> active# X, active# U91(X1, X2, X3, X4) -> U91#(active X1, X2, X3, X4))
(active# U32 X -> active# X, active# U91(X1, X2, X3, X4) -> active# X1)
(active# U32 X -> active# X, active# take(s M, cons(N, IL)) -> isNatKind# M)
(active# U32 X -> active# X, active# take(s M, cons(N, IL)) -> isNatKind# N)
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(active# U32 X -> active# X, active# take(X1, X2) -> take#(active X1, X2))
(active# U32 X -> active# X, active# take(X1, X2) -> take#(X1, active X2))
(active# U32 X -> active# X, active# take(X1, X2) -> active# X2)
(active# U32 X -> active# X, active# take(X1, X2) -> active# X1)
(active# U32 X -> active# X, active# U81 X -> U81# active X)
(active# U32 X -> active# X, active# U81 X -> active# X)
(active# U32 X -> active# X, active# U71(tt(), L) -> length# L)
(active# U32 X -> active# X, active# U71(tt(), L) -> s# length L)
(active# U32 X -> active# X, active# U71(X1, X2) -> U71#(active X1, X2))
(active# U32 X -> active# X, active# U71(X1, X2) -> active# X1)
(active# U32 X -> active# X, active# length cons(N, L) -> isNatKind# N)
(active# U32 X -> active# X, active# length cons(N, L) -> isNatIListKind# L)
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(active# U32 X -> active# X, active# length X -> length# active X)
(active# U32 X -> active# X, active# length X -> active# X)
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(active# U32 X -> active# X, active# U63 X -> U63# active X)
(active# U32 X -> active# X, active# U63 X -> active# X)
(active# U32 X -> active# X, active# U61(tt(), V1, V2) -> U62#(isNat V1, V2))
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(active# U32 X -> active# X, active# U61(X1, X2, X3) -> active# X1)
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(active# U32 X -> active# X, active# U62(X1, X2) -> active# X1)
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(active# U32 X -> active# X, active# U52(X1, X2) -> active# X1)
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(active# U32 X -> active# X, active# isNatIList V -> isNatIListKind# V)
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(active# U32 X -> active# X, active# U41(X1, X2, X3) -> active# X1)
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(active# U32 X -> active# X, active# U42(X1, X2) -> U42#(active X1, X2))
(active# U32 X -> active# X, active# U42(X1, X2) -> active# X1)
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(active# U32 X -> active# X, active# isNat length V1 -> isNatIListKind# V1)
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(active# U32 X -> active# X, active# U11(tt(), V1) -> isNatList# V1)
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(active# U32 X -> active# X, active# U11(X1, X2) -> U11#(active X1, X2))
(active# U32 X -> active# X, active# U11(X1, X2) -> active# X1)
(active# U32 X -> active# X, active# isNatList take(V1, V2) -> isNatKind# V1)
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(active# U32 X -> active# X, active# isNatList take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U32 X -> active# X, active# isNatList take(V1, V2) -> U61#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U32 X -> active# X, active# isNatList cons(V1, V2) -> isNatKind# V1)
(active# U32 X -> active# X, active# isNatList cons(V1, V2) -> isNatIListKind# V2)
(active# U32 X -> active# X, active# isNatList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U32 X -> active# X, active# isNatList cons(V1, V2) -> U51#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U32 X -> active# X, active# U12 X -> U12# active X)
(active# U32 X -> active# X, active# U12 X -> active# X)
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(active# U32 X -> active# X, active# cons(X1, X2) -> active# X1)
(active# U32 X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2))
(active# U53 X -> active# X, active# isNatKind length V1 -> isNatIListKind# V1)
(active# U53 X -> active# X, active# isNatKind s V1 -> isNatKind# V1)
(active# U53 X -> active# X, active# isNatIListKind take(V1, V2) -> isNatKind# V1)
(active# U53 X -> active# X, active# isNatIListKind take(V1, V2) -> isNatIListKind# V2)
(active# U53 X -> active# X, active# isNatIListKind take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U53 X -> active# X, active# isNatIListKind cons(V1, V2) -> isNatKind# V1)
(active# U53 X -> active# X, active# isNatIListKind cons(V1, V2) -> isNatIListKind# V2)
(active# U53 X -> active# X, active# isNatIListKind cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U53 X -> active# X, active# and(X1, X2) -> and#(active X1, X2))
(active# U53 X -> active# X, active# and(X1, X2) -> active# X1)
(active# U53 X -> active# X, active# U91(tt(), IL, M, N) -> take#(M, IL))
(active# U53 X -> active# X, active# U91(tt(), IL, M, N) -> cons#(N, take(M, IL)))
(active# U53 X -> active# X, active# U91(X1, X2, X3, X4) -> U91#(active X1, X2, X3, X4))
(active# U53 X -> active# X, active# U91(X1, X2, X3, X4) -> active# X1)
(active# U53 X -> active# X, active# take(s M, cons(N, IL)) -> isNatKind# M)
(active# U53 X -> active# X, active# take(s M, cons(N, IL)) -> isNatKind# N)
(active# U53 X -> active# X, active# take(s M, cons(N, IL)) -> isNatIListKind# IL)
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(active# U53 X -> active# X, active# take(X1, X2) -> active# X2)
(active# U53 X -> active# X, active# take(X1, X2) -> active# X1)
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(active# U53 X -> active# X, active# U71(X1, X2) -> active# X1)
(active# U53 X -> active# X, active# length cons(N, L) -> isNatKind# N)
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(active# U53 X -> active# X, active# U63 X -> U63# active X)
(active# U53 X -> active# X, active# U63 X -> active# X)
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(active# U53 X -> active# X, active# U61(X1, X2, X3) -> active# X1)
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(active# U53 X -> active# X, active# U62(X1, X2) -> active# X1)
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(active# U53 X -> active# X, active# U51(X1, X2, X3) -> active# X1)
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(active# U53 X -> active# X, active# U52(X1, X2) -> active# X1)
(active# U53 X -> active# X, active# isNatIList cons(V1, V2) -> isNatKind# V1)
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(active# U53 X -> active# X, active# isNatIList V -> isNatIListKind# V)
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(active# U53 X -> active# X, active# U43 X -> active# X)
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(active# U53 X -> active# X, active# U41(X1, X2, X3) -> active# X1)
(active# U53 X -> active# X, active# U42(tt(), V2) -> isNatIList# V2)
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(active# U53 X -> active# X, active# U42(X1, X2) -> U42#(active X1, X2))
(active# U53 X -> active# X, active# U42(X1, X2) -> active# X1)
(active# U53 X -> active# X, active# U31(tt(), V) -> U32# isNatList V)
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(active# U53 X -> active# X, active# U31(X1, X2) -> U31#(active X1, X2))
(active# U53 X -> active# X, active# U31(X1, X2) -> active# X1)
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(active# U53 X -> active# X, active# U32 X -> active# X)
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(active# U53 X -> active# X, active# U21(X1, X2) -> active# X1)
(active# U53 X -> active# X, active# isNat length V1 -> isNatIListKind# V1)
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(active# U53 X -> active# X, active# U22 X -> active# X)
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(active# U53 X -> active# X, active# U12 X -> active# X)
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(active# U53 X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2))
(active# s X -> active# X, active# isNatKind length V1 -> isNatIListKind# V1)
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(active# s X -> active# X, active# isNatIListKind take(V1, V2) -> isNatKind# V1)
(active# s X -> active# X, active# isNatIListKind take(V1, V2) -> isNatIListKind# V2)
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(active# s X -> active# X, active# isNatIListKind cons(V1, V2) -> isNatKind# V1)
(active# s X -> active# X, active# isNatIListKind cons(V1, V2) -> isNatIListKind# V2)
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(active# s X -> active# X, active# take(s M, cons(N, IL)) -> isNatKind# M)
(active# s X -> active# X, active# take(s M, cons(N, IL)) -> isNatKind# N)
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(active# s X -> active# X, active# take(X1, X2) -> take#(X1, active X2))
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(active# s X -> active# X, active# U71(X1, X2) -> active# X1)
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(active# s X -> active# X, active# length X -> active# X)
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(active# s X -> active# X, active# U42(X1, X2) -> active# X1)
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(active# s X -> active# X, active# U21(X1, X2) -> active# X1)
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(active# s X -> active# X, active# U11(tt(), V1) -> U12# isNatList V1)
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(active# s X -> active# X, active# U11(X1, X2) -> active# X1)
(active# s X -> active# X, active# isNatList take(V1, V2) -> isNatKind# V1)
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(active# s X -> active# X, active# isNatList take(V1, V2) -> U61#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# s X -> active# X, active# isNatList cons(V1, V2) -> isNatKind# V1)
(active# s X -> active# X, active# isNatList cons(V1, V2) -> isNatIListKind# V2)
(active# s X -> active# X, active# isNatList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# s X -> active# X, active# isNatList cons(V1, V2) -> U51#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# s X -> active# X, active# U12 X -> U12# active X)
(active# s X -> active# X, active# U12 X -> active# X)
(active# s X -> active# X, active# zeros() -> cons#(0(), zeros()))
(active# s X -> active# X, active# cons(X1, X2) -> active# X1)
(active# s X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2))
(active# U81 X -> active# X, active# isNatKind length V1 -> isNatIListKind# V1)
(active# U81 X -> active# X, active# isNatKind s V1 -> isNatKind# V1)
(active# U81 X -> active# X, active# isNatIListKind take(V1, V2) -> isNatKind# V1)
(active# U81 X -> active# X, active# isNatIListKind take(V1, V2) -> isNatIListKind# V2)
(active# U81 X -> active# X, active# isNatIListKind take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U81 X -> active# X, active# isNatIListKind cons(V1, V2) -> isNatKind# V1)
(active# U81 X -> active# X, active# isNatIListKind cons(V1, V2) -> isNatIListKind# V2)
(active# U81 X -> active# X, active# isNatIListKind cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U81 X -> active# X, active# and(X1, X2) -> and#(active X1, X2))
(active# U81 X -> active# X, active# and(X1, X2) -> active# X1)
(active# U81 X -> active# X, active# U91(tt(), IL, M, N) -> take#(M, IL))
(active# U81 X -> active# X, active# U91(tt(), IL, M, N) -> cons#(N, take(M, IL)))
(active# U81 X -> active# X, active# U91(X1, X2, X3, X4) -> U91#(active X1, X2, X3, X4))
(active# U81 X -> active# X, active# U91(X1, X2, X3, X4) -> active# X1)
(active# U81 X -> active# X, active# take(s M, cons(N, IL)) -> isNatKind# M)
(active# U81 X -> active# X, active# take(s M, cons(N, IL)) -> isNatKind# N)
(active# U81 X -> active# X, active# take(s M, cons(N, IL)) -> isNatIListKind# IL)
(active# U81 X -> active# X, active# take(s M, cons(N, IL)) -> and#(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))))
(active# U81 X -> active# X, active# take(s M, cons(N, IL)) -> and#(and(isNat M, isNatKind M), and(isNat N, isNatKind N)))
(active# U81 X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, isNatIListKind IL))
(active# U81 X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNat M, isNatKind M))
(active# U81 X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNat N, isNatKind N))
(active# U81 X -> active# X, active# take(s M, cons(N, IL)) -> U91#(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N))
(active# U81 X -> active# X, active# take(s M, cons(N, IL)) -> isNatIList# IL)
(active# U81 X -> active# X, active# take(s M, cons(N, IL)) -> isNat# M)
(active# U81 X -> active# X, active# take(s M, cons(N, IL)) -> isNat# N)
(active# U81 X -> active# X, active# take(0(), IL) -> isNatIListKind# IL)
(active# U81 X -> active# X, active# take(0(), IL) -> and#(isNatIList IL, isNatIListKind IL))
(active# U81 X -> active# X, active# take(0(), IL) -> U81# and(isNatIList IL, isNatIListKind IL))
(active# U81 X -> active# X, active# take(0(), IL) -> isNatIList# IL)
(active# U81 X -> active# X, active# take(X1, X2) -> take#(active X1, X2))
(active# U81 X -> active# X, active# take(X1, X2) -> take#(X1, active X2))
(active# U81 X -> active# X, active# take(X1, X2) -> active# X2)
(active# U81 X -> active# X, active# take(X1, X2) -> active# X1)
(active# U81 X -> active# X, active# U81 X -> U81# active X)
(active# U81 X -> active# X, active# U81 X -> active# X)
(active# U81 X -> active# X, active# U71(tt(), L) -> length# L)
(active# U81 X -> active# X, active# U71(tt(), L) -> s# length L)
(active# U81 X -> active# X, active# U71(X1, X2) -> U71#(active X1, X2))
(active# U81 X -> active# X, active# U71(X1, X2) -> active# X1)
(active# U81 X -> active# X, active# length cons(N, L) -> isNatKind# N)
(active# U81 X -> active# X, active# length cons(N, L) -> isNatIListKind# L)
(active# U81 X -> active# X, active# length cons(N, L) -> and#(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)))
(active# U81 X -> active# X, active# length cons(N, L) -> and#(isNat N, isNatKind N))
(active# U81 X -> active# X, active# length cons(N, L) -> and#(isNatList L, isNatIListKind L))
(active# U81 X -> active# X, active# length cons(N, L) -> U71#(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L))
(active# U81 X -> active# X, active# length cons(N, L) -> isNat# N)
(active# U81 X -> active# X, active# length cons(N, L) -> isNatList# L)
(active# U81 X -> active# X, active# length X -> length# active X)
(active# U81 X -> active# X, active# length X -> active# X)
(active# U81 X -> active# X, active# s X -> s# active X)
(active# U81 X -> active# X, active# s X -> active# X)
(active# U81 X -> active# X, active# U63 X -> U63# active X)
(active# U81 X -> active# X, active# U63 X -> active# X)
(active# U81 X -> active# X, active# U61(tt(), V1, V2) -> U62#(isNat V1, V2))
(active# U81 X -> active# X, active# U61(tt(), V1, V2) -> isNat# V1)
(active# U81 X -> active# X, active# U61(X1, X2, X3) -> U61#(active X1, X2, X3))
(active# U81 X -> active# X, active# U61(X1, X2, X3) -> active# X1)
(active# U81 X -> active# X, active# U62(tt(), V2) -> U63# isNatIList V2)
(active# U81 X -> active# X, active# U62(tt(), V2) -> isNatIList# V2)
(active# U81 X -> active# X, active# U62(X1, X2) -> U62#(active X1, X2))
(active# U81 X -> active# X, active# U62(X1, X2) -> active# X1)
(active# U81 X -> active# X, active# U53 X -> U53# active X)
(active# U81 X -> active# X, active# U53 X -> active# X)
(active# U81 X -> active# X, active# U51(tt(), V1, V2) -> U52#(isNat V1, V2))
(active# U81 X -> active# X, active# U51(tt(), V1, V2) -> isNat# V1)
(active# U81 X -> active# X, active# U51(X1, X2, X3) -> U51#(active X1, X2, X3))
(active# U81 X -> active# X, active# U51(X1, X2, X3) -> active# X1)
(active# U81 X -> active# X, active# U52(tt(), V2) -> U53# isNatList V2)
(active# U81 X -> active# X, active# U52(tt(), V2) -> isNatList# V2)
(active# U81 X -> active# X, active# U52(X1, X2) -> U52#(active X1, X2))
(active# U81 X -> active# X, active# U52(X1, X2) -> active# X1)
(active# U81 X -> active# X, active# isNatIList cons(V1, V2) -> isNatKind# V1)
(active# U81 X -> active# X, active# isNatIList cons(V1, V2) -> isNatIListKind# V2)
(active# U81 X -> active# X, active# isNatIList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U81 X -> active# X, active# isNatIList cons(V1, V2) -> U41#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U81 X -> active# X, active# isNatIList V -> isNatIListKind# V)
(active# U81 X -> active# X, active# isNatIList V -> U31#(isNatIListKind V, V))
(active# U81 X -> active# X, active# U43 X -> U43# active X)
(active# U81 X -> active# X, active# U43 X -> active# X)
(active# U81 X -> active# X, active# U41(tt(), V1, V2) -> U42#(isNat V1, V2))
(active# U81 X -> active# X, active# U41(tt(), V1, V2) -> isNat# V1)
(active# U81 X -> active# X, active# U41(X1, X2, X3) -> U41#(active X1, X2, X3))
(active# U81 X -> active# X, active# U41(X1, X2, X3) -> active# X1)
(active# U81 X -> active# X, active# U42(tt(), V2) -> isNatIList# V2)
(active# U81 X -> active# X, active# U42(tt(), V2) -> U43# isNatIList V2)
(active# U81 X -> active# X, active# U42(X1, X2) -> U42#(active X1, X2))
(active# U81 X -> active# X, active# U42(X1, X2) -> active# X1)
(active# U81 X -> active# X, active# U31(tt(), V) -> U32# isNatList V)
(active# U81 X -> active# X, active# U31(tt(), V) -> isNatList# V)
(active# U81 X -> active# X, active# U31(X1, X2) -> U31#(active X1, X2))
(active# U81 X -> active# X, active# U31(X1, X2) -> active# X1)
(active# U81 X -> active# X, active# U32 X -> U32# active X)
(active# U81 X -> active# X, active# U32 X -> active# X)
(active# U81 X -> active# X, active# U21(tt(), V1) -> isNat# V1)
(active# U81 X -> active# X, active# U21(tt(), V1) -> U22# isNat V1)
(active# U81 X -> active# X, active# U21(X1, X2) -> U21#(active X1, X2))
(active# U81 X -> active# X, active# U21(X1, X2) -> active# X1)
(active# U81 X -> active# X, active# isNat length V1 -> isNatIListKind# V1)
(active# U81 X -> active# X, active# isNat length V1 -> U11#(isNatIListKind V1, V1))
(active# U81 X -> active# X, active# isNat s V1 -> isNatKind# V1)
(active# U81 X -> active# X, active# isNat s V1 -> U21#(isNatKind V1, V1))
(active# U81 X -> active# X, active# U22 X -> U22# active X)
(active# U81 X -> active# X, active# U22 X -> active# X)
(active# U81 X -> active# X, active# U11(tt(), V1) -> isNatList# V1)
(active# U81 X -> active# X, active# U11(tt(), V1) -> U12# isNatList V1)
(active# U81 X -> active# X, active# U11(X1, X2) -> U11#(active X1, X2))
(active# U81 X -> active# X, active# U11(X1, X2) -> active# X1)
(active# U81 X -> active# X, active# isNatList take(V1, V2) -> isNatKind# V1)
(active# U81 X -> active# X, active# isNatList take(V1, V2) -> isNatIListKind# V2)
(active# U81 X -> active# X, active# isNatList take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U81 X -> active# X, active# isNatList take(V1, V2) -> U61#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U81 X -> active# X, active# isNatList cons(V1, V2) -> isNatKind# V1)
(active# U81 X -> active# X, active# isNatList cons(V1, V2) -> isNatIListKind# V2)
(active# U81 X -> active# X, active# isNatList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U81 X -> active# X, active# isNatList cons(V1, V2) -> U51#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U81 X -> active# X, active# U12 X -> U12# active X)
(active# U81 X -> active# X, active# U12 X -> active# X)
(active# U81 X -> active# X, active# zeros() -> cons#(0(), zeros()))
(active# U81 X -> active# X, active# cons(X1, X2) -> active# X1)
(active# U81 X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2))
(U12# mark X -> U12# X, U12# ok X -> U12# X)
(U12# mark X -> U12# X, U12# mark X -> U12# X)
(isNatList# ok X -> isNatList# X, isNatList# ok X -> isNatList# X)
(U22# ok X -> U22# X, U22# ok X -> U22# X)
(U22# ok X -> U22# X, U22# mark X -> U22# X)
(U32# mark X -> U32# X, U32# ok X -> U32# X)
(U32# mark X -> U32# X, U32# mark X -> U32# X)
(U43# mark X -> U43# X, U43# ok X -> U43# X)
(U43# mark X -> U43# X, U43# mark X -> U43# X)
(isNatIList# ok X -> isNatIList# X, isNatIList# ok X -> isNatIList# X)
(U53# ok X -> U53# X, U53# ok X -> U53# X)
(U53# ok X -> U53# X, U53# mark X -> U53# X)
(U63# ok X -> U63# X, U63# ok X -> U63# X)
(U63# ok X -> U63# X, U63# mark X -> U63# X)
(s# ok X -> s# X, s# ok X -> s# X)
(s# ok X -> s# X, s# mark X -> s# X)
(length# ok X -> length# X, length# ok X -> length# X)
(length# ok X -> length# X, length# mark X -> length# X)
(U81# ok X -> U81# X, U81# ok X -> U81# X)
(U81# ok X -> U81# X, U81# mark X -> U81# X)
(isNatKind# ok X -> isNatKind# X, isNatKind# ok X -> isNatKind# X)
(proper# isNatList X -> proper# X, proper# isNatKind X -> proper# X)
(proper# isNatList X -> proper# X, proper# isNatKind X -> isNatKind# proper X)
(proper# isNatList X -> proper# X, proper# isNatIListKind X -> proper# X)
(proper# isNatList X -> proper# X, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# isNatList X -> proper# X, proper# and(X1, X2) -> proper# X2)
(proper# isNatList X -> proper# X, proper# and(X1, X2) -> proper# X1)
(proper# isNatList X -> proper# X, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# isNatList X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# isNatList X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# isNatList X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# isNatList X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# isNatList X -> proper# X, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# isNatList X -> proper# X, proper# take(X1, X2) -> proper# X2)
(proper# isNatList X -> proper# X, proper# take(X1, X2) -> proper# X1)
(proper# isNatList X -> proper# X, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# isNatList X -> proper# X, proper# U81 X -> proper# X)
(proper# isNatList X -> proper# X, proper# U81 X -> U81# proper X)
(proper# isNatList X -> proper# X, proper# U71(X1, X2) -> proper# X2)
(proper# isNatList X -> proper# X, proper# U71(X1, X2) -> proper# X1)
(proper# isNatList X -> proper# X, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# isNatList X -> proper# X, proper# length X -> proper# X)
(proper# isNatList X -> proper# X, proper# length X -> length# proper X)
(proper# isNatList X -> proper# X, proper# s X -> proper# X)
(proper# isNatList X -> proper# X, proper# s X -> s# proper X)
(proper# isNatList X -> proper# X, proper# U63 X -> proper# X)
(proper# isNatList X -> proper# X, proper# U63 X -> U63# proper X)
(proper# isNatList X -> proper# X, proper# U61(X1, X2, X3) -> proper# X3)
(proper# isNatList X -> proper# X, proper# U61(X1, X2, X3) -> proper# X2)
(proper# isNatList X -> proper# X, proper# U61(X1, X2, X3) -> proper# X1)
(proper# isNatList X -> proper# X, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# isNatList X -> proper# X, proper# U62(X1, X2) -> proper# X2)
(proper# isNatList X -> proper# X, proper# U62(X1, X2) -> proper# X1)
(proper# isNatList X -> proper# X, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# isNatList X -> proper# X, proper# U53 X -> proper# X)
(proper# isNatList X -> proper# X, proper# U53 X -> U53# proper X)
(proper# isNatList X -> proper# X, proper# U51(X1, X2, X3) -> proper# X3)
(proper# isNatList X -> proper# X, proper# U51(X1, X2, X3) -> proper# X2)
(proper# isNatList X -> proper# X, proper# U51(X1, X2, X3) -> proper# X1)
(proper# isNatList X -> proper# X, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# isNatList X -> proper# X, proper# U52(X1, X2) -> proper# X2)
(proper# isNatList X -> proper# X, proper# U52(X1, X2) -> proper# X1)
(proper# isNatList X -> proper# X, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# isNatList X -> proper# X, proper# isNatIList X -> proper# X)
(proper# isNatList X -> proper# X, proper# isNatIList X -> isNatIList# proper X)
(proper# isNatList X -> proper# X, proper# U43 X -> proper# X)
(proper# isNatList X -> proper# X, proper# U43 X -> U43# proper X)
(proper# isNatList X -> proper# X, proper# U41(X1, X2, X3) -> proper# X3)
(proper# isNatList X -> proper# X, proper# U41(X1, X2, X3) -> proper# X2)
(proper# isNatList X -> proper# X, proper# U41(X1, X2, X3) -> proper# X1)
(proper# isNatList X -> proper# X, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# isNatList X -> proper# X, proper# U42(X1, X2) -> proper# X2)
(proper# isNatList X -> proper# X, proper# U42(X1, X2) -> proper# X1)
(proper# isNatList X -> proper# X, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# isNatList X -> proper# X, proper# U31(X1, X2) -> proper# X2)
(proper# isNatList X -> proper# X, proper# U31(X1, X2) -> proper# X1)
(proper# isNatList X -> proper# X, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# isNatList X -> proper# X, proper# U32 X -> proper# X)
(proper# isNatList X -> proper# X, proper# U32 X -> U32# proper X)
(proper# isNatList X -> proper# X, proper# U21(X1, X2) -> proper# X2)
(proper# isNatList X -> proper# X, proper# U21(X1, X2) -> proper# X1)
(proper# isNatList X -> proper# X, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# isNatList X -> proper# X, proper# isNat X -> proper# X)
(proper# isNatList X -> proper# X, proper# isNat X -> isNat# proper X)
(proper# isNatList X -> proper# X, proper# U22 X -> proper# X)
(proper# isNatList X -> proper# X, proper# U22 X -> U22# proper X)
(proper# isNatList X -> proper# X, proper# U11(X1, X2) -> proper# X2)
(proper# isNatList X -> proper# X, proper# U11(X1, X2) -> proper# X1)
(proper# isNatList X -> proper# X, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# isNatList X -> proper# X, proper# isNatList X -> proper# X)
(proper# isNatList X -> proper# X, proper# isNatList X -> isNatList# proper X)
(proper# isNatList X -> proper# X, proper# U12 X -> proper# X)
(proper# isNatList X -> proper# X, proper# U12 X -> U12# proper X)
(proper# isNatList X -> proper# X, proper# cons(X1, X2) -> proper# X2)
(proper# isNatList X -> proper# X, proper# cons(X1, X2) -> proper# X1)
(proper# isNatList X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# isNat X -> proper# X, proper# isNatKind X -> proper# X)
(proper# isNat X -> proper# X, proper# isNatKind X -> isNatKind# proper X)
(proper# isNat X -> proper# X, proper# isNatIListKind X -> proper# X)
(proper# isNat X -> proper# X, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# isNat X -> proper# X, proper# and(X1, X2) -> proper# X2)
(proper# isNat X -> proper# X, proper# and(X1, X2) -> proper# X1)
(proper# isNat X -> proper# X, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# isNat X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# isNat X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# isNat X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# isNat X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# isNat X -> proper# X, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# isNat X -> proper# X, proper# take(X1, X2) -> proper# X2)
(proper# isNat X -> proper# X, proper# take(X1, X2) -> proper# X1)
(proper# isNat X -> proper# X, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# isNat X -> proper# X, proper# U81 X -> proper# X)
(proper# isNat X -> proper# X, proper# U81 X -> U81# proper X)
(proper# isNat X -> proper# X, proper# U71(X1, X2) -> proper# X2)
(proper# isNat X -> proper# X, proper# U71(X1, X2) -> proper# X1)
(proper# isNat X -> proper# X, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# isNat X -> proper# X, proper# length X -> proper# X)
(proper# isNat X -> proper# X, proper# length X -> length# proper X)
(proper# isNat X -> proper# X, proper# s X -> proper# X)
(proper# isNat X -> proper# X, proper# s X -> s# proper X)
(proper# isNat X -> proper# X, proper# U63 X -> proper# X)
(proper# isNat X -> proper# X, proper# U63 X -> U63# proper X)
(proper# isNat X -> proper# X, proper# U61(X1, X2, X3) -> proper# X3)
(proper# isNat X -> proper# X, proper# U61(X1, X2, X3) -> proper# X2)
(proper# isNat X -> proper# X, proper# U61(X1, X2, X3) -> proper# X1)
(proper# isNat X -> proper# X, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# isNat X -> proper# X, proper# U62(X1, X2) -> proper# X2)
(proper# isNat X -> proper# X, proper# U62(X1, X2) -> proper# X1)
(proper# isNat X -> proper# X, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# isNat X -> proper# X, proper# U53 X -> proper# X)
(proper# isNat X -> proper# X, proper# U53 X -> U53# proper X)
(proper# isNat X -> proper# X, proper# U51(X1, X2, X3) -> proper# X3)
(proper# isNat X -> proper# X, proper# U51(X1, X2, X3) -> proper# X2)
(proper# isNat X -> proper# X, proper# U51(X1, X2, X3) -> proper# X1)
(proper# isNat X -> proper# X, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# isNat X -> proper# X, proper# U52(X1, X2) -> proper# X2)
(proper# isNat X -> proper# X, proper# U52(X1, X2) -> proper# X1)
(proper# isNat X -> proper# X, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# isNat X -> proper# X, proper# isNatIList X -> proper# X)
(proper# isNat X -> proper# X, proper# isNatIList X -> isNatIList# proper X)
(proper# isNat X -> proper# X, proper# U43 X -> proper# X)
(proper# isNat X -> proper# X, proper# U43 X -> U43# proper X)
(proper# isNat X -> proper# X, proper# U41(X1, X2, X3) -> proper# X3)
(proper# isNat X -> proper# X, proper# U41(X1, X2, X3) -> proper# X2)
(proper# isNat X -> proper# X, proper# U41(X1, X2, X3) -> proper# X1)
(proper# isNat X -> proper# X, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# isNat X -> proper# X, proper# U42(X1, X2) -> proper# X2)
(proper# isNat X -> proper# X, proper# U42(X1, X2) -> proper# X1)
(proper# isNat X -> proper# X, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# isNat X -> proper# X, proper# U31(X1, X2) -> proper# X2)
(proper# isNat X -> proper# X, proper# U31(X1, X2) -> proper# X1)
(proper# isNat X -> proper# X, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# isNat X -> proper# X, proper# U32 X -> proper# X)
(proper# isNat X -> proper# X, proper# U32 X -> U32# proper X)
(proper# isNat X -> proper# X, proper# U21(X1, X2) -> proper# X2)
(proper# isNat X -> proper# X, proper# U21(X1, X2) -> proper# X1)
(proper# isNat X -> proper# X, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# isNat X -> proper# X, proper# isNat X -> proper# X)
(proper# isNat X -> proper# X, proper# isNat X -> isNat# proper X)
(proper# isNat X -> proper# X, proper# U22 X -> proper# X)
(proper# isNat X -> proper# X, proper# U22 X -> U22# proper X)
(proper# isNat X -> proper# X, proper# U11(X1, X2) -> proper# X2)
(proper# isNat X -> proper# X, proper# U11(X1, X2) -> proper# X1)
(proper# isNat X -> proper# X, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# isNat X -> proper# X, proper# isNatList X -> proper# X)
(proper# isNat X -> proper# X, proper# isNatList X -> isNatList# proper X)
(proper# isNat X -> proper# X, proper# U12 X -> proper# X)
(proper# isNat X -> proper# X, proper# U12 X -> U12# proper X)
(proper# isNat X -> proper# X, proper# cons(X1, X2) -> proper# X2)
(proper# isNat X -> proper# X, proper# cons(X1, X2) -> proper# X1)
(proper# isNat X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# U43 X -> proper# X, proper# isNatKind X -> proper# X)
(proper# U43 X -> proper# X, proper# isNatKind X -> isNatKind# proper X)
(proper# U43 X -> proper# X, proper# isNatIListKind X -> proper# X)
(proper# U43 X -> proper# X, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# U43 X -> proper# X, proper# and(X1, X2) -> proper# X2)
(proper# U43 X -> proper# X, proper# and(X1, X2) -> proper# X1)
(proper# U43 X -> proper# X, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# U43 X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# U43 X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# U43 X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# U43 X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# U43 X -> proper# X, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# U43 X -> proper# X, proper# take(X1, X2) -> proper# X2)
(proper# U43 X -> proper# X, proper# take(X1, X2) -> proper# X1)
(proper# U43 X -> proper# X, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# U43 X -> proper# X, proper# U81 X -> proper# X)
(proper# U43 X -> proper# X, proper# U81 X -> U81# proper X)
(proper# U43 X -> proper# X, proper# U71(X1, X2) -> proper# X2)
(proper# U43 X -> proper# X, proper# U71(X1, X2) -> proper# X1)
(proper# U43 X -> proper# X, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# U43 X -> proper# X, proper# length X -> proper# X)
(proper# U43 X -> proper# X, proper# length X -> length# proper X)
(proper# U43 X -> proper# X, proper# s X -> proper# X)
(proper# U43 X -> proper# X, proper# s X -> s# proper X)
(proper# U43 X -> proper# X, proper# U63 X -> proper# X)
(proper# U43 X -> proper# X, proper# U63 X -> U63# proper X)
(proper# U43 X -> proper# X, proper# U61(X1, X2, X3) -> proper# X3)
(proper# U43 X -> proper# X, proper# U61(X1, X2, X3) -> proper# X2)
(proper# U43 X -> proper# X, proper# U61(X1, X2, X3) -> proper# X1)
(proper# U43 X -> proper# X, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# U43 X -> proper# X, proper# U62(X1, X2) -> proper# X2)
(proper# U43 X -> proper# X, proper# U62(X1, X2) -> proper# X1)
(proper# U43 X -> proper# X, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# U43 X -> proper# X, proper# U53 X -> proper# X)
(proper# U43 X -> proper# X, proper# U53 X -> U53# proper X)
(proper# U43 X -> proper# X, proper# U51(X1, X2, X3) -> proper# X3)
(proper# U43 X -> proper# X, proper# U51(X1, X2, X3) -> proper# X2)
(proper# U43 X -> proper# X, proper# U51(X1, X2, X3) -> proper# X1)
(proper# U43 X -> proper# X, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# U43 X -> proper# X, proper# U52(X1, X2) -> proper# X2)
(proper# U43 X -> proper# X, proper# U52(X1, X2) -> proper# X1)
(proper# U43 X -> proper# X, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# U43 X -> proper# X, proper# isNatIList X -> proper# X)
(proper# U43 X -> proper# X, proper# isNatIList X -> isNatIList# proper X)
(proper# U43 X -> proper# X, proper# U43 X -> proper# X)
(proper# U43 X -> proper# X, proper# U43 X -> U43# proper X)
(proper# U43 X -> proper# X, proper# U41(X1, X2, X3) -> proper# X3)
(proper# U43 X -> proper# X, proper# U41(X1, X2, X3) -> proper# X2)
(proper# U43 X -> proper# X, proper# U41(X1, X2, X3) -> proper# X1)
(proper# U43 X -> proper# X, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# U43 X -> proper# X, proper# U42(X1, X2) -> proper# X2)
(proper# U43 X -> proper# X, proper# U42(X1, X2) -> proper# X1)
(proper# U43 X -> proper# X, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# U43 X -> proper# X, proper# U31(X1, X2) -> proper# X2)
(proper# U43 X -> proper# X, proper# U31(X1, X2) -> proper# X1)
(proper# U43 X -> proper# X, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# U43 X -> proper# X, proper# U32 X -> proper# X)
(proper# U43 X -> proper# X, proper# U32 X -> U32# proper X)
(proper# U43 X -> proper# X, proper# U21(X1, X2) -> proper# X2)
(proper# U43 X -> proper# X, proper# U21(X1, X2) -> proper# X1)
(proper# U43 X -> proper# X, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# U43 X -> proper# X, proper# isNat X -> proper# X)
(proper# U43 X -> proper# X, proper# isNat X -> isNat# proper X)
(proper# U43 X -> proper# X, proper# U22 X -> proper# X)
(proper# U43 X -> proper# X, proper# U22 X -> U22# proper X)
(proper# U43 X -> proper# X, proper# U11(X1, X2) -> proper# X2)
(proper# U43 X -> proper# X, proper# U11(X1, X2) -> proper# X1)
(proper# U43 X -> proper# X, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# U43 X -> proper# X, proper# isNatList X -> proper# X)
(proper# U43 X -> proper# X, proper# isNatList X -> isNatList# proper X)
(proper# U43 X -> proper# X, proper# U12 X -> proper# X)
(proper# U43 X -> proper# X, proper# U12 X -> U12# proper X)
(proper# U43 X -> proper# X, proper# cons(X1, X2) -> proper# X2)
(proper# U43 X -> proper# X, proper# cons(X1, X2) -> proper# X1)
(proper# U43 X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# U53 X -> proper# X, proper# isNatKind X -> proper# X)
(proper# U53 X -> proper# X, proper# isNatKind X -> isNatKind# proper X)
(proper# U53 X -> proper# X, proper# isNatIListKind X -> proper# X)
(proper# U53 X -> proper# X, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# U53 X -> proper# X, proper# and(X1, X2) -> proper# X2)
(proper# U53 X -> proper# X, proper# and(X1, X2) -> proper# X1)
(proper# U53 X -> proper# X, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# U53 X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# U53 X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# U53 X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# U53 X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# U53 X -> proper# X, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# U53 X -> proper# X, proper# take(X1, X2) -> proper# X2)
(proper# U53 X -> proper# X, proper# take(X1, X2) -> proper# X1)
(proper# U53 X -> proper# X, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# U53 X -> proper# X, proper# U81 X -> proper# X)
(proper# U53 X -> proper# X, proper# U81 X -> U81# proper X)
(proper# U53 X -> proper# X, proper# U71(X1, X2) -> proper# X2)
(proper# U53 X -> proper# X, proper# U71(X1, X2) -> proper# X1)
(proper# U53 X -> proper# X, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# U53 X -> proper# X, proper# length X -> proper# X)
(proper# U53 X -> proper# X, proper# length X -> length# proper X)
(proper# U53 X -> proper# X, proper# s X -> proper# X)
(proper# U53 X -> proper# X, proper# s X -> s# proper X)
(proper# U53 X -> proper# X, proper# U63 X -> proper# X)
(proper# U53 X -> proper# X, proper# U63 X -> U63# proper X)
(proper# U53 X -> proper# X, proper# U61(X1, X2, X3) -> proper# X3)
(proper# U53 X -> proper# X, proper# U61(X1, X2, X3) -> proper# X2)
(proper# U53 X -> proper# X, proper# U61(X1, X2, X3) -> proper# X1)
(proper# U53 X -> proper# X, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# U53 X -> proper# X, proper# U62(X1, X2) -> proper# X2)
(proper# U53 X -> proper# X, proper# U62(X1, X2) -> proper# X1)
(proper# U53 X -> proper# X, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# U53 X -> proper# X, proper# U53 X -> proper# X)
(proper# U53 X -> proper# X, proper# U53 X -> U53# proper X)
(proper# U53 X -> proper# X, proper# U51(X1, X2, X3) -> proper# X3)
(proper# U53 X -> proper# X, proper# U51(X1, X2, X3) -> proper# X2)
(proper# U53 X -> proper# X, proper# U51(X1, X2, X3) -> proper# X1)
(proper# U53 X -> proper# X, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# U53 X -> proper# X, proper# U52(X1, X2) -> proper# X2)
(proper# U53 X -> proper# X, proper# U52(X1, X2) -> proper# X1)
(proper# U53 X -> proper# X, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# U53 X -> proper# X, proper# isNatIList X -> proper# X)
(proper# U53 X -> proper# X, proper# isNatIList X -> isNatIList# proper X)
(proper# U53 X -> proper# X, proper# U43 X -> proper# X)
(proper# U53 X -> proper# X, proper# U43 X -> U43# proper X)
(proper# U53 X -> proper# X, proper# U41(X1, X2, X3) -> proper# X3)
(proper# U53 X -> proper# X, proper# U41(X1, X2, X3) -> proper# X2)
(proper# U53 X -> proper# X, proper# U41(X1, X2, X3) -> proper# X1)
(proper# U53 X -> proper# X, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# U53 X -> proper# X, proper# U42(X1, X2) -> proper# X2)
(proper# U53 X -> proper# X, proper# U42(X1, X2) -> proper# X1)
(proper# U53 X -> proper# X, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# U53 X -> proper# X, proper# U31(X1, X2) -> proper# X2)
(proper# U53 X -> proper# X, proper# U31(X1, X2) -> proper# X1)
(proper# U53 X -> proper# X, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# U53 X -> proper# X, proper# U32 X -> proper# X)
(proper# U53 X -> proper# X, proper# U32 X -> U32# proper X)
(proper# U53 X -> proper# X, proper# U21(X1, X2) -> proper# X2)
(proper# U53 X -> proper# X, proper# U21(X1, X2) -> proper# X1)
(proper# U53 X -> proper# X, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# U53 X -> proper# X, proper# isNat X -> proper# X)
(proper# U53 X -> proper# X, proper# isNat X -> isNat# proper X)
(proper# U53 X -> proper# X, proper# U22 X -> proper# X)
(proper# U53 X -> proper# X, proper# U22 X -> U22# proper X)
(proper# U53 X -> proper# X, proper# U11(X1, X2) -> proper# X2)
(proper# U53 X -> proper# X, proper# U11(X1, X2) -> proper# X1)
(proper# U53 X -> proper# X, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# U53 X -> proper# X, proper# isNatList X -> proper# X)
(proper# U53 X -> proper# X, proper# isNatList X -> isNatList# proper X)
(proper# U53 X -> proper# X, proper# U12 X -> proper# X)
(proper# U53 X -> proper# X, proper# U12 X -> U12# proper X)
(proper# U53 X -> proper# X, proper# cons(X1, X2) -> proper# X2)
(proper# U53 X -> proper# X, proper# cons(X1, X2) -> proper# X1)
(proper# U53 X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# s X -> proper# X, proper# isNatKind X -> proper# X)
(proper# s X -> proper# X, proper# isNatKind X -> isNatKind# proper X)
(proper# s X -> proper# X, proper# isNatIListKind X -> proper# X)
(proper# s X -> proper# X, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# s X -> proper# X, proper# and(X1, X2) -> proper# X2)
(proper# s X -> proper# X, proper# and(X1, X2) -> proper# X1)
(proper# s X -> proper# X, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# s X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# s X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# s X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# s X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# s X -> proper# X, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# s X -> proper# X, proper# take(X1, X2) -> proper# X2)
(proper# s X -> proper# X, proper# take(X1, X2) -> proper# X1)
(proper# s X -> proper# X, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# s X -> proper# X, proper# U81 X -> proper# X)
(proper# s X -> proper# X, proper# U81 X -> U81# proper X)
(proper# s X -> proper# X, proper# U71(X1, X2) -> proper# X2)
(proper# s X -> proper# X, proper# U71(X1, X2) -> proper# X1)
(proper# s X -> proper# X, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# s X -> proper# X, proper# length X -> proper# X)
(proper# s X -> proper# X, proper# length X -> length# proper X)
(proper# s X -> proper# X, proper# s X -> proper# X)
(proper# s X -> proper# X, proper# s X -> s# proper X)
(proper# s X -> proper# X, proper# U63 X -> proper# X)
(proper# s X -> proper# X, proper# U63 X -> U63# proper X)
(proper# s X -> proper# X, proper# U61(X1, X2, X3) -> proper# X3)
(proper# s X -> proper# X, proper# U61(X1, X2, X3) -> proper# X2)
(proper# s X -> proper# X, proper# U61(X1, X2, X3) -> proper# X1)
(proper# s X -> proper# X, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# s X -> proper# X, proper# U62(X1, X2) -> proper# X2)
(proper# s X -> proper# X, proper# U62(X1, X2) -> proper# X1)
(proper# s X -> proper# X, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# s X -> proper# X, proper# U53 X -> proper# X)
(proper# s X -> proper# X, proper# U53 X -> U53# proper X)
(proper# s X -> proper# X, proper# U51(X1, X2, X3) -> proper# X3)
(proper# s X -> proper# X, proper# U51(X1, X2, X3) -> proper# X2)
(proper# s X -> proper# X, proper# U51(X1, X2, X3) -> proper# X1)
(proper# s X -> proper# X, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# s X -> proper# X, proper# U52(X1, X2) -> proper# X2)
(proper# s X -> proper# X, proper# U52(X1, X2) -> proper# X1)
(proper# s X -> proper# X, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# s X -> proper# X, proper# isNatIList X -> proper# X)
(proper# s X -> proper# X, proper# isNatIList X -> isNatIList# proper X)
(proper# s X -> proper# X, proper# U43 X -> proper# X)
(proper# s X -> proper# X, proper# U43 X -> U43# proper X)
(proper# s X -> proper# X, proper# U41(X1, X2, X3) -> proper# X3)
(proper# s X -> proper# X, proper# U41(X1, X2, X3) -> proper# X2)
(proper# s X -> proper# X, proper# U41(X1, X2, X3) -> proper# X1)
(proper# s X -> proper# X, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# s X -> proper# X, proper# U42(X1, X2) -> proper# X2)
(proper# s X -> proper# X, proper# U42(X1, X2) -> proper# X1)
(proper# s X -> proper# X, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# s X -> proper# X, proper# U31(X1, X2) -> proper# X2)
(proper# s X -> proper# X, proper# U31(X1, X2) -> proper# X1)
(proper# s X -> proper# X, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# s X -> proper# X, proper# U32 X -> proper# X)
(proper# s X -> proper# X, proper# U32 X -> U32# proper X)
(proper# s X -> proper# X, proper# U21(X1, X2) -> proper# X2)
(proper# s X -> proper# X, proper# U21(X1, X2) -> proper# X1)
(proper# s X -> proper# X, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# s X -> proper# X, proper# isNat X -> proper# X)
(proper# s X -> proper# X, proper# isNat X -> isNat# proper X)
(proper# s X -> proper# X, proper# U22 X -> proper# X)
(proper# s X -> proper# X, proper# U22 X -> U22# proper X)
(proper# s X -> proper# X, proper# U11(X1, X2) -> proper# X2)
(proper# s X -> proper# X, proper# U11(X1, X2) -> proper# X1)
(proper# s X -> proper# X, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# s X -> proper# X, proper# isNatList X -> proper# X)
(proper# s X -> proper# X, proper# isNatList X -> isNatList# proper X)
(proper# s X -> proper# X, proper# U12 X -> proper# X)
(proper# s X -> proper# X, proper# U12 X -> U12# proper X)
(proper# s X -> proper# X, proper# cons(X1, X2) -> proper# X2)
(proper# s X -> proper# X, proper# cons(X1, X2) -> proper# X1)
(proper# s X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# U81 X -> proper# X, proper# isNatKind X -> proper# X)
(proper# U81 X -> proper# X, proper# isNatKind X -> isNatKind# proper X)
(proper# U81 X -> proper# X, proper# isNatIListKind X -> proper# X)
(proper# U81 X -> proper# X, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# U81 X -> proper# X, proper# and(X1, X2) -> proper# X2)
(proper# U81 X -> proper# X, proper# and(X1, X2) -> proper# X1)
(proper# U81 X -> proper# X, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# U81 X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# U81 X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# U81 X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# U81 X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# U81 X -> proper# X, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# U81 X -> proper# X, proper# take(X1, X2) -> proper# X2)
(proper# U81 X -> proper# X, proper# take(X1, X2) -> proper# X1)
(proper# U81 X -> proper# X, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# U81 X -> proper# X, proper# U81 X -> proper# X)
(proper# U81 X -> proper# X, proper# U81 X -> U81# proper X)
(proper# U81 X -> proper# X, proper# U71(X1, X2) -> proper# X2)
(proper# U81 X -> proper# X, proper# U71(X1, X2) -> proper# X1)
(proper# U81 X -> proper# X, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# U81 X -> proper# X, proper# length X -> proper# X)
(proper# U81 X -> proper# X, proper# length X -> length# proper X)
(proper# U81 X -> proper# X, proper# s X -> proper# X)
(proper# U81 X -> proper# X, proper# s X -> s# proper X)
(proper# U81 X -> proper# X, proper# U63 X -> proper# X)
(proper# U81 X -> proper# X, proper# U63 X -> U63# proper X)
(proper# U81 X -> proper# X, proper# U61(X1, X2, X3) -> proper# X3)
(proper# U81 X -> proper# X, proper# U61(X1, X2, X3) -> proper# X2)
(proper# U81 X -> proper# X, proper# U61(X1, X2, X3) -> proper# X1)
(proper# U81 X -> proper# X, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# U81 X -> proper# X, proper# U62(X1, X2) -> proper# X2)
(proper# U81 X -> proper# X, proper# U62(X1, X2) -> proper# X1)
(proper# U81 X -> proper# X, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# U81 X -> proper# X, proper# U53 X -> proper# X)
(proper# U81 X -> proper# X, proper# U53 X -> U53# proper X)
(proper# U81 X -> proper# X, proper# U51(X1, X2, X3) -> proper# X3)
(proper# U81 X -> proper# X, proper# U51(X1, X2, X3) -> proper# X2)
(proper# U81 X -> proper# X, proper# U51(X1, X2, X3) -> proper# X1)
(proper# U81 X -> proper# X, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# U81 X -> proper# X, proper# U52(X1, X2) -> proper# X2)
(proper# U81 X -> proper# X, proper# U52(X1, X2) -> proper# X1)
(proper# U81 X -> proper# X, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# U81 X -> proper# X, proper# isNatIList X -> proper# X)
(proper# U81 X -> proper# X, proper# isNatIList X -> isNatIList# proper X)
(proper# U81 X -> proper# X, proper# U43 X -> proper# X)
(proper# U81 X -> proper# X, proper# U43 X -> U43# proper X)
(proper# U81 X -> proper# X, proper# U41(X1, X2, X3) -> proper# X3)
(proper# U81 X -> proper# X, proper# U41(X1, X2, X3) -> proper# X2)
(proper# U81 X -> proper# X, proper# U41(X1, X2, X3) -> proper# X1)
(proper# U81 X -> proper# X, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# U81 X -> proper# X, proper# U42(X1, X2) -> proper# X2)
(proper# U81 X -> proper# X, proper# U42(X1, X2) -> proper# X1)
(proper# U81 X -> proper# X, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# U81 X -> proper# X, proper# U31(X1, X2) -> proper# X2)
(proper# U81 X -> proper# X, proper# U31(X1, X2) -> proper# X1)
(proper# U81 X -> proper# X, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# U81 X -> proper# X, proper# U32 X -> proper# X)
(proper# U81 X -> proper# X, proper# U32 X -> U32# proper X)
(proper# U81 X -> proper# X, proper# U21(X1, X2) -> proper# X2)
(proper# U81 X -> proper# X, proper# U21(X1, X2) -> proper# X1)
(proper# U81 X -> proper# X, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# U81 X -> proper# X, proper# isNat X -> proper# X)
(proper# U81 X -> proper# X, proper# isNat X -> isNat# proper X)
(proper# U81 X -> proper# X, proper# U22 X -> proper# X)
(proper# U81 X -> proper# X, proper# U22 X -> U22# proper X)
(proper# U81 X -> proper# X, proper# U11(X1, X2) -> proper# X2)
(proper# U81 X -> proper# X, proper# U11(X1, X2) -> proper# X1)
(proper# U81 X -> proper# X, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# U81 X -> proper# X, proper# isNatList X -> proper# X)
(proper# U81 X -> proper# X, proper# isNatList X -> isNatList# proper X)
(proper# U81 X -> proper# X, proper# U12 X -> proper# X)
(proper# U81 X -> proper# X, proper# U12 X -> U12# proper X)
(proper# U81 X -> proper# X, proper# cons(X1, X2) -> proper# X2)
(proper# U81 X -> proper# X, proper# cons(X1, X2) -> proper# X1)
(proper# U81 X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# isNatKind X -> proper# X, proper# isNatKind X -> proper# X)
(proper# isNatKind X -> proper# X, proper# isNatKind X -> isNatKind# proper X)
(proper# isNatKind X -> proper# X, proper# isNatIListKind X -> proper# X)
(proper# isNatKind X -> proper# X, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# isNatKind X -> proper# X, proper# and(X1, X2) -> proper# X2)
(proper# isNatKind X -> proper# X, proper# and(X1, X2) -> proper# X1)
(proper# isNatKind X -> proper# X, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# isNatKind X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# isNatKind X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# isNatKind X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# isNatKind X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# isNatKind X -> proper# X, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# isNatKind X -> proper# X, proper# take(X1, X2) -> proper# X2)
(proper# isNatKind X -> proper# X, proper# take(X1, X2) -> proper# X1)
(proper# isNatKind X -> proper# X, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# isNatKind X -> proper# X, proper# U81 X -> proper# X)
(proper# isNatKind X -> proper# X, proper# U81 X -> U81# proper X)
(proper# isNatKind X -> proper# X, proper# U71(X1, X2) -> proper# X2)
(proper# isNatKind X -> proper# X, proper# U71(X1, X2) -> proper# X1)
(proper# isNatKind X -> proper# X, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# isNatKind X -> proper# X, proper# length X -> proper# X)
(proper# isNatKind X -> proper# X, proper# length X -> length# proper X)
(proper# isNatKind X -> proper# X, proper# s X -> proper# X)
(proper# isNatKind X -> proper# X, proper# s X -> s# proper X)
(proper# isNatKind X -> proper# X, proper# U63 X -> proper# X)
(proper# isNatKind X -> proper# X, proper# U63 X -> U63# proper X)
(proper# isNatKind X -> proper# X, proper# U61(X1, X2, X3) -> proper# X3)
(proper# isNatKind X -> proper# X, proper# U61(X1, X2, X3) -> proper# X2)
(proper# isNatKind X -> proper# X, proper# U61(X1, X2, X3) -> proper# X1)
(proper# isNatKind X -> proper# X, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# isNatKind X -> proper# X, proper# U62(X1, X2) -> proper# X2)
(proper# isNatKind X -> proper# X, proper# U62(X1, X2) -> proper# X1)
(proper# isNatKind X -> proper# X, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# isNatKind X -> proper# X, proper# U53 X -> proper# X)
(proper# isNatKind X -> proper# X, proper# U53 X -> U53# proper X)
(proper# isNatKind X -> proper# X, proper# U51(X1, X2, X3) -> proper# X3)
(proper# isNatKind X -> proper# X, proper# U51(X1, X2, X3) -> proper# X2)
(proper# isNatKind X -> proper# X, proper# U51(X1, X2, X3) -> proper# X1)
(proper# isNatKind X -> proper# X, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# isNatKind X -> proper# X, proper# U52(X1, X2) -> proper# X2)
(proper# isNatKind X -> proper# X, proper# U52(X1, X2) -> proper# X1)
(proper# isNatKind X -> proper# X, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# isNatKind X -> proper# X, proper# isNatIList X -> proper# X)
(proper# isNatKind X -> proper# X, proper# isNatIList X -> isNatIList# proper X)
(proper# isNatKind X -> proper# X, proper# U43 X -> proper# X)
(proper# isNatKind X -> proper# X, proper# U43 X -> U43# proper X)
(proper# isNatKind X -> proper# X, proper# U41(X1, X2, X3) -> proper# X3)
(proper# isNatKind X -> proper# X, proper# U41(X1, X2, X3) -> proper# X2)
(proper# isNatKind X -> proper# X, proper# U41(X1, X2, X3) -> proper# X1)
(proper# isNatKind X -> proper# X, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# isNatKind X -> proper# X, proper# U42(X1, X2) -> proper# X2)
(proper# isNatKind X -> proper# X, proper# U42(X1, X2) -> proper# X1)
(proper# isNatKind X -> proper# X, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# isNatKind X -> proper# X, proper# U31(X1, X2) -> proper# X2)
(proper# isNatKind X -> proper# X, proper# U31(X1, X2) -> proper# X1)
(proper# isNatKind X -> proper# X, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# isNatKind X -> proper# X, proper# U32 X -> proper# X)
(proper# isNatKind X -> proper# X, proper# U32 X -> U32# proper X)
(proper# isNatKind X -> proper# X, proper# U21(X1, X2) -> proper# X2)
(proper# isNatKind X -> proper# X, proper# U21(X1, X2) -> proper# X1)
(proper# isNatKind X -> proper# X, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# isNatKind X -> proper# X, proper# isNat X -> proper# X)
(proper# isNatKind X -> proper# X, proper# isNat X -> isNat# proper X)
(proper# isNatKind X -> proper# X, proper# U22 X -> proper# X)
(proper# isNatKind X -> proper# X, proper# U22 X -> U22# proper X)
(proper# isNatKind X -> proper# X, proper# U11(X1, X2) -> proper# X2)
(proper# isNatKind X -> proper# X, proper# U11(X1, X2) -> proper# X1)
(proper# isNatKind X -> proper# X, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# isNatKind X -> proper# X, proper# isNatList X -> proper# X)
(proper# isNatKind X -> proper# X, proper# isNatList X -> isNatList# proper X)
(proper# isNatKind X -> proper# X, proper# U12 X -> proper# X)
(proper# isNatKind X -> proper# X, proper# U12 X -> U12# proper X)
(proper# isNatKind X -> proper# X, proper# cons(X1, X2) -> proper# X2)
(proper# isNatKind X -> proper# X, proper# cons(X1, X2) -> proper# X1)
(proper# isNatKind X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(top# ok X -> active# X, active# isNatKind length V1 -> isNatIListKind# V1)
(top# ok X -> active# X, active# isNatKind s V1 -> isNatKind# V1)
(top# ok X -> active# X, active# isNatIListKind take(V1, V2) -> isNatKind# V1)
(top# ok X -> active# X, active# isNatIListKind take(V1, V2) -> isNatIListKind# V2)
(top# ok X -> active# X, active# isNatIListKind take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(top# ok X -> active# X, active# isNatIListKind cons(V1, V2) -> isNatKind# V1)
(top# ok X -> active# X, active# isNatIListKind cons(V1, V2) -> isNatIListKind# V2)
(top# ok X -> active# X, active# isNatIListKind cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(top# ok X -> active# X, active# and(X1, X2) -> and#(active X1, X2))
(top# ok X -> active# X, active# and(X1, X2) -> active# X1)
(top# ok X -> active# X, active# U91(tt(), IL, M, N) -> take#(M, IL))
(top# ok X -> active# X, active# U91(tt(), IL, M, N) -> cons#(N, take(M, IL)))
(top# ok X -> active# X, active# U91(X1, X2, X3, X4) -> U91#(active X1, X2, X3, X4))
(top# ok X -> active# X, active# U91(X1, X2, X3, X4) -> active# X1)
(top# ok X -> active# X, active# take(s M, cons(N, IL)) -> isNatKind# M)
(top# ok X -> active# X, active# take(s M, cons(N, IL)) -> isNatKind# N)
(top# ok X -> active# X, active# take(s M, cons(N, IL)) -> isNatIListKind# IL)
(top# ok X -> active# X, active# take(s M, cons(N, IL)) -> and#(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))))
(top# ok X -> active# X, active# take(s M, cons(N, IL)) -> and#(and(isNat M, isNatKind M), and(isNat N, isNatKind N)))
(top# ok X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, isNatIListKind IL))
(top# ok X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNat M, isNatKind M))
(top# ok X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNat N, isNatKind N))
(top# ok X -> active# X, active# take(s M, cons(N, IL)) -> U91#(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N))
(top# ok X -> active# X, active# take(s M, cons(N, IL)) -> isNatIList# IL)
(top# ok X -> active# X, active# take(s M, cons(N, IL)) -> isNat# M)
(top# ok X -> active# X, active# take(s M, cons(N, IL)) -> isNat# N)
(top# ok X -> active# X, active# take(0(), IL) -> isNatIListKind# IL)
(top# ok X -> active# X, active# take(0(), IL) -> and#(isNatIList IL, isNatIListKind IL))
(top# ok X -> active# X, active# take(0(), IL) -> U81# and(isNatIList IL, isNatIListKind IL))
(top# ok X -> active# X, active# take(0(), IL) -> isNatIList# IL)
(top# ok X -> active# X, active# take(X1, X2) -> take#(active X1, X2))
(top# ok X -> active# X, active# take(X1, X2) -> take#(X1, active X2))
(top# ok X -> active# X, active# take(X1, X2) -> active# X2)
(top# ok X -> active# X, active# take(X1, X2) -> active# X1)
(top# ok X -> active# X, active# U81 X -> U81# active X)
(top# ok X -> active# X, active# U81 X -> active# X)
(top# ok X -> active# X, active# U71(tt(), L) -> length# L)
(top# ok X -> active# X, active# U71(tt(), L) -> s# length L)
(top# ok X -> active# X, active# U71(X1, X2) -> U71#(active X1, X2))
(top# ok X -> active# X, active# U71(X1, X2) -> active# X1)
(top# ok X -> active# X, active# length cons(N, L) -> isNatKind# N)
(top# ok X -> active# X, active# length cons(N, L) -> isNatIListKind# L)
(top# ok X -> active# X, active# length cons(N, L) -> and#(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)))
(top# ok X -> active# X, active# length cons(N, L) -> and#(isNat N, isNatKind N))
(top# ok X -> active# X, active# length cons(N, L) -> and#(isNatList L, isNatIListKind L))
(top# ok X -> active# X, active# length cons(N, L) -> U71#(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L))
(top# ok X -> active# X, active# length cons(N, L) -> isNat# N)
(top# ok X -> active# X, active# length cons(N, L) -> isNatList# L)
(top# ok X -> active# X, active# length X -> length# active X)
(top# ok X -> active# X, active# length X -> active# X)
(top# ok X -> active# X, active# s X -> s# active X)
(top# ok X -> active# X, active# s X -> active# X)
(top# ok X -> active# X, active# U63 X -> U63# active X)
(top# ok X -> active# X, active# U63 X -> active# X)
(top# ok X -> active# X, active# U61(tt(), V1, V2) -> U62#(isNat V1, V2))
(top# ok X -> active# X, active# U61(tt(), V1, V2) -> isNat# V1)
(top# ok X -> active# X, active# U61(X1, X2, X3) -> U61#(active X1, X2, X3))
(top# ok X -> active# X, active# U61(X1, X2, X3) -> active# X1)
(top# ok X -> active# X, active# U62(tt(), V2) -> U63# isNatIList V2)
(top# ok X -> active# X, active# U62(tt(), V2) -> isNatIList# V2)
(top# ok X -> active# X, active# U62(X1, X2) -> U62#(active X1, X2))
(top# ok X -> active# X, active# U62(X1, X2) -> active# X1)
(top# ok X -> active# X, active# U53 X -> U53# active X)
(top# ok X -> active# X, active# U53 X -> active# X)
(top# ok X -> active# X, active# U51(tt(), V1, V2) -> U52#(isNat V1, V2))
(top# ok X -> active# X, active# U51(tt(), V1, V2) -> isNat# V1)
(top# ok X -> active# X, active# U51(X1, X2, X3) -> U51#(active X1, X2, X3))
(top# ok X -> active# X, active# U51(X1, X2, X3) -> active# X1)
(top# ok X -> active# X, active# U52(tt(), V2) -> U53# isNatList V2)
(top# ok X -> active# X, active# U52(tt(), V2) -> isNatList# V2)
(top# ok X -> active# X, active# U52(X1, X2) -> U52#(active X1, X2))
(top# ok X -> active# X, active# U52(X1, X2) -> active# X1)
(top# ok X -> active# X, active# isNatIList cons(V1, V2) -> isNatKind# V1)
(top# ok X -> active# X, active# isNatIList cons(V1, V2) -> isNatIListKind# V2)
(top# ok X -> active# X, active# isNatIList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(top# ok X -> active# X, active# isNatIList cons(V1, V2) -> U41#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(top# ok X -> active# X, active# isNatIList V -> isNatIListKind# V)
(top# ok X -> active# X, active# isNatIList V -> U31#(isNatIListKind V, V))
(top# ok X -> active# X, active# U43 X -> U43# active X)
(top# ok X -> active# X, active# U43 X -> active# X)
(top# ok X -> active# X, active# U41(tt(), V1, V2) -> U42#(isNat V1, V2))
(top# ok X -> active# X, active# U41(tt(), V1, V2) -> isNat# V1)
(top# ok X -> active# X, active# U41(X1, X2, X3) -> U41#(active X1, X2, X3))
(top# ok X -> active# X, active# U41(X1, X2, X3) -> active# X1)
(top# ok X -> active# X, active# U42(tt(), V2) -> isNatIList# V2)
(top# ok X -> active# X, active# U42(tt(), V2) -> U43# isNatIList V2)
(top# ok X -> active# X, active# U42(X1, X2) -> U42#(active X1, X2))
(top# ok X -> active# X, active# U42(X1, X2) -> active# X1)
(top# ok X -> active# X, active# U31(tt(), V) -> U32# isNatList V)
(top# ok X -> active# X, active# U31(tt(), V) -> isNatList# V)
(top# ok X -> active# X, active# U31(X1, X2) -> U31#(active X1, X2))
(top# ok X -> active# X, active# U31(X1, X2) -> active# X1)
(top# ok X -> active# X, active# U32 X -> U32# active X)
(top# ok X -> active# X, active# U32 X -> active# X)
(top# ok X -> active# X, active# U21(tt(), V1) -> isNat# V1)
(top# ok X -> active# X, active# U21(tt(), V1) -> U22# isNat V1)
(top# ok X -> active# X, active# U21(X1, X2) -> U21#(active X1, X2))
(top# ok X -> active# X, active# U21(X1, X2) -> active# X1)
(top# ok X -> active# X, active# isNat length V1 -> isNatIListKind# V1)
(top# ok X -> active# X, active# isNat length V1 -> U11#(isNatIListKind V1, V1))
(top# ok X -> active# X, active# isNat s V1 -> isNatKind# V1)
(top# ok X -> active# X, active# isNat s V1 -> U21#(isNatKind V1, V1))
(top# ok X -> active# X, active# U22 X -> U22# active X)
(top# ok X -> active# X, active# U22 X -> active# X)
(top# ok X -> active# X, active# U11(tt(), V1) -> isNatList# V1)
(top# ok X -> active# X, active# U11(tt(), V1) -> U12# isNatList V1)
(top# ok X -> active# X, active# U11(X1, X2) -> U11#(active X1, X2))
(top# ok X -> active# X, active# U11(X1, X2) -> active# X1)
(top# ok X -> active# X, active# isNatList take(V1, V2) -> isNatKind# V1)
(top# ok X -> active# X, active# isNatList take(V1, V2) -> isNatIListKind# V2)
(top# ok X -> active# X, active# isNatList take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(top# ok X -> active# X, active# isNatList take(V1, V2) -> U61#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(top# ok X -> active# X, active# isNatList cons(V1, V2) -> isNatKind# V1)
(top# ok X -> active# X, active# isNatList cons(V1, V2) -> isNatIListKind# V2)
(top# ok X -> active# X, active# isNatList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(top# ok X -> active# X, active# isNatList cons(V1, V2) -> U51#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(top# ok X -> active# X, active# U12 X -> U12# active X)
(top# ok X -> active# X, active# U12 X -> active# X)
(top# ok X -> active# X, active# zeros() -> cons#(0(), zeros()))
(top# ok X -> active# X, active# cons(X1, X2) -> active# X1)
(top# ok X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2))
(top# mark X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(top# mark X -> proper# X, proper# cons(X1, X2) -> proper# X1)
(top# mark X -> proper# X, proper# cons(X1, X2) -> proper# X2)
(top# mark X -> proper# X, proper# U12 X -> U12# proper X)
(top# mark X -> proper# X, proper# U12 X -> proper# X)
(top# mark X -> proper# X, proper# isNatList X -> isNatList# proper X)
(top# mark X -> proper# X, proper# isNatList X -> proper# X)
(top# mark X -> proper# X, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(top# mark X -> proper# X, proper# U11(X1, X2) -> proper# X1)
(top# mark X -> proper# X, proper# U11(X1, X2) -> proper# X2)
(top# mark X -> proper# X, proper# U22 X -> U22# proper X)
(top# mark X -> proper# X, proper# U22 X -> proper# X)
(top# mark X -> proper# X, proper# isNat X -> isNat# proper X)
(top# mark X -> proper# X, proper# isNat X -> proper# X)
(top# mark X -> proper# X, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(top# mark X -> proper# X, proper# U21(X1, X2) -> proper# X1)
(top# mark X -> proper# X, proper# U21(X1, X2) -> proper# X2)
(top# mark X -> proper# X, proper# U32 X -> U32# proper X)
(top# mark X -> proper# X, proper# U32 X -> proper# X)
(top# mark X -> proper# X, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(top# mark X -> proper# X, proper# U31(X1, X2) -> proper# X1)
(top# mark X -> proper# X, proper# U31(X1, X2) -> proper# X2)
(top# mark X -> proper# X, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(top# mark X -> proper# X, proper# U42(X1, X2) -> proper# X1)
(top# mark X -> proper# X, proper# U42(X1, X2) -> proper# X2)
(top# mark X -> proper# X, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(top# mark X -> proper# X, proper# U41(X1, X2, X3) -> proper# X1)
(top# mark X -> proper# X, proper# U41(X1, X2, X3) -> proper# X2)
(top# mark X -> proper# X, proper# U41(X1, X2, X3) -> proper# X3)
(top# mark X -> proper# X, proper# U43 X -> U43# proper X)
(top# mark X -> proper# X, proper# U43 X -> proper# X)
(top# mark X -> proper# X, proper# isNatIList X -> isNatIList# proper X)
(top# mark X -> proper# X, proper# isNatIList X -> proper# X)
(top# mark X -> proper# X, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(top# mark X -> proper# X, proper# U52(X1, X2) -> proper# X1)
(top# mark X -> proper# X, proper# U52(X1, X2) -> proper# X2)
(top# mark X -> proper# X, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(top# mark X -> proper# X, proper# U51(X1, X2, X3) -> proper# X1)
(top# mark X -> proper# X, proper# U51(X1, X2, X3) -> proper# X2)
(top# mark X -> proper# X, proper# U51(X1, X2, X3) -> proper# X3)
(top# mark X -> proper# X, proper# U53 X -> U53# proper X)
(top# mark X -> proper# X, proper# U53 X -> proper# X)
(top# mark X -> proper# X, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(top# mark X -> proper# X, proper# U62(X1, X2) -> proper# X1)
(top# mark X -> proper# X, proper# U62(X1, X2) -> proper# X2)
(top# mark X -> proper# X, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(top# mark X -> proper# X, proper# U61(X1, X2, X3) -> proper# X1)
(top# mark X -> proper# X, proper# U61(X1, X2, X3) -> proper# X2)
(top# mark X -> proper# X, proper# U61(X1, X2, X3) -> proper# X3)
(top# mark X -> proper# X, proper# U63 X -> U63# proper X)
(top# mark X -> proper# X, proper# U63 X -> proper# X)
(top# mark X -> proper# X, proper# s X -> s# proper X)
(top# mark X -> proper# X, proper# s X -> proper# X)
(top# mark X -> proper# X, proper# length X -> length# proper X)
(top# mark X -> proper# X, proper# length X -> proper# X)
(top# mark X -> proper# X, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(top# mark X -> proper# X, proper# U71(X1, X2) -> proper# X1)
(top# mark X -> proper# X, proper# U71(X1, X2) -> proper# X2)
(top# mark X -> proper# X, proper# U81 X -> U81# proper X)
(top# mark X -> proper# X, proper# U81 X -> proper# X)
(top# mark X -> proper# X, proper# take(X1, X2) -> take#(proper X1, proper X2))
(top# mark X -> proper# X, proper# take(X1, X2) -> proper# X1)
(top# mark X -> proper# X, proper# take(X1, X2) -> proper# X2)
(top# mark X -> proper# X, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(top# mark X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X1)
(top# mark X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X2)
(top# mark X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X3)
(top# mark X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X4)
(top# mark X -> proper# X, proper# and(X1, X2) -> and#(proper X1, proper X2))
(top# mark X -> proper# X, proper# and(X1, X2) -> proper# X1)
(top# mark X -> proper# X, proper# and(X1, X2) -> proper# X2)
(top# mark X -> proper# X, proper# isNatIListKind X -> isNatIListKind# proper X)
(top# mark X -> proper# X, proper# isNatIListKind X -> proper# X)
(top# mark X -> proper# X, proper# isNatKind X -> isNatKind# proper X)
(top# mark X -> proper# X, proper# isNatKind X -> proper# X)
(proper# isNatIListKind X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# isNatIListKind X -> proper# X, proper# cons(X1, X2) -> proper# X1)
(proper# isNatIListKind X -> proper# X, proper# cons(X1, X2) -> proper# X2)
(proper# isNatIListKind X -> proper# X, proper# U12 X -> U12# proper X)
(proper# isNatIListKind X -> proper# X, proper# U12 X -> proper# X)
(proper# isNatIListKind X -> proper# X, proper# isNatList X -> isNatList# proper X)
(proper# isNatIListKind X -> proper# X, proper# isNatList X -> proper# X)
(proper# isNatIListKind X -> proper# X, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# isNatIListKind X -> proper# X, proper# U11(X1, X2) -> proper# X1)
(proper# isNatIListKind X -> proper# X, proper# U11(X1, X2) -> proper# X2)
(proper# isNatIListKind X -> proper# X, proper# U22 X -> U22# proper X)
(proper# isNatIListKind X -> proper# X, proper# U22 X -> proper# X)
(proper# isNatIListKind X -> proper# X, proper# isNat X -> isNat# proper X)
(proper# isNatIListKind X -> proper# X, proper# isNat X -> proper# X)
(proper# isNatIListKind X -> proper# X, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# isNatIListKind X -> proper# X, proper# U21(X1, X2) -> proper# X1)
(proper# isNatIListKind X -> proper# X, proper# U21(X1, X2) -> proper# X2)
(proper# isNatIListKind X -> proper# X, proper# U32 X -> U32# proper X)
(proper# isNatIListKind X -> proper# X, proper# U32 X -> proper# X)
(proper# isNatIListKind X -> proper# X, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# isNatIListKind X -> proper# X, proper# U31(X1, X2) -> proper# X1)
(proper# isNatIListKind X -> proper# X, proper# U31(X1, X2) -> proper# X2)
(proper# isNatIListKind X -> proper# X, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# isNatIListKind X -> proper# X, proper# U42(X1, X2) -> proper# X1)
(proper# isNatIListKind X -> proper# X, proper# U42(X1, X2) -> proper# X2)
(proper# isNatIListKind X -> proper# X, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# isNatIListKind X -> proper# X, proper# U41(X1, X2, X3) -> proper# X1)
(proper# isNatIListKind X -> proper# X, proper# U41(X1, X2, X3) -> proper# X2)
(proper# isNatIListKind X -> proper# X, proper# U41(X1, X2, X3) -> proper# X3)
(proper# isNatIListKind X -> proper# X, proper# U43 X -> U43# proper X)
(proper# isNatIListKind X -> proper# X, proper# U43 X -> proper# X)
(proper# isNatIListKind X -> proper# X, proper# isNatIList X -> isNatIList# proper X)
(proper# isNatIListKind X -> proper# X, proper# isNatIList X -> proper# X)
(proper# isNatIListKind X -> proper# X, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# isNatIListKind X -> proper# X, proper# U52(X1, X2) -> proper# X1)
(proper# isNatIListKind X -> proper# X, proper# U52(X1, X2) -> proper# X2)
(proper# isNatIListKind X -> proper# X, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# isNatIListKind X -> proper# X, proper# U51(X1, X2, X3) -> proper# X1)
(proper# isNatIListKind X -> proper# X, proper# U51(X1, X2, X3) -> proper# X2)
(proper# isNatIListKind X -> proper# X, proper# U51(X1, X2, X3) -> proper# X3)
(proper# isNatIListKind X -> proper# X, proper# U53 X -> U53# proper X)
(proper# isNatIListKind X -> proper# X, proper# U53 X -> proper# X)
(proper# isNatIListKind X -> proper# X, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# isNatIListKind X -> proper# X, proper# U62(X1, X2) -> proper# X1)
(proper# isNatIListKind X -> proper# X, proper# U62(X1, X2) -> proper# X2)
(proper# isNatIListKind X -> proper# X, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# isNatIListKind X -> proper# X, proper# U61(X1, X2, X3) -> proper# X1)
(proper# isNatIListKind X -> proper# X, proper# U61(X1, X2, X3) -> proper# X2)
(proper# isNatIListKind X -> proper# X, proper# U61(X1, X2, X3) -> proper# X3)
(proper# isNatIListKind X -> proper# X, proper# U63 X -> U63# proper X)
(proper# isNatIListKind X -> proper# X, proper# U63 X -> proper# X)
(proper# isNatIListKind X -> proper# X, proper# s X -> s# proper X)
(proper# isNatIListKind X -> proper# X, proper# s X -> proper# X)
(proper# isNatIListKind X -> proper# X, proper# length X -> length# proper X)
(proper# isNatIListKind X -> proper# X, proper# length X -> proper# X)
(proper# isNatIListKind X -> proper# X, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# isNatIListKind X -> proper# X, proper# U71(X1, X2) -> proper# X1)
(proper# isNatIListKind X -> proper# X, proper# U71(X1, X2) -> proper# X2)
(proper# isNatIListKind X -> proper# X, proper# U81 X -> U81# proper X)
(proper# isNatIListKind X -> proper# X, proper# U81 X -> proper# X)
(proper# isNatIListKind X -> proper# X, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# isNatIListKind X -> proper# X, proper# take(X1, X2) -> proper# X1)
(proper# isNatIListKind X -> proper# X, proper# take(X1, X2) -> proper# X2)
(proper# isNatIListKind X -> proper# X, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# isNatIListKind X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# isNatIListKind X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# isNatIListKind X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# isNatIListKind X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# isNatIListKind X -> proper# X, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# isNatIListKind X -> proper# X, proper# and(X1, X2) -> proper# X1)
(proper# isNatIListKind X -> proper# X, proper# and(X1, X2) -> proper# X2)
(proper# isNatIListKind X -> proper# X, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# isNatIListKind X -> proper# X, proper# isNatIListKind X -> proper# X)
(proper# isNatIListKind X -> proper# X, proper# isNatKind X -> isNatKind# proper X)
(proper# isNatIListKind X -> proper# X, proper# isNatKind X -> proper# X)
(proper# length X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# length X -> proper# X, proper# cons(X1, X2) -> proper# X1)
(proper# length X -> proper# X, proper# cons(X1, X2) -> proper# X2)
(proper# length X -> proper# X, proper# U12 X -> U12# proper X)
(proper# length X -> proper# X, proper# U12 X -> proper# X)
(proper# length X -> proper# X, proper# isNatList X -> isNatList# proper X)
(proper# length X -> proper# X, proper# isNatList X -> proper# X)
(proper# length X -> proper# X, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# length X -> proper# X, proper# U11(X1, X2) -> proper# X1)
(proper# length X -> proper# X, proper# U11(X1, X2) -> proper# X2)
(proper# length X -> proper# X, proper# U22 X -> U22# proper X)
(proper# length X -> proper# X, proper# U22 X -> proper# X)
(proper# length X -> proper# X, proper# isNat X -> isNat# proper X)
(proper# length X -> proper# X, proper# isNat X -> proper# X)
(proper# length X -> proper# X, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# length X -> proper# X, proper# U21(X1, X2) -> proper# X1)
(proper# length X -> proper# X, proper# U21(X1, X2) -> proper# X2)
(proper# length X -> proper# X, proper# U32 X -> U32# proper X)
(proper# length X -> proper# X, proper# U32 X -> proper# X)
(proper# length X -> proper# X, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# length X -> proper# X, proper# U31(X1, X2) -> proper# X1)
(proper# length X -> proper# X, proper# U31(X1, X2) -> proper# X2)
(proper# length X -> proper# X, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# length X -> proper# X, proper# U42(X1, X2) -> proper# X1)
(proper# length X -> proper# X, proper# U42(X1, X2) -> proper# X2)
(proper# length X -> proper# X, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# length X -> proper# X, proper# U41(X1, X2, X3) -> proper# X1)
(proper# length X -> proper# X, proper# U41(X1, X2, X3) -> proper# X2)
(proper# length X -> proper# X, proper# U41(X1, X2, X3) -> proper# X3)
(proper# length X -> proper# X, proper# U43 X -> U43# proper X)
(proper# length X -> proper# X, proper# U43 X -> proper# X)
(proper# length X -> proper# X, proper# isNatIList X -> isNatIList# proper X)
(proper# length X -> proper# X, proper# isNatIList X -> proper# X)
(proper# length X -> proper# X, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# length X -> proper# X, proper# U52(X1, X2) -> proper# X1)
(proper# length X -> proper# X, proper# U52(X1, X2) -> proper# X2)
(proper# length X -> proper# X, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# length X -> proper# X, proper# U51(X1, X2, X3) -> proper# X1)
(proper# length X -> proper# X, proper# U51(X1, X2, X3) -> proper# X2)
(proper# length X -> proper# X, proper# U51(X1, X2, X3) -> proper# X3)
(proper# length X -> proper# X, proper# U53 X -> U53# proper X)
(proper# length X -> proper# X, proper# U53 X -> proper# X)
(proper# length X -> proper# X, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# length X -> proper# X, proper# U62(X1, X2) -> proper# X1)
(proper# length X -> proper# X, proper# U62(X1, X2) -> proper# X2)
(proper# length X -> proper# X, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# length X -> proper# X, proper# U61(X1, X2, X3) -> proper# X1)
(proper# length X -> proper# X, proper# U61(X1, X2, X3) -> proper# X2)
(proper# length X -> proper# X, proper# U61(X1, X2, X3) -> proper# X3)
(proper# length X -> proper# X, proper# U63 X -> U63# proper X)
(proper# length X -> proper# X, proper# U63 X -> proper# X)
(proper# length X -> proper# X, proper# s X -> s# proper X)
(proper# length X -> proper# X, proper# s X -> proper# X)
(proper# length X -> proper# X, proper# length X -> length# proper X)
(proper# length X -> proper# X, proper# length X -> proper# X)
(proper# length X -> proper# X, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# length X -> proper# X, proper# U71(X1, X2) -> proper# X1)
(proper# length X -> proper# X, proper# U71(X1, X2) -> proper# X2)
(proper# length X -> proper# X, proper# U81 X -> U81# proper X)
(proper# length X -> proper# X, proper# U81 X -> proper# X)
(proper# length X -> proper# X, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# length X -> proper# X, proper# take(X1, X2) -> proper# X1)
(proper# length X -> proper# X, proper# take(X1, X2) -> proper# X2)
(proper# length X -> proper# X, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# length X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# length X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# length X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# length X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# length X -> proper# X, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# length X -> proper# X, proper# and(X1, X2) -> proper# X1)
(proper# length X -> proper# X, proper# and(X1, X2) -> proper# X2)
(proper# length X -> proper# X, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# length X -> proper# X, proper# isNatIListKind X -> proper# X)
(proper# length X -> proper# X, proper# isNatKind X -> isNatKind# proper X)
(proper# length X -> proper# X, proper# isNatKind X -> proper# X)
(proper# U63 X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# U63 X -> proper# X, proper# cons(X1, X2) -> proper# X1)
(proper# U63 X -> proper# X, proper# cons(X1, X2) -> proper# X2)
(proper# U63 X -> proper# X, proper# U12 X -> U12# proper X)
(proper# U63 X -> proper# X, proper# U12 X -> proper# X)
(proper# U63 X -> proper# X, proper# isNatList X -> isNatList# proper X)
(proper# U63 X -> proper# X, proper# isNatList X -> proper# X)
(proper# U63 X -> proper# X, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# U63 X -> proper# X, proper# U11(X1, X2) -> proper# X1)
(proper# U63 X -> proper# X, proper# U11(X1, X2) -> proper# X2)
(proper# U63 X -> proper# X, proper# U22 X -> U22# proper X)
(proper# U63 X -> proper# X, proper# U22 X -> proper# X)
(proper# U63 X -> proper# X, proper# isNat X -> isNat# proper X)
(proper# U63 X -> proper# X, proper# isNat X -> proper# X)
(proper# U63 X -> proper# X, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# U63 X -> proper# X, proper# U21(X1, X2) -> proper# X1)
(proper# U63 X -> proper# X, proper# U21(X1, X2) -> proper# X2)
(proper# U63 X -> proper# X, proper# U32 X -> U32# proper X)
(proper# U63 X -> proper# X, proper# U32 X -> proper# X)
(proper# U63 X -> proper# X, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# U63 X -> proper# X, proper# U31(X1, X2) -> proper# X1)
(proper# U63 X -> proper# X, proper# U31(X1, X2) -> proper# X2)
(proper# U63 X -> proper# X, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# U63 X -> proper# X, proper# U42(X1, X2) -> proper# X1)
(proper# U63 X -> proper# X, proper# U42(X1, X2) -> proper# X2)
(proper# U63 X -> proper# X, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# U63 X -> proper# X, proper# U41(X1, X2, X3) -> proper# X1)
(proper# U63 X -> proper# X, proper# U41(X1, X2, X3) -> proper# X2)
(proper# U63 X -> proper# X, proper# U41(X1, X2, X3) -> proper# X3)
(proper# U63 X -> proper# X, proper# U43 X -> U43# proper X)
(proper# U63 X -> proper# X, proper# U43 X -> proper# X)
(proper# U63 X -> proper# X, proper# isNatIList X -> isNatIList# proper X)
(proper# U63 X -> proper# X, proper# isNatIList X -> proper# X)
(proper# U63 X -> proper# X, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# U63 X -> proper# X, proper# U52(X1, X2) -> proper# X1)
(proper# U63 X -> proper# X, proper# U52(X1, X2) -> proper# X2)
(proper# U63 X -> proper# X, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# U63 X -> proper# X, proper# U51(X1, X2, X3) -> proper# X1)
(proper# U63 X -> proper# X, proper# U51(X1, X2, X3) -> proper# X2)
(proper# U63 X -> proper# X, proper# U51(X1, X2, X3) -> proper# X3)
(proper# U63 X -> proper# X, proper# U53 X -> U53# proper X)
(proper# U63 X -> proper# X, proper# U53 X -> proper# X)
(proper# U63 X -> proper# X, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# U63 X -> proper# X, proper# U62(X1, X2) -> proper# X1)
(proper# U63 X -> proper# X, proper# U62(X1, X2) -> proper# X2)
(proper# U63 X -> proper# X, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# U63 X -> proper# X, proper# U61(X1, X2, X3) -> proper# X1)
(proper# U63 X -> proper# X, proper# U61(X1, X2, X3) -> proper# X2)
(proper# U63 X -> proper# X, proper# U61(X1, X2, X3) -> proper# X3)
(proper# U63 X -> proper# X, proper# U63 X -> U63# proper X)
(proper# U63 X -> proper# X, proper# U63 X -> proper# X)
(proper# U63 X -> proper# X, proper# s X -> s# proper X)
(proper# U63 X -> proper# X, proper# s X -> proper# X)
(proper# U63 X -> proper# X, proper# length X -> length# proper X)
(proper# U63 X -> proper# X, proper# length X -> proper# X)
(proper# U63 X -> proper# X, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# U63 X -> proper# X, proper# U71(X1, X2) -> proper# X1)
(proper# U63 X -> proper# X, proper# U71(X1, X2) -> proper# X2)
(proper# U63 X -> proper# X, proper# U81 X -> U81# proper X)
(proper# U63 X -> proper# X, proper# U81 X -> proper# X)
(proper# U63 X -> proper# X, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# U63 X -> proper# X, proper# take(X1, X2) -> proper# X1)
(proper# U63 X -> proper# X, proper# take(X1, X2) -> proper# X2)
(proper# U63 X -> proper# X, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# U63 X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# U63 X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# U63 X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# U63 X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# U63 X -> proper# X, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# U63 X -> proper# X, proper# and(X1, X2) -> proper# X1)
(proper# U63 X -> proper# X, proper# and(X1, X2) -> proper# X2)
(proper# U63 X -> proper# X, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# U63 X -> proper# X, proper# isNatIListKind X -> proper# X)
(proper# U63 X -> proper# X, proper# isNatKind X -> isNatKind# proper X)
(proper# U63 X -> proper# X, proper# isNatKind X -> proper# X)
(proper# isNatIList X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# isNatIList X -> proper# X, proper# cons(X1, X2) -> proper# X1)
(proper# isNatIList X -> proper# X, proper# cons(X1, X2) -> proper# X2)
(proper# isNatIList X -> proper# X, proper# U12 X -> U12# proper X)
(proper# isNatIList X -> proper# X, proper# U12 X -> proper# X)
(proper# isNatIList X -> proper# X, proper# isNatList X -> isNatList# proper X)
(proper# isNatIList X -> proper# X, proper# isNatList X -> proper# X)
(proper# isNatIList X -> proper# X, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# isNatIList X -> proper# X, proper# U11(X1, X2) -> proper# X1)
(proper# isNatIList X -> proper# X, proper# U11(X1, X2) -> proper# X2)
(proper# isNatIList X -> proper# X, proper# U22 X -> U22# proper X)
(proper# isNatIList X -> proper# X, proper# U22 X -> proper# X)
(proper# isNatIList X -> proper# X, proper# isNat X -> isNat# proper X)
(proper# isNatIList X -> proper# X, proper# isNat X -> proper# X)
(proper# isNatIList X -> proper# X, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# isNatIList X -> proper# X, proper# U21(X1, X2) -> proper# X1)
(proper# isNatIList X -> proper# X, proper# U21(X1, X2) -> proper# X2)
(proper# isNatIList X -> proper# X, proper# U32 X -> U32# proper X)
(proper# isNatIList X -> proper# X, proper# U32 X -> proper# X)
(proper# isNatIList X -> proper# X, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# isNatIList X -> proper# X, proper# U31(X1, X2) -> proper# X1)
(proper# isNatIList X -> proper# X, proper# U31(X1, X2) -> proper# X2)
(proper# isNatIList X -> proper# X, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# isNatIList X -> proper# X, proper# U42(X1, X2) -> proper# X1)
(proper# isNatIList X -> proper# X, proper# U42(X1, X2) -> proper# X2)
(proper# isNatIList X -> proper# X, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# isNatIList X -> proper# X, proper# U41(X1, X2, X3) -> proper# X1)
(proper# isNatIList X -> proper# X, proper# U41(X1, X2, X3) -> proper# X2)
(proper# isNatIList X -> proper# X, proper# U41(X1, X2, X3) -> proper# X3)
(proper# isNatIList X -> proper# X, proper# U43 X -> U43# proper X)
(proper# isNatIList X -> proper# X, proper# U43 X -> proper# X)
(proper# isNatIList X -> proper# X, proper# isNatIList X -> isNatIList# proper X)
(proper# isNatIList X -> proper# X, proper# isNatIList X -> proper# X)
(proper# isNatIList X -> proper# X, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# isNatIList X -> proper# X, proper# U52(X1, X2) -> proper# X1)
(proper# isNatIList X -> proper# X, proper# U52(X1, X2) -> proper# X2)
(proper# isNatIList X -> proper# X, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# isNatIList X -> proper# X, proper# U51(X1, X2, X3) -> proper# X1)
(proper# isNatIList X -> proper# X, proper# U51(X1, X2, X3) -> proper# X2)
(proper# isNatIList X -> proper# X, proper# U51(X1, X2, X3) -> proper# X3)
(proper# isNatIList X -> proper# X, proper# U53 X -> U53# proper X)
(proper# isNatIList X -> proper# X, proper# U53 X -> proper# X)
(proper# isNatIList X -> proper# X, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# isNatIList X -> proper# X, proper# U62(X1, X2) -> proper# X1)
(proper# isNatIList X -> proper# X, proper# U62(X1, X2) -> proper# X2)
(proper# isNatIList X -> proper# X, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# isNatIList X -> proper# X, proper# U61(X1, X2, X3) -> proper# X1)
(proper# isNatIList X -> proper# X, proper# U61(X1, X2, X3) -> proper# X2)
(proper# isNatIList X -> proper# X, proper# U61(X1, X2, X3) -> proper# X3)
(proper# isNatIList X -> proper# X, proper# U63 X -> U63# proper X)
(proper# isNatIList X -> proper# X, proper# U63 X -> proper# X)
(proper# isNatIList X -> proper# X, proper# s X -> s# proper X)
(proper# isNatIList X -> proper# X, proper# s X -> proper# X)
(proper# isNatIList X -> proper# X, proper# length X -> length# proper X)
(proper# isNatIList X -> proper# X, proper# length X -> proper# X)
(proper# isNatIList X -> proper# X, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# isNatIList X -> proper# X, proper# U71(X1, X2) -> proper# X1)
(proper# isNatIList X -> proper# X, proper# U71(X1, X2) -> proper# X2)
(proper# isNatIList X -> proper# X, proper# U81 X -> U81# proper X)
(proper# isNatIList X -> proper# X, proper# U81 X -> proper# X)
(proper# isNatIList X -> proper# X, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# isNatIList X -> proper# X, proper# take(X1, X2) -> proper# X1)
(proper# isNatIList X -> proper# X, proper# take(X1, X2) -> proper# X2)
(proper# isNatIList X -> proper# X, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# isNatIList X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# isNatIList X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# isNatIList X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# isNatIList X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# isNatIList X -> proper# X, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# isNatIList X -> proper# X, proper# and(X1, X2) -> proper# X1)
(proper# isNatIList X -> proper# X, proper# and(X1, X2) -> proper# X2)
(proper# isNatIList X -> proper# X, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# isNatIList X -> proper# X, proper# isNatIListKind X -> proper# X)
(proper# isNatIList X -> proper# X, proper# isNatKind X -> isNatKind# proper X)
(proper# isNatIList X -> proper# X, proper# isNatKind X -> proper# X)
(proper# U32 X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# U32 X -> proper# X, proper# cons(X1, X2) -> proper# X1)
(proper# U32 X -> proper# X, proper# cons(X1, X2) -> proper# X2)
(proper# U32 X -> proper# X, proper# U12 X -> U12# proper X)
(proper# U32 X -> proper# X, proper# U12 X -> proper# X)
(proper# U32 X -> proper# X, proper# isNatList X -> isNatList# proper X)
(proper# U32 X -> proper# X, proper# isNatList X -> proper# X)
(proper# U32 X -> proper# X, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# U32 X -> proper# X, proper# U11(X1, X2) -> proper# X1)
(proper# U32 X -> proper# X, proper# U11(X1, X2) -> proper# X2)
(proper# U32 X -> proper# X, proper# U22 X -> U22# proper X)
(proper# U32 X -> proper# X, proper# U22 X -> proper# X)
(proper# U32 X -> proper# X, proper# isNat X -> isNat# proper X)
(proper# U32 X -> proper# X, proper# isNat X -> proper# X)
(proper# U32 X -> proper# X, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# U32 X -> proper# X, proper# U21(X1, X2) -> proper# X1)
(proper# U32 X -> proper# X, proper# U21(X1, X2) -> proper# X2)
(proper# U32 X -> proper# X, proper# U32 X -> U32# proper X)
(proper# U32 X -> proper# X, proper# U32 X -> proper# X)
(proper# U32 X -> proper# X, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# U32 X -> proper# X, proper# U31(X1, X2) -> proper# X1)
(proper# U32 X -> proper# X, proper# U31(X1, X2) -> proper# X2)
(proper# U32 X -> proper# X, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# U32 X -> proper# X, proper# U42(X1, X2) -> proper# X1)
(proper# U32 X -> proper# X, proper# U42(X1, X2) -> proper# X2)
(proper# U32 X -> proper# X, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# U32 X -> proper# X, proper# U41(X1, X2, X3) -> proper# X1)
(proper# U32 X -> proper# X, proper# U41(X1, X2, X3) -> proper# X2)
(proper# U32 X -> proper# X, proper# U41(X1, X2, X3) -> proper# X3)
(proper# U32 X -> proper# X, proper# U43 X -> U43# proper X)
(proper# U32 X -> proper# X, proper# U43 X -> proper# X)
(proper# U32 X -> proper# X, proper# isNatIList X -> isNatIList# proper X)
(proper# U32 X -> proper# X, proper# isNatIList X -> proper# X)
(proper# U32 X -> proper# X, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# U32 X -> proper# X, proper# U52(X1, X2) -> proper# X1)
(proper# U32 X -> proper# X, proper# U52(X1, X2) -> proper# X2)
(proper# U32 X -> proper# X, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# U32 X -> proper# X, proper# U51(X1, X2, X3) -> proper# X1)
(proper# U32 X -> proper# X, proper# U51(X1, X2, X3) -> proper# X2)
(proper# U32 X -> proper# X, proper# U51(X1, X2, X3) -> proper# X3)
(proper# U32 X -> proper# X, proper# U53 X -> U53# proper X)
(proper# U32 X -> proper# X, proper# U53 X -> proper# X)
(proper# U32 X -> proper# X, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# U32 X -> proper# X, proper# U62(X1, X2) -> proper# X1)
(proper# U32 X -> proper# X, proper# U62(X1, X2) -> proper# X2)
(proper# U32 X -> proper# X, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# U32 X -> proper# X, proper# U61(X1, X2, X3) -> proper# X1)
(proper# U32 X -> proper# X, proper# U61(X1, X2, X3) -> proper# X2)
(proper# U32 X -> proper# X, proper# U61(X1, X2, X3) -> proper# X3)
(proper# U32 X -> proper# X, proper# U63 X -> U63# proper X)
(proper# U32 X -> proper# X, proper# U63 X -> proper# X)
(proper# U32 X -> proper# X, proper# s X -> s# proper X)
(proper# U32 X -> proper# X, proper# s X -> proper# X)
(proper# U32 X -> proper# X, proper# length X -> length# proper X)
(proper# U32 X -> proper# X, proper# length X -> proper# X)
(proper# U32 X -> proper# X, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# U32 X -> proper# X, proper# U71(X1, X2) -> proper# X1)
(proper# U32 X -> proper# X, proper# U71(X1, X2) -> proper# X2)
(proper# U32 X -> proper# X, proper# U81 X -> U81# proper X)
(proper# U32 X -> proper# X, proper# U81 X -> proper# X)
(proper# U32 X -> proper# X, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# U32 X -> proper# X, proper# take(X1, X2) -> proper# X1)
(proper# U32 X -> proper# X, proper# take(X1, X2) -> proper# X2)
(proper# U32 X -> proper# X, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# U32 X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# U32 X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# U32 X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# U32 X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# U32 X -> proper# X, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# U32 X -> proper# X, proper# and(X1, X2) -> proper# X1)
(proper# U32 X -> proper# X, proper# and(X1, X2) -> proper# X2)
(proper# U32 X -> proper# X, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# U32 X -> proper# X, proper# isNatIListKind X -> proper# X)
(proper# U32 X -> proper# X, proper# isNatKind X -> isNatKind# proper X)
(proper# U32 X -> proper# X, proper# isNatKind X -> proper# X)
(proper# U22 X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# U22 X -> proper# X, proper# cons(X1, X2) -> proper# X1)
(proper# U22 X -> proper# X, proper# cons(X1, X2) -> proper# X2)
(proper# U22 X -> proper# X, proper# U12 X -> U12# proper X)
(proper# U22 X -> proper# X, proper# U12 X -> proper# X)
(proper# U22 X -> proper# X, proper# isNatList X -> isNatList# proper X)
(proper# U22 X -> proper# X, proper# isNatList X -> proper# X)
(proper# U22 X -> proper# X, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# U22 X -> proper# X, proper# U11(X1, X2) -> proper# X1)
(proper# U22 X -> proper# X, proper# U11(X1, X2) -> proper# X2)
(proper# U22 X -> proper# X, proper# U22 X -> U22# proper X)
(proper# U22 X -> proper# X, proper# U22 X -> proper# X)
(proper# U22 X -> proper# X, proper# isNat X -> isNat# proper X)
(proper# U22 X -> proper# X, proper# isNat X -> proper# X)
(proper# U22 X -> proper# X, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# U22 X -> proper# X, proper# U21(X1, X2) -> proper# X1)
(proper# U22 X -> proper# X, proper# U21(X1, X2) -> proper# X2)
(proper# U22 X -> proper# X, proper# U32 X -> U32# proper X)
(proper# U22 X -> proper# X, proper# U32 X -> proper# X)
(proper# U22 X -> proper# X, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# U22 X -> proper# X, proper# U31(X1, X2) -> proper# X1)
(proper# U22 X -> proper# X, proper# U31(X1, X2) -> proper# X2)
(proper# U22 X -> proper# X, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# U22 X -> proper# X, proper# U42(X1, X2) -> proper# X1)
(proper# U22 X -> proper# X, proper# U42(X1, X2) -> proper# X2)
(proper# U22 X -> proper# X, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# U22 X -> proper# X, proper# U41(X1, X2, X3) -> proper# X1)
(proper# U22 X -> proper# X, proper# U41(X1, X2, X3) -> proper# X2)
(proper# U22 X -> proper# X, proper# U41(X1, X2, X3) -> proper# X3)
(proper# U22 X -> proper# X, proper# U43 X -> U43# proper X)
(proper# U22 X -> proper# X, proper# U43 X -> proper# X)
(proper# U22 X -> proper# X, proper# isNatIList X -> isNatIList# proper X)
(proper# U22 X -> proper# X, proper# isNatIList X -> proper# X)
(proper# U22 X -> proper# X, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# U22 X -> proper# X, proper# U52(X1, X2) -> proper# X1)
(proper# U22 X -> proper# X, proper# U52(X1, X2) -> proper# X2)
(proper# U22 X -> proper# X, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# U22 X -> proper# X, proper# U51(X1, X2, X3) -> proper# X1)
(proper# U22 X -> proper# X, proper# U51(X1, X2, X3) -> proper# X2)
(proper# U22 X -> proper# X, proper# U51(X1, X2, X3) -> proper# X3)
(proper# U22 X -> proper# X, proper# U53 X -> U53# proper X)
(proper# U22 X -> proper# X, proper# U53 X -> proper# X)
(proper# U22 X -> proper# X, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# U22 X -> proper# X, proper# U62(X1, X2) -> proper# X1)
(proper# U22 X -> proper# X, proper# U62(X1, X2) -> proper# X2)
(proper# U22 X -> proper# X, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# U22 X -> proper# X, proper# U61(X1, X2, X3) -> proper# X1)
(proper# U22 X -> proper# X, proper# U61(X1, X2, X3) -> proper# X2)
(proper# U22 X -> proper# X, proper# U61(X1, X2, X3) -> proper# X3)
(proper# U22 X -> proper# X, proper# U63 X -> U63# proper X)
(proper# U22 X -> proper# X, proper# U63 X -> proper# X)
(proper# U22 X -> proper# X, proper# s X -> s# proper X)
(proper# U22 X -> proper# X, proper# s X -> proper# X)
(proper# U22 X -> proper# X, proper# length X -> length# proper X)
(proper# U22 X -> proper# X, proper# length X -> proper# X)
(proper# U22 X -> proper# X, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# U22 X -> proper# X, proper# U71(X1, X2) -> proper# X1)
(proper# U22 X -> proper# X, proper# U71(X1, X2) -> proper# X2)
(proper# U22 X -> proper# X, proper# U81 X -> U81# proper X)
(proper# U22 X -> proper# X, proper# U81 X -> proper# X)
(proper# U22 X -> proper# X, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# U22 X -> proper# X, proper# take(X1, X2) -> proper# X1)
(proper# U22 X -> proper# X, proper# take(X1, X2) -> proper# X2)
(proper# U22 X -> proper# X, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# U22 X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# U22 X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# U22 X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# U22 X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# U22 X -> proper# X, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# U22 X -> proper# X, proper# and(X1, X2) -> proper# X1)
(proper# U22 X -> proper# X, proper# and(X1, X2) -> proper# X2)
(proper# U22 X -> proper# X, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# U22 X -> proper# X, proper# isNatIListKind X -> proper# X)
(proper# U22 X -> proper# X, proper# isNatKind X -> isNatKind# proper X)
(proper# U22 X -> proper# X, proper# isNatKind X -> proper# X)
(proper# U12 X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# U12 X -> proper# X, proper# cons(X1, X2) -> proper# X1)
(proper# U12 X -> proper# X, proper# cons(X1, X2) -> proper# X2)
(proper# U12 X -> proper# X, proper# U12 X -> U12# proper X)
(proper# U12 X -> proper# X, proper# U12 X -> proper# X)
(proper# U12 X -> proper# X, proper# isNatList X -> isNatList# proper X)
(proper# U12 X -> proper# X, proper# isNatList X -> proper# X)
(proper# U12 X -> proper# X, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# U12 X -> proper# X, proper# U11(X1, X2) -> proper# X1)
(proper# U12 X -> proper# X, proper# U11(X1, X2) -> proper# X2)
(proper# U12 X -> proper# X, proper# U22 X -> U22# proper X)
(proper# U12 X -> proper# X, proper# U22 X -> proper# X)
(proper# U12 X -> proper# X, proper# isNat X -> isNat# proper X)
(proper# U12 X -> proper# X, proper# isNat X -> proper# X)
(proper# U12 X -> proper# X, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# U12 X -> proper# X, proper# U21(X1, X2) -> proper# X1)
(proper# U12 X -> proper# X, proper# U21(X1, X2) -> proper# X2)
(proper# U12 X -> proper# X, proper# U32 X -> U32# proper X)
(proper# U12 X -> proper# X, proper# U32 X -> proper# X)
(proper# U12 X -> proper# X, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# U12 X -> proper# X, proper# U31(X1, X2) -> proper# X1)
(proper# U12 X -> proper# X, proper# U31(X1, X2) -> proper# X2)
(proper# U12 X -> proper# X, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# U12 X -> proper# X, proper# U42(X1, X2) -> proper# X1)
(proper# U12 X -> proper# X, proper# U42(X1, X2) -> proper# X2)
(proper# U12 X -> proper# X, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# U12 X -> proper# X, proper# U41(X1, X2, X3) -> proper# X1)
(proper# U12 X -> proper# X, proper# U41(X1, X2, X3) -> proper# X2)
(proper# U12 X -> proper# X, proper# U41(X1, X2, X3) -> proper# X3)
(proper# U12 X -> proper# X, proper# U43 X -> U43# proper X)
(proper# U12 X -> proper# X, proper# U43 X -> proper# X)
(proper# U12 X -> proper# X, proper# isNatIList X -> isNatIList# proper X)
(proper# U12 X -> proper# X, proper# isNatIList X -> proper# X)
(proper# U12 X -> proper# X, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# U12 X -> proper# X, proper# U52(X1, X2) -> proper# X1)
(proper# U12 X -> proper# X, proper# U52(X1, X2) -> proper# X2)
(proper# U12 X -> proper# X, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# U12 X -> proper# X, proper# U51(X1, X2, X3) -> proper# X1)
(proper# U12 X -> proper# X, proper# U51(X1, X2, X3) -> proper# X2)
(proper# U12 X -> proper# X, proper# U51(X1, X2, X3) -> proper# X3)
(proper# U12 X -> proper# X, proper# U53 X -> U53# proper X)
(proper# U12 X -> proper# X, proper# U53 X -> proper# X)
(proper# U12 X -> proper# X, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# U12 X -> proper# X, proper# U62(X1, X2) -> proper# X1)
(proper# U12 X -> proper# X, proper# U62(X1, X2) -> proper# X2)
(proper# U12 X -> proper# X, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# U12 X -> proper# X, proper# U61(X1, X2, X3) -> proper# X1)
(proper# U12 X -> proper# X, proper# U61(X1, X2, X3) -> proper# X2)
(proper# U12 X -> proper# X, proper# U61(X1, X2, X3) -> proper# X3)
(proper# U12 X -> proper# X, proper# U63 X -> U63# proper X)
(proper# U12 X -> proper# X, proper# U63 X -> proper# X)
(proper# U12 X -> proper# X, proper# s X -> s# proper X)
(proper# U12 X -> proper# X, proper# s X -> proper# X)
(proper# U12 X -> proper# X, proper# length X -> length# proper X)
(proper# U12 X -> proper# X, proper# length X -> proper# X)
(proper# U12 X -> proper# X, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# U12 X -> proper# X, proper# U71(X1, X2) -> proper# X1)
(proper# U12 X -> proper# X, proper# U71(X1, X2) -> proper# X2)
(proper# U12 X -> proper# X, proper# U81 X -> U81# proper X)
(proper# U12 X -> proper# X, proper# U81 X -> proper# X)
(proper# U12 X -> proper# X, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# U12 X -> proper# X, proper# take(X1, X2) -> proper# X1)
(proper# U12 X -> proper# X, proper# take(X1, X2) -> proper# X2)
(proper# U12 X -> proper# X, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# U12 X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# U12 X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# U12 X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# U12 X -> proper# X, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# U12 X -> proper# X, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# U12 X -> proper# X, proper# and(X1, X2) -> proper# X1)
(proper# U12 X -> proper# X, proper# and(X1, X2) -> proper# X2)
(proper# U12 X -> proper# X, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# U12 X -> proper# X, proper# isNatIListKind X -> proper# X)
(proper# U12 X -> proper# X, proper# isNatKind X -> isNatKind# proper X)
(proper# U12 X -> proper# X, proper# isNatKind X -> proper# X)
(isNatIListKind# ok X -> isNatIListKind# X, isNatIListKind# ok X -> isNatIListKind# X)
(U81# mark X -> U81# X, U81# mark X -> U81# X)
(U81# mark X -> U81# X, U81# ok X -> U81# X)
(length# mark X -> length# X, length# mark X -> length# X)
(length# mark X -> length# X, length# ok X -> length# X)
(s# mark X -> s# X, s# mark X -> s# X)
(s# mark X -> s# X, s# ok X -> s# X)
(U63# mark X -> U63# X, U63# mark X -> U63# X)
(U63# mark X -> U63# X, U63# ok X -> U63# X)
(U53# mark X -> U53# X, U53# mark X -> U53# X)
(U53# mark X -> U53# X, U53# ok X -> U53# X)
(U43# ok X -> U43# X, U43# mark X -> U43# X)
(U43# ok X -> U43# X, U43# ok X -> U43# X)
(U32# ok X -> U32# X, U32# mark X -> U32# X)
(U32# ok X -> U32# X, U32# ok X -> U32# X)
(isNat# ok X -> isNat# X, isNat# ok X -> isNat# X)
(U22# mark X -> U22# X, U22# mark X -> U22# X)
(U22# mark X -> U22# X, U22# ok X -> U22# X)
(U12# ok X -> U12# X, U12# mark X -> U12# X)
(U12# ok X -> U12# X, U12# ok X -> U12# X)
(active# take(0(), IL) -> U81# and(isNatIList IL, isNatIListKind IL), U81# mark X -> U81# X)
(active# take(0(), IL) -> U81# and(isNatIList IL, isNatIListKind IL), U81# ok X -> U81# X)
(active# length X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2))
(active# length X -> active# X, active# cons(X1, X2) -> active# X1)
(active# length X -> active# X, active# zeros() -> cons#(0(), zeros()))
(active# length X -> active# X, active# U12 X -> active# X)
(active# length X -> active# X, active# U12 X -> U12# active X)
(active# length X -> active# X, active# isNatList cons(V1, V2) -> U51#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# length X -> active# X, active# isNatList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# length X -> active# X, active# isNatList cons(V1, V2) -> isNatIListKind# V2)
(active# length X -> active# X, active# isNatList cons(V1, V2) -> isNatKind# V1)
(active# length X -> active# X, active# isNatList take(V1, V2) -> U61#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# length X -> active# X, active# isNatList take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# length X -> active# X, active# isNatList take(V1, V2) -> isNatIListKind# V2)
(active# length X -> active# X, active# isNatList take(V1, V2) -> isNatKind# V1)
(active# length X -> active# X, active# U11(X1, X2) -> active# X1)
(active# length X -> active# X, active# U11(X1, X2) -> U11#(active X1, X2))
(active# length X -> active# X, active# U11(tt(), V1) -> U12# isNatList V1)
(active# length X -> active# X, active# U11(tt(), V1) -> isNatList# V1)
(active# length X -> active# X, active# U22 X -> active# X)
(active# length X -> active# X, active# U22 X -> U22# active X)
(active# length X -> active# X, active# isNat s V1 -> U21#(isNatKind V1, V1))
(active# length X -> active# X, active# isNat s V1 -> isNatKind# V1)
(active# length X -> active# X, active# isNat length V1 -> U11#(isNatIListKind V1, V1))
(active# length X -> active# X, active# isNat length V1 -> isNatIListKind# V1)
(active# length X -> active# X, active# U21(X1, X2) -> active# X1)
(active# length X -> active# X, active# U21(X1, X2) -> U21#(active X1, X2))
(active# length X -> active# X, active# U21(tt(), V1) -> U22# isNat V1)
(active# length X -> active# X, active# U21(tt(), V1) -> isNat# V1)
(active# length X -> active# X, active# U32 X -> active# X)
(active# length X -> active# X, active# U32 X -> U32# active X)
(active# length X -> active# X, active# U31(X1, X2) -> active# X1)
(active# length X -> active# X, active# U31(X1, X2) -> U31#(active X1, X2))
(active# length X -> active# X, active# U31(tt(), V) -> isNatList# V)
(active# length X -> active# X, active# U31(tt(), V) -> U32# isNatList V)
(active# length X -> active# X, active# U42(X1, X2) -> active# X1)
(active# length X -> active# X, active# U42(X1, X2) -> U42#(active X1, X2))
(active# length X -> active# X, active# U42(tt(), V2) -> U43# isNatIList V2)
(active# length X -> active# X, active# U42(tt(), V2) -> isNatIList# V2)
(active# length X -> active# X, active# U41(X1, X2, X3) -> active# X1)
(active# length X -> active# X, active# U41(X1, X2, X3) -> U41#(active X1, X2, X3))
(active# length X -> active# X, active# U41(tt(), V1, V2) -> isNat# V1)
(active# length X -> active# X, active# U41(tt(), V1, V2) -> U42#(isNat V1, V2))
(active# length X -> active# X, active# U43 X -> active# X)
(active# length X -> active# X, active# U43 X -> U43# active X)
(active# length X -> active# X, active# isNatIList V -> U31#(isNatIListKind V, V))
(active# length X -> active# X, active# isNatIList V -> isNatIListKind# V)
(active# length X -> active# X, active# isNatIList cons(V1, V2) -> U41#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# length X -> active# X, active# isNatIList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# length X -> active# X, active# isNatIList cons(V1, V2) -> isNatIListKind# V2)
(active# length X -> active# X, active# isNatIList cons(V1, V2) -> isNatKind# V1)
(active# length X -> active# X, active# U52(X1, X2) -> active# X1)
(active# length X -> active# X, active# U52(X1, X2) -> U52#(active X1, X2))
(active# length X -> active# X, active# U52(tt(), V2) -> isNatList# V2)
(active# length X -> active# X, active# U52(tt(), V2) -> U53# isNatList V2)
(active# length X -> active# X, active# U51(X1, X2, X3) -> active# X1)
(active# length X -> active# X, active# U51(X1, X2, X3) -> U51#(active X1, X2, X3))
(active# length X -> active# X, active# U51(tt(), V1, V2) -> isNat# V1)
(active# length X -> active# X, active# U51(tt(), V1, V2) -> U52#(isNat V1, V2))
(active# length X -> active# X, active# U53 X -> active# X)
(active# length X -> active# X, active# U53 X -> U53# active X)
(active# length X -> active# X, active# U62(X1, X2) -> active# X1)
(active# length X -> active# X, active# U62(X1, X2) -> U62#(active X1, X2))
(active# length X -> active# X, active# U62(tt(), V2) -> isNatIList# V2)
(active# length X -> active# X, active# U62(tt(), V2) -> U63# isNatIList V2)
(active# length X -> active# X, active# U61(X1, X2, X3) -> active# X1)
(active# length X -> active# X, active# U61(X1, X2, X3) -> U61#(active X1, X2, X3))
(active# length X -> active# X, active# U61(tt(), V1, V2) -> isNat# V1)
(active# length X -> active# X, active# U61(tt(), V1, V2) -> U62#(isNat V1, V2))
(active# length X -> active# X, active# U63 X -> active# X)
(active# length X -> active# X, active# U63 X -> U63# active X)
(active# length X -> active# X, active# s X -> active# X)
(active# length X -> active# X, active# s X -> s# active X)
(active# length X -> active# X, active# length X -> active# X)
(active# length X -> active# X, active# length X -> length# active X)
(active# length X -> active# X, active# length cons(N, L) -> isNatList# L)
(active# length X -> active# X, active# length cons(N, L) -> isNat# N)
(active# length X -> active# X, active# length cons(N, L) -> U71#(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L))
(active# length X -> active# X, active# length cons(N, L) -> and#(isNatList L, isNatIListKind L))
(active# length X -> active# X, active# length cons(N, L) -> and#(isNat N, isNatKind N))
(active# length X -> active# X, active# length cons(N, L) -> and#(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)))
(active# length X -> active# X, active# length cons(N, L) -> isNatIListKind# L)
(active# length X -> active# X, active# length cons(N, L) -> isNatKind# N)
(active# length X -> active# X, active# U71(X1, X2) -> active# X1)
(active# length X -> active# X, active# U71(X1, X2) -> U71#(active X1, X2))
(active# length X -> active# X, active# U71(tt(), L) -> s# length L)
(active# length X -> active# X, active# U71(tt(), L) -> length# L)
(active# length X -> active# X, active# U81 X -> active# X)
(active# length X -> active# X, active# U81 X -> U81# active X)
(active# length X -> active# X, active# take(X1, X2) -> active# X1)
(active# length X -> active# X, active# take(X1, X2) -> active# X2)
(active# length X -> active# X, active# take(X1, X2) -> take#(X1, active X2))
(active# length X -> active# X, active# take(X1, X2) -> take#(active X1, X2))
(active# length X -> active# X, active# take(0(), IL) -> isNatIList# IL)
(active# length X -> active# X, active# take(0(), IL) -> U81# and(isNatIList IL, isNatIListKind IL))
(active# length X -> active# X, active# take(0(), IL) -> and#(isNatIList IL, isNatIListKind IL))
(active# length X -> active# X, active# take(0(), IL) -> isNatIListKind# IL)
(active# length X -> active# X, active# take(s M, cons(N, IL)) -> isNat# N)
(active# length X -> active# X, active# take(s M, cons(N, IL)) -> isNat# M)
(active# length X -> active# X, active# take(s M, cons(N, IL)) -> isNatIList# IL)
(active# length X -> active# X, active# take(s M, cons(N, IL)) -> U91#(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N))
(active# length X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNat N, isNatKind N))
(active# length X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNat M, isNatKind M))
(active# length X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, isNatIListKind IL))
(active# length X -> active# X, active# take(s M, cons(N, IL)) -> and#(and(isNat M, isNatKind M), and(isNat N, isNatKind N)))
(active# length X -> active# X, active# take(s M, cons(N, IL)) -> and#(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))))
(active# length X -> active# X, active# take(s M, cons(N, IL)) -> isNatIListKind# IL)
(active# length X -> active# X, active# take(s M, cons(N, IL)) -> isNatKind# N)
(active# length X -> active# X, active# take(s M, cons(N, IL)) -> isNatKind# M)
(active# length X -> active# X, active# U91(X1, X2, X3, X4) -> active# X1)
(active# length X -> active# X, active# U91(X1, X2, X3, X4) -> U91#(active X1, X2, X3, X4))
(active# length X -> active# X, active# U91(tt(), IL, M, N) -> cons#(N, take(M, IL)))
(active# length X -> active# X, active# U91(tt(), IL, M, N) -> take#(M, IL))
(active# length X -> active# X, active# and(X1, X2) -> active# X1)
(active# length X -> active# X, active# and(X1, X2) -> and#(active X1, X2))
(active# length X -> active# X, active# isNatIListKind cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# length X -> active# X, active# isNatIListKind cons(V1, V2) -> isNatIListKind# V2)
(active# length X -> active# X, active# isNatIListKind cons(V1, V2) -> isNatKind# V1)
(active# length X -> active# X, active# isNatIListKind take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# length X -> active# X, active# isNatIListKind take(V1, V2) -> isNatIListKind# V2)
(active# length X -> active# X, active# isNatIListKind take(V1, V2) -> isNatKind# V1)
(active# length X -> active# X, active# isNatKind s V1 -> isNatKind# V1)
(active# length X -> active# X, active# isNatKind length V1 -> isNatIListKind# V1)
(active# U63 X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2))
(active# U63 X -> active# X, active# cons(X1, X2) -> active# X1)
(active# U63 X -> active# X, active# zeros() -> cons#(0(), zeros()))
(active# U63 X -> active# X, active# U12 X -> active# X)
(active# U63 X -> active# X, active# U12 X -> U12# active X)
(active# U63 X -> active# X, active# isNatList cons(V1, V2) -> U51#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U63 X -> active# X, active# isNatList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U63 X -> active# X, active# isNatList cons(V1, V2) -> isNatIListKind# V2)
(active# U63 X -> active# X, active# isNatList cons(V1, V2) -> isNatKind# V1)
(active# U63 X -> active# X, active# isNatList take(V1, V2) -> U61#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U63 X -> active# X, active# isNatList take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U63 X -> active# X, active# isNatList take(V1, V2) -> isNatIListKind# V2)
(active# U63 X -> active# X, active# isNatList take(V1, V2) -> isNatKind# V1)
(active# U63 X -> active# X, active# U11(X1, X2) -> active# X1)
(active# U63 X -> active# X, active# U11(X1, X2) -> U11#(active X1, X2))
(active# U63 X -> active# X, active# U11(tt(), V1) -> U12# isNatList V1)
(active# U63 X -> active# X, active# U11(tt(), V1) -> isNatList# V1)
(active# U63 X -> active# X, active# U22 X -> active# X)
(active# U63 X -> active# X, active# U22 X -> U22# active X)
(active# U63 X -> active# X, active# isNat s V1 -> U21#(isNatKind V1, V1))
(active# U63 X -> active# X, active# isNat s V1 -> isNatKind# V1)
(active# U63 X -> active# X, active# isNat length V1 -> U11#(isNatIListKind V1, V1))
(active# U63 X -> active# X, active# isNat length V1 -> isNatIListKind# V1)
(active# U63 X -> active# X, active# U21(X1, X2) -> active# X1)
(active# U63 X -> active# X, active# U21(X1, X2) -> U21#(active X1, X2))
(active# U63 X -> active# X, active# U21(tt(), V1) -> U22# isNat V1)
(active# U63 X -> active# X, active# U21(tt(), V1) -> isNat# V1)
(active# U63 X -> active# X, active# U32 X -> active# X)
(active# U63 X -> active# X, active# U32 X -> U32# active X)
(active# U63 X -> active# X, active# U31(X1, X2) -> active# X1)
(active# U63 X -> active# X, active# U31(X1, X2) -> U31#(active X1, X2))
(active# U63 X -> active# X, active# U31(tt(), V) -> isNatList# V)
(active# U63 X -> active# X, active# U31(tt(), V) -> U32# isNatList V)
(active# U63 X -> active# X, active# U42(X1, X2) -> active# X1)
(active# U63 X -> active# X, active# U42(X1, X2) -> U42#(active X1, X2))
(active# U63 X -> active# X, active# U42(tt(), V2) -> U43# isNatIList V2)
(active# U63 X -> active# X, active# U42(tt(), V2) -> isNatIList# V2)
(active# U63 X -> active# X, active# U41(X1, X2, X3) -> active# X1)
(active# U63 X -> active# X, active# U41(X1, X2, X3) -> U41#(active X1, X2, X3))
(active# U63 X -> active# X, active# U41(tt(), V1, V2) -> isNat# V1)
(active# U63 X -> active# X, active# U41(tt(), V1, V2) -> U42#(isNat V1, V2))
(active# U63 X -> active# X, active# U43 X -> active# X)
(active# U63 X -> active# X, active# U43 X -> U43# active X)
(active# U63 X -> active# X, active# isNatIList V -> U31#(isNatIListKind V, V))
(active# U63 X -> active# X, active# isNatIList V -> isNatIListKind# V)
(active# U63 X -> active# X, active# isNatIList cons(V1, V2) -> U41#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U63 X -> active# X, active# isNatIList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U63 X -> active# X, active# isNatIList cons(V1, V2) -> isNatIListKind# V2)
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(active# U22 X -> active# X, active# U43 X -> active# X)
(active# U22 X -> active# X, active# U43 X -> U43# active X)
(active# U22 X -> active# X, active# isNatIList V -> U31#(isNatIListKind V, V))
(active# U22 X -> active# X, active# isNatIList V -> isNatIListKind# V)
(active# U22 X -> active# X, active# isNatIList cons(V1, V2) -> U41#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U22 X -> active# X, active# isNatIList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U22 X -> active# X, active# isNatIList cons(V1, V2) -> isNatIListKind# V2)
(active# U22 X -> active# X, active# isNatIList cons(V1, V2) -> isNatKind# V1)
(active# U22 X -> active# X, active# U52(X1, X2) -> active# X1)
(active# U22 X -> active# X, active# U52(X1, X2) -> U52#(active X1, X2))
(active# U22 X -> active# X, active# U52(tt(), V2) -> isNatList# V2)
(active# U22 X -> active# X, active# U52(tt(), V2) -> U53# isNatList V2)
(active# U22 X -> active# X, active# U51(X1, X2, X3) -> active# X1)
(active# U22 X -> active# X, active# U51(X1, X2, X3) -> U51#(active X1, X2, X3))
(active# U22 X -> active# X, active# U51(tt(), V1, V2) -> isNat# V1)
(active# U22 X -> active# X, active# U51(tt(), V1, V2) -> U52#(isNat V1, V2))
(active# U22 X -> active# X, active# U53 X -> active# X)
(active# U22 X -> active# X, active# U53 X -> U53# active X)
(active# U22 X -> active# X, active# U62(X1, X2) -> active# X1)
(active# U22 X -> active# X, active# U62(X1, X2) -> U62#(active X1, X2))
(active# U22 X -> active# X, active# U62(tt(), V2) -> isNatIList# V2)
(active# U22 X -> active# X, active# U62(tt(), V2) -> U63# isNatIList V2)
(active# U22 X -> active# X, active# U61(X1, X2, X3) -> active# X1)
(active# U22 X -> active# X, active# U61(X1, X2, X3) -> U61#(active X1, X2, X3))
(active# U22 X -> active# X, active# U61(tt(), V1, V2) -> isNat# V1)
(active# U22 X -> active# X, active# U61(tt(), V1, V2) -> U62#(isNat V1, V2))
(active# U22 X -> active# X, active# U63 X -> active# X)
(active# U22 X -> active# X, active# U63 X -> U63# active X)
(active# U22 X -> active# X, active# s X -> active# X)
(active# U22 X -> active# X, active# s X -> s# active X)
(active# U22 X -> active# X, active# length X -> active# X)
(active# U22 X -> active# X, active# length X -> length# active X)
(active# U22 X -> active# X, active# length cons(N, L) -> isNatList# L)
(active# U22 X -> active# X, active# length cons(N, L) -> isNat# N)
(active# U22 X -> active# X, active# length cons(N, L) -> U71#(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L))
(active# U22 X -> active# X, active# length cons(N, L) -> and#(isNatList L, isNatIListKind L))
(active# U22 X -> active# X, active# length cons(N, L) -> and#(isNat N, isNatKind N))
(active# U22 X -> active# X, active# length cons(N, L) -> and#(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)))
(active# U22 X -> active# X, active# length cons(N, L) -> isNatIListKind# L)
(active# U22 X -> active# X, active# length cons(N, L) -> isNatKind# N)
(active# U22 X -> active# X, active# U71(X1, X2) -> active# X1)
(active# U22 X -> active# X, active# U71(X1, X2) -> U71#(active X1, X2))
(active# U22 X -> active# X, active# U71(tt(), L) -> s# length L)
(active# U22 X -> active# X, active# U71(tt(), L) -> length# L)
(active# U22 X -> active# X, active# U81 X -> active# X)
(active# U22 X -> active# X, active# U81 X -> U81# active X)
(active# U22 X -> active# X, active# take(X1, X2) -> active# X1)
(active# U22 X -> active# X, active# take(X1, X2) -> active# X2)
(active# U22 X -> active# X, active# take(X1, X2) -> take#(X1, active X2))
(active# U22 X -> active# X, active# take(X1, X2) -> take#(active X1, X2))
(active# U22 X -> active# X, active# take(0(), IL) -> isNatIList# IL)
(active# U22 X -> active# X, active# take(0(), IL) -> U81# and(isNatIList IL, isNatIListKind IL))
(active# U22 X -> active# X, active# take(0(), IL) -> and#(isNatIList IL, isNatIListKind IL))
(active# U22 X -> active# X, active# take(0(), IL) -> isNatIListKind# IL)
(active# U22 X -> active# X, active# take(s M, cons(N, IL)) -> isNat# N)
(active# U22 X -> active# X, active# take(s M, cons(N, IL)) -> isNat# M)
(active# U22 X -> active# X, active# take(s M, cons(N, IL)) -> isNatIList# IL)
(active# U22 X -> active# X, active# take(s M, cons(N, IL)) -> U91#(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N))
(active# U22 X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNat N, isNatKind N))
(active# U22 X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNat M, isNatKind M))
(active# U22 X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, isNatIListKind IL))
(active# U22 X -> active# X, active# take(s M, cons(N, IL)) -> and#(and(isNat M, isNatKind M), and(isNat N, isNatKind N)))
(active# U22 X -> active# X, active# take(s M, cons(N, IL)) -> and#(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))))
(active# U22 X -> active# X, active# take(s M, cons(N, IL)) -> isNatIListKind# IL)
(active# U22 X -> active# X, active# take(s M, cons(N, IL)) -> isNatKind# N)
(active# U22 X -> active# X, active# take(s M, cons(N, IL)) -> isNatKind# M)
(active# U22 X -> active# X, active# U91(X1, X2, X3, X4) -> active# X1)
(active# U22 X -> active# X, active# U91(X1, X2, X3, X4) -> U91#(active X1, X2, X3, X4))
(active# U22 X -> active# X, active# U91(tt(), IL, M, N) -> cons#(N, take(M, IL)))
(active# U22 X -> active# X, active# U91(tt(), IL, M, N) -> take#(M, IL))
(active# U22 X -> active# X, active# and(X1, X2) -> active# X1)
(active# U22 X -> active# X, active# and(X1, X2) -> and#(active X1, X2))
(active# U22 X -> active# X, active# isNatIListKind cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U22 X -> active# X, active# isNatIListKind cons(V1, V2) -> isNatIListKind# V2)
(active# U22 X -> active# X, active# isNatIListKind cons(V1, V2) -> isNatKind# V1)
(active# U22 X -> active# X, active# isNatIListKind take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U22 X -> active# X, active# isNatIListKind take(V1, V2) -> isNatIListKind# V2)
(active# U22 X -> active# X, active# isNatIListKind take(V1, V2) -> isNatKind# V1)
(active# U22 X -> active# X, active# isNatKind s V1 -> isNatKind# V1)
(active# U22 X -> active# X, active# isNatKind length V1 -> isNatIListKind# V1)
(proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4), U91#(mark X1, X2, X3, X4) -> U91#(X1, X2, X3, X4))
(proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4), U91#(ok X1, ok X2, ok X3, ok X4) -> U91#(X1, X2, X3, X4))
(active# isNatIListKind cons(V1, V2) -> isNatIListKind# V2, isNatIListKind# ok X -> isNatIListKind# X)
(active# U52(tt(), V2) -> isNatList# V2, isNatList# ok X -> isNatList# X)
(active# U42(tt(), V2) -> isNatIList# V2, isNatIList# ok X -> isNatIList# X)
(active# isNatList cons(V1, V2) -> isNatIListKind# V2, isNatIListKind# ok X -> isNatIListKind# X)
(active# isNat s V1 -> U21#(isNatKind V1, V1), U21#(mark X1, X2) -> U21#(X1, X2))
(active# isNat s V1 -> U21#(isNatKind V1, V1), U21#(ok X1, ok X2) -> U21#(X1, X2))
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# cons(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# cons(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U12 X -> U12# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U12 X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# isNatList X -> isNatList# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# isNatList X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U11(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U11(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U22 X -> U22# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U22 X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# isNat X -> isNat# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# isNat X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U21(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U21(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U32 X -> U32# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U32 X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U31(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U31(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U42(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U42(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X3)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U43 X -> U43# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U43 X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# isNatIList X -> isNatIList# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# isNatIList X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U52(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U52(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X3)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U53 X -> U53# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U53 X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U62(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U62(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X3)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U63 X -> U63# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U63 X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# s X -> s# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# s X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# length X -> length# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# length X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U71(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U71(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U81 X -> U81# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U81 X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# take(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# take(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# and(X1, X2) -> proper# X1)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# and(X1, X2) -> proper# X2)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# isNatIListKind X -> proper# X)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# isNatKind X -> isNatKind# proper X)
(proper# U91(X1, X2, X3, X4) -> proper# X2, proper# isNatKind X -> proper# X)
(proper# U71(X1, X2) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# U71(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1)
(proper# U71(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X2)
(proper# U71(X1, X2) -> proper# X2, proper# U12 X -> U12# proper X)
(proper# U71(X1, X2) -> proper# X2, proper# U12 X -> proper# X)
(proper# U71(X1, X2) -> proper# X2, proper# isNatList X -> isNatList# proper X)
(proper# U71(X1, X2) -> proper# X2, proper# isNatList X -> proper# X)
(proper# U71(X1, X2) -> proper# X2, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# U71(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X1)
(proper# U71(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X2)
(proper# U71(X1, X2) -> proper# X2, proper# U22 X -> U22# proper X)
(proper# U71(X1, X2) -> proper# X2, proper# U22 X -> proper# X)
(proper# U71(X1, X2) -> proper# X2, proper# isNat X -> isNat# proper X)
(proper# U71(X1, X2) -> proper# X2, proper# isNat X -> proper# X)
(proper# U71(X1, X2) -> proper# X2, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# U71(X1, X2) -> proper# X2, proper# U21(X1, X2) -> proper# X1)
(proper# U71(X1, X2) -> proper# X2, proper# U21(X1, X2) -> proper# X2)
(proper# U71(X1, X2) -> proper# X2, proper# U32 X -> U32# proper X)
(proper# U71(X1, X2) -> proper# X2, proper# U32 X -> proper# X)
(proper# U71(X1, X2) -> proper# X2, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# U71(X1, X2) -> proper# X2, proper# U31(X1, X2) -> proper# X1)
(proper# U71(X1, X2) -> proper# X2, proper# U31(X1, X2) -> proper# X2)
(proper# U71(X1, X2) -> proper# X2, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# U71(X1, X2) -> proper# X2, proper# U42(X1, X2) -> proper# X1)
(proper# U71(X1, X2) -> proper# X2, proper# U42(X1, X2) -> proper# X2)
(proper# U71(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# U71(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X1)
(proper# U71(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X2)
(proper# U71(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X3)
(proper# U71(X1, X2) -> proper# X2, proper# U43 X -> U43# proper X)
(proper# U71(X1, X2) -> proper# X2, proper# U43 X -> proper# X)
(proper# U71(X1, X2) -> proper# X2, proper# isNatIList X -> isNatIList# proper X)
(proper# U71(X1, X2) -> proper# X2, proper# isNatIList X -> proper# X)
(proper# U71(X1, X2) -> proper# X2, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# U71(X1, X2) -> proper# X2, proper# U52(X1, X2) -> proper# X1)
(proper# U71(X1, X2) -> proper# X2, proper# U52(X1, X2) -> proper# X2)
(proper# U71(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# U71(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X1)
(proper# U71(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X2)
(proper# U71(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X3)
(proper# U71(X1, X2) -> proper# X2, proper# U53 X -> U53# proper X)
(proper# U71(X1, X2) -> proper# X2, proper# U53 X -> proper# X)
(proper# U71(X1, X2) -> proper# X2, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# U71(X1, X2) -> proper# X2, proper# U62(X1, X2) -> proper# X1)
(proper# U71(X1, X2) -> proper# X2, proper# U62(X1, X2) -> proper# X2)
(proper# U71(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# U71(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X1)
(proper# U71(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X2)
(proper# U71(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X3)
(proper# U71(X1, X2) -> proper# X2, proper# U63 X -> U63# proper X)
(proper# U71(X1, X2) -> proper# X2, proper# U63 X -> proper# X)
(proper# U71(X1, X2) -> proper# X2, proper# s X -> s# proper X)
(proper# U71(X1, X2) -> proper# X2, proper# s X -> proper# X)
(proper# U71(X1, X2) -> proper# X2, proper# length X -> length# proper X)
(proper# U71(X1, X2) -> proper# X2, proper# length X -> proper# X)
(proper# U71(X1, X2) -> proper# X2, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# U71(X1, X2) -> proper# X2, proper# U71(X1, X2) -> proper# X1)
(proper# U71(X1, X2) -> proper# X2, proper# U71(X1, X2) -> proper# X2)
(proper# U71(X1, X2) -> proper# X2, proper# U81 X -> U81# proper X)
(proper# U71(X1, X2) -> proper# X2, proper# U81 X -> proper# X)
(proper# U71(X1, X2) -> proper# X2, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# U71(X1, X2) -> proper# X2, proper# take(X1, X2) -> proper# X1)
(proper# U71(X1, X2) -> proper# X2, proper# take(X1, X2) -> proper# X2)
(proper# U71(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# U71(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# U71(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# U71(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# U71(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# U71(X1, X2) -> proper# X2, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# U71(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X1)
(proper# U71(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X2)
(proper# U71(X1, X2) -> proper# X2, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# U71(X1, X2) -> proper# X2, proper# isNatIListKind X -> proper# X)
(proper# U71(X1, X2) -> proper# X2, proper# isNatKind X -> isNatKind# proper X)
(proper# U71(X1, X2) -> proper# X2, proper# isNatKind X -> proper# X)
(proper# U62(X1, X2) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# U62(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1)
(proper# U62(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X2)
(proper# U62(X1, X2) -> proper# X2, proper# U12 X -> U12# proper X)
(proper# U62(X1, X2) -> proper# X2, proper# U12 X -> proper# X)
(proper# U62(X1, X2) -> proper# X2, proper# isNatList X -> isNatList# proper X)
(proper# U62(X1, X2) -> proper# X2, proper# isNatList X -> proper# X)
(proper# U62(X1, X2) -> proper# X2, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# U62(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X1)
(proper# U62(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X2)
(proper# U62(X1, X2) -> proper# X2, proper# U22 X -> U22# proper X)
(proper# U62(X1, X2) -> proper# X2, proper# U22 X -> proper# X)
(proper# U62(X1, X2) -> proper# X2, proper# isNat X -> isNat# proper X)
(proper# U62(X1, X2) -> proper# X2, proper# isNat X -> proper# X)
(proper# U62(X1, X2) -> proper# X2, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# U62(X1, X2) -> proper# X2, proper# U21(X1, X2) -> proper# X1)
(proper# U62(X1, X2) -> proper# X2, proper# U21(X1, X2) -> proper# X2)
(proper# U62(X1, X2) -> proper# X2, proper# U32 X -> U32# proper X)
(proper# U62(X1, X2) -> proper# X2, proper# U32 X -> proper# X)
(proper# U62(X1, X2) -> proper# X2, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# U62(X1, X2) -> proper# X2, proper# U31(X1, X2) -> proper# X1)
(proper# U62(X1, X2) -> proper# X2, proper# U31(X1, X2) -> proper# X2)
(proper# U62(X1, X2) -> proper# X2, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# U62(X1, X2) -> proper# X2, proper# U42(X1, X2) -> proper# X1)
(proper# U62(X1, X2) -> proper# X2, proper# U42(X1, X2) -> proper# X2)
(proper# U62(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# U62(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X1)
(proper# U62(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X2)
(proper# U62(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X3)
(proper# U62(X1, X2) -> proper# X2, proper# U43 X -> U43# proper X)
(proper# U62(X1, X2) -> proper# X2, proper# U43 X -> proper# X)
(proper# U62(X1, X2) -> proper# X2, proper# isNatIList X -> isNatIList# proper X)
(proper# U62(X1, X2) -> proper# X2, proper# isNatIList X -> proper# X)
(proper# U62(X1, X2) -> proper# X2, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# U62(X1, X2) -> proper# X2, proper# U52(X1, X2) -> proper# X1)
(proper# U62(X1, X2) -> proper# X2, proper# U52(X1, X2) -> proper# X2)
(proper# U62(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# U62(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X1)
(proper# U62(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X2)
(proper# U62(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X3)
(proper# U62(X1, X2) -> proper# X2, proper# U53 X -> U53# proper X)
(proper# U62(X1, X2) -> proper# X2, proper# U53 X -> proper# X)
(proper# U62(X1, X2) -> proper# X2, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# U62(X1, X2) -> proper# X2, proper# U62(X1, X2) -> proper# X1)
(proper# U62(X1, X2) -> proper# X2, proper# U62(X1, X2) -> proper# X2)
(proper# U62(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# U62(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X1)
(proper# U62(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X2)
(proper# U62(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X3)
(proper# U62(X1, X2) -> proper# X2, proper# U63 X -> U63# proper X)
(proper# U62(X1, X2) -> proper# X2, proper# U63 X -> proper# X)
(proper# U62(X1, X2) -> proper# X2, proper# s X -> s# proper X)
(proper# U62(X1, X2) -> proper# X2, proper# s X -> proper# X)
(proper# U62(X1, X2) -> proper# X2, proper# length X -> length# proper X)
(proper# U62(X1, X2) -> proper# X2, proper# length X -> proper# X)
(proper# U62(X1, X2) -> proper# X2, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# U62(X1, X2) -> proper# X2, proper# U71(X1, X2) -> proper# X1)
(proper# U62(X1, X2) -> proper# X2, proper# U71(X1, X2) -> proper# X2)
(proper# U62(X1, X2) -> proper# X2, proper# U81 X -> U81# proper X)
(proper# U62(X1, X2) -> proper# X2, proper# U81 X -> proper# X)
(proper# U62(X1, X2) -> proper# X2, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# U62(X1, X2) -> proper# X2, proper# take(X1, X2) -> proper# X1)
(proper# U62(X1, X2) -> proper# X2, proper# take(X1, X2) -> proper# X2)
(proper# U62(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# U62(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# U62(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# U62(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# U62(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# U62(X1, X2) -> proper# X2, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# U62(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X1)
(proper# U62(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X2)
(proper# U62(X1, X2) -> proper# X2, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# U62(X1, X2) -> proper# X2, proper# isNatIListKind X -> proper# X)
(proper# U62(X1, X2) -> proper# X2, proper# isNatKind X -> isNatKind# proper X)
(proper# U62(X1, X2) -> proper# X2, proper# isNatKind X -> proper# X)
(proper# U52(X1, X2) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# U52(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1)
(proper# U52(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X2)
(proper# U52(X1, X2) -> proper# X2, proper# U12 X -> U12# proper X)
(proper# U52(X1, X2) -> proper# X2, proper# U12 X -> proper# X)
(proper# U52(X1, X2) -> proper# X2, proper# isNatList X -> isNatList# proper X)
(proper# U52(X1, X2) -> proper# X2, proper# isNatList X -> proper# X)
(proper# U52(X1, X2) -> proper# X2, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# U52(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X1)
(proper# U52(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X2)
(proper# U52(X1, X2) -> proper# X2, proper# U22 X -> U22# proper X)
(proper# U52(X1, X2) -> proper# X2, proper# U22 X -> proper# X)
(proper# U52(X1, X2) -> proper# X2, proper# isNat X -> isNat# proper X)
(proper# U52(X1, X2) -> proper# X2, proper# isNat X -> proper# X)
(proper# U52(X1, X2) -> proper# X2, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# U52(X1, X2) -> proper# X2, proper# U21(X1, X2) -> proper# X1)
(proper# U52(X1, X2) -> proper# X2, proper# U21(X1, X2) -> proper# X2)
(proper# U52(X1, X2) -> proper# X2, proper# U32 X -> U32# proper X)
(proper# U52(X1, X2) -> proper# X2, proper# U32 X -> proper# X)
(proper# U52(X1, X2) -> proper# X2, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# U52(X1, X2) -> proper# X2, proper# U31(X1, X2) -> proper# X1)
(proper# U52(X1, X2) -> proper# X2, proper# U31(X1, X2) -> proper# X2)
(proper# U52(X1, X2) -> proper# X2, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# U52(X1, X2) -> proper# X2, proper# U42(X1, X2) -> proper# X1)
(proper# U52(X1, X2) -> proper# X2, proper# U42(X1, X2) -> proper# X2)
(proper# U52(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# U52(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X1)
(proper# U52(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X2)
(proper# U52(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X3)
(proper# U52(X1, X2) -> proper# X2, proper# U43 X -> U43# proper X)
(proper# U52(X1, X2) -> proper# X2, proper# U43 X -> proper# X)
(proper# U52(X1, X2) -> proper# X2, proper# isNatIList X -> isNatIList# proper X)
(proper# U52(X1, X2) -> proper# X2, proper# isNatIList X -> proper# X)
(proper# U52(X1, X2) -> proper# X2, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# U52(X1, X2) -> proper# X2, proper# U52(X1, X2) -> proper# X1)
(proper# U52(X1, X2) -> proper# X2, proper# U52(X1, X2) -> proper# X2)
(proper# U52(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# U52(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X1)
(proper# U52(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X2)
(proper# U52(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X3)
(proper# U52(X1, X2) -> proper# X2, proper# U53 X -> U53# proper X)
(proper# U52(X1, X2) -> proper# X2, proper# U53 X -> proper# X)
(proper# U52(X1, X2) -> proper# X2, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# U52(X1, X2) -> proper# X2, proper# U62(X1, X2) -> proper# X1)
(proper# U52(X1, X2) -> proper# X2, proper# U62(X1, X2) -> proper# X2)
(proper# U52(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# U52(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X1)
(proper# U52(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X2)
(proper# U52(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X3)
(proper# U52(X1, X2) -> proper# X2, proper# U63 X -> U63# proper X)
(proper# U52(X1, X2) -> proper# X2, proper# U63 X -> proper# X)
(proper# U52(X1, X2) -> proper# X2, proper# s X -> s# proper X)
(proper# U52(X1, X2) -> proper# X2, proper# s X -> proper# X)
(proper# U52(X1, X2) -> proper# X2, proper# length X -> length# proper X)
(proper# U52(X1, X2) -> proper# X2, proper# length X -> proper# X)
(proper# U52(X1, X2) -> proper# X2, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# U52(X1, X2) -> proper# X2, proper# U71(X1, X2) -> proper# X1)
(proper# U52(X1, X2) -> proper# X2, proper# U71(X1, X2) -> proper# X2)
(proper# U52(X1, X2) -> proper# X2, proper# U81 X -> U81# proper X)
(proper# U52(X1, X2) -> proper# X2, proper# U81 X -> proper# X)
(proper# U52(X1, X2) -> proper# X2, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# U52(X1, X2) -> proper# X2, proper# take(X1, X2) -> proper# X1)
(proper# U52(X1, X2) -> proper# X2, proper# take(X1, X2) -> proper# X2)
(proper# U52(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# U52(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# U52(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# U52(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# U52(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# U52(X1, X2) -> proper# X2, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# U52(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X1)
(proper# U52(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X2)
(proper# U52(X1, X2) -> proper# X2, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# U52(X1, X2) -> proper# X2, proper# isNatIListKind X -> proper# X)
(proper# U52(X1, X2) -> proper# X2, proper# isNatKind X -> isNatKind# proper X)
(proper# U52(X1, X2) -> proper# X2, proper# isNatKind X -> proper# X)
(proper# U42(X1, X2) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# U42(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1)
(proper# U42(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X2)
(proper# U42(X1, X2) -> proper# X2, proper# U12 X -> U12# proper X)
(proper# U42(X1, X2) -> proper# X2, proper# U12 X -> proper# X)
(proper# U42(X1, X2) -> proper# X2, proper# isNatList X -> isNatList# proper X)
(proper# U42(X1, X2) -> proper# X2, proper# isNatList X -> proper# X)
(proper# U42(X1, X2) -> proper# X2, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# U42(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X1)
(proper# U42(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X2)
(proper# U42(X1, X2) -> proper# X2, proper# U22 X -> U22# proper X)
(proper# U42(X1, X2) -> proper# X2, proper# U22 X -> proper# X)
(proper# U42(X1, X2) -> proper# X2, proper# isNat X -> isNat# proper X)
(proper# U42(X1, X2) -> proper# X2, proper# isNat X -> proper# X)
(proper# U42(X1, X2) -> proper# X2, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# U42(X1, X2) -> proper# X2, proper# U21(X1, X2) -> proper# X1)
(proper# U42(X1, X2) -> proper# X2, proper# U21(X1, X2) -> proper# X2)
(proper# U42(X1, X2) -> proper# X2, proper# U32 X -> U32# proper X)
(proper# U42(X1, X2) -> proper# X2, proper# U32 X -> proper# X)
(proper# U42(X1, X2) -> proper# X2, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# U42(X1, X2) -> proper# X2, proper# U31(X1, X2) -> proper# X1)
(proper# U42(X1, X2) -> proper# X2, proper# U31(X1, X2) -> proper# X2)
(proper# U42(X1, X2) -> proper# X2, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# U42(X1, X2) -> proper# X2, proper# U42(X1, X2) -> proper# X1)
(proper# U42(X1, X2) -> proper# X2, proper# U42(X1, X2) -> proper# X2)
(proper# U42(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# U42(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X1)
(proper# U42(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X2)
(proper# U42(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X3)
(proper# U42(X1, X2) -> proper# X2, proper# U43 X -> U43# proper X)
(proper# U42(X1, X2) -> proper# X2, proper# U43 X -> proper# X)
(proper# U42(X1, X2) -> proper# X2, proper# isNatIList X -> isNatIList# proper X)
(proper# U42(X1, X2) -> proper# X2, proper# isNatIList X -> proper# X)
(proper# U42(X1, X2) -> proper# X2, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# U42(X1, X2) -> proper# X2, proper# U52(X1, X2) -> proper# X1)
(proper# U42(X1, X2) -> proper# X2, proper# U52(X1, X2) -> proper# X2)
(proper# U42(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# U42(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X1)
(proper# U42(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X2)
(proper# U42(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X3)
(proper# U42(X1, X2) -> proper# X2, proper# U53 X -> U53# proper X)
(proper# U42(X1, X2) -> proper# X2, proper# U53 X -> proper# X)
(proper# U42(X1, X2) -> proper# X2, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# U42(X1, X2) -> proper# X2, proper# U62(X1, X2) -> proper# X1)
(proper# U42(X1, X2) -> proper# X2, proper# U62(X1, X2) -> proper# X2)
(proper# U42(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# U42(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X1)
(proper# U42(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X2)
(proper# U42(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X3)
(proper# U42(X1, X2) -> proper# X2, proper# U63 X -> U63# proper X)
(proper# U42(X1, X2) -> proper# X2, proper# U63 X -> proper# X)
(proper# U42(X1, X2) -> proper# X2, proper# s X -> s# proper X)
(proper# U42(X1, X2) -> proper# X2, proper# s X -> proper# X)
(proper# U42(X1, X2) -> proper# X2, proper# length X -> length# proper X)
(proper# U42(X1, X2) -> proper# X2, proper# length X -> proper# X)
(proper# U42(X1, X2) -> proper# X2, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# U42(X1, X2) -> proper# X2, proper# U71(X1, X2) -> proper# X1)
(proper# U42(X1, X2) -> proper# X2, proper# U71(X1, X2) -> proper# X2)
(proper# U42(X1, X2) -> proper# X2, proper# U81 X -> U81# proper X)
(proper# U42(X1, X2) -> proper# X2, proper# U81 X -> proper# X)
(proper# U42(X1, X2) -> proper# X2, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# U42(X1, X2) -> proper# X2, proper# take(X1, X2) -> proper# X1)
(proper# U42(X1, X2) -> proper# X2, proper# take(X1, X2) -> proper# X2)
(proper# U42(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# U42(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# U42(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# U42(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# U42(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# U42(X1, X2) -> proper# X2, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# U42(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X1)
(proper# U42(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X2)
(proper# U42(X1, X2) -> proper# X2, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# U42(X1, X2) -> proper# X2, proper# isNatIListKind X -> proper# X)
(proper# U42(X1, X2) -> proper# X2, proper# isNatKind X -> isNatKind# proper X)
(proper# U42(X1, X2) -> proper# X2, proper# isNatKind X -> proper# X)
(proper# U21(X1, X2) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# U21(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1)
(proper# U21(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X2)
(proper# U21(X1, X2) -> proper# X2, proper# U12 X -> U12# proper X)
(proper# U21(X1, X2) -> proper# X2, proper# U12 X -> proper# X)
(proper# U21(X1, X2) -> proper# X2, proper# isNatList X -> isNatList# proper X)
(proper# U21(X1, X2) -> proper# X2, proper# isNatList X -> proper# X)
(proper# U21(X1, X2) -> proper# X2, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# U21(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X1)
(proper# U21(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X2)
(proper# U21(X1, X2) -> proper# X2, proper# U22 X -> U22# proper X)
(proper# U21(X1, X2) -> proper# X2, proper# U22 X -> proper# X)
(proper# U21(X1, X2) -> proper# X2, proper# isNat X -> isNat# proper X)
(proper# U21(X1, X2) -> proper# X2, proper# isNat X -> proper# X)
(proper# U21(X1, X2) -> proper# X2, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# U21(X1, X2) -> proper# X2, proper# U21(X1, X2) -> proper# X1)
(proper# U21(X1, X2) -> proper# X2, proper# U21(X1, X2) -> proper# X2)
(proper# U21(X1, X2) -> proper# X2, proper# U32 X -> U32# proper X)
(proper# U21(X1, X2) -> proper# X2, proper# U32 X -> proper# X)
(proper# U21(X1, X2) -> proper# X2, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# U21(X1, X2) -> proper# X2, proper# U31(X1, X2) -> proper# X1)
(proper# U21(X1, X2) -> proper# X2, proper# U31(X1, X2) -> proper# X2)
(proper# U21(X1, X2) -> proper# X2, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# U21(X1, X2) -> proper# X2, proper# U42(X1, X2) -> proper# X1)
(proper# U21(X1, X2) -> proper# X2, proper# U42(X1, X2) -> proper# X2)
(proper# U21(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# U21(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X1)
(proper# U21(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X2)
(proper# U21(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X3)
(proper# U21(X1, X2) -> proper# X2, proper# U43 X -> U43# proper X)
(proper# U21(X1, X2) -> proper# X2, proper# U43 X -> proper# X)
(proper# U21(X1, X2) -> proper# X2, proper# isNatIList X -> isNatIList# proper X)
(proper# U21(X1, X2) -> proper# X2, proper# isNatIList X -> proper# X)
(proper# U21(X1, X2) -> proper# X2, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# U21(X1, X2) -> proper# X2, proper# U52(X1, X2) -> proper# X1)
(proper# U21(X1, X2) -> proper# X2, proper# U52(X1, X2) -> proper# X2)
(proper# U21(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# U21(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X1)
(proper# U21(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X2)
(proper# U21(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X3)
(proper# U21(X1, X2) -> proper# X2, proper# U53 X -> U53# proper X)
(proper# U21(X1, X2) -> proper# X2, proper# U53 X -> proper# X)
(proper# U21(X1, X2) -> proper# X2, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# U21(X1, X2) -> proper# X2, proper# U62(X1, X2) -> proper# X1)
(proper# U21(X1, X2) -> proper# X2, proper# U62(X1, X2) -> proper# X2)
(proper# U21(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# U21(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X1)
(proper# U21(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X2)
(proper# U21(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X3)
(proper# U21(X1, X2) -> proper# X2, proper# U63 X -> U63# proper X)
(proper# U21(X1, X2) -> proper# X2, proper# U63 X -> proper# X)
(proper# U21(X1, X2) -> proper# X2, proper# s X -> s# proper X)
(proper# U21(X1, X2) -> proper# X2, proper# s X -> proper# X)
(proper# U21(X1, X2) -> proper# X2, proper# length X -> length# proper X)
(proper# U21(X1, X2) -> proper# X2, proper# length X -> proper# X)
(proper# U21(X1, X2) -> proper# X2, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# U21(X1, X2) -> proper# X2, proper# U71(X1, X2) -> proper# X1)
(proper# U21(X1, X2) -> proper# X2, proper# U71(X1, X2) -> proper# X2)
(proper# U21(X1, X2) -> proper# X2, proper# U81 X -> U81# proper X)
(proper# U21(X1, X2) -> proper# X2, proper# U81 X -> proper# X)
(proper# U21(X1, X2) -> proper# X2, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# U21(X1, X2) -> proper# X2, proper# take(X1, X2) -> proper# X1)
(proper# U21(X1, X2) -> proper# X2, proper# take(X1, X2) -> proper# X2)
(proper# U21(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# U21(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# U21(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# U21(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# U21(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# U21(X1, X2) -> proper# X2, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# U21(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X1)
(proper# U21(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X2)
(proper# U21(X1, X2) -> proper# X2, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# U21(X1, X2) -> proper# X2, proper# isNatIListKind X -> proper# X)
(proper# U21(X1, X2) -> proper# X2, proper# isNatKind X -> isNatKind# proper X)
(proper# U21(X1, X2) -> proper# X2, proper# isNatKind X -> proper# X)
(proper# cons(X1, X2) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# cons(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1)
(proper# cons(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X2)
(proper# cons(X1, X2) -> proper# X2, proper# U12 X -> U12# proper X)
(proper# cons(X1, X2) -> proper# X2, proper# U12 X -> proper# X)
(proper# cons(X1, X2) -> proper# X2, proper# isNatList X -> isNatList# proper X)
(proper# cons(X1, X2) -> proper# X2, proper# isNatList X -> proper# X)
(proper# cons(X1, X2) -> proper# X2, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# cons(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X1)
(proper# cons(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X2)
(proper# cons(X1, X2) -> proper# X2, proper# U22 X -> U22# proper X)
(proper# cons(X1, X2) -> proper# X2, proper# U22 X -> proper# X)
(proper# cons(X1, X2) -> proper# X2, proper# isNat X -> isNat# proper X)
(proper# cons(X1, X2) -> proper# X2, proper# isNat X -> proper# X)
(proper# cons(X1, X2) -> proper# X2, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# cons(X1, X2) -> proper# X2, proper# U21(X1, X2) -> proper# X1)
(proper# cons(X1, X2) -> proper# X2, proper# U21(X1, X2) -> proper# X2)
(proper# cons(X1, X2) -> proper# X2, proper# U32 X -> U32# proper X)
(proper# cons(X1, X2) -> proper# X2, proper# U32 X -> proper# X)
(proper# cons(X1, X2) -> proper# X2, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# cons(X1, X2) -> proper# X2, proper# U31(X1, X2) -> proper# X1)
(proper# cons(X1, X2) -> proper# X2, proper# U31(X1, X2) -> proper# X2)
(proper# cons(X1, X2) -> proper# X2, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# cons(X1, X2) -> proper# X2, proper# U42(X1, X2) -> proper# X1)
(proper# cons(X1, X2) -> proper# X2, proper# U42(X1, X2) -> proper# X2)
(proper# cons(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# cons(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X1)
(proper# cons(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X2)
(proper# cons(X1, X2) -> proper# X2, proper# U41(X1, X2, X3) -> proper# X3)
(proper# cons(X1, X2) -> proper# X2, proper# U43 X -> U43# proper X)
(proper# cons(X1, X2) -> proper# X2, proper# U43 X -> proper# X)
(proper# cons(X1, X2) -> proper# X2, proper# isNatIList X -> isNatIList# proper X)
(proper# cons(X1, X2) -> proper# X2, proper# isNatIList X -> proper# X)
(proper# cons(X1, X2) -> proper# X2, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# cons(X1, X2) -> proper# X2, proper# U52(X1, X2) -> proper# X1)
(proper# cons(X1, X2) -> proper# X2, proper# U52(X1, X2) -> proper# X2)
(proper# cons(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# cons(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X1)
(proper# cons(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X2)
(proper# cons(X1, X2) -> proper# X2, proper# U51(X1, X2, X3) -> proper# X3)
(proper# cons(X1, X2) -> proper# X2, proper# U53 X -> U53# proper X)
(proper# cons(X1, X2) -> proper# X2, proper# U53 X -> proper# X)
(proper# cons(X1, X2) -> proper# X2, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# cons(X1, X2) -> proper# X2, proper# U62(X1, X2) -> proper# X1)
(proper# cons(X1, X2) -> proper# X2, proper# U62(X1, X2) -> proper# X2)
(proper# cons(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# cons(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X1)
(proper# cons(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X2)
(proper# cons(X1, X2) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X3)
(proper# cons(X1, X2) -> proper# X2, proper# U63 X -> U63# proper X)
(proper# cons(X1, X2) -> proper# X2, proper# U63 X -> proper# X)
(proper# cons(X1, X2) -> proper# X2, proper# s X -> s# proper X)
(proper# cons(X1, X2) -> proper# X2, proper# s X -> proper# X)
(proper# cons(X1, X2) -> proper# X2, proper# length X -> length# proper X)
(proper# cons(X1, X2) -> proper# X2, proper# length X -> proper# X)
(proper# cons(X1, X2) -> proper# X2, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# cons(X1, X2) -> proper# X2, proper# U71(X1, X2) -> proper# X1)
(proper# cons(X1, X2) -> proper# X2, proper# U71(X1, X2) -> proper# X2)
(proper# cons(X1, X2) -> proper# X2, proper# U81 X -> U81# proper X)
(proper# cons(X1, X2) -> proper# X2, proper# U81 X -> proper# X)
(proper# cons(X1, X2) -> proper# X2, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# cons(X1, X2) -> proper# X2, proper# take(X1, X2) -> proper# X1)
(proper# cons(X1, X2) -> proper# X2, proper# take(X1, X2) -> proper# X2)
(proper# cons(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# cons(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# cons(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# cons(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# cons(X1, X2) -> proper# X2, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# cons(X1, X2) -> proper# X2, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# cons(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X1)
(proper# cons(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X2)
(proper# cons(X1, X2) -> proper# X2, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# cons(X1, X2) -> proper# X2, proper# isNatIListKind X -> proper# X)
(proper# cons(X1, X2) -> proper# X2, proper# isNatKind X -> isNatKind# proper X)
(proper# cons(X1, X2) -> proper# X2, proper# isNatKind X -> proper# X)
(active# take(s M, cons(N, IL)) -> isNatKind# N, isNatKind# ok X -> isNatKind# X)
(active# length cons(N, L) -> isNatKind# N, isNatKind# ok X -> isNatKind# X)
(active# length cons(N, L) -> U71#(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L), U71#(mark X1, X2) -> U71#(X1, X2))
(active# length cons(N, L) -> U71#(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L), U71#(ok X1, ok X2) -> U71#(X1, X2))
(active# U91(tt(), IL, M, N) -> take#(M, IL), take#(X1, mark X2) -> take#(X1, X2))
(active# U91(tt(), IL, M, N) -> take#(M, IL), take#(mark X1, X2) -> take#(X1, X2))
(active# U91(tt(), IL, M, N) -> take#(M, IL), take#(ok X1, ok X2) -> take#(X1, X2))
(proper# take(X1, X2) -> take#(proper X1, proper X2), take#(X1, mark X2) -> take#(X1, X2))
(proper# take(X1, X2) -> take#(proper X1, proper X2), take#(mark X1, X2) -> take#(X1, X2))
(proper# take(X1, X2) -> take#(proper X1, proper X2), take#(ok X1, ok X2) -> take#(X1, X2))
(proper# U62(X1, X2) -> U62#(proper X1, proper X2), U62#(mark X1, X2) -> U62#(X1, X2))
(proper# U62(X1, X2) -> U62#(proper X1, proper X2), U62#(ok X1, ok X2) -> U62#(X1, X2))
(proper# U42(X1, X2) -> U42#(proper X1, proper X2), U42#(mark X1, X2) -> U42#(X1, X2))
(proper# U42(X1, X2) -> U42#(proper X1, proper X2), U42#(ok X1, ok X2) -> U42#(X1, X2))
(proper# U21(X1, X2) -> U21#(proper X1, proper X2), U21#(mark X1, X2) -> U21#(X1, X2))
(proper# U21(X1, X2) -> U21#(proper X1, proper X2), U21#(ok X1, ok X2) -> U21#(X1, X2))
(proper# cons(X1, X2) -> cons#(proper X1, proper X2), cons#(mark X1, X2) -> cons#(X1, X2))
(proper# cons(X1, X2) -> cons#(proper X1, proper X2), cons#(ok X1, ok X2) -> cons#(X1, X2))
(active# isNatIListKind cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2), and#(mark X1, X2) -> and#(X1, X2))
(active# isNatIListKind cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2), and#(ok X1, ok X2) -> and#(X1, X2))
(active# take(s M, cons(N, IL)) -> and#(isNat M, isNatKind M), and#(mark X1, X2) -> and#(X1, X2))
(active# take(s M, cons(N, IL)) -> and#(isNat M, isNatKind M), and#(ok X1, ok X2) -> and#(X1, X2))
(active# take(0(), IL) -> and#(isNatIList IL, isNatIListKind IL), and#(mark X1, X2) -> and#(X1, X2))
(active# take(0(), IL) -> and#(isNatIList IL, isNatIListKind IL), and#(ok X1, ok X2) -> and#(X1, X2))
(active# length cons(N, L) -> and#(isNat N, isNatKind N), and#(mark X1, X2) -> and#(X1, X2))
(active# length cons(N, L) -> and#(isNat N, isNatKind N), and#(ok X1, ok X2) -> and#(X1, X2))
(active# isNatIList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2), and#(mark X1, X2) -> and#(X1, X2))
(active# isNatIList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2), and#(ok X1, ok X2) -> and#(X1, X2))
(active# isNatList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2), and#(mark X1, X2) -> and#(X1, X2))
(active# isNatList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2), and#(ok X1, ok X2) -> and#(X1, X2))
(U91#(mark X1, X2, X3, X4) -> U91#(X1, X2, X3, X4), U91#(mark X1, X2, X3, X4) -> U91#(X1, X2, X3, X4))
(U91#(mark X1, X2, X3, X4) -> U91#(X1, X2, X3, X4), U91#(ok X1, ok X2, ok X3, ok X4) -> U91#(X1, X2, X3, X4))
(active# take(s M, cons(N, IL)) -> isNatIListKind# IL, isNatIListKind# ok X -> isNatIListKind# X)
(active# take(0(), IL) -> isNatIListKind# IL, isNatIListKind# ok X -> isNatIListKind# X)
(active# U21(tt(), V1) -> U22# isNat V1, U22# mark X -> U22# X)
(active# U21(tt(), V1) -> U22# isNat V1, U22# ok X -> U22# X)
(active# U31(tt(), V) -> U32# isNatList V, U32# mark X -> U32# X)
(active# U31(tt(), V) -> U32# isNatList V, U32# ok X -> U32# X)
(active# U52(tt(), V2) -> U53# isNatList V2, U53# mark X -> U53# X)
(active# U52(tt(), V2) -> U53# isNatList V2, U53# ok X -> U53# X)
(active# U71(tt(), L) -> s# length L, s# mark X -> s# X)
(active# U71(tt(), L) -> s# length L, s# ok X -> s# X)
(top# mark X -> top# proper X, top# mark X -> proper# X)
(top# mark X -> top# proper X, top# mark X -> top# proper X)
(top# mark X -> top# proper X, top# ok X -> active# X)
(top# mark X -> top# proper X, top# ok X -> top# active X)
(proper# isNatIListKind X -> isNatIListKind# proper X, isNatIListKind# ok X -> isNatIListKind# X)
(proper# length X -> length# proper X, length# mark X -> length# X)
(proper# length X -> length# proper X, length# ok X -> length# X)
(proper# U63 X -> U63# proper X, U63# mark X -> U63# X)
(proper# U63 X -> U63# proper X, U63# ok X -> U63# X)
(proper# isNatIList X -> isNatIList# proper X, isNatIList# ok X -> isNatIList# X)
(proper# U32 X -> U32# proper X, U32# mark X -> U32# X)
(proper# U32 X -> U32# proper X, U32# ok X -> U32# X)
(proper# U22 X -> U22# proper X, U22# mark X -> U22# X)
(proper# U22 X -> U22# proper X, U22# ok X -> U22# X)
(proper# U12 X -> U12# proper X, U12# mark X -> U12# X)
(proper# U12 X -> U12# proper X, U12# ok X -> U12# X)
(active# length X -> length# active X, length# mark X -> length# X)
(active# length X -> length# active X, length# ok X -> length# X)
(active# U63 X -> U63# active X, U63# mark X -> U63# X)
(active# U63 X -> U63# active X, U63# ok X -> U63# X)
(active# U43 X -> U43# active X, U43# mark X -> U43# X)
(active# U43 X -> U43# active X, U43# ok X -> U43# X)
(active# U22 X -> U22# active X, U22# mark X -> U22# X)
(active# U22 X -> U22# active X, U22# ok X -> U22# X)
(proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3), U61#(mark X1, X2, X3) -> U61#(X1, X2, X3))
(proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3), U61#(ok X1, ok X2, ok X3) -> U61#(X1, X2, X3))
(proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3), U41#(mark X1, X2, X3) -> U41#(X1, X2, X3))
(proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3), U41#(ok X1, ok X2, ok X3) -> U41#(X1, X2, X3))
(active# U31(tt(), V) -> isNatList# V, isNatList# ok X -> isNatList# X)
(active# isNatList take(V1, V2) -> U61#(and(isNatKind V1, isNatIListKind V2), V1, V2), U61#(mark X1, X2, X3) -> U61#(X1, X2, X3))
(active# isNatList take(V1, V2) -> U61#(and(isNatKind V1, isNatIListKind V2), V1, V2), U61#(ok X1, ok X2, ok X3) -> U61#(X1, X2, X3))
(and#(ok X1, ok X2) -> and#(X1, X2), and#(mark X1, X2) -> and#(X1, X2))
(and#(ok X1, ok X2) -> and#(X1, X2), and#(ok X1, ok X2) -> and#(X1, X2))
(take#(ok X1, ok X2) -> take#(X1, X2), take#(X1, mark X2) -> take#(X1, X2))
(take#(ok X1, ok X2) -> take#(X1, X2), take#(mark X1, X2) -> take#(X1, X2))
(take#(ok X1, ok X2) -> take#(X1, X2), take#(ok X1, ok X2) -> take#(X1, X2))
(take#(X1, mark X2) -> take#(X1, X2), take#(X1, mark X2) -> take#(X1, X2))
(take#(X1, mark X2) -> take#(X1, X2), take#(mark X1, X2) -> take#(X1, X2))
(take#(X1, mark X2) -> take#(X1, X2), take#(ok X1, ok X2) -> take#(X1, X2))
(U71#(mark X1, X2) -> U71#(X1, X2), U71#(mark X1, X2) -> U71#(X1, X2))
(U71#(mark X1, X2) -> U71#(X1, X2), U71#(ok X1, ok X2) -> U71#(X1, X2))
(U62#(mark X1, X2) -> U62#(X1, X2), U62#(mark X1, X2) -> U62#(X1, X2))
(U62#(mark X1, X2) -> U62#(X1, X2), U62#(ok X1, ok X2) -> U62#(X1, X2))
(U52#(mark X1, X2) -> U52#(X1, X2), U52#(mark X1, X2) -> U52#(X1, X2))
(U52#(mark X1, X2) -> U52#(X1, X2), U52#(ok X1, ok X2) -> U52#(X1, X2))
(U42#(mark X1, X2) -> U42#(X1, X2), U42#(mark X1, X2) -> U42#(X1, X2))
(U42#(mark X1, X2) -> U42#(X1, X2), U42#(ok X1, ok X2) -> U42#(X1, X2))
(U31#(mark X1, X2) -> U31#(X1, X2), U31#(mark X1, X2) -> U31#(X1, X2))
(U31#(mark X1, X2) -> U31#(X1, X2), U31#(ok X1, ok X2) -> U31#(X1, X2))
(U21#(mark X1, X2) -> U21#(X1, X2), U21#(mark X1, X2) -> U21#(X1, X2))
(U21#(mark X1, X2) -> U21#(X1, X2), U21#(ok X1, ok X2) -> U21#(X1, X2))
(U11#(mark X1, X2) -> U11#(X1, X2), U11#(mark X1, X2) -> U11#(X1, X2))
(U11#(mark X1, X2) -> U11#(X1, X2), U11#(ok X1, ok X2) -> U11#(X1, X2))
(cons#(mark X1, X2) -> cons#(X1, X2), cons#(mark X1, X2) -> cons#(X1, X2))
(cons#(mark X1, X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2))
(active# U51(tt(), V1, V2) -> U52#(isNat V1, V2), U52#(mark X1, X2) -> U52#(X1, X2))
(active# U51(tt(), V1, V2) -> U52#(isNat V1, V2), U52#(ok X1, ok X2) -> U52#(X1, X2))
(proper# and(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# and(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1)
(proper# and(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2)
(proper# and(X1, X2) -> proper# X1, proper# U12 X -> U12# proper X)
(proper# and(X1, X2) -> proper# X1, proper# U12 X -> proper# X)
(proper# and(X1, X2) -> proper# X1, proper# isNatList X -> isNatList# proper X)
(proper# and(X1, X2) -> proper# X1, proper# isNatList X -> proper# X)
(proper# and(X1, X2) -> proper# X1, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# and(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X1)
(proper# and(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X2)
(proper# and(X1, X2) -> proper# X1, proper# U22 X -> U22# proper X)
(proper# and(X1, X2) -> proper# X1, proper# U22 X -> proper# X)
(proper# and(X1, X2) -> proper# X1, proper# isNat X -> isNat# proper X)
(proper# and(X1, X2) -> proper# X1, proper# isNat X -> proper# X)
(proper# and(X1, X2) -> proper# X1, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# and(X1, X2) -> proper# X1, proper# U21(X1, X2) -> proper# X1)
(proper# and(X1, X2) -> proper# X1, proper# U21(X1, X2) -> proper# X2)
(proper# and(X1, X2) -> proper# X1, proper# U32 X -> U32# proper X)
(proper# and(X1, X2) -> proper# X1, proper# U32 X -> proper# X)
(proper# and(X1, X2) -> proper# X1, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# and(X1, X2) -> proper# X1, proper# U31(X1, X2) -> proper# X1)
(proper# and(X1, X2) -> proper# X1, proper# U31(X1, X2) -> proper# X2)
(proper# and(X1, X2) -> proper# X1, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# and(X1, X2) -> proper# X1, proper# U42(X1, X2) -> proper# X1)
(proper# and(X1, X2) -> proper# X1, proper# U42(X1, X2) -> proper# X2)
(proper# and(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# and(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X1)
(proper# and(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X2)
(proper# and(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X3)
(proper# and(X1, X2) -> proper# X1, proper# U43 X -> U43# proper X)
(proper# and(X1, X2) -> proper# X1, proper# U43 X -> proper# X)
(proper# and(X1, X2) -> proper# X1, proper# isNatIList X -> isNatIList# proper X)
(proper# and(X1, X2) -> proper# X1, proper# isNatIList X -> proper# X)
(proper# and(X1, X2) -> proper# X1, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# and(X1, X2) -> proper# X1, proper# U52(X1, X2) -> proper# X1)
(proper# and(X1, X2) -> proper# X1, proper# U52(X1, X2) -> proper# X2)
(proper# and(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# and(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X1)
(proper# and(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X2)
(proper# and(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X3)
(proper# and(X1, X2) -> proper# X1, proper# U53 X -> U53# proper X)
(proper# and(X1, X2) -> proper# X1, proper# U53 X -> proper# X)
(proper# and(X1, X2) -> proper# X1, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# and(X1, X2) -> proper# X1, proper# U62(X1, X2) -> proper# X1)
(proper# and(X1, X2) -> proper# X1, proper# U62(X1, X2) -> proper# X2)
(proper# and(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# and(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X1)
(proper# and(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X2)
(proper# and(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X3)
(proper# and(X1, X2) -> proper# X1, proper# U63 X -> U63# proper X)
(proper# and(X1, X2) -> proper# X1, proper# U63 X -> proper# X)
(proper# and(X1, X2) -> proper# X1, proper# s X -> s# proper X)
(proper# and(X1, X2) -> proper# X1, proper# s X -> proper# X)
(proper# and(X1, X2) -> proper# X1, proper# length X -> length# proper X)
(proper# and(X1, X2) -> proper# X1, proper# length X -> proper# X)
(proper# and(X1, X2) -> proper# X1, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# and(X1, X2) -> proper# X1, proper# U71(X1, X2) -> proper# X1)
(proper# and(X1, X2) -> proper# X1, proper# U71(X1, X2) -> proper# X2)
(proper# and(X1, X2) -> proper# X1, proper# U81 X -> U81# proper X)
(proper# and(X1, X2) -> proper# X1, proper# U81 X -> proper# X)
(proper# and(X1, X2) -> proper# X1, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# and(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X1)
(proper# and(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X2)
(proper# and(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# and(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# and(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# and(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# and(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X1)
(proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2)
(proper# and(X1, X2) -> proper# X1, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# and(X1, X2) -> proper# X1, proper# isNatIListKind X -> proper# X)
(proper# and(X1, X2) -> proper# X1, proper# isNatKind X -> isNatKind# proper X)
(proper# and(X1, X2) -> proper# X1, proper# isNatKind X -> proper# X)
(proper# take(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# take(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1)
(proper# take(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2)
(proper# take(X1, X2) -> proper# X1, proper# U12 X -> U12# proper X)
(proper# take(X1, X2) -> proper# X1, proper# U12 X -> proper# X)
(proper# take(X1, X2) -> proper# X1, proper# isNatList X -> isNatList# proper X)
(proper# take(X1, X2) -> proper# X1, proper# isNatList X -> proper# X)
(proper# take(X1, X2) -> proper# X1, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# take(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X1)
(proper# take(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X2)
(proper# take(X1, X2) -> proper# X1, proper# U22 X -> U22# proper X)
(proper# take(X1, X2) -> proper# X1, proper# U22 X -> proper# X)
(proper# take(X1, X2) -> proper# X1, proper# isNat X -> isNat# proper X)
(proper# take(X1, X2) -> proper# X1, proper# isNat X -> proper# X)
(proper# take(X1, X2) -> proper# X1, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# take(X1, X2) -> proper# X1, proper# U21(X1, X2) -> proper# X1)
(proper# take(X1, X2) -> proper# X1, proper# U21(X1, X2) -> proper# X2)
(proper# take(X1, X2) -> proper# X1, proper# U32 X -> U32# proper X)
(proper# take(X1, X2) -> proper# X1, proper# U32 X -> proper# X)
(proper# take(X1, X2) -> proper# X1, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# take(X1, X2) -> proper# X1, proper# U31(X1, X2) -> proper# X1)
(proper# take(X1, X2) -> proper# X1, proper# U31(X1, X2) -> proper# X2)
(proper# take(X1, X2) -> proper# X1, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# take(X1, X2) -> proper# X1, proper# U42(X1, X2) -> proper# X1)
(proper# take(X1, X2) -> proper# X1, proper# U42(X1, X2) -> proper# X2)
(proper# take(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# take(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X1)
(proper# take(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X2)
(proper# take(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X3)
(proper# take(X1, X2) -> proper# X1, proper# U43 X -> U43# proper X)
(proper# take(X1, X2) -> proper# X1, proper# U43 X -> proper# X)
(proper# take(X1, X2) -> proper# X1, proper# isNatIList X -> isNatIList# proper X)
(proper# take(X1, X2) -> proper# X1, proper# isNatIList X -> proper# X)
(proper# take(X1, X2) -> proper# X1, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# take(X1, X2) -> proper# X1, proper# U52(X1, X2) -> proper# X1)
(proper# take(X1, X2) -> proper# X1, proper# U52(X1, X2) -> proper# X2)
(proper# take(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# take(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X1)
(proper# take(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X2)
(proper# take(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X3)
(proper# take(X1, X2) -> proper# X1, proper# U53 X -> U53# proper X)
(proper# take(X1, X2) -> proper# X1, proper# U53 X -> proper# X)
(proper# take(X1, X2) -> proper# X1, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# take(X1, X2) -> proper# X1, proper# U62(X1, X2) -> proper# X1)
(proper# take(X1, X2) -> proper# X1, proper# U62(X1, X2) -> proper# X2)
(proper# take(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# take(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X1)
(proper# take(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X2)
(proper# take(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X3)
(proper# take(X1, X2) -> proper# X1, proper# U63 X -> U63# proper X)
(proper# take(X1, X2) -> proper# X1, proper# U63 X -> proper# X)
(proper# take(X1, X2) -> proper# X1, proper# s X -> s# proper X)
(proper# take(X1, X2) -> proper# X1, proper# s X -> proper# X)
(proper# take(X1, X2) -> proper# X1, proper# length X -> length# proper X)
(proper# take(X1, X2) -> proper# X1, proper# length X -> proper# X)
(proper# take(X1, X2) -> proper# X1, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# take(X1, X2) -> proper# X1, proper# U71(X1, X2) -> proper# X1)
(proper# take(X1, X2) -> proper# X1, proper# U71(X1, X2) -> proper# X2)
(proper# take(X1, X2) -> proper# X1, proper# U81 X -> U81# proper X)
(proper# take(X1, X2) -> proper# X1, proper# U81 X -> proper# X)
(proper# take(X1, X2) -> proper# X1, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# take(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X1)
(proper# take(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X2)
(proper# take(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# take(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# take(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# take(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# take(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# take(X1, X2) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# take(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X1)
(proper# take(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2)
(proper# take(X1, X2) -> proper# X1, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# take(X1, X2) -> proper# X1, proper# isNatIListKind X -> proper# X)
(proper# take(X1, X2) -> proper# X1, proper# isNatKind X -> isNatKind# proper X)
(proper# take(X1, X2) -> proper# X1, proper# isNatKind X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# U61(X1, X2, X3) -> proper# X1, proper# cons(X1, X2) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X1, proper# cons(X1, X2) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U12 X -> U12# proper X)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U12 X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X1, proper# isNatList X -> isNatList# proper X)
(proper# U61(X1, X2, X3) -> proper# X1, proper# isNatList X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# U61(X1, X2, X3) -> proper# X1, proper# U11(X1, X2) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U11(X1, X2) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U22 X -> U22# proper X)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U22 X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X1, proper# isNat X -> isNat# proper X)
(proper# U61(X1, X2, X3) -> proper# X1, proper# isNat X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# U61(X1, X2, X3) -> proper# X1, proper# U21(X1, X2) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U21(X1, X2) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U32 X -> U32# proper X)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U32 X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# U61(X1, X2, X3) -> proper# X1, proper# U31(X1, X2) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U31(X1, X2) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# U61(X1, X2, X3) -> proper# X1, proper# U42(X1, X2) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U42(X1, X2) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# U61(X1, X2, X3) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X3)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U43 X -> U43# proper X)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U43 X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X1, proper# isNatIList X -> isNatIList# proper X)
(proper# U61(X1, X2, X3) -> proper# X1, proper# isNatIList X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# U61(X1, X2, X3) -> proper# X1, proper# U52(X1, X2) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U52(X1, X2) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# U61(X1, X2, X3) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X3)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U53 X -> U53# proper X)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U53 X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# U61(X1, X2, X3) -> proper# X1, proper# U62(X1, X2) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U62(X1, X2) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# U61(X1, X2, X3) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X3)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U63 X -> U63# proper X)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U63 X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X1, proper# s X -> s# proper X)
(proper# U61(X1, X2, X3) -> proper# X1, proper# s X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X1, proper# length X -> length# proper X)
(proper# U61(X1, X2, X3) -> proper# X1, proper# length X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# U61(X1, X2, X3) -> proper# X1, proper# U71(X1, X2) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U71(X1, X2) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U81 X -> U81# proper X)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U81 X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X1, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# U61(X1, X2, X3) -> proper# X1, proper# take(X1, X2) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X1, proper# take(X1, X2) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# U61(X1, X2, X3) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# U61(X1, X2, X3) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# U61(X1, X2, X3) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# U61(X1, X2, X3) -> proper# X1, proper# and(X1, X2) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X1, proper# and(X1, X2) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X1, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# U61(X1, X2, X3) -> proper# X1, proper# isNatIListKind X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X1, proper# isNatKind X -> isNatKind# proper X)
(proper# U61(X1, X2, X3) -> proper# X1, proper# isNatKind X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# U51(X1, X2, X3) -> proper# X1, proper# cons(X1, X2) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X1, proper# cons(X1, X2) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U12 X -> U12# proper X)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U12 X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X1, proper# isNatList X -> isNatList# proper X)
(proper# U51(X1, X2, X3) -> proper# X1, proper# isNatList X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# U51(X1, X2, X3) -> proper# X1, proper# U11(X1, X2) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U11(X1, X2) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U22 X -> U22# proper X)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U22 X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X1, proper# isNat X -> isNat# proper X)
(proper# U51(X1, X2, X3) -> proper# X1, proper# isNat X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# U51(X1, X2, X3) -> proper# X1, proper# U21(X1, X2) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U21(X1, X2) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U32 X -> U32# proper X)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U32 X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# U51(X1, X2, X3) -> proper# X1, proper# U31(X1, X2) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U31(X1, X2) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# U51(X1, X2, X3) -> proper# X1, proper# U42(X1, X2) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U42(X1, X2) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# U51(X1, X2, X3) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X3)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U43 X -> U43# proper X)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U43 X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X1, proper# isNatIList X -> isNatIList# proper X)
(proper# U51(X1, X2, X3) -> proper# X1, proper# isNatIList X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# U51(X1, X2, X3) -> proper# X1, proper# U52(X1, X2) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U52(X1, X2) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# U51(X1, X2, X3) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X3)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U53 X -> U53# proper X)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U53 X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# U51(X1, X2, X3) -> proper# X1, proper# U62(X1, X2) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U62(X1, X2) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# U51(X1, X2, X3) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X3)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U63 X -> U63# proper X)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U63 X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X1, proper# s X -> s# proper X)
(proper# U51(X1, X2, X3) -> proper# X1, proper# s X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X1, proper# length X -> length# proper X)
(proper# U51(X1, X2, X3) -> proper# X1, proper# length X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# U51(X1, X2, X3) -> proper# X1, proper# U71(X1, X2) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U71(X1, X2) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U81 X -> U81# proper X)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U81 X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X1, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# U51(X1, X2, X3) -> proper# X1, proper# take(X1, X2) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X1, proper# take(X1, X2) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# U51(X1, X2, X3) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# U51(X1, X2, X3) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# U51(X1, X2, X3) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# U51(X1, X2, X3) -> proper# X1, proper# and(X1, X2) -> proper# X1)
(proper# U51(X1, X2, X3) -> proper# X1, proper# and(X1, X2) -> proper# X2)
(proper# U51(X1, X2, X3) -> proper# X1, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# U51(X1, X2, X3) -> proper# X1, proper# isNatIListKind X -> proper# X)
(proper# U51(X1, X2, X3) -> proper# X1, proper# isNatKind X -> isNatKind# proper X)
(proper# U51(X1, X2, X3) -> proper# X1, proper# isNatKind X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# U41(X1, X2, X3) -> proper# X1, proper# cons(X1, X2) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X1, proper# cons(X1, X2) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U12 X -> U12# proper X)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U12 X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X1, proper# isNatList X -> isNatList# proper X)
(proper# U41(X1, X2, X3) -> proper# X1, proper# isNatList X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# U41(X1, X2, X3) -> proper# X1, proper# U11(X1, X2) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U11(X1, X2) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U22 X -> U22# proper X)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U22 X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X1, proper# isNat X -> isNat# proper X)
(proper# U41(X1, X2, X3) -> proper# X1, proper# isNat X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# U41(X1, X2, X3) -> proper# X1, proper# U21(X1, X2) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U21(X1, X2) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U32 X -> U32# proper X)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U32 X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# U41(X1, X2, X3) -> proper# X1, proper# U31(X1, X2) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U31(X1, X2) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# U41(X1, X2, X3) -> proper# X1, proper# U42(X1, X2) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U42(X1, X2) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# U41(X1, X2, X3) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X3)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U43 X -> U43# proper X)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U43 X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X1, proper# isNatIList X -> isNatIList# proper X)
(proper# U41(X1, X2, X3) -> proper# X1, proper# isNatIList X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# U41(X1, X2, X3) -> proper# X1, proper# U52(X1, X2) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U52(X1, X2) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# U41(X1, X2, X3) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X3)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U53 X -> U53# proper X)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U53 X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# U41(X1, X2, X3) -> proper# X1, proper# U62(X1, X2) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U62(X1, X2) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# U41(X1, X2, X3) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X3)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U63 X -> U63# proper X)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U63 X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X1, proper# s X -> s# proper X)
(proper# U41(X1, X2, X3) -> proper# X1, proper# s X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X1, proper# length X -> length# proper X)
(proper# U41(X1, X2, X3) -> proper# X1, proper# length X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# U41(X1, X2, X3) -> proper# X1, proper# U71(X1, X2) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U71(X1, X2) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U81 X -> U81# proper X)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U81 X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X1, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# U41(X1, X2, X3) -> proper# X1, proper# take(X1, X2) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X1, proper# take(X1, X2) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# U41(X1, X2, X3) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# U41(X1, X2, X3) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# U41(X1, X2, X3) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# U41(X1, X2, X3) -> proper# X1, proper# and(X1, X2) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X1, proper# and(X1, X2) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X1, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# U41(X1, X2, X3) -> proper# X1, proper# isNatIListKind X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X1, proper# isNatKind X -> isNatKind# proper X)
(proper# U41(X1, X2, X3) -> proper# X1, proper# isNatKind X -> proper# X)
(proper# U31(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# U31(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1)
(proper# U31(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2)
(proper# U31(X1, X2) -> proper# X1, proper# U12 X -> U12# proper X)
(proper# U31(X1, X2) -> proper# X1, proper# U12 X -> proper# X)
(proper# U31(X1, X2) -> proper# X1, proper# isNatList X -> isNatList# proper X)
(proper# U31(X1, X2) -> proper# X1, proper# isNatList X -> proper# X)
(proper# U31(X1, X2) -> proper# X1, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# U31(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X1)
(proper# U31(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X2)
(proper# U31(X1, X2) -> proper# X1, proper# U22 X -> U22# proper X)
(proper# U31(X1, X2) -> proper# X1, proper# U22 X -> proper# X)
(proper# U31(X1, X2) -> proper# X1, proper# isNat X -> isNat# proper X)
(proper# U31(X1, X2) -> proper# X1, proper# isNat X -> proper# X)
(proper# U31(X1, X2) -> proper# X1, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# U31(X1, X2) -> proper# X1, proper# U21(X1, X2) -> proper# X1)
(proper# U31(X1, X2) -> proper# X1, proper# U21(X1, X2) -> proper# X2)
(proper# U31(X1, X2) -> proper# X1, proper# U32 X -> U32# proper X)
(proper# U31(X1, X2) -> proper# X1, proper# U32 X -> proper# X)
(proper# U31(X1, X2) -> proper# X1, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# U31(X1, X2) -> proper# X1, proper# U31(X1, X2) -> proper# X1)
(proper# U31(X1, X2) -> proper# X1, proper# U31(X1, X2) -> proper# X2)
(proper# U31(X1, X2) -> proper# X1, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# U31(X1, X2) -> proper# X1, proper# U42(X1, X2) -> proper# X1)
(proper# U31(X1, X2) -> proper# X1, proper# U42(X1, X2) -> proper# X2)
(proper# U31(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# U31(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X1)
(proper# U31(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X2)
(proper# U31(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X3)
(proper# U31(X1, X2) -> proper# X1, proper# U43 X -> U43# proper X)
(proper# U31(X1, X2) -> proper# X1, proper# U43 X -> proper# X)
(proper# U31(X1, X2) -> proper# X1, proper# isNatIList X -> isNatIList# proper X)
(proper# U31(X1, X2) -> proper# X1, proper# isNatIList X -> proper# X)
(proper# U31(X1, X2) -> proper# X1, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# U31(X1, X2) -> proper# X1, proper# U52(X1, X2) -> proper# X1)
(proper# U31(X1, X2) -> proper# X1, proper# U52(X1, X2) -> proper# X2)
(proper# U31(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# U31(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X1)
(proper# U31(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X2)
(proper# U31(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X3)
(proper# U31(X1, X2) -> proper# X1, proper# U53 X -> U53# proper X)
(proper# U31(X1, X2) -> proper# X1, proper# U53 X -> proper# X)
(proper# U31(X1, X2) -> proper# X1, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# U31(X1, X2) -> proper# X1, proper# U62(X1, X2) -> proper# X1)
(proper# U31(X1, X2) -> proper# X1, proper# U62(X1, X2) -> proper# X2)
(proper# U31(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# U31(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X1)
(proper# U31(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X2)
(proper# U31(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X3)
(proper# U31(X1, X2) -> proper# X1, proper# U63 X -> U63# proper X)
(proper# U31(X1, X2) -> proper# X1, proper# U63 X -> proper# X)
(proper# U31(X1, X2) -> proper# X1, proper# s X -> s# proper X)
(proper# U31(X1, X2) -> proper# X1, proper# s X -> proper# X)
(proper# U31(X1, X2) -> proper# X1, proper# length X -> length# proper X)
(proper# U31(X1, X2) -> proper# X1, proper# length X -> proper# X)
(proper# U31(X1, X2) -> proper# X1, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# U31(X1, X2) -> proper# X1, proper# U71(X1, X2) -> proper# X1)
(proper# U31(X1, X2) -> proper# X1, proper# U71(X1, X2) -> proper# X2)
(proper# U31(X1, X2) -> proper# X1, proper# U81 X -> U81# proper X)
(proper# U31(X1, X2) -> proper# X1, proper# U81 X -> proper# X)
(proper# U31(X1, X2) -> proper# X1, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# U31(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X1)
(proper# U31(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X2)
(proper# U31(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# U31(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# U31(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# U31(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# U31(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# U31(X1, X2) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# U31(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X1)
(proper# U31(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2)
(proper# U31(X1, X2) -> proper# X1, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# U31(X1, X2) -> proper# X1, proper# isNatIListKind X -> proper# X)
(proper# U31(X1, X2) -> proper# X1, proper# isNatKind X -> isNatKind# proper X)
(proper# U31(X1, X2) -> proper# X1, proper# isNatKind X -> proper# X)
(proper# U11(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# U11(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1)
(proper# U11(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2)
(proper# U11(X1, X2) -> proper# X1, proper# U12 X -> U12# proper X)
(proper# U11(X1, X2) -> proper# X1, proper# U12 X -> proper# X)
(proper# U11(X1, X2) -> proper# X1, proper# isNatList X -> isNatList# proper X)
(proper# U11(X1, X2) -> proper# X1, proper# isNatList X -> proper# X)
(proper# U11(X1, X2) -> proper# X1, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# U11(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X1)
(proper# U11(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X2)
(proper# U11(X1, X2) -> proper# X1, proper# U22 X -> U22# proper X)
(proper# U11(X1, X2) -> proper# X1, proper# U22 X -> proper# X)
(proper# U11(X1, X2) -> proper# X1, proper# isNat X -> isNat# proper X)
(proper# U11(X1, X2) -> proper# X1, proper# isNat X -> proper# X)
(proper# U11(X1, X2) -> proper# X1, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# U11(X1, X2) -> proper# X1, proper# U21(X1, X2) -> proper# X1)
(proper# U11(X1, X2) -> proper# X1, proper# U21(X1, X2) -> proper# X2)
(proper# U11(X1, X2) -> proper# X1, proper# U32 X -> U32# proper X)
(proper# U11(X1, X2) -> proper# X1, proper# U32 X -> proper# X)
(proper# U11(X1, X2) -> proper# X1, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# U11(X1, X2) -> proper# X1, proper# U31(X1, X2) -> proper# X1)
(proper# U11(X1, X2) -> proper# X1, proper# U31(X1, X2) -> proper# X2)
(proper# U11(X1, X2) -> proper# X1, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# U11(X1, X2) -> proper# X1, proper# U42(X1, X2) -> proper# X1)
(proper# U11(X1, X2) -> proper# X1, proper# U42(X1, X2) -> proper# X2)
(proper# U11(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# U11(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X1)
(proper# U11(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X2)
(proper# U11(X1, X2) -> proper# X1, proper# U41(X1, X2, X3) -> proper# X3)
(proper# U11(X1, X2) -> proper# X1, proper# U43 X -> U43# proper X)
(proper# U11(X1, X2) -> proper# X1, proper# U43 X -> proper# X)
(proper# U11(X1, X2) -> proper# X1, proper# isNatIList X -> isNatIList# proper X)
(proper# U11(X1, X2) -> proper# X1, proper# isNatIList X -> proper# X)
(proper# U11(X1, X2) -> proper# X1, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# U11(X1, X2) -> proper# X1, proper# U52(X1, X2) -> proper# X1)
(proper# U11(X1, X2) -> proper# X1, proper# U52(X1, X2) -> proper# X2)
(proper# U11(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# U11(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X1)
(proper# U11(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X2)
(proper# U11(X1, X2) -> proper# X1, proper# U51(X1, X2, X3) -> proper# X3)
(proper# U11(X1, X2) -> proper# X1, proper# U53 X -> U53# proper X)
(proper# U11(X1, X2) -> proper# X1, proper# U53 X -> proper# X)
(proper# U11(X1, X2) -> proper# X1, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# U11(X1, X2) -> proper# X1, proper# U62(X1, X2) -> proper# X1)
(proper# U11(X1, X2) -> proper# X1, proper# U62(X1, X2) -> proper# X2)
(proper# U11(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# U11(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X1)
(proper# U11(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X2)
(proper# U11(X1, X2) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X3)
(proper# U11(X1, X2) -> proper# X1, proper# U63 X -> U63# proper X)
(proper# U11(X1, X2) -> proper# X1, proper# U63 X -> proper# X)
(proper# U11(X1, X2) -> proper# X1, proper# s X -> s# proper X)
(proper# U11(X1, X2) -> proper# X1, proper# s X -> proper# X)
(proper# U11(X1, X2) -> proper# X1, proper# length X -> length# proper X)
(proper# U11(X1, X2) -> proper# X1, proper# length X -> proper# X)
(proper# U11(X1, X2) -> proper# X1, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# U11(X1, X2) -> proper# X1, proper# U71(X1, X2) -> proper# X1)
(proper# U11(X1, X2) -> proper# X1, proper# U71(X1, X2) -> proper# X2)
(proper# U11(X1, X2) -> proper# X1, proper# U81 X -> U81# proper X)
(proper# U11(X1, X2) -> proper# X1, proper# U81 X -> proper# X)
(proper# U11(X1, X2) -> proper# X1, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# U11(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X1)
(proper# U11(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X2)
(proper# U11(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# U11(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# U11(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# U11(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# U11(X1, X2) -> proper# X1, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# U11(X1, X2) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# U11(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X1)
(proper# U11(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2)
(proper# U11(X1, X2) -> proper# X1, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# U11(X1, X2) -> proper# X1, proper# isNatIListKind X -> proper# X)
(proper# U11(X1, X2) -> proper# X1, proper# isNatKind X -> isNatKind# proper X)
(proper# U11(X1, X2) -> proper# X1, proper# isNatKind X -> proper# X)
(active# and(X1, X2) -> and#(active X1, X2), and#(mark X1, X2) -> and#(X1, X2))
(active# and(X1, X2) -> and#(active X1, X2), and#(ok X1, ok X2) -> and#(X1, X2))
(active# U91(X1, X2, X3, X4) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2))
(active# U91(X1, X2, X3, X4) -> active# X1, active# cons(X1, X2) -> active# X1)
(active# U91(X1, X2, X3, X4) -> active# X1, active# zeros() -> cons#(0(), zeros()))
(active# U91(X1, X2, X3, X4) -> active# X1, active# U12 X -> active# X)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U12 X -> U12# active X)
(active# U91(X1, X2, X3, X4) -> active# X1, active# isNatList cons(V1, V2) -> U51#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U91(X1, X2, X3, X4) -> active# X1, active# isNatList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U91(X1, X2, X3, X4) -> active# X1, active# isNatList cons(V1, V2) -> isNatIListKind# V2)
(active# U91(X1, X2, X3, X4) -> active# X1, active# isNatList cons(V1, V2) -> isNatKind# V1)
(active# U91(X1, X2, X3, X4) -> active# X1, active# isNatList take(V1, V2) -> U61#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U91(X1, X2, X3, X4) -> active# X1, active# isNatList take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U91(X1, X2, X3, X4) -> active# X1, active# isNatList take(V1, V2) -> isNatIListKind# V2)
(active# U91(X1, X2, X3, X4) -> active# X1, active# isNatList take(V1, V2) -> isNatKind# V1)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U11(X1, X2) -> active# X1)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U11(X1, X2) -> U11#(active X1, X2))
(active# U91(X1, X2, X3, X4) -> active# X1, active# U11(tt(), V1) -> U12# isNatList V1)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U11(tt(), V1) -> isNatList# V1)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U22 X -> active# X)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U22 X -> U22# active X)
(active# U91(X1, X2, X3, X4) -> active# X1, active# isNat s V1 -> U21#(isNatKind V1, V1))
(active# U91(X1, X2, X3, X4) -> active# X1, active# isNat s V1 -> isNatKind# V1)
(active# U91(X1, X2, X3, X4) -> active# X1, active# isNat length V1 -> U11#(isNatIListKind V1, V1))
(active# U91(X1, X2, X3, X4) -> active# X1, active# isNat length V1 -> isNatIListKind# V1)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U21(X1, X2) -> active# X1)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U21(X1, X2) -> U21#(active X1, X2))
(active# U91(X1, X2, X3, X4) -> active# X1, active# U21(tt(), V1) -> U22# isNat V1)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U21(tt(), V1) -> isNat# V1)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U32 X -> active# X)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U32 X -> U32# active X)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U31(X1, X2) -> active# X1)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U31(X1, X2) -> U31#(active X1, X2))
(active# U91(X1, X2, X3, X4) -> active# X1, active# U31(tt(), V) -> isNatList# V)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U31(tt(), V) -> U32# isNatList V)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U42(X1, X2) -> active# X1)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U42(X1, X2) -> U42#(active X1, X2))
(active# U91(X1, X2, X3, X4) -> active# X1, active# U42(tt(), V2) -> U43# isNatIList V2)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U42(tt(), V2) -> isNatIList# V2)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U41(X1, X2, X3) -> active# X1)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U41(X1, X2, X3) -> U41#(active X1, X2, X3))
(active# U91(X1, X2, X3, X4) -> active# X1, active# U41(tt(), V1, V2) -> isNat# V1)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U41(tt(), V1, V2) -> U42#(isNat V1, V2))
(active# U91(X1, X2, X3, X4) -> active# X1, active# U43 X -> active# X)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U43 X -> U43# active X)
(active# U91(X1, X2, X3, X4) -> active# X1, active# isNatIList V -> U31#(isNatIListKind V, V))
(active# U91(X1, X2, X3, X4) -> active# X1, active# isNatIList V -> isNatIListKind# V)
(active# U91(X1, X2, X3, X4) -> active# X1, active# isNatIList cons(V1, V2) -> U41#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U91(X1, X2, X3, X4) -> active# X1, active# isNatIList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U91(X1, X2, X3, X4) -> active# X1, active# isNatIList cons(V1, V2) -> isNatIListKind# V2)
(active# U91(X1, X2, X3, X4) -> active# X1, active# isNatIList cons(V1, V2) -> isNatKind# V1)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U52(X1, X2) -> active# X1)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U52(X1, X2) -> U52#(active X1, X2))
(active# U91(X1, X2, X3, X4) -> active# X1, active# U52(tt(), V2) -> isNatList# V2)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U52(tt(), V2) -> U53# isNatList V2)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U51(X1, X2, X3) -> active# X1)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U51(X1, X2, X3) -> U51#(active X1, X2, X3))
(active# U91(X1, X2, X3, X4) -> active# X1, active# U51(tt(), V1, V2) -> isNat# V1)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U51(tt(), V1, V2) -> U52#(isNat V1, V2))
(active# U91(X1, X2, X3, X4) -> active# X1, active# U53 X -> active# X)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U53 X -> U53# active X)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U62(X1, X2) -> active# X1)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U62(X1, X2) -> U62#(active X1, X2))
(active# U91(X1, X2, X3, X4) -> active# X1, active# U62(tt(), V2) -> isNatIList# V2)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U62(tt(), V2) -> U63# isNatIList V2)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U61(X1, X2, X3) -> active# X1)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U61(X1, X2, X3) -> U61#(active X1, X2, X3))
(active# U91(X1, X2, X3, X4) -> active# X1, active# U61(tt(), V1, V2) -> isNat# V1)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U61(tt(), V1, V2) -> U62#(isNat V1, V2))
(active# U91(X1, X2, X3, X4) -> active# X1, active# U63 X -> active# X)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U63 X -> U63# active X)
(active# U91(X1, X2, X3, X4) -> active# X1, active# s X -> active# X)
(active# U91(X1, X2, X3, X4) -> active# X1, active# s X -> s# active X)
(active# U91(X1, X2, X3, X4) -> active# X1, active# length X -> active# X)
(active# U91(X1, X2, X3, X4) -> active# X1, active# length X -> length# active X)
(active# U91(X1, X2, X3, X4) -> active# X1, active# length cons(N, L) -> isNatList# L)
(active# U91(X1, X2, X3, X4) -> active# X1, active# length cons(N, L) -> isNat# N)
(active# U91(X1, X2, X3, X4) -> active# X1, active# length cons(N, L) -> U71#(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L))
(active# U91(X1, X2, X3, X4) -> active# X1, active# length cons(N, L) -> and#(isNatList L, isNatIListKind L))
(active# U91(X1, X2, X3, X4) -> active# X1, active# length cons(N, L) -> and#(isNat N, isNatKind N))
(active# U91(X1, X2, X3, X4) -> active# X1, active# length cons(N, L) -> and#(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)))
(active# U91(X1, X2, X3, X4) -> active# X1, active# length cons(N, L) -> isNatIListKind# L)
(active# U91(X1, X2, X3, X4) -> active# X1, active# length cons(N, L) -> isNatKind# N)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U71(X1, X2) -> active# X1)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U71(X1, X2) -> U71#(active X1, X2))
(active# U91(X1, X2, X3, X4) -> active# X1, active# U71(tt(), L) -> s# length L)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U71(tt(), L) -> length# L)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U81 X -> active# X)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U81 X -> U81# active X)
(active# U91(X1, X2, X3, X4) -> active# X1, active# take(X1, X2) -> active# X1)
(active# U91(X1, X2, X3, X4) -> active# X1, active# take(X1, X2) -> active# X2)
(active# U91(X1, X2, X3, X4) -> active# X1, active# take(X1, X2) -> take#(X1, active X2))
(active# U91(X1, X2, X3, X4) -> active# X1, active# take(X1, X2) -> take#(active X1, X2))
(active# U91(X1, X2, X3, X4) -> active# X1, active# take(0(), IL) -> isNatIList# IL)
(active# U91(X1, X2, X3, X4) -> active# X1, active# take(0(), IL) -> U81# and(isNatIList IL, isNatIListKind IL))
(active# U91(X1, X2, X3, X4) -> active# X1, active# take(0(), IL) -> and#(isNatIList IL, isNatIListKind IL))
(active# U91(X1, X2, X3, X4) -> active# X1, active# take(0(), IL) -> isNatIListKind# IL)
(active# U91(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# N)
(active# U91(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# M)
(active# U91(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIList# IL)
(active# U91(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> U91#(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N))
(active# U91(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat N, isNatKind N))
(active# U91(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat M, isNatKind M))
(active# U91(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, isNatIListKind IL))
(active# U91(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> and#(and(isNat M, isNatKind M), and(isNat N, isNatKind N)))
(active# U91(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> and#(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))))
(active# U91(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIListKind# IL)
(active# U91(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> isNatKind# N)
(active# U91(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> isNatKind# M)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U91(X1, X2, X3, X4) -> active# X1)
(active# U91(X1, X2, X3, X4) -> active# X1, active# U91(X1, X2, X3, X4) -> U91#(active X1, X2, X3, X4))
(active# U91(X1, X2, X3, X4) -> active# X1, active# U91(tt(), IL, M, N) -> cons#(N, take(M, IL)))
(active# U91(X1, X2, X3, X4) -> active# X1, active# U91(tt(), IL, M, N) -> take#(M, IL))
(active# U91(X1, X2, X3, X4) -> active# X1, active# and(X1, X2) -> active# X1)
(active# U91(X1, X2, X3, X4) -> active# X1, active# and(X1, X2) -> and#(active X1, X2))
(active# U91(X1, X2, X3, X4) -> active# X1, active# isNatIListKind cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U91(X1, X2, X3, X4) -> active# X1, active# isNatIListKind cons(V1, V2) -> isNatIListKind# V2)
(active# U91(X1, X2, X3, X4) -> active# X1, active# isNatIListKind cons(V1, V2) -> isNatKind# V1)
(active# U91(X1, X2, X3, X4) -> active# X1, active# isNatIListKind take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U91(X1, X2, X3, X4) -> active# X1, active# isNatIListKind take(V1, V2) -> isNatIListKind# V2)
(active# U91(X1, X2, X3, X4) -> active# X1, active# isNatIListKind take(V1, V2) -> isNatKind# V1)
(active# U91(X1, X2, X3, X4) -> active# X1, active# isNatKind s V1 -> isNatKind# V1)
(active# U91(X1, X2, X3, X4) -> active# X1, active# isNatKind length V1 -> isNatIListKind# V1)
(active# take(X1, X2) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2))
(active# take(X1, X2) -> active# X1, active# cons(X1, X2) -> active# X1)
(active# take(X1, X2) -> active# X1, active# zeros() -> cons#(0(), zeros()))
(active# take(X1, X2) -> active# X1, active# U12 X -> active# X)
(active# take(X1, X2) -> active# X1, active# U12 X -> U12# active X)
(active# take(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> U51#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# take(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# take(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> isNatIListKind# V2)
(active# take(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> isNatKind# V1)
(active# take(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> U61#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# take(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# take(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> isNatIListKind# V2)
(active# take(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> isNatKind# V1)
(active# take(X1, X2) -> active# X1, active# U11(X1, X2) -> active# X1)
(active# take(X1, X2) -> active# X1, active# U11(X1, X2) -> U11#(active X1, X2))
(active# take(X1, X2) -> active# X1, active# U11(tt(), V1) -> U12# isNatList V1)
(active# take(X1, X2) -> active# X1, active# U11(tt(), V1) -> isNatList# V1)
(active# take(X1, X2) -> active# X1, active# U22 X -> active# X)
(active# take(X1, X2) -> active# X1, active# U22 X -> U22# active X)
(active# take(X1, X2) -> active# X1, active# isNat s V1 -> U21#(isNatKind V1, V1))
(active# take(X1, X2) -> active# X1, active# isNat s V1 -> isNatKind# V1)
(active# take(X1, X2) -> active# X1, active# isNat length V1 -> U11#(isNatIListKind V1, V1))
(active# take(X1, X2) -> active# X1, active# isNat length V1 -> isNatIListKind# V1)
(active# take(X1, X2) -> active# X1, active# U21(X1, X2) -> active# X1)
(active# take(X1, X2) -> active# X1, active# U21(X1, X2) -> U21#(active X1, X2))
(active# take(X1, X2) -> active# X1, active# U21(tt(), V1) -> U22# isNat V1)
(active# take(X1, X2) -> active# X1, active# U21(tt(), V1) -> isNat# V1)
(active# take(X1, X2) -> active# X1, active# U32 X -> active# X)
(active# take(X1, X2) -> active# X1, active# U32 X -> U32# active X)
(active# take(X1, X2) -> active# X1, active# U31(X1, X2) -> active# X1)
(active# take(X1, X2) -> active# X1, active# U31(X1, X2) -> U31#(active X1, X2))
(active# take(X1, X2) -> active# X1, active# U31(tt(), V) -> isNatList# V)
(active# take(X1, X2) -> active# X1, active# U31(tt(), V) -> U32# isNatList V)
(active# take(X1, X2) -> active# X1, active# U42(X1, X2) -> active# X1)
(active# take(X1, X2) -> active# X1, active# U42(X1, X2) -> U42#(active X1, X2))
(active# take(X1, X2) -> active# X1, active# U42(tt(), V2) -> U43# isNatIList V2)
(active# take(X1, X2) -> active# X1, active# U42(tt(), V2) -> isNatIList# V2)
(active# take(X1, X2) -> active# X1, active# U41(X1, X2, X3) -> active# X1)
(active# take(X1, X2) -> active# X1, active# U41(X1, X2, X3) -> U41#(active X1, X2, X3))
(active# take(X1, X2) -> active# X1, active# U41(tt(), V1, V2) -> isNat# V1)
(active# take(X1, X2) -> active# X1, active# U41(tt(), V1, V2) -> U42#(isNat V1, V2))
(active# take(X1, X2) -> active# X1, active# U43 X -> active# X)
(active# take(X1, X2) -> active# X1, active# U43 X -> U43# active X)
(active# take(X1, X2) -> active# X1, active# isNatIList V -> U31#(isNatIListKind V, V))
(active# take(X1, X2) -> active# X1, active# isNatIList V -> isNatIListKind# V)
(active# take(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> U41#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# take(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# take(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNatIListKind# V2)
(active# take(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNatKind# V1)
(active# take(X1, X2) -> active# X1, active# U52(X1, X2) -> active# X1)
(active# take(X1, X2) -> active# X1, active# U52(X1, X2) -> U52#(active X1, X2))
(active# take(X1, X2) -> active# X1, active# U52(tt(), V2) -> isNatList# V2)
(active# take(X1, X2) -> active# X1, active# U52(tt(), V2) -> U53# isNatList V2)
(active# take(X1, X2) -> active# X1, active# U51(X1, X2, X3) -> active# X1)
(active# take(X1, X2) -> active# X1, active# U51(X1, X2, X3) -> U51#(active X1, X2, X3))
(active# take(X1, X2) -> active# X1, active# U51(tt(), V1, V2) -> isNat# V1)
(active# take(X1, X2) -> active# X1, active# U51(tt(), V1, V2) -> U52#(isNat V1, V2))
(active# take(X1, X2) -> active# X1, active# U53 X -> active# X)
(active# take(X1, X2) -> active# X1, active# U53 X -> U53# active X)
(active# take(X1, X2) -> active# X1, active# U62(X1, X2) -> active# X1)
(active# take(X1, X2) -> active# X1, active# U62(X1, X2) -> U62#(active X1, X2))
(active# take(X1, X2) -> active# X1, active# U62(tt(), V2) -> isNatIList# V2)
(active# take(X1, X2) -> active# X1, active# U62(tt(), V2) -> U63# isNatIList V2)
(active# take(X1, X2) -> active# X1, active# U61(X1, X2, X3) -> active# X1)
(active# take(X1, X2) -> active# X1, active# U61(X1, X2, X3) -> U61#(active X1, X2, X3))
(active# take(X1, X2) -> active# X1, active# U61(tt(), V1, V2) -> isNat# V1)
(active# take(X1, X2) -> active# X1, active# U61(tt(), V1, V2) -> U62#(isNat V1, V2))
(active# take(X1, X2) -> active# X1, active# U63 X -> active# X)
(active# take(X1, X2) -> active# X1, active# U63 X -> U63# active X)
(active# take(X1, X2) -> active# X1, active# s X -> active# X)
(active# take(X1, X2) -> active# X1, active# s X -> s# active X)
(active# take(X1, X2) -> active# X1, active# length X -> active# X)
(active# take(X1, X2) -> active# X1, active# length X -> length# active X)
(active# take(X1, X2) -> active# X1, active# length cons(N, L) -> isNatList# L)
(active# take(X1, X2) -> active# X1, active# length cons(N, L) -> isNat# N)
(active# take(X1, X2) -> active# X1, active# length cons(N, L) -> U71#(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L))
(active# take(X1, X2) -> active# X1, active# length cons(N, L) -> and#(isNatList L, isNatIListKind L))
(active# take(X1, X2) -> active# X1, active# length cons(N, L) -> and#(isNat N, isNatKind N))
(active# take(X1, X2) -> active# X1, active# length cons(N, L) -> and#(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)))
(active# take(X1, X2) -> active# X1, active# length cons(N, L) -> isNatIListKind# L)
(active# take(X1, X2) -> active# X1, active# length cons(N, L) -> isNatKind# N)
(active# take(X1, X2) -> active# X1, active# U71(X1, X2) -> active# X1)
(active# take(X1, X2) -> active# X1, active# U71(X1, X2) -> U71#(active X1, X2))
(active# take(X1, X2) -> active# X1, active# U71(tt(), L) -> s# length L)
(active# take(X1, X2) -> active# X1, active# U71(tt(), L) -> length# L)
(active# take(X1, X2) -> active# X1, active# U81 X -> active# X)
(active# take(X1, X2) -> active# X1, active# U81 X -> U81# active X)
(active# take(X1, X2) -> active# X1, active# take(X1, X2) -> active# X1)
(active# take(X1, X2) -> active# X1, active# take(X1, X2) -> active# X2)
(active# take(X1, X2) -> active# X1, active# take(X1, X2) -> take#(X1, active X2))
(active# take(X1, X2) -> active# X1, active# take(X1, X2) -> take#(active X1, X2))
(active# take(X1, X2) -> active# X1, active# take(0(), IL) -> isNatIList# IL)
(active# take(X1, X2) -> active# X1, active# take(0(), IL) -> U81# and(isNatIList IL, isNatIListKind IL))
(active# take(X1, X2) -> active# X1, active# take(0(), IL) -> and#(isNatIList IL, isNatIListKind IL))
(active# take(X1, X2) -> active# X1, active# take(0(), IL) -> isNatIListKind# IL)
(active# take(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# N)
(active# take(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# M)
(active# take(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIList# IL)
(active# take(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> U91#(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N))
(active# take(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat N, isNatKind N))
(active# take(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat M, isNatKind M))
(active# take(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, isNatIListKind IL))
(active# take(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(and(isNat M, isNatKind M), and(isNat N, isNatKind N)))
(active# take(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))))
(active# take(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIListKind# IL)
(active# take(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatKind# N)
(active# take(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatKind# M)
(active# take(X1, X2) -> active# X1, active# U91(X1, X2, X3, X4) -> active# X1)
(active# take(X1, X2) -> active# X1, active# U91(X1, X2, X3, X4) -> U91#(active X1, X2, X3, X4))
(active# take(X1, X2) -> active# X1, active# U91(tt(), IL, M, N) -> cons#(N, take(M, IL)))
(active# take(X1, X2) -> active# X1, active# U91(tt(), IL, M, N) -> take#(M, IL))
(active# take(X1, X2) -> active# X1, active# and(X1, X2) -> active# X1)
(active# take(X1, X2) -> active# X1, active# and(X1, X2) -> and#(active X1, X2))
(active# take(X1, X2) -> active# X1, active# isNatIListKind cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# take(X1, X2) -> active# X1, active# isNatIListKind cons(V1, V2) -> isNatIListKind# V2)
(active# take(X1, X2) -> active# X1, active# isNatIListKind cons(V1, V2) -> isNatKind# V1)
(active# take(X1, X2) -> active# X1, active# isNatIListKind take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# take(X1, X2) -> active# X1, active# isNatIListKind take(V1, V2) -> isNatIListKind# V2)
(active# take(X1, X2) -> active# X1, active# isNatIListKind take(V1, V2) -> isNatKind# V1)
(active# take(X1, X2) -> active# X1, active# isNatKind s V1 -> isNatKind# V1)
(active# take(X1, X2) -> active# X1, active# isNatKind length V1 -> isNatIListKind# V1)
(active# U71(X1, X2) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2))
(active# U71(X1, X2) -> active# X1, active# cons(X1, X2) -> active# X1)
(active# U71(X1, X2) -> active# X1, active# zeros() -> cons#(0(), zeros()))
(active# U71(X1, X2) -> active# X1, active# U12 X -> active# X)
(active# U71(X1, X2) -> active# X1, active# U12 X -> U12# active X)
(active# U71(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> U51#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U71(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U71(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> isNatIListKind# V2)
(active# U71(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> isNatKind# V1)
(active# U71(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> U61#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U71(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U71(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> isNatIListKind# V2)
(active# U71(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> isNatKind# V1)
(active# U71(X1, X2) -> active# X1, active# U11(X1, X2) -> active# X1)
(active# U71(X1, X2) -> active# X1, active# U11(X1, X2) -> U11#(active X1, X2))
(active# U71(X1, X2) -> active# X1, active# U11(tt(), V1) -> U12# isNatList V1)
(active# U71(X1, X2) -> active# X1, active# U11(tt(), V1) -> isNatList# V1)
(active# U71(X1, X2) -> active# X1, active# U22 X -> active# X)
(active# U71(X1, X2) -> active# X1, active# U22 X -> U22# active X)
(active# U71(X1, X2) -> active# X1, active# isNat s V1 -> U21#(isNatKind V1, V1))
(active# U71(X1, X2) -> active# X1, active# isNat s V1 -> isNatKind# V1)
(active# U71(X1, X2) -> active# X1, active# isNat length V1 -> U11#(isNatIListKind V1, V1))
(active# U71(X1, X2) -> active# X1, active# isNat length V1 -> isNatIListKind# V1)
(active# U71(X1, X2) -> active# X1, active# U21(X1, X2) -> active# X1)
(active# U71(X1, X2) -> active# X1, active# U21(X1, X2) -> U21#(active X1, X2))
(active# U71(X1, X2) -> active# X1, active# U21(tt(), V1) -> U22# isNat V1)
(active# U71(X1, X2) -> active# X1, active# U21(tt(), V1) -> isNat# V1)
(active# U71(X1, X2) -> active# X1, active# U32 X -> active# X)
(active# U71(X1, X2) -> active# X1, active# U32 X -> U32# active X)
(active# U71(X1, X2) -> active# X1, active# U31(X1, X2) -> active# X1)
(active# U71(X1, X2) -> active# X1, active# U31(X1, X2) -> U31#(active X1, X2))
(active# U71(X1, X2) -> active# X1, active# U31(tt(), V) -> isNatList# V)
(active# U71(X1, X2) -> active# X1, active# U31(tt(), V) -> U32# isNatList V)
(active# U71(X1, X2) -> active# X1, active# U42(X1, X2) -> active# X1)
(active# U71(X1, X2) -> active# X1, active# U42(X1, X2) -> U42#(active X1, X2))
(active# U71(X1, X2) -> active# X1, active# U42(tt(), V2) -> U43# isNatIList V2)
(active# U71(X1, X2) -> active# X1, active# U42(tt(), V2) -> isNatIList# V2)
(active# U71(X1, X2) -> active# X1, active# U41(X1, X2, X3) -> active# X1)
(active# U71(X1, X2) -> active# X1, active# U41(X1, X2, X3) -> U41#(active X1, X2, X3))
(active# U71(X1, X2) -> active# X1, active# U41(tt(), V1, V2) -> isNat# V1)
(active# U71(X1, X2) -> active# X1, active# U41(tt(), V1, V2) -> U42#(isNat V1, V2))
(active# U71(X1, X2) -> active# X1, active# U43 X -> active# X)
(active# U71(X1, X2) -> active# X1, active# U43 X -> U43# active X)
(active# U71(X1, X2) -> active# X1, active# isNatIList V -> U31#(isNatIListKind V, V))
(active# U71(X1, X2) -> active# X1, active# isNatIList V -> isNatIListKind# V)
(active# U71(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> U41#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U71(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U71(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNatIListKind# V2)
(active# U71(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNatKind# V1)
(active# U71(X1, X2) -> active# X1, active# U52(X1, X2) -> active# X1)
(active# U71(X1, X2) -> active# X1, active# U52(X1, X2) -> U52#(active X1, X2))
(active# U71(X1, X2) -> active# X1, active# U52(tt(), V2) -> isNatList# V2)
(active# U71(X1, X2) -> active# X1, active# U52(tt(), V2) -> U53# isNatList V2)
(active# U71(X1, X2) -> active# X1, active# U51(X1, X2, X3) -> active# X1)
(active# U71(X1, X2) -> active# X1, active# U51(X1, X2, X3) -> U51#(active X1, X2, X3))
(active# U71(X1, X2) -> active# X1, active# U51(tt(), V1, V2) -> isNat# V1)
(active# U71(X1, X2) -> active# X1, active# U51(tt(), V1, V2) -> U52#(isNat V1, V2))
(active# U71(X1, X2) -> active# X1, active# U53 X -> active# X)
(active# U71(X1, X2) -> active# X1, active# U53 X -> U53# active X)
(active# U71(X1, X2) -> active# X1, active# U62(X1, X2) -> active# X1)
(active# U71(X1, X2) -> active# X1, active# U62(X1, X2) -> U62#(active X1, X2))
(active# U71(X1, X2) -> active# X1, active# U62(tt(), V2) -> isNatIList# V2)
(active# U71(X1, X2) -> active# X1, active# U62(tt(), V2) -> U63# isNatIList V2)
(active# U71(X1, X2) -> active# X1, active# U61(X1, X2, X3) -> active# X1)
(active# U71(X1, X2) -> active# X1, active# U61(X1, X2, X3) -> U61#(active X1, X2, X3))
(active# U71(X1, X2) -> active# X1, active# U61(tt(), V1, V2) -> isNat# V1)
(active# U71(X1, X2) -> active# X1, active# U61(tt(), V1, V2) -> U62#(isNat V1, V2))
(active# U71(X1, X2) -> active# X1, active# U63 X -> active# X)
(active# U71(X1, X2) -> active# X1, active# U63 X -> U63# active X)
(active# U71(X1, X2) -> active# X1, active# s X -> active# X)
(active# U71(X1, X2) -> active# X1, active# s X -> s# active X)
(active# U71(X1, X2) -> active# X1, active# length X -> active# X)
(active# U71(X1, X2) -> active# X1, active# length X -> length# active X)
(active# U71(X1, X2) -> active# X1, active# length cons(N, L) -> isNatList# L)
(active# U71(X1, X2) -> active# X1, active# length cons(N, L) -> isNat# N)
(active# U71(X1, X2) -> active# X1, active# length cons(N, L) -> U71#(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L))
(active# U71(X1, X2) -> active# X1, active# length cons(N, L) -> and#(isNatList L, isNatIListKind L))
(active# U71(X1, X2) -> active# X1, active# length cons(N, L) -> and#(isNat N, isNatKind N))
(active# U71(X1, X2) -> active# X1, active# length cons(N, L) -> and#(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)))
(active# U71(X1, X2) -> active# X1, active# length cons(N, L) -> isNatIListKind# L)
(active# U71(X1, X2) -> active# X1, active# length cons(N, L) -> isNatKind# N)
(active# U71(X1, X2) -> active# X1, active# U71(X1, X2) -> active# X1)
(active# U71(X1, X2) -> active# X1, active# U71(X1, X2) -> U71#(active X1, X2))
(active# U71(X1, X2) -> active# X1, active# U71(tt(), L) -> s# length L)
(active# U71(X1, X2) -> active# X1, active# U71(tt(), L) -> length# L)
(active# U71(X1, X2) -> active# X1, active# U81 X -> active# X)
(active# U71(X1, X2) -> active# X1, active# U81 X -> U81# active X)
(active# U71(X1, X2) -> active# X1, active# take(X1, X2) -> active# X1)
(active# U71(X1, X2) -> active# X1, active# take(X1, X2) -> active# X2)
(active# U71(X1, X2) -> active# X1, active# take(X1, X2) -> take#(X1, active X2))
(active# U71(X1, X2) -> active# X1, active# take(X1, X2) -> take#(active X1, X2))
(active# U71(X1, X2) -> active# X1, active# take(0(), IL) -> isNatIList# IL)
(active# U71(X1, X2) -> active# X1, active# take(0(), IL) -> U81# and(isNatIList IL, isNatIListKind IL))
(active# U71(X1, X2) -> active# X1, active# take(0(), IL) -> and#(isNatIList IL, isNatIListKind IL))
(active# U71(X1, X2) -> active# X1, active# take(0(), IL) -> isNatIListKind# IL)
(active# U71(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# N)
(active# U71(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# M)
(active# U71(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIList# IL)
(active# U71(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> U91#(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N))
(active# U71(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat N, isNatKind N))
(active# U71(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat M, isNatKind M))
(active# U71(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, isNatIListKind IL))
(active# U71(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(and(isNat M, isNatKind M), and(isNat N, isNatKind N)))
(active# U71(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))))
(active# U71(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIListKind# IL)
(active# U71(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatKind# N)
(active# U71(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatKind# M)
(active# U71(X1, X2) -> active# X1, active# U91(X1, X2, X3, X4) -> active# X1)
(active# U71(X1, X2) -> active# X1, active# U91(X1, X2, X3, X4) -> U91#(active X1, X2, X3, X4))
(active# U71(X1, X2) -> active# X1, active# U91(tt(), IL, M, N) -> cons#(N, take(M, IL)))
(active# U71(X1, X2) -> active# X1, active# U91(tt(), IL, M, N) -> take#(M, IL))
(active# U71(X1, X2) -> active# X1, active# and(X1, X2) -> active# X1)
(active# U71(X1, X2) -> active# X1, active# and(X1, X2) -> and#(active X1, X2))
(active# U71(X1, X2) -> active# X1, active# isNatIListKind cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U71(X1, X2) -> active# X1, active# isNatIListKind cons(V1, V2) -> isNatIListKind# V2)
(active# U71(X1, X2) -> active# X1, active# isNatIListKind cons(V1, V2) -> isNatKind# V1)
(active# U71(X1, X2) -> active# X1, active# isNatIListKind take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U71(X1, X2) -> active# X1, active# isNatIListKind take(V1, V2) -> isNatIListKind# V2)
(active# U71(X1, X2) -> active# X1, active# isNatIListKind take(V1, V2) -> isNatKind# V1)
(active# U71(X1, X2) -> active# X1, active# isNatKind s V1 -> isNatKind# V1)
(active# U71(X1, X2) -> active# X1, active# isNatKind length V1 -> isNatIListKind# V1)
(active# U62(X1, X2) -> U62#(active X1, X2), U62#(mark X1, X2) -> U62#(X1, X2))
(active# U62(X1, X2) -> U62#(active X1, X2), U62#(ok X1, ok X2) -> U62#(X1, X2))
(active# U51(X1, X2, X3) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2))
(active# U51(X1, X2, X3) -> active# X1, active# cons(X1, X2) -> active# X1)
(active# U51(X1, X2, X3) -> active# X1, active# zeros() -> cons#(0(), zeros()))
(active# U51(X1, X2, X3) -> active# X1, active# U12 X -> active# X)
(active# U51(X1, X2, X3) -> active# X1, active# U12 X -> U12# active X)
(active# U51(X1, X2, X3) -> active# X1, active# isNatList cons(V1, V2) -> U51#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U51(X1, X2, X3) -> active# X1, active# isNatList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U51(X1, X2, X3) -> active# X1, active# isNatList cons(V1, V2) -> isNatIListKind# V2)
(active# U51(X1, X2, X3) -> active# X1, active# isNatList cons(V1, V2) -> isNatKind# V1)
(active# U51(X1, X2, X3) -> active# X1, active# isNatList take(V1, V2) -> U61#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U51(X1, X2, X3) -> active# X1, active# isNatList take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U51(X1, X2, X3) -> active# X1, active# isNatList take(V1, V2) -> isNatIListKind# V2)
(active# U51(X1, X2, X3) -> active# X1, active# isNatList take(V1, V2) -> isNatKind# V1)
(active# U51(X1, X2, X3) -> active# X1, active# U11(X1, X2) -> active# X1)
(active# U51(X1, X2, X3) -> active# X1, active# U11(X1, X2) -> U11#(active X1, X2))
(active# U51(X1, X2, X3) -> active# X1, active# U11(tt(), V1) -> U12# isNatList V1)
(active# U51(X1, X2, X3) -> active# X1, active# U11(tt(), V1) -> isNatList# V1)
(active# U51(X1, X2, X3) -> active# X1, active# U22 X -> active# X)
(active# U51(X1, X2, X3) -> active# X1, active# U22 X -> U22# active X)
(active# U51(X1, X2, X3) -> active# X1, active# isNat s V1 -> U21#(isNatKind V1, V1))
(active# U51(X1, X2, X3) -> active# X1, active# isNat s V1 -> isNatKind# V1)
(active# U51(X1, X2, X3) -> active# X1, active# isNat length V1 -> U11#(isNatIListKind V1, V1))
(active# U51(X1, X2, X3) -> active# X1, active# isNat length V1 -> isNatIListKind# V1)
(active# U51(X1, X2, X3) -> active# X1, active# U21(X1, X2) -> active# X1)
(active# U51(X1, X2, X3) -> active# X1, active# U21(X1, X2) -> U21#(active X1, X2))
(active# U51(X1, X2, X3) -> active# X1, active# U21(tt(), V1) -> U22# isNat V1)
(active# U51(X1, X2, X3) -> active# X1, active# U21(tt(), V1) -> isNat# V1)
(active# U51(X1, X2, X3) -> active# X1, active# U32 X -> active# X)
(active# U51(X1, X2, X3) -> active# X1, active# U32 X -> U32# active X)
(active# U51(X1, X2, X3) -> active# X1, active# U31(X1, X2) -> active# X1)
(active# U51(X1, X2, X3) -> active# X1, active# U31(X1, X2) -> U31#(active X1, X2))
(active# U51(X1, X2, X3) -> active# X1, active# U31(tt(), V) -> isNatList# V)
(active# U51(X1, X2, X3) -> active# X1, active# U31(tt(), V) -> U32# isNatList V)
(active# U51(X1, X2, X3) -> active# X1, active# U42(X1, X2) -> active# X1)
(active# U51(X1, X2, X3) -> active# X1, active# U42(X1, X2) -> U42#(active X1, X2))
(active# U51(X1, X2, X3) -> active# X1, active# U42(tt(), V2) -> U43# isNatIList V2)
(active# U51(X1, X2, X3) -> active# X1, active# U42(tt(), V2) -> isNatIList# V2)
(active# U51(X1, X2, X3) -> active# X1, active# U41(X1, X2, X3) -> active# X1)
(active# U51(X1, X2, X3) -> active# X1, active# U41(X1, X2, X3) -> U41#(active X1, X2, X3))
(active# U51(X1, X2, X3) -> active# X1, active# U41(tt(), V1, V2) -> isNat# V1)
(active# U51(X1, X2, X3) -> active# X1, active# U41(tt(), V1, V2) -> U42#(isNat V1, V2))
(active# U51(X1, X2, X3) -> active# X1, active# U43 X -> active# X)
(active# U51(X1, X2, X3) -> active# X1, active# U43 X -> U43# active X)
(active# U51(X1, X2, X3) -> active# X1, active# isNatIList V -> U31#(isNatIListKind V, V))
(active# U51(X1, X2, X3) -> active# X1, active# isNatIList V -> isNatIListKind# V)
(active# U51(X1, X2, X3) -> active# X1, active# isNatIList cons(V1, V2) -> U41#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U51(X1, X2, X3) -> active# X1, active# isNatIList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U51(X1, X2, X3) -> active# X1, active# isNatIList cons(V1, V2) -> isNatIListKind# V2)
(active# U51(X1, X2, X3) -> active# X1, active# isNatIList cons(V1, V2) -> isNatKind# V1)
(active# U51(X1, X2, X3) -> active# X1, active# U52(X1, X2) -> active# X1)
(active# U51(X1, X2, X3) -> active# X1, active# U52(X1, X2) -> U52#(active X1, X2))
(active# U51(X1, X2, X3) -> active# X1, active# U52(tt(), V2) -> isNatList# V2)
(active# U51(X1, X2, X3) -> active# X1, active# U52(tt(), V2) -> U53# isNatList V2)
(active# U51(X1, X2, X3) -> active# X1, active# U51(X1, X2, X3) -> active# X1)
(active# U51(X1, X2, X3) -> active# X1, active# U51(X1, X2, X3) -> U51#(active X1, X2, X3))
(active# U51(X1, X2, X3) -> active# X1, active# U51(tt(), V1, V2) -> isNat# V1)
(active# U51(X1, X2, X3) -> active# X1, active# U51(tt(), V1, V2) -> U52#(isNat V1, V2))
(active# U51(X1, X2, X3) -> active# X1, active# U53 X -> active# X)
(active# U51(X1, X2, X3) -> active# X1, active# U53 X -> U53# active X)
(active# U51(X1, X2, X3) -> active# X1, active# U62(X1, X2) -> active# X1)
(active# U51(X1, X2, X3) -> active# X1, active# U62(X1, X2) -> U62#(active X1, X2))
(active# U51(X1, X2, X3) -> active# X1, active# U62(tt(), V2) -> isNatIList# V2)
(active# U51(X1, X2, X3) -> active# X1, active# U62(tt(), V2) -> U63# isNatIList V2)
(active# U51(X1, X2, X3) -> active# X1, active# U61(X1, X2, X3) -> active# X1)
(active# U51(X1, X2, X3) -> active# X1, active# U61(X1, X2, X3) -> U61#(active X1, X2, X3))
(active# U51(X1, X2, X3) -> active# X1, active# U61(tt(), V1, V2) -> isNat# V1)
(active# U51(X1, X2, X3) -> active# X1, active# U61(tt(), V1, V2) -> U62#(isNat V1, V2))
(active# U51(X1, X2, X3) -> active# X1, active# U63 X -> active# X)
(active# U51(X1, X2, X3) -> active# X1, active# U63 X -> U63# active X)
(active# U51(X1, X2, X3) -> active# X1, active# s X -> active# X)
(active# U51(X1, X2, X3) -> active# X1, active# s X -> s# active X)
(active# U51(X1, X2, X3) -> active# X1, active# length X -> active# X)
(active# U51(X1, X2, X3) -> active# X1, active# length X -> length# active X)
(active# U51(X1, X2, X3) -> active# X1, active# length cons(N, L) -> isNatList# L)
(active# U51(X1, X2, X3) -> active# X1, active# length cons(N, L) -> isNat# N)
(active# U51(X1, X2, X3) -> active# X1, active# length cons(N, L) -> U71#(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L))
(active# U51(X1, X2, X3) -> active# X1, active# length cons(N, L) -> and#(isNatList L, isNatIListKind L))
(active# U51(X1, X2, X3) -> active# X1, active# length cons(N, L) -> and#(isNat N, isNatKind N))
(active# U51(X1, X2, X3) -> active# X1, active# length cons(N, L) -> and#(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)))
(active# U51(X1, X2, X3) -> active# X1, active# length cons(N, L) -> isNatIListKind# L)
(active# U51(X1, X2, X3) -> active# X1, active# length cons(N, L) -> isNatKind# N)
(active# U51(X1, X2, X3) -> active# X1, active# U71(X1, X2) -> active# X1)
(active# U51(X1, X2, X3) -> active# X1, active# U71(X1, X2) -> U71#(active X1, X2))
(active# U51(X1, X2, X3) -> active# X1, active# U71(tt(), L) -> s# length L)
(active# U51(X1, X2, X3) -> active# X1, active# U71(tt(), L) -> length# L)
(active# U51(X1, X2, X3) -> active# X1, active# U81 X -> active# X)
(active# U51(X1, X2, X3) -> active# X1, active# U81 X -> U81# active X)
(active# U51(X1, X2, X3) -> active# X1, active# take(X1, X2) -> active# X1)
(active# U51(X1, X2, X3) -> active# X1, active# take(X1, X2) -> active# X2)
(active# U51(X1, X2, X3) -> active# X1, active# take(X1, X2) -> take#(X1, active X2))
(active# U51(X1, X2, X3) -> active# X1, active# take(X1, X2) -> take#(active X1, X2))
(active# U51(X1, X2, X3) -> active# X1, active# take(0(), IL) -> isNatIList# IL)
(active# U51(X1, X2, X3) -> active# X1, active# take(0(), IL) -> U81# and(isNatIList IL, isNatIListKind IL))
(active# U51(X1, X2, X3) -> active# X1, active# take(0(), IL) -> and#(isNatIList IL, isNatIListKind IL))
(active# U51(X1, X2, X3) -> active# X1, active# take(0(), IL) -> isNatIListKind# IL)
(active# U51(X1, X2, X3) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# N)
(active# U51(X1, X2, X3) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# M)
(active# U51(X1, X2, X3) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIList# IL)
(active# U51(X1, X2, X3) -> active# X1, active# take(s M, cons(N, IL)) -> U91#(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N))
(active# U51(X1, X2, X3) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat N, isNatKind N))
(active# U51(X1, X2, X3) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat M, isNatKind M))
(active# U51(X1, X2, X3) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, isNatIListKind IL))
(active# U51(X1, X2, X3) -> active# X1, active# take(s M, cons(N, IL)) -> and#(and(isNat M, isNatKind M), and(isNat N, isNatKind N)))
(active# U51(X1, X2, X3) -> active# X1, active# take(s M, cons(N, IL)) -> and#(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))))
(active# U51(X1, X2, X3) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIListKind# IL)
(active# U51(X1, X2, X3) -> active# X1, active# take(s M, cons(N, IL)) -> isNatKind# N)
(active# U51(X1, X2, X3) -> active# X1, active# take(s M, cons(N, IL)) -> isNatKind# M)
(active# U51(X1, X2, X3) -> active# X1, active# U91(X1, X2, X3, X4) -> active# X1)
(active# U51(X1, X2, X3) -> active# X1, active# U91(X1, X2, X3, X4) -> U91#(active X1, X2, X3, X4))
(active# U51(X1, X2, X3) -> active# X1, active# U91(tt(), IL, M, N) -> cons#(N, take(M, IL)))
(active# U51(X1, X2, X3) -> active# X1, active# U91(tt(), IL, M, N) -> take#(M, IL))
(active# U51(X1, X2, X3) -> active# X1, active# and(X1, X2) -> active# X1)
(active# U51(X1, X2, X3) -> active# X1, active# and(X1, X2) -> and#(active X1, X2))
(active# U51(X1, X2, X3) -> active# X1, active# isNatIListKind cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U51(X1, X2, X3) -> active# X1, active# isNatIListKind cons(V1, V2) -> isNatIListKind# V2)
(active# U51(X1, X2, X3) -> active# X1, active# isNatIListKind cons(V1, V2) -> isNatKind# V1)
(active# U51(X1, X2, X3) -> active# X1, active# isNatIListKind take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U51(X1, X2, X3) -> active# X1, active# isNatIListKind take(V1, V2) -> isNatIListKind# V2)
(active# U51(X1, X2, X3) -> active# X1, active# isNatIListKind take(V1, V2) -> isNatKind# V1)
(active# U51(X1, X2, X3) -> active# X1, active# isNatKind s V1 -> isNatKind# V1)
(active# U51(X1, X2, X3) -> active# X1, active# isNatKind length V1 -> isNatIListKind# V1)
(active# U52(X1, X2) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2))
(active# U52(X1, X2) -> active# X1, active# cons(X1, X2) -> active# X1)
(active# U52(X1, X2) -> active# X1, active# zeros() -> cons#(0(), zeros()))
(active# U52(X1, X2) -> active# X1, active# U12 X -> active# X)
(active# U52(X1, X2) -> active# X1, active# U12 X -> U12# active X)
(active# U52(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> U51#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U52(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U52(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> isNatIListKind# V2)
(active# U52(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> isNatKind# V1)
(active# U52(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> U61#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U52(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U52(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> isNatIListKind# V2)
(active# U52(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> isNatKind# V1)
(active# U52(X1, X2) -> active# X1, active# U11(X1, X2) -> active# X1)
(active# U52(X1, X2) -> active# X1, active# U11(X1, X2) -> U11#(active X1, X2))
(active# U52(X1, X2) -> active# X1, active# U11(tt(), V1) -> U12# isNatList V1)
(active# U52(X1, X2) -> active# X1, active# U11(tt(), V1) -> isNatList# V1)
(active# U52(X1, X2) -> active# X1, active# U22 X -> active# X)
(active# U52(X1, X2) -> active# X1, active# U22 X -> U22# active X)
(active# U52(X1, X2) -> active# X1, active# isNat s V1 -> U21#(isNatKind V1, V1))
(active# U52(X1, X2) -> active# X1, active# isNat s V1 -> isNatKind# V1)
(active# U52(X1, X2) -> active# X1, active# isNat length V1 -> U11#(isNatIListKind V1, V1))
(active# U52(X1, X2) -> active# X1, active# isNat length V1 -> isNatIListKind# V1)
(active# U52(X1, X2) -> active# X1, active# U21(X1, X2) -> active# X1)
(active# U52(X1, X2) -> active# X1, active# U21(X1, X2) -> U21#(active X1, X2))
(active# U52(X1, X2) -> active# X1, active# U21(tt(), V1) -> U22# isNat V1)
(active# U52(X1, X2) -> active# X1, active# U21(tt(), V1) -> isNat# V1)
(active# U52(X1, X2) -> active# X1, active# U32 X -> active# X)
(active# U52(X1, X2) -> active# X1, active# U32 X -> U32# active X)
(active# U52(X1, X2) -> active# X1, active# U31(X1, X2) -> active# X1)
(active# U52(X1, X2) -> active# X1, active# U31(X1, X2) -> U31#(active X1, X2))
(active# U52(X1, X2) -> active# X1, active# U31(tt(), V) -> isNatList# V)
(active# U52(X1, X2) -> active# X1, active# U31(tt(), V) -> U32# isNatList V)
(active# U52(X1, X2) -> active# X1, active# U42(X1, X2) -> active# X1)
(active# U52(X1, X2) -> active# X1, active# U42(X1, X2) -> U42#(active X1, X2))
(active# U52(X1, X2) -> active# X1, active# U42(tt(), V2) -> U43# isNatIList V2)
(active# U52(X1, X2) -> active# X1, active# U42(tt(), V2) -> isNatIList# V2)
(active# U52(X1, X2) -> active# X1, active# U41(X1, X2, X3) -> active# X1)
(active# U52(X1, X2) -> active# X1, active# U41(X1, X2, X3) -> U41#(active X1, X2, X3))
(active# U52(X1, X2) -> active# X1, active# U41(tt(), V1, V2) -> isNat# V1)
(active# U52(X1, X2) -> active# X1, active# U41(tt(), V1, V2) -> U42#(isNat V1, V2))
(active# U52(X1, X2) -> active# X1, active# U43 X -> active# X)
(active# U52(X1, X2) -> active# X1, active# U43 X -> U43# active X)
(active# U52(X1, X2) -> active# X1, active# isNatIList V -> U31#(isNatIListKind V, V))
(active# U52(X1, X2) -> active# X1, active# isNatIList V -> isNatIListKind# V)
(active# U52(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> U41#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# U52(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U52(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNatIListKind# V2)
(active# U52(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNatKind# V1)
(active# U52(X1, X2) -> active# X1, active# U52(X1, X2) -> active# X1)
(active# U52(X1, X2) -> active# X1, active# U52(X1, X2) -> U52#(active X1, X2))
(active# U52(X1, X2) -> active# X1, active# U52(tt(), V2) -> isNatList# V2)
(active# U52(X1, X2) -> active# X1, active# U52(tt(), V2) -> U53# isNatList V2)
(active# U52(X1, X2) -> active# X1, active# U51(X1, X2, X3) -> active# X1)
(active# U52(X1, X2) -> active# X1, active# U51(X1, X2, X3) -> U51#(active X1, X2, X3))
(active# U52(X1, X2) -> active# X1, active# U51(tt(), V1, V2) -> isNat# V1)
(active# U52(X1, X2) -> active# X1, active# U51(tt(), V1, V2) -> U52#(isNat V1, V2))
(active# U52(X1, X2) -> active# X1, active# U53 X -> active# X)
(active# U52(X1, X2) -> active# X1, active# U53 X -> U53# active X)
(active# U52(X1, X2) -> active# X1, active# U62(X1, X2) -> active# X1)
(active# U52(X1, X2) -> active# X1, active# U62(X1, X2) -> U62#(active X1, X2))
(active# U52(X1, X2) -> active# X1, active# U62(tt(), V2) -> isNatIList# V2)
(active# U52(X1, X2) -> active# X1, active# U62(tt(), V2) -> U63# isNatIList V2)
(active# U52(X1, X2) -> active# X1, active# U61(X1, X2, X3) -> active# X1)
(active# U52(X1, X2) -> active# X1, active# U61(X1, X2, X3) -> U61#(active X1, X2, X3))
(active# U52(X1, X2) -> active# X1, active# U61(tt(), V1, V2) -> isNat# V1)
(active# U52(X1, X2) -> active# X1, active# U61(tt(), V1, V2) -> U62#(isNat V1, V2))
(active# U52(X1, X2) -> active# X1, active# U63 X -> active# X)
(active# U52(X1, X2) -> active# X1, active# U63 X -> U63# active X)
(active# U52(X1, X2) -> active# X1, active# s X -> active# X)
(active# U52(X1, X2) -> active# X1, active# s X -> s# active X)
(active# U52(X1, X2) -> active# X1, active# length X -> active# X)
(active# U52(X1, X2) -> active# X1, active# length X -> length# active X)
(active# U52(X1, X2) -> active# X1, active# length cons(N, L) -> isNatList# L)
(active# U52(X1, X2) -> active# X1, active# length cons(N, L) -> isNat# N)
(active# U52(X1, X2) -> active# X1, active# length cons(N, L) -> U71#(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L))
(active# U52(X1, X2) -> active# X1, active# length cons(N, L) -> and#(isNatList L, isNatIListKind L))
(active# U52(X1, X2) -> active# X1, active# length cons(N, L) -> and#(isNat N, isNatKind N))
(active# U52(X1, X2) -> active# X1, active# length cons(N, L) -> and#(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)))
(active# U52(X1, X2) -> active# X1, active# length cons(N, L) -> isNatIListKind# L)
(active# U52(X1, X2) -> active# X1, active# length cons(N, L) -> isNatKind# N)
(active# U52(X1, X2) -> active# X1, active# U71(X1, X2) -> active# X1)
(active# U52(X1, X2) -> active# X1, active# U71(X1, X2) -> U71#(active X1, X2))
(active# U52(X1, X2) -> active# X1, active# U71(tt(), L) -> s# length L)
(active# U52(X1, X2) -> active# X1, active# U71(tt(), L) -> length# L)
(active# U52(X1, X2) -> active# X1, active# U81 X -> active# X)
(active# U52(X1, X2) -> active# X1, active# U81 X -> U81# active X)
(active# U52(X1, X2) -> active# X1, active# take(X1, X2) -> active# X1)
(active# U52(X1, X2) -> active# X1, active# take(X1, X2) -> active# X2)
(active# U52(X1, X2) -> active# X1, active# take(X1, X2) -> take#(X1, active X2))
(active# U52(X1, X2) -> active# X1, active# take(X1, X2) -> take#(active X1, X2))
(active# U52(X1, X2) -> active# X1, active# take(0(), IL) -> isNatIList# IL)
(active# U52(X1, X2) -> active# X1, active# take(0(), IL) -> U81# and(isNatIList IL, isNatIListKind IL))
(active# U52(X1, X2) -> active# X1, active# take(0(), IL) -> and#(isNatIList IL, isNatIListKind IL))
(active# U52(X1, X2) -> active# X1, active# take(0(), IL) -> isNatIListKind# IL)
(active# U52(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# N)
(active# U52(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# M)
(active# U52(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIList# IL)
(active# U52(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> U91#(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N))
(active# U52(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat N, isNatKind N))
(active# U52(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat M, isNatKind M))
(active# U52(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, isNatIListKind IL))
(active# U52(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(and(isNat M, isNatKind M), and(isNat N, isNatKind N)))
(active# U52(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))))
(active# U52(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIListKind# IL)
(active# U52(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatKind# N)
(active# U52(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatKind# M)
(active# U52(X1, X2) -> active# X1, active# U91(X1, X2, X3, X4) -> active# X1)
(active# U52(X1, X2) -> active# X1, active# U91(X1, X2, X3, X4) -> U91#(active X1, X2, X3, X4))
(active# U52(X1, X2) -> active# X1, active# U91(tt(), IL, M, N) -> cons#(N, take(M, IL)))
(active# U52(X1, X2) -> active# X1, active# U91(tt(), IL, M, N) -> take#(M, IL))
(active# U52(X1, X2) -> active# X1, active# and(X1, X2) -> active# X1)
(active# U52(X1, X2) -> active# X1, active# and(X1, X2) -> and#(active X1, X2))
(active# U52(X1, X2) -> active# X1, active# isNatIListKind cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U52(X1, X2) -> active# X1, active# isNatIListKind cons(V1, V2) -> isNatIListKind# V2)
(active# U52(X1, X2) -> active# X1, active# isNatIListKind cons(V1, V2) -> isNatKind# V1)
(active# U52(X1, X2) -> active# X1, active# isNatIListKind take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# U52(X1, X2) -> active# X1, active# isNatIListKind take(V1, V2) -> isNatIListKind# V2)
(active# U52(X1, X2) -> active# X1, active# isNatIListKind take(V1, V2) -> isNatKind# V1)
(active# U52(X1, X2) -> active# X1, active# isNatKind s V1 -> isNatKind# V1)
(active# U52(X1, X2) -> active# X1, active# isNatKind length V1 -> isNatIListKind# V1)
(active# U42(X1, X2) -> U42#(active X1, X2), U42#(mark X1, X2) -> U42#(X1, X2))
(active# U42(X1, X2) -> U42#(active X1, X2), U42#(ok X1, ok X2) -> U42#(X1, X2))
(active# U31(X1, X2) -> U31#(active X1, X2), U31#(mark X1, X2) -> U31#(X1, X2))
(active# U31(X1, X2) -> U31#(active X1, X2), U31#(ok X1, ok X2) -> U31#(X1, X2))
(active# U21(X1, X2) -> U21#(active X1, X2), U21#(mark X1, X2) -> U21#(X1, X2))
(active# U21(X1, X2) -> U21#(active X1, X2), U21#(ok X1, ok X2) -> U21#(X1, X2))
(active# U11(X1, X2) -> U11#(active X1, X2), U11#(mark X1, X2) -> U11#(X1, X2))
(active# U11(X1, X2) -> U11#(active X1, X2), U11#(ok X1, ok X2) -> U11#(X1, X2))
(active# cons(X1, X2) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2))
(active# cons(X1, X2) -> active# X1, active# cons(X1, X2) -> active# X1)
(active# cons(X1, X2) -> active# X1, active# zeros() -> cons#(0(), zeros()))
(active# cons(X1, X2) -> active# X1, active# U12 X -> active# X)
(active# cons(X1, X2) -> active# X1, active# U12 X -> U12# active X)
(active# cons(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> U51#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# cons(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# cons(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> isNatIListKind# V2)
(active# cons(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> isNatKind# V1)
(active# cons(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> U61#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# cons(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# cons(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> isNatIListKind# V2)
(active# cons(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> isNatKind# V1)
(active# cons(X1, X2) -> active# X1, active# U11(X1, X2) -> active# X1)
(active# cons(X1, X2) -> active# X1, active# U11(X1, X2) -> U11#(active X1, X2))
(active# cons(X1, X2) -> active# X1, active# U11(tt(), V1) -> U12# isNatList V1)
(active# cons(X1, X2) -> active# X1, active# U11(tt(), V1) -> isNatList# V1)
(active# cons(X1, X2) -> active# X1, active# U22 X -> active# X)
(active# cons(X1, X2) -> active# X1, active# U22 X -> U22# active X)
(active# cons(X1, X2) -> active# X1, active# isNat s V1 -> U21#(isNatKind V1, V1))
(active# cons(X1, X2) -> active# X1, active# isNat s V1 -> isNatKind# V1)
(active# cons(X1, X2) -> active# X1, active# isNat length V1 -> U11#(isNatIListKind V1, V1))
(active# cons(X1, X2) -> active# X1, active# isNat length V1 -> isNatIListKind# V1)
(active# cons(X1, X2) -> active# X1, active# U21(X1, X2) -> active# X1)
(active# cons(X1, X2) -> active# X1, active# U21(X1, X2) -> U21#(active X1, X2))
(active# cons(X1, X2) -> active# X1, active# U21(tt(), V1) -> U22# isNat V1)
(active# cons(X1, X2) -> active# X1, active# U21(tt(), V1) -> isNat# V1)
(active# cons(X1, X2) -> active# X1, active# U32 X -> active# X)
(active# cons(X1, X2) -> active# X1, active# U32 X -> U32# active X)
(active# cons(X1, X2) -> active# X1, active# U31(X1, X2) -> active# X1)
(active# cons(X1, X2) -> active# X1, active# U31(X1, X2) -> U31#(active X1, X2))
(active# cons(X1, X2) -> active# X1, active# U31(tt(), V) -> isNatList# V)
(active# cons(X1, X2) -> active# X1, active# U31(tt(), V) -> U32# isNatList V)
(active# cons(X1, X2) -> active# X1, active# U42(X1, X2) -> active# X1)
(active# cons(X1, X2) -> active# X1, active# U42(X1, X2) -> U42#(active X1, X2))
(active# cons(X1, X2) -> active# X1, active# U42(tt(), V2) -> U43# isNatIList V2)
(active# cons(X1, X2) -> active# X1, active# U42(tt(), V2) -> isNatIList# V2)
(active# cons(X1, X2) -> active# X1, active# U41(X1, X2, X3) -> active# X1)
(active# cons(X1, X2) -> active# X1, active# U41(X1, X2, X3) -> U41#(active X1, X2, X3))
(active# cons(X1, X2) -> active# X1, active# U41(tt(), V1, V2) -> isNat# V1)
(active# cons(X1, X2) -> active# X1, active# U41(tt(), V1, V2) -> U42#(isNat V1, V2))
(active# cons(X1, X2) -> active# X1, active# U43 X -> active# X)
(active# cons(X1, X2) -> active# X1, active# U43 X -> U43# active X)
(active# cons(X1, X2) -> active# X1, active# isNatIList V -> U31#(isNatIListKind V, V))
(active# cons(X1, X2) -> active# X1, active# isNatIList V -> isNatIListKind# V)
(active# cons(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> U41#(and(isNatKind V1, isNatIListKind V2), V1, V2))
(active# cons(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# cons(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNatIListKind# V2)
(active# cons(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNatKind# V1)
(active# cons(X1, X2) -> active# X1, active# U52(X1, X2) -> active# X1)
(active# cons(X1, X2) -> active# X1, active# U52(X1, X2) -> U52#(active X1, X2))
(active# cons(X1, X2) -> active# X1, active# U52(tt(), V2) -> isNatList# V2)
(active# cons(X1, X2) -> active# X1, active# U52(tt(), V2) -> U53# isNatList V2)
(active# cons(X1, X2) -> active# X1, active# U51(X1, X2, X3) -> active# X1)
(active# cons(X1, X2) -> active# X1, active# U51(X1, X2, X3) -> U51#(active X1, X2, X3))
(active# cons(X1, X2) -> active# X1, active# U51(tt(), V1, V2) -> isNat# V1)
(active# cons(X1, X2) -> active# X1, active# U51(tt(), V1, V2) -> U52#(isNat V1, V2))
(active# cons(X1, X2) -> active# X1, active# U53 X -> active# X)
(active# cons(X1, X2) -> active# X1, active# U53 X -> U53# active X)
(active# cons(X1, X2) -> active# X1, active# U62(X1, X2) -> active# X1)
(active# cons(X1, X2) -> active# X1, active# U62(X1, X2) -> U62#(active X1, X2))
(active# cons(X1, X2) -> active# X1, active# U62(tt(), V2) -> isNatIList# V2)
(active# cons(X1, X2) -> active# X1, active# U62(tt(), V2) -> U63# isNatIList V2)
(active# cons(X1, X2) -> active# X1, active# U61(X1, X2, X3) -> active# X1)
(active# cons(X1, X2) -> active# X1, active# U61(X1, X2, X3) -> U61#(active X1, X2, X3))
(active# cons(X1, X2) -> active# X1, active# U61(tt(), V1, V2) -> isNat# V1)
(active# cons(X1, X2) -> active# X1, active# U61(tt(), V1, V2) -> U62#(isNat V1, V2))
(active# cons(X1, X2) -> active# X1, active# U63 X -> active# X)
(active# cons(X1, X2) -> active# X1, active# U63 X -> U63# active X)
(active# cons(X1, X2) -> active# X1, active# s X -> active# X)
(active# cons(X1, X2) -> active# X1, active# s X -> s# active X)
(active# cons(X1, X2) -> active# X1, active# length X -> active# X)
(active# cons(X1, X2) -> active# X1, active# length X -> length# active X)
(active# cons(X1, X2) -> active# X1, active# length cons(N, L) -> isNatList# L)
(active# cons(X1, X2) -> active# X1, active# length cons(N, L) -> isNat# N)
(active# cons(X1, X2) -> active# X1, active# length cons(N, L) -> U71#(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L))
(active# cons(X1, X2) -> active# X1, active# length cons(N, L) -> and#(isNatList L, isNatIListKind L))
(active# cons(X1, X2) -> active# X1, active# length cons(N, L) -> and#(isNat N, isNatKind N))
(active# cons(X1, X2) -> active# X1, active# length cons(N, L) -> and#(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)))
(active# cons(X1, X2) -> active# X1, active# length cons(N, L) -> isNatIListKind# L)
(active# cons(X1, X2) -> active# X1, active# length cons(N, L) -> isNatKind# N)
(active# cons(X1, X2) -> active# X1, active# U71(X1, X2) -> active# X1)
(active# cons(X1, X2) -> active# X1, active# U71(X1, X2) -> U71#(active X1, X2))
(active# cons(X1, X2) -> active# X1, active# U71(tt(), L) -> s# length L)
(active# cons(X1, X2) -> active# X1, active# U71(tt(), L) -> length# L)
(active# cons(X1, X2) -> active# X1, active# U81 X -> active# X)
(active# cons(X1, X2) -> active# X1, active# U81 X -> U81# active X)
(active# cons(X1, X2) -> active# X1, active# take(X1, X2) -> active# X1)
(active# cons(X1, X2) -> active# X1, active# take(X1, X2) -> active# X2)
(active# cons(X1, X2) -> active# X1, active# take(X1, X2) -> take#(X1, active X2))
(active# cons(X1, X2) -> active# X1, active# take(X1, X2) -> take#(active X1, X2))
(active# cons(X1, X2) -> active# X1, active# take(0(), IL) -> isNatIList# IL)
(active# cons(X1, X2) -> active# X1, active# take(0(), IL) -> U81# and(isNatIList IL, isNatIListKind IL))
(active# cons(X1, X2) -> active# X1, active# take(0(), IL) -> and#(isNatIList IL, isNatIListKind IL))
(active# cons(X1, X2) -> active# X1, active# take(0(), IL) -> isNatIListKind# IL)
(active# cons(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# N)
(active# cons(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# M)
(active# cons(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIList# IL)
(active# cons(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> U91#(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N))
(active# cons(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat N, isNatKind N))
(active# cons(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat M, isNatKind M))
(active# cons(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, isNatIListKind IL))
(active# cons(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(and(isNat M, isNatKind M), and(isNat N, isNatKind N)))
(active# cons(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))))
(active# cons(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIListKind# IL)
(active# cons(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatKind# N)
(active# cons(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatKind# M)
(active# cons(X1, X2) -> active# X1, active# U91(X1, X2, X3, X4) -> active# X1)
(active# cons(X1, X2) -> active# X1, active# U91(X1, X2, X3, X4) -> U91#(active X1, X2, X3, X4))
(active# cons(X1, X2) -> active# X1, active# U91(tt(), IL, M, N) -> cons#(N, take(M, IL)))
(active# cons(X1, X2) -> active# X1, active# U91(tt(), IL, M, N) -> take#(M, IL))
(active# cons(X1, X2) -> active# X1, active# and(X1, X2) -> active# X1)
(active# cons(X1, X2) -> active# X1, active# and(X1, X2) -> and#(active X1, X2))
(active# cons(X1, X2) -> active# X1, active# isNatIListKind cons(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# cons(X1, X2) -> active# X1, active# isNatIListKind cons(V1, V2) -> isNatIListKind# V2)
(active# cons(X1, X2) -> active# X1, active# isNatIListKind cons(V1, V2) -> isNatKind# V1)
(active# cons(X1, X2) -> active# X1, active# isNatIListKind take(V1, V2) -> and#(isNatKind V1, isNatIListKind V2))
(active# cons(X1, X2) -> active# X1, active# isNatIListKind take(V1, V2) -> isNatIListKind# V2)
(active# cons(X1, X2) -> active# X1, active# isNatIListKind take(V1, V2) -> isNatKind# V1)
(active# cons(X1, X2) -> active# X1, active# isNatKind s V1 -> isNatKind# V1)
(active# cons(X1, X2) -> active# X1, active# isNatKind length V1 -> isNatIListKind# V1)
(active# U71(tt(), L) -> length# L, length# mark X -> length# X)
(active# U71(tt(), L) -> length# L, length# ok X -> length# X)
(active# length cons(N, L) -> isNatList# L, isNatList# ok X -> isNatList# X)
(proper# U61(X1, X2, X3) -> proper# X3, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# U61(X1, X2, X3) -> proper# X3, proper# cons(X1, X2) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X3, proper# cons(X1, X2) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U12 X -> U12# proper X)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U12 X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X3, proper# isNatList X -> isNatList# proper X)
(proper# U61(X1, X2, X3) -> proper# X3, proper# isNatList X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# U61(X1, X2, X3) -> proper# X3, proper# U11(X1, X2) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U11(X1, X2) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U22 X -> U22# proper X)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U22 X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X3, proper# isNat X -> isNat# proper X)
(proper# U61(X1, X2, X3) -> proper# X3, proper# isNat X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# U61(X1, X2, X3) -> proper# X3, proper# U21(X1, X2) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U21(X1, X2) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U32 X -> U32# proper X)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U32 X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# U61(X1, X2, X3) -> proper# X3, proper# U31(X1, X2) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U31(X1, X2) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# U61(X1, X2, X3) -> proper# X3, proper# U42(X1, X2) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U42(X1, X2) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# U61(X1, X2, X3) -> proper# X3, proper# U41(X1, X2, X3) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U41(X1, X2, X3) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U41(X1, X2, X3) -> proper# X3)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U43 X -> U43# proper X)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U43 X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X3, proper# isNatIList X -> isNatIList# proper X)
(proper# U61(X1, X2, X3) -> proper# X3, proper# isNatIList X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# U61(X1, X2, X3) -> proper# X3, proper# U52(X1, X2) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U52(X1, X2) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# U61(X1, X2, X3) -> proper# X3, proper# U51(X1, X2, X3) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U51(X1, X2, X3) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U51(X1, X2, X3) -> proper# X3)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U53 X -> U53# proper X)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U53 X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# U61(X1, X2, X3) -> proper# X3, proper# U62(X1, X2) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U62(X1, X2) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# U61(X1, X2, X3) -> proper# X3, proper# U61(X1, X2, X3) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U61(X1, X2, X3) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U61(X1, X2, X3) -> proper# X3)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U63 X -> U63# proper X)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U63 X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X3, proper# s X -> s# proper X)
(proper# U61(X1, X2, X3) -> proper# X3, proper# s X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X3, proper# length X -> length# proper X)
(proper# U61(X1, X2, X3) -> proper# X3, proper# length X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# U61(X1, X2, X3) -> proper# X3, proper# U71(X1, X2) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U71(X1, X2) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U81 X -> U81# proper X)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U81 X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X3, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# U61(X1, X2, X3) -> proper# X3, proper# take(X1, X2) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X3, proper# take(X1, X2) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# U61(X1, X2, X3) -> proper# X3, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# U61(X1, X2, X3) -> proper# X3, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# U61(X1, X2, X3) -> proper# X3, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# U61(X1, X2, X3) -> proper# X3, proper# and(X1, X2) -> proper# X1)
(proper# U61(X1, X2, X3) -> proper# X3, proper# and(X1, X2) -> proper# X2)
(proper# U61(X1, X2, X3) -> proper# X3, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# U61(X1, X2, X3) -> proper# X3, proper# isNatIListKind X -> proper# X)
(proper# U61(X1, X2, X3) -> proper# X3, proper# isNatKind X -> isNatKind# proper X)
(proper# U61(X1, X2, X3) -> proper# X3, proper# isNatKind X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X3, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# U41(X1, X2, X3) -> proper# X3, proper# cons(X1, X2) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X3, proper# cons(X1, X2) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U12 X -> U12# proper X)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U12 X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X3, proper# isNatList X -> isNatList# proper X)
(proper# U41(X1, X2, X3) -> proper# X3, proper# isNatList X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U11(X1, X2) -> U11#(proper X1, proper X2))
(proper# U41(X1, X2, X3) -> proper# X3, proper# U11(X1, X2) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U11(X1, X2) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U22 X -> U22# proper X)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U22 X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X3, proper# isNat X -> isNat# proper X)
(proper# U41(X1, X2, X3) -> proper# X3, proper# isNat X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U21(X1, X2) -> U21#(proper X1, proper X2))
(proper# U41(X1, X2, X3) -> proper# X3, proper# U21(X1, X2) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U21(X1, X2) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U32 X -> U32# proper X)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U32 X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U31(X1, X2) -> U31#(proper X1, proper X2))
(proper# U41(X1, X2, X3) -> proper# X3, proper# U31(X1, X2) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U31(X1, X2) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U42(X1, X2) -> U42#(proper X1, proper X2))
(proper# U41(X1, X2, X3) -> proper# X3, proper# U42(X1, X2) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U42(X1, X2) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U41(X1, X2, X3) -> U41#(proper X1, proper X2, proper X3))
(proper# U41(X1, X2, X3) -> proper# X3, proper# U41(X1, X2, X3) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U41(X1, X2, X3) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U41(X1, X2, X3) -> proper# X3)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U43 X -> U43# proper X)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U43 X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X3, proper# isNatIList X -> isNatIList# proper X)
(proper# U41(X1, X2, X3) -> proper# X3, proper# isNatIList X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U52(X1, X2) -> U52#(proper X1, proper X2))
(proper# U41(X1, X2, X3) -> proper# X3, proper# U52(X1, X2) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U52(X1, X2) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U51(X1, X2, X3) -> U51#(proper X1, proper X2, proper X3))
(proper# U41(X1, X2, X3) -> proper# X3, proper# U51(X1, X2, X3) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U51(X1, X2, X3) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U51(X1, X2, X3) -> proper# X3)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U53 X -> U53# proper X)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U53 X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U62(X1, X2) -> U62#(proper X1, proper X2))
(proper# U41(X1, X2, X3) -> proper# X3, proper# U62(X1, X2) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U62(X1, X2) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3))
(proper# U41(X1, X2, X3) -> proper# X3, proper# U61(X1, X2, X3) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U61(X1, X2, X3) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U61(X1, X2, X3) -> proper# X3)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U63 X -> U63# proper X)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U63 X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X3, proper# s X -> s# proper X)
(proper# U41(X1, X2, X3) -> proper# X3, proper# s X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X3, proper# length X -> length# proper X)
(proper# U41(X1, X2, X3) -> proper# X3, proper# length X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U71(X1, X2) -> U71#(proper X1, proper X2))
(proper# U41(X1, X2, X3) -> proper# X3, proper# U71(X1, X2) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U71(X1, X2) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U81 X -> U81# proper X)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U81 X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X3, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# U41(X1, X2, X3) -> proper# X3, proper# take(X1, X2) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X3, proper# take(X1, X2) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U91(X1, X2, X3, X4) -> U91#(proper X1, proper X2, proper X3, proper X4))
(proper# U41(X1, X2, X3) -> proper# X3, proper# U91(X1, X2, X3, X4) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U91(X1, X2, X3, X4) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U91(X1, X2, X3, X4) -> proper# X3)
(proper# U41(X1, X2, X3) -> proper# X3, proper# U91(X1, X2, X3, X4) -> proper# X4)
(proper# U41(X1, X2, X3) -> proper# X3, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# U41(X1, X2, X3) -> proper# X3, proper# and(X1, X2) -> proper# X1)
(proper# U41(X1, X2, X3) -> proper# X3, proper# and(X1, X2) -> proper# X2)
(proper# U41(X1, X2, X3) -> proper# X3, proper# isNatIListKind X -> isNatIListKind# proper X)
(proper# U41(X1, X2, X3) -> proper# X3, proper# isNatIListKind X -> proper# X)
(proper# U41(X1, X2, X3) -> proper# X3, proper# isNatKind X -> isNatKind# proper X)
(proper# U41(X1, X2, X3) -> proper# X3, proper# isNatKind X -> proper# X)
(U61#(ok X1, ok X2, ok X3) -> U61#(X1, X2, X3), U61#(mark X1, X2, X3) -> U61#(X1, X2, X3))
(U61#(ok X1, ok X2, ok X3) -> U61#(X1, X2, X3), U61#(ok X1, ok X2, ok X3) -> U61#(X1, X2, X3))
(U51#(ok X1, ok X2, ok X3) -> U51#(X1, X2, X3), U51#(mark X1, X2, X3) -> U51#(X1, X2, X3))
(U51#(ok X1, ok X2, ok X3) -> U51#(X1, X2, X3), U51#(ok X1, ok X2, ok X3) -> U51#(X1, X2, X3))
(U41#(ok X1, ok X2, ok X3) -> U41#(X1, X2, X3), U41#(mark X1, X2, X3) -> U41#(X1, X2, X3))
(U41#(ok X1, ok X2, ok X3) -> U41#(X1, X2, X3), U41#(ok X1, ok X2, ok X3) -> U41#(X1, X2, X3))
(active# U61(X1, X2, X3) -> U61#(active X1, X2, X3), U61#(mark X1, X2, X3) -> U61#(X1, X2, X3))
(active# U61(X1, X2, X3) -> U61#(active X1, X2, X3), U61#(ok X1, ok X2, ok X3) -> U61#(X1, X2, X3))
(active# U41(X1, X2, X3) -> U41#(active X1, X2, X3), U41#(mark X1, X2, X3) -> U41#(X1, X2, X3))
(active# U41(X1, X2, X3) -> U41#(active X1, X2, X3), U41#(ok X1, ok X2, ok X3) -> U41#(X1, X2, X3))
(active# take(s M, cons(N, IL)) -> and#(and(isNat M, isNatKind M), and(isNat N, isNatKind N)), and#(mark X1, X2) -> and#(X1, X2))
(active# take(s M, cons(N, IL)) -> and#(and(isNat M, isNatKind M), and(isNat N, isNatKind N)), and#(ok X1, ok X2) -> and#(X1, X2))
(active# take(s M, cons(N, IL)) -> isNatKind# M, isNatKind# ok X -> isNatKind# X)
(active# isNatIList V -> U31#(isNatIListKind V, V), U31#(mark X1, X2) -> U31#(X1, X2))
(active# isNatIList V -> U31#(isNatIListKind V, V), U31#(ok X1, ok X2) -> U31#(X1, X2))
(active# isNatKind s V1 -> isNatKind# V1, isNatKind# ok X -> isNatKind# X)
(active# isNatIListKind cons(V1, V2) -> isNatKind# V1, isNatKind# ok X -> isNatKind# X)
(active# U51(tt(), V1, V2) -> isNat# V1, isNat# ok X -> isNat# X)
(active# U41(tt(), V1, V2) -> isNat# V1, isNat# ok X -> isNat# X)
(active# isNat length V1 -> isNatIListKind# V1, isNatIListKind# ok X -> isNatIListKind# X)
(active# U11(tt(), V1) -> isNatList# V1, isNatList# ok X -> isNatList# X)
(active# isNatList cons(V1, V2) -> isNatKind# V1, isNatKind# ok X -> isNatKind# X)
}
STATUS:
arrows: 0.890621
SCCS (31):
Scc:
{top# mark X -> top# proper X,
top# ok X -> top# active X}
Scc:
{ active# cons(X1, X2) -> active# X1,
active# U12 X -> active# X,
active# U11(X1, X2) -> active# X1,
active# U22 X -> active# X,
active# U21(X1, X2) -> active# X1,
active# U32 X -> active# X,
active# U31(X1, X2) -> active# X1,
active# U42(X1, X2) -> active# X1,
active# U41(X1, X2, X3) -> active# X1,
active# U43 X -> active# X,
active# U52(X1, X2) -> active# X1,
active# U51(X1, X2, X3) -> active# X1,
active# U53 X -> active# X,
active# U62(X1, X2) -> active# X1,
active# U61(X1, X2, X3) -> active# X1,
active# U63 X -> active# X,
active# s X -> active# X,
active# length X -> active# X,
active# U71(X1, X2) -> active# X1,
active# U81 X -> active# X,
active# take(X1, X2) -> active# X1,
active# take(X1, X2) -> active# X2,
active# U91(X1, X2, X3, X4) -> active# X1,
active# and(X1, X2) -> active# X1}
Scc:
{ proper# cons(X1, X2) -> proper# X1,
proper# cons(X1, X2) -> proper# X2,
proper# U12 X -> proper# X,
proper# isNatList X -> proper# X,
proper# U11(X1, X2) -> proper# X1,
proper# U11(X1, X2) -> proper# X2,
proper# U22 X -> proper# X,
proper# isNat X -> proper# X,
proper# U21(X1, X2) -> proper# X1,
proper# U21(X1, X2) -> proper# X2,
proper# U32 X -> proper# X,
proper# U31(X1, X2) -> proper# X1,
proper# U31(X1, X2) -> proper# X2,
proper# U42(X1, X2) -> proper# X1,
proper# U42(X1, X2) -> proper# X2,
proper# U41(X1, X2, X3) -> proper# X1,
proper# U41(X1, X2, X3) -> proper# X2,
proper# U41(X1, X2, X3) -> proper# X3,
proper# U43 X -> proper# X,
proper# isNatIList X -> proper# X,
proper# U52(X1, X2) -> proper# X1,
proper# U52(X1, X2) -> proper# X2,
proper# U51(X1, X2, X3) -> proper# X1,
proper# U51(X1, X2, X3) -> proper# X2,
proper# U51(X1, X2, X3) -> proper# X3,
proper# U53 X -> proper# X,
proper# U62(X1, X2) -> proper# X1,
proper# U62(X1, X2) -> proper# X2,
proper# U61(X1, X2, X3) -> proper# X1,
proper# U61(X1, X2, X3) -> proper# X2,
proper# U61(X1, X2, X3) -> proper# X3,
proper# U63 X -> proper# X,
proper# s X -> proper# X,
proper# length X -> proper# X,
proper# U71(X1, X2) -> proper# X1,
proper# U71(X1, X2) -> proper# X2,
proper# U81 X -> proper# X,
proper# take(X1, X2) -> proper# X1,
proper# take(X1, X2) -> proper# X2,
proper# U91(X1, X2, X3, X4) -> proper# X1,
proper# U91(X1, X2, X3, X4) -> proper# X2,
proper# U91(X1, X2, X3, X4) -> proper# X3,
proper# U91(X1, X2, X3, X4) -> proper# X4,
proper# and(X1, X2) -> proper# X1,
proper# and(X1, X2) -> proper# X2,
proper# isNatIListKind X -> proper# X,
proper# isNatKind X -> proper# X}
Scc:
{ U91#(mark X1, X2, X3, X4) -> U91#(X1, X2, X3, X4),
U91#(ok X1, ok X2, ok X3, ok X4) -> U91#(X1, X2, X3, X4)}
Scc:
{ take#(X1, mark X2) -> take#(X1, X2),
take#(mark X1, X2) -> take#(X1, X2),
take#(ok X1, ok X2) -> take#(X1, X2)}
Scc:
{U81# mark X -> U81# X,
U81# ok X -> U81# X}
Scc:
{ U71#(mark X1, X2) -> U71#(X1, X2),
U71#(ok X1, ok X2) -> U71#(X1, X2)}
Scc:
{length# mark X -> length# X,
length# ok X -> length# X}
Scc:
{s# mark X -> s# X,
s# ok X -> s# X}
Scc:
{U63# mark X -> U63# X,
U63# ok X -> U63# X}
Scc:
{ U62#(mark X1, X2) -> U62#(X1, X2),
U62#(ok X1, ok X2) -> U62#(X1, X2)}
Scc:
{U53# mark X -> U53# X,
U53# ok X -> U53# X}
Scc:
{ U52#(mark X1, X2) -> U52#(X1, X2),
U52#(ok X1, ok X2) -> U52#(X1, X2)}
Scc:
{isNatIList# ok X -> isNatIList# X}
Scc:
{U43# mark X -> U43# X,
U43# ok X -> U43# X}
Scc:
{ U42#(mark X1, X2) -> U42#(X1, X2),
U42#(ok X1, ok X2) -> U42#(X1, X2)}
Scc:
{U32# mark X -> U32# X,
U32# ok X -> U32# X}
Scc:
{ U21#(mark X1, X2) -> U21#(X1, X2),
U21#(ok X1, ok X2) -> U21#(X1, X2)}
Scc:
{U22# mark X -> U22# X,
U22# ok X -> U22# X}
Scc:
{ U11#(mark X1, X2) -> U11#(X1, X2),
U11#(ok X1, ok X2) -> U11#(X1, X2)}
Scc:
{U12# mark X -> U12# X,
U12# ok X -> U12# X}
Scc:
{ cons#(mark X1, X2) -> cons#(X1, X2),
cons#(ok X1, ok X2) -> cons#(X1, X2)}
Scc:
{ U61#(mark X1, X2, X3) -> U61#(X1, X2, X3),
U61#(ok X1, ok X2, ok X3) -> U61#(X1, X2, X3)}
Scc:
{ U51#(mark X1, X2, X3) -> U51#(X1, X2, X3),
U51#(ok X1, ok X2, ok X3) -> U51#(X1, X2, X3)}
Scc:
{ U41#(mark X1, X2, X3) -> U41#(X1, X2, X3),
U41#(ok X1, ok X2, ok X3) -> U41#(X1, X2, X3)}
Scc:
{ and#(mark X1, X2) -> and#(X1, X2),
and#(ok X1, ok X2) -> and#(X1, X2)}
Scc:
{ U31#(mark X1, X2) -> U31#(X1, X2),
U31#(ok X1, ok X2) -> U31#(X1, X2)}
Scc:
{isNat# ok X -> isNat# X}
Scc:
{isNatIListKind# ok X -> isNatIListKind# X}
Scc:
{isNatList# ok X -> isNatList# X}
Scc:
{isNatKind# ok X -> isNatKind# X}
SCC (2):
Strict:
{top# mark X -> top# proper X,
top# ok X -> top# active X}
Weak:
{ cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
active cons(X1, X2) -> cons(active X1, X2),
active zeros() -> mark cons(0(), zeros()),
active U12 X -> U12 active X,
active U12 tt() -> mark tt(),
active isNatList cons(V1, V2) -> mark U51(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatList nil() -> mark tt(),
active isNatList take(V1, V2) -> mark U61(and(isNatKind V1, isNatIListKind V2), V1, V2),
active U11(X1, X2) -> U11(active X1, X2),
active U11(tt(), V1) -> mark U12 isNatList V1,
active U22 X -> U22 active X,
active U22 tt() -> mark tt(),
active isNat 0() -> mark tt(),
active isNat s V1 -> mark U21(isNatKind V1, V1),
active isNat length V1 -> mark U11(isNatIListKind V1, V1),
active U21(X1, X2) -> U21(active X1, X2),
active U21(tt(), V1) -> mark U22 isNat V1,
active U32 X -> U32 active X,
active U32 tt() -> mark tt(),
active U31(X1, X2) -> U31(active X1, X2),
active U31(tt(), V) -> mark U32 isNatList V,
active U42(X1, X2) -> U42(active X1, X2),
active U42(tt(), V2) -> mark U43 isNatIList V2,
active U41(X1, X2, X3) -> U41(active X1, X2, X3),
active U41(tt(), V1, V2) -> mark U42(isNat V1, V2),
active U43 X -> U43 active X,
active U43 tt() -> mark tt(),
active isNatIList V -> mark U31(isNatIListKind V, V),
active isNatIList cons(V1, V2) -> mark U41(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatIList zeros() -> mark tt(),
active U52(X1, X2) -> U52(active X1, X2),
active U52(tt(), V2) -> mark U53 isNatList V2,
active U51(X1, X2, X3) -> U51(active X1, X2, X3),
active U51(tt(), V1, V2) -> mark U52(isNat V1, V2),
active U53 X -> U53 active X,
active U53 tt() -> mark tt(),
active U62(X1, X2) -> U62(active X1, X2),
active U62(tt(), V2) -> mark U63 isNatIList V2,
active U61(X1, X2, X3) -> U61(active X1, X2, X3),
active U61(tt(), V1, V2) -> mark U62(isNat V1, V2),
active U63 X -> U63 active X,
active U63 tt() -> mark tt(),
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark U71(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L),
active length nil() -> mark 0(),
active U71(X1, X2) -> U71(active X1, X2),
active U71(tt(), L) -> mark s length L,
active U81 X -> U81 active X,
active U81 tt() -> mark nil(),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark U81 and(isNatIList IL, isNatIListKind IL),
active take(s M, cons(N, IL)) -> mark U91(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N),
active U91(X1, X2, X3, X4) -> U91(active X1, X2, X3, X4),
active U91(tt(), IL, M, N) -> mark cons(N, take(M, IL)),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), X) -> mark X,
active isNatIListKind cons(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatIListKind zeros() -> mark tt(),
active isNatIListKind nil() -> mark tt(),
active isNatIListKind take(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatKind 0() -> mark tt(),
active isNatKind s V1 -> mark isNatKind V1,
active isNatKind length V1 -> mark isNatIListKind V1,
U12 mark X -> mark U12 X,
U12 ok X -> ok U12 X,
isNatList ok X -> ok isNatList X,
U11(mark X1, X2) -> mark U11(X1, X2),
U11(ok X1, ok X2) -> ok U11(X1, X2),
U22 mark X -> mark U22 X,
U22 ok X -> ok U22 X,
isNat ok X -> ok isNat X,
U21(mark X1, X2) -> mark U21(X1, X2),
U21(ok X1, ok X2) -> ok U21(X1, X2),
U32 mark X -> mark U32 X,
U32 ok X -> ok U32 X,
U31(mark X1, X2) -> mark U31(X1, X2),
U31(ok X1, ok X2) -> ok U31(X1, X2),
U42(mark X1, X2) -> mark U42(X1, X2),
U42(ok X1, ok X2) -> ok U42(X1, X2),
U41(mark X1, X2, X3) -> mark U41(X1, X2, X3),
U41(ok X1, ok X2, ok X3) -> ok U41(X1, X2, X3),
U43 mark X -> mark U43 X,
U43 ok X -> ok U43 X,
isNatIList ok X -> ok isNatIList X,
U52(mark X1, X2) -> mark U52(X1, X2),
U52(ok X1, ok X2) -> ok U52(X1, X2),
U51(mark X1, X2, X3) -> mark U51(X1, X2, X3),
U51(ok X1, ok X2, ok X3) -> ok U51(X1, X2, X3),
U53 mark X -> mark U53 X,
U53 ok X -> ok U53 X,
U62(mark X1, X2) -> mark U62(X1, X2),
U62(ok X1, ok X2) -> ok U62(X1, X2),
U61(mark X1, X2, X3) -> mark U61(X1, X2, X3),
U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3),
U63 mark X -> mark U63 X,
U63 ok X -> ok U63 X,
s mark X -> mark s X,
s ok X -> ok s X,
length mark X -> mark length X,
length ok X -> ok length X,
U71(mark X1, X2) -> mark U71(X1, X2),
U71(ok X1, ok X2) -> ok U71(X1, X2),
U81 mark X -> mark U81 X,
U81 ok X -> ok U81 X,
take(X1, mark X2) -> mark take(X1, X2),
take(mark X1, X2) -> mark take(X1, X2),
take(ok X1, ok X2) -> ok take(X1, X2),
U91(mark X1, X2, X3, X4) -> mark U91(X1, X2, X3, X4),
U91(ok X1, ok X2, ok X3, ok X4) -> ok U91(X1, X2, X3, X4),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatIListKind ok X -> ok isNatIListKind X,
isNatKind ok X -> ok isNatKind X,
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper 0() -> ok 0(),
proper zeros() -> ok zeros(),
proper U12 X -> U12 proper X,
proper isNatList X -> isNatList proper X,
proper U11(X1, X2) -> U11(proper X1, proper X2),
proper tt() -> ok tt(),
proper U22 X -> U22 proper X,
proper isNat X -> isNat proper X,
proper U21(X1, X2) -> U21(proper X1, proper X2),
proper U32 X -> U32 proper X,
proper U31(X1, X2) -> U31(proper X1, proper X2),
proper U42(X1, X2) -> U42(proper X1, proper X2),
proper U41(X1, X2, X3) -> U41(proper X1, proper X2, proper X3),
proper U43 X -> U43 proper X,
proper isNatIList X -> isNatIList proper X,
proper U52(X1, X2) -> U52(proper X1, proper X2),
proper U51(X1, X2, X3) -> U51(proper X1, proper X2, proper X3),
proper U53 X -> U53 proper X,
proper U62(X1, X2) -> U62(proper X1, proper X2),
proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3),
proper U63 X -> U63 proper X,
proper s X -> s proper X,
proper length X -> length proper X,
proper U71(X1, X2) -> U71(proper X1, proper X2),
proper nil() -> ok nil(),
proper U81 X -> U81 proper X,
proper take(X1, X2) -> take(proper X1, proper X2),
proper U91(X1, X2, X3, X4) -> U91(proper X1, proper X2, proper X3, proper X4),
proper and(X1, X2) -> and(proper X1, proper X2),
proper isNatIListKind X -> isNatIListKind proper X,
proper isNatKind X -> isNatKind proper X,
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (24):
Strict:
{ active# cons(X1, X2) -> active# X1,
active# U12 X -> active# X,
active# U11(X1, X2) -> active# X1,
active# U22 X -> active# X,
active# U21(X1, X2) -> active# X1,
active# U32 X -> active# X,
active# U31(X1, X2) -> active# X1,
active# U42(X1, X2) -> active# X1,
active# U41(X1, X2, X3) -> active# X1,
active# U43 X -> active# X,
active# U52(X1, X2) -> active# X1,
active# U51(X1, X2, X3) -> active# X1,
active# U53 X -> active# X,
active# U62(X1, X2) -> active# X1,
active# U61(X1, X2, X3) -> active# X1,
active# U63 X -> active# X,
active# s X -> active# X,
active# length X -> active# X,
active# U71(X1, X2) -> active# X1,
active# U81 X -> active# X,
active# take(X1, X2) -> active# X1,
active# take(X1, X2) -> active# X2,
active# U91(X1, X2, X3, X4) -> active# X1,
active# and(X1, X2) -> active# X1}
Weak:
{ cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
active cons(X1, X2) -> cons(active X1, X2),
active zeros() -> mark cons(0(), zeros()),
active U12 X -> U12 active X,
active U12 tt() -> mark tt(),
active isNatList cons(V1, V2) -> mark U51(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatList nil() -> mark tt(),
active isNatList take(V1, V2) -> mark U61(and(isNatKind V1, isNatIListKind V2), V1, V2),
active U11(X1, X2) -> U11(active X1, X2),
active U11(tt(), V1) -> mark U12 isNatList V1,
active U22 X -> U22 active X,
active U22 tt() -> mark tt(),
active isNat 0() -> mark tt(),
active isNat s V1 -> mark U21(isNatKind V1, V1),
active isNat length V1 -> mark U11(isNatIListKind V1, V1),
active U21(X1, X2) -> U21(active X1, X2),
active U21(tt(), V1) -> mark U22 isNat V1,
active U32 X -> U32 active X,
active U32 tt() -> mark tt(),
active U31(X1, X2) -> U31(active X1, X2),
active U31(tt(), V) -> mark U32 isNatList V,
active U42(X1, X2) -> U42(active X1, X2),
active U42(tt(), V2) -> mark U43 isNatIList V2,
active U41(X1, X2, X3) -> U41(active X1, X2, X3),
active U41(tt(), V1, V2) -> mark U42(isNat V1, V2),
active U43 X -> U43 active X,
active U43 tt() -> mark tt(),
active isNatIList V -> mark U31(isNatIListKind V, V),
active isNatIList cons(V1, V2) -> mark U41(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatIList zeros() -> mark tt(),
active U52(X1, X2) -> U52(active X1, X2),
active U52(tt(), V2) -> mark U53 isNatList V2,
active U51(X1, X2, X3) -> U51(active X1, X2, X3),
active U51(tt(), V1, V2) -> mark U52(isNat V1, V2),
active U53 X -> U53 active X,
active U53 tt() -> mark tt(),
active U62(X1, X2) -> U62(active X1, X2),
active U62(tt(), V2) -> mark U63 isNatIList V2,
active U61(X1, X2, X3) -> U61(active X1, X2, X3),
active U61(tt(), V1, V2) -> mark U62(isNat V1, V2),
active U63 X -> U63 active X,
active U63 tt() -> mark tt(),
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark U71(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L),
active length nil() -> mark 0(),
active U71(X1, X2) -> U71(active X1, X2),
active U71(tt(), L) -> mark s length L,
active U81 X -> U81 active X,
active U81 tt() -> mark nil(),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark U81 and(isNatIList IL, isNatIListKind IL),
active take(s M, cons(N, IL)) -> mark U91(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N),
active U91(X1, X2, X3, X4) -> U91(active X1, X2, X3, X4),
active U91(tt(), IL, M, N) -> mark cons(N, take(M, IL)),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), X) -> mark X,
active isNatIListKind cons(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatIListKind zeros() -> mark tt(),
active isNatIListKind nil() -> mark tt(),
active isNatIListKind take(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatKind 0() -> mark tt(),
active isNatKind s V1 -> mark isNatKind V1,
active isNatKind length V1 -> mark isNatIListKind V1,
U12 mark X -> mark U12 X,
U12 ok X -> ok U12 X,
isNatList ok X -> ok isNatList X,
U11(mark X1, X2) -> mark U11(X1, X2),
U11(ok X1, ok X2) -> ok U11(X1, X2),
U22 mark X -> mark U22 X,
U22 ok X -> ok U22 X,
isNat ok X -> ok isNat X,
U21(mark X1, X2) -> mark U21(X1, X2),
U21(ok X1, ok X2) -> ok U21(X1, X2),
U32 mark X -> mark U32 X,
U32 ok X -> ok U32 X,
U31(mark X1, X2) -> mark U31(X1, X2),
U31(ok X1, ok X2) -> ok U31(X1, X2),
U42(mark X1, X2) -> mark U42(X1, X2),
U42(ok X1, ok X2) -> ok U42(X1, X2),
U41(mark X1, X2, X3) -> mark U41(X1, X2, X3),
U41(ok X1, ok X2, ok X3) -> ok U41(X1, X2, X3),
U43 mark X -> mark U43 X,
U43 ok X -> ok U43 X,
isNatIList ok X -> ok isNatIList X,
U52(mark X1, X2) -> mark U52(X1, X2),
U52(ok X1, ok X2) -> ok U52(X1, X2),
U51(mark X1, X2, X3) -> mark U51(X1, X2, X3),
U51(ok X1, ok X2, ok X3) -> ok U51(X1, X2, X3),
U53 mark X -> mark U53 X,
U53 ok X -> ok U53 X,
U62(mark X1, X2) -> mark U62(X1, X2),
U62(ok X1, ok X2) -> ok U62(X1, X2),
U61(mark X1, X2, X3) -> mark U61(X1, X2, X3),
U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3),
U63 mark X -> mark U63 X,
U63 ok X -> ok U63 X,
s mark X -> mark s X,
s ok X -> ok s X,
length mark X -> mark length X,
length ok X -> ok length X,
U71(mark X1, X2) -> mark U71(X1, X2),
U71(ok X1, ok X2) -> ok U71(X1, X2),
U81 mark X -> mark U81 X,
U81 ok X -> ok U81 X,
take(X1, mark X2) -> mark take(X1, X2),
take(mark X1, X2) -> mark take(X1, X2),
take(ok X1, ok X2) -> ok take(X1, X2),
U91(mark X1, X2, X3, X4) -> mark U91(X1, X2, X3, X4),
U91(ok X1, ok X2, ok X3, ok X4) -> ok U91(X1, X2, X3, X4),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatIListKind ok X -> ok isNatIListKind X,
isNatKind ok X -> ok isNatKind X,
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper 0() -> ok 0(),
proper zeros() -> ok zeros(),
proper U12 X -> U12 proper X,
proper isNatList X -> isNatList proper X,
proper U11(X1, X2) -> U11(proper X1, proper X2),
proper tt() -> ok tt(),
proper U22 X -> U22 proper X,
proper isNat X -> isNat proper X,
proper U21(X1, X2) -> U21(proper X1, proper X2),
proper U32 X -> U32 proper X,
proper U31(X1, X2) -> U31(proper X1, proper X2),
proper U42(X1, X2) -> U42(proper X1, proper X2),
proper U41(X1, X2, X3) -> U41(proper X1, proper X2, proper X3),
proper U43 X -> U43 proper X,
proper isNatIList X -> isNatIList proper X,
proper U52(X1, X2) -> U52(proper X1, proper X2),
proper U51(X1, X2, X3) -> U51(proper X1, proper X2, proper X3),
proper U53 X -> U53 proper X,
proper U62(X1, X2) -> U62(proper X1, proper X2),
proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3),
proper U63 X -> U63 proper X,
proper s X -> s proper X,
proper length X -> length proper X,
proper U71(X1, X2) -> U71(proper X1, proper X2),
proper nil() -> ok nil(),
proper U81 X -> U81 proper X,
proper take(X1, X2) -> take(proper X1, proper X2),
proper U91(X1, X2, X3, X4) -> U91(proper X1, proper X2, proper X3, proper X4),
proper and(X1, X2) -> and(proper X1, proper X2),
proper isNatIListKind X -> isNatIListKind proper X,
proper isNatKind X -> isNatKind proper X,
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (47):
Strict:
{ proper# cons(X1, X2) -> proper# X1,
proper# cons(X1, X2) -> proper# X2,
proper# U12 X -> proper# X,
proper# isNatList X -> proper# X,
proper# U11(X1, X2) -> proper# X1,
proper# U11(X1, X2) -> proper# X2,
proper# U22 X -> proper# X,
proper# isNat X -> proper# X,
proper# U21(X1, X2) -> proper# X1,
proper# U21(X1, X2) -> proper# X2,
proper# U32 X -> proper# X,
proper# U31(X1, X2) -> proper# X1,
proper# U31(X1, X2) -> proper# X2,
proper# U42(X1, X2) -> proper# X1,
proper# U42(X1, X2) -> proper# X2,
proper# U41(X1, X2, X3) -> proper# X1,
proper# U41(X1, X2, X3) -> proper# X2,
proper# U41(X1, X2, X3) -> proper# X3,
proper# U43 X -> proper# X,
proper# isNatIList X -> proper# X,
proper# U52(X1, X2) -> proper# X1,
proper# U52(X1, X2) -> proper# X2,
proper# U51(X1, X2, X3) -> proper# X1,
proper# U51(X1, X2, X3) -> proper# X2,
proper# U51(X1, X2, X3) -> proper# X3,
proper# U53 X -> proper# X,
proper# U62(X1, X2) -> proper# X1,
proper# U62(X1, X2) -> proper# X2,
proper# U61(X1, X2, X3) -> proper# X1,
proper# U61(X1, X2, X3) -> proper# X2,
proper# U61(X1, X2, X3) -> proper# X3,
proper# U63 X -> proper# X,
proper# s X -> proper# X,
proper# length X -> proper# X,
proper# U71(X1, X2) -> proper# X1,
proper# U71(X1, X2) -> proper# X2,
proper# U81 X -> proper# X,
proper# take(X1, X2) -> proper# X1,
proper# take(X1, X2) -> proper# X2,
proper# U91(X1, X2, X3, X4) -> proper# X1,
proper# U91(X1, X2, X3, X4) -> proper# X2,
proper# U91(X1, X2, X3, X4) -> proper# X3,
proper# U91(X1, X2, X3, X4) -> proper# X4,
proper# and(X1, X2) -> proper# X1,
proper# and(X1, X2) -> proper# X2,
proper# isNatIListKind X -> proper# X,
proper# isNatKind X -> proper# X}
Weak:
{ cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
active cons(X1, X2) -> cons(active X1, X2),
active zeros() -> mark cons(0(), zeros()),
active U12 X -> U12 active X,
active U12 tt() -> mark tt(),
active isNatList cons(V1, V2) -> mark U51(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatList nil() -> mark tt(),
active isNatList take(V1, V2) -> mark U61(and(isNatKind V1, isNatIListKind V2), V1, V2),
active U11(X1, X2) -> U11(active X1, X2),
active U11(tt(), V1) -> mark U12 isNatList V1,
active U22 X -> U22 active X,
active U22 tt() -> mark tt(),
active isNat 0() -> mark tt(),
active isNat s V1 -> mark U21(isNatKind V1, V1),
active isNat length V1 -> mark U11(isNatIListKind V1, V1),
active U21(X1, X2) -> U21(active X1, X2),
active U21(tt(), V1) -> mark U22 isNat V1,
active U32 X -> U32 active X,
active U32 tt() -> mark tt(),
active U31(X1, X2) -> U31(active X1, X2),
active U31(tt(), V) -> mark U32 isNatList V,
active U42(X1, X2) -> U42(active X1, X2),
active U42(tt(), V2) -> mark U43 isNatIList V2,
active U41(X1, X2, X3) -> U41(active X1, X2, X3),
active U41(tt(), V1, V2) -> mark U42(isNat V1, V2),
active U43 X -> U43 active X,
active U43 tt() -> mark tt(),
active isNatIList V -> mark U31(isNatIListKind V, V),
active isNatIList cons(V1, V2) -> mark U41(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatIList zeros() -> mark tt(),
active U52(X1, X2) -> U52(active X1, X2),
active U52(tt(), V2) -> mark U53 isNatList V2,
active U51(X1, X2, X3) -> U51(active X1, X2, X3),
active U51(tt(), V1, V2) -> mark U52(isNat V1, V2),
active U53 X -> U53 active X,
active U53 tt() -> mark tt(),
active U62(X1, X2) -> U62(active X1, X2),
active U62(tt(), V2) -> mark U63 isNatIList V2,
active U61(X1, X2, X3) -> U61(active X1, X2, X3),
active U61(tt(), V1, V2) -> mark U62(isNat V1, V2),
active U63 X -> U63 active X,
active U63 tt() -> mark tt(),
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark U71(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L),
active length nil() -> mark 0(),
active U71(X1, X2) -> U71(active X1, X2),
active U71(tt(), L) -> mark s length L,
active U81 X -> U81 active X,
active U81 tt() -> mark nil(),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark U81 and(isNatIList IL, isNatIListKind IL),
active take(s M, cons(N, IL)) -> mark U91(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N),
active U91(X1, X2, X3, X4) -> U91(active X1, X2, X3, X4),
active U91(tt(), IL, M, N) -> mark cons(N, take(M, IL)),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), X) -> mark X,
active isNatIListKind cons(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatIListKind zeros() -> mark tt(),
active isNatIListKind nil() -> mark tt(),
active isNatIListKind take(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatKind 0() -> mark tt(),
active isNatKind s V1 -> mark isNatKind V1,
active isNatKind length V1 -> mark isNatIListKind V1,
U12 mark X -> mark U12 X,
U12 ok X -> ok U12 X,
isNatList ok X -> ok isNatList X,
U11(mark X1, X2) -> mark U11(X1, X2),
U11(ok X1, ok X2) -> ok U11(X1, X2),
U22 mark X -> mark U22 X,
U22 ok X -> ok U22 X,
isNat ok X -> ok isNat X,
U21(mark X1, X2) -> mark U21(X1, X2),
U21(ok X1, ok X2) -> ok U21(X1, X2),
U32 mark X -> mark U32 X,
U32 ok X -> ok U32 X,
U31(mark X1, X2) -> mark U31(X1, X2),
U31(ok X1, ok X2) -> ok U31(X1, X2),
U42(mark X1, X2) -> mark U42(X1, X2),
U42(ok X1, ok X2) -> ok U42(X1, X2),
U41(mark X1, X2, X3) -> mark U41(X1, X2, X3),
U41(ok X1, ok X2, ok X3) -> ok U41(X1, X2, X3),
U43 mark X -> mark U43 X,
U43 ok X -> ok U43 X,
isNatIList ok X -> ok isNatIList X,
U52(mark X1, X2) -> mark U52(X1, X2),
U52(ok X1, ok X2) -> ok U52(X1, X2),
U51(mark X1, X2, X3) -> mark U51(X1, X2, X3),
U51(ok X1, ok X2, ok X3) -> ok U51(X1, X2, X3),
U53 mark X -> mark U53 X,
U53 ok X -> ok U53 X,
U62(mark X1, X2) -> mark U62(X1, X2),
U62(ok X1, ok X2) -> ok U62(X1, X2),
U61(mark X1, X2, X3) -> mark U61(X1, X2, X3),
U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3),
U63 mark X -> mark U63 X,
U63 ok X -> ok U63 X,
s mark X -> mark s X,
s ok X -> ok s X,
length mark X -> mark length X,
length ok X -> ok length X,
U71(mark X1, X2) -> mark U71(X1, X2),
U71(ok X1, ok X2) -> ok U71(X1, X2),
U81 mark X -> mark U81 X,
U81 ok X -> ok U81 X,
take(X1, mark X2) -> mark take(X1, X2),
take(mark X1, X2) -> mark take(X1, X2),
take(ok X1, ok X2) -> ok take(X1, X2),
U91(mark X1, X2, X3, X4) -> mark U91(X1, X2, X3, X4),
U91(ok X1, ok X2, ok X3, ok X4) -> ok U91(X1, X2, X3, X4),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatIListKind ok X -> ok isNatIListKind X,
isNatKind ok X -> ok isNatKind X,
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper 0() -> ok 0(),
proper zeros() -> ok zeros(),
proper U12 X -> U12 proper X,
proper isNatList X -> isNatList proper X,
proper U11(X1, X2) -> U11(proper X1, proper X2),
proper tt() -> ok tt(),
proper U22 X -> U22 proper X,
proper isNat X -> isNat proper X,
proper U21(X1, X2) -> U21(proper X1, proper X2),
proper U32 X -> U32 proper X,
proper U31(X1, X2) -> U31(proper X1, proper X2),
proper U42(X1, X2) -> U42(proper X1, proper X2),
proper U41(X1, X2, X3) -> U41(proper X1, proper X2, proper X3),
proper U43 X -> U43 proper X,
proper isNatIList X -> isNatIList proper X,
proper U52(X1, X2) -> U52(proper X1, proper X2),
proper U51(X1, X2, X3) -> U51(proper X1, proper X2, proper X3),
proper U53 X -> U53 proper X,
proper U62(X1, X2) -> U62(proper X1, proper X2),
proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3),
proper U63 X -> U63 proper X,
proper s X -> s proper X,
proper length X -> length proper X,
proper U71(X1, X2) -> U71(proper X1, proper X2),
proper nil() -> ok nil(),
proper U81 X -> U81 proper X,
proper take(X1, X2) -> take(proper X1, proper X2),
proper U91(X1, X2, X3, X4) -> U91(proper X1, proper X2, proper X3, proper X4),
proper and(X1, X2) -> and(proper X1, proper X2),
proper isNatIListKind X -> isNatIListKind proper X,
proper isNatKind X -> isNatKind proper X,
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (2):
Strict:
{ U91#(mark X1, X2, X3, X4) -> U91#(X1, X2, X3, X4),
U91#(ok X1, ok X2, ok X3, ok X4) -> U91#(X1, X2, X3, X4)}
Weak:
{ cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
active cons(X1, X2) -> cons(active X1, X2),
active zeros() -> mark cons(0(), zeros()),
active U12 X -> U12 active X,
active U12 tt() -> mark tt(),
active isNatList cons(V1, V2) -> mark U51(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatList nil() -> mark tt(),
active isNatList take(V1, V2) -> mark U61(and(isNatKind V1, isNatIListKind V2), V1, V2),
active U11(X1, X2) -> U11(active X1, X2),
active U11(tt(), V1) -> mark U12 isNatList V1,
active U22 X -> U22 active X,
active U22 tt() -> mark tt(),
active isNat 0() -> mark tt(),
active isNat s V1 -> mark U21(isNatKind V1, V1),
active isNat length V1 -> mark U11(isNatIListKind V1, V1),
active U21(X1, X2) -> U21(active X1, X2),
active U21(tt(), V1) -> mark U22 isNat V1,
active U32 X -> U32 active X,
active U32 tt() -> mark tt(),
active U31(X1, X2) -> U31(active X1, X2),
active U31(tt(), V) -> mark U32 isNatList V,
active U42(X1, X2) -> U42(active X1, X2),
active U42(tt(), V2) -> mark U43 isNatIList V2,
active U41(X1, X2, X3) -> U41(active X1, X2, X3),
active U41(tt(), V1, V2) -> mark U42(isNat V1, V2),
active U43 X -> U43 active X,
active U43 tt() -> mark tt(),
active isNatIList V -> mark U31(isNatIListKind V, V),
active isNatIList cons(V1, V2) -> mark U41(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatIList zeros() -> mark tt(),
active U52(X1, X2) -> U52(active X1, X2),
active U52(tt(), V2) -> mark U53 isNatList V2,
active U51(X1, X2, X3) -> U51(active X1, X2, X3),
active U51(tt(), V1, V2) -> mark U52(isNat V1, V2),
active U53 X -> U53 active X,
active U53 tt() -> mark tt(),
active U62(X1, X2) -> U62(active X1, X2),
active U62(tt(), V2) -> mark U63 isNatIList V2,
active U61(X1, X2, X3) -> U61(active X1, X2, X3),
active U61(tt(), V1, V2) -> mark U62(isNat V1, V2),
active U63 X -> U63 active X,
active U63 tt() -> mark tt(),
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark U71(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L),
active length nil() -> mark 0(),
active U71(X1, X2) -> U71(active X1, X2),
active U71(tt(), L) -> mark s length L,
active U81 X -> U81 active X,
active U81 tt() -> mark nil(),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark U81 and(isNatIList IL, isNatIListKind IL),
active take(s M, cons(N, IL)) -> mark U91(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N),
active U91(X1, X2, X3, X4) -> U91(active X1, X2, X3, X4),
active U91(tt(), IL, M, N) -> mark cons(N, take(M, IL)),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), X) -> mark X,
active isNatIListKind cons(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatIListKind zeros() -> mark tt(),
active isNatIListKind nil() -> mark tt(),
active isNatIListKind take(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatKind 0() -> mark tt(),
active isNatKind s V1 -> mark isNatKind V1,
active isNatKind length V1 -> mark isNatIListKind V1,
U12 mark X -> mark U12 X,
U12 ok X -> ok U12 X,
isNatList ok X -> ok isNatList X,
U11(mark X1, X2) -> mark U11(X1, X2),
U11(ok X1, ok X2) -> ok U11(X1, X2),
U22 mark X -> mark U22 X,
U22 ok X -> ok U22 X,
isNat ok X -> ok isNat X,
U21(mark X1, X2) -> mark U21(X1, X2),
U21(ok X1, ok X2) -> ok U21(X1, X2),
U32 mark X -> mark U32 X,
U32 ok X -> ok U32 X,
U31(mark X1, X2) -> mark U31(X1, X2),
U31(ok X1, ok X2) -> ok U31(X1, X2),
U42(mark X1, X2) -> mark U42(X1, X2),
U42(ok X1, ok X2) -> ok U42(X1, X2),
U41(mark X1, X2, X3) -> mark U41(X1, X2, X3),
U41(ok X1, ok X2, ok X3) -> ok U41(X1, X2, X3),
U43 mark X -> mark U43 X,
U43 ok X -> ok U43 X,
isNatIList ok X -> ok isNatIList X,
U52(mark X1, X2) -> mark U52(X1, X2),
U52(ok X1, ok X2) -> ok U52(X1, X2),
U51(mark X1, X2, X3) -> mark U51(X1, X2, X3),
U51(ok X1, ok X2, ok X3) -> ok U51(X1, X2, X3),
U53 mark X -> mark U53 X,
U53 ok X -> ok U53 X,
U62(mark X1, X2) -> mark U62(X1, X2),
U62(ok X1, ok X2) -> ok U62(X1, X2),
U61(mark X1, X2, X3) -> mark U61(X1, X2, X3),
U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3),
U63 mark X -> mark U63 X,
U63 ok X -> ok U63 X,
s mark X -> mark s X,
s ok X -> ok s X,
length mark X -> mark length X,
length ok X -> ok length X,
U71(mark X1, X2) -> mark U71(X1, X2),
U71(ok X1, ok X2) -> ok U71(X1, X2),
U81 mark X -> mark U81 X,
U81 ok X -> ok U81 X,
take(X1, mark X2) -> mark take(X1, X2),
take(mark X1, X2) -> mark take(X1, X2),
take(ok X1, ok X2) -> ok take(X1, X2),
U91(mark X1, X2, X3, X4) -> mark U91(X1, X2, X3, X4),
U91(ok X1, ok X2, ok X3, ok X4) -> ok U91(X1, X2, X3, X4),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatIListKind ok X -> ok isNatIListKind X,
isNatKind ok X -> ok isNatKind X,
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper 0() -> ok 0(),
proper zeros() -> ok zeros(),
proper U12 X -> U12 proper X,
proper isNatList X -> isNatList proper X,
proper U11(X1, X2) -> U11(proper X1, proper X2),
proper tt() -> ok tt(),
proper U22 X -> U22 proper X,
proper isNat X -> isNat proper X,
proper U21(X1, X2) -> U21(proper X1, proper X2),
proper U32 X -> U32 proper X,
proper U31(X1, X2) -> U31(proper X1, proper X2),
proper U42(X1, X2) -> U42(proper X1, proper X2),
proper U41(X1, X2, X3) -> U41(proper X1, proper X2, proper X3),
proper U43 X -> U43 proper X,
proper isNatIList X -> isNatIList proper X,
proper U52(X1, X2) -> U52(proper X1, proper X2),
proper U51(X1, X2, X3) -> U51(proper X1, proper X2, proper X3),
proper U53 X -> U53 proper X,
proper U62(X1, X2) -> U62(proper X1, proper X2),
proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3),
proper U63 X -> U63 proper X,
proper s X -> s proper X,
proper length X -> length proper X,
proper U71(X1, X2) -> U71(proper X1, proper X2),
proper nil() -> ok nil(),
proper U81 X -> U81 proper X,
proper take(X1, X2) -> take(proper X1, proper X2),
proper U91(X1, X2, X3, X4) -> U91(proper X1, proper X2, proper X3, proper X4),
proper and(X1, X2) -> and(proper X1, proper X2),
proper isNatIListKind X -> isNatIListKind proper X,
proper isNatKind X -> isNatKind proper X,
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (3):
Strict:
{ take#(X1, mark X2) -> take#(X1, X2),
take#(mark X1, X2) -> take#(X1, X2),
take#(ok X1, ok X2) -> take#(X1, X2)}
Weak:
{ cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
active cons(X1, X2) -> cons(active X1, X2),
active zeros() -> mark cons(0(), zeros()),
active U12 X -> U12 active X,
active U12 tt() -> mark tt(),
active isNatList cons(V1, V2) -> mark U51(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatList nil() -> mark tt(),
active isNatList take(V1, V2) -> mark U61(and(isNatKind V1, isNatIListKind V2), V1, V2),
active U11(X1, X2) -> U11(active X1, X2),
active U11(tt(), V1) -> mark U12 isNatList V1,
active U22 X -> U22 active X,
active U22 tt() -> mark tt(),
active isNat 0() -> mark tt(),
active isNat s V1 -> mark U21(isNatKind V1, V1),
active isNat length V1 -> mark U11(isNatIListKind V1, V1),
active U21(X1, X2) -> U21(active X1, X2),
active U21(tt(), V1) -> mark U22 isNat V1,
active U32 X -> U32 active X,
active U32 tt() -> mark tt(),
active U31(X1, X2) -> U31(active X1, X2),
active U31(tt(), V) -> mark U32 isNatList V,
active U42(X1, X2) -> U42(active X1, X2),
active U42(tt(), V2) -> mark U43 isNatIList V2,
active U41(X1, X2, X3) -> U41(active X1, X2, X3),
active U41(tt(), V1, V2) -> mark U42(isNat V1, V2),
active U43 X -> U43 active X,
active U43 tt() -> mark tt(),
active isNatIList V -> mark U31(isNatIListKind V, V),
active isNatIList cons(V1, V2) -> mark U41(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatIList zeros() -> mark tt(),
active U52(X1, X2) -> U52(active X1, X2),
active U52(tt(), V2) -> mark U53 isNatList V2,
active U51(X1, X2, X3) -> U51(active X1, X2, X3),
active U51(tt(), V1, V2) -> mark U52(isNat V1, V2),
active U53 X -> U53 active X,
active U53 tt() -> mark tt(),
active U62(X1, X2) -> U62(active X1, X2),
active U62(tt(), V2) -> mark U63 isNatIList V2,
active U61(X1, X2, X3) -> U61(active X1, X2, X3),
active U61(tt(), V1, V2) -> mark U62(isNat V1, V2),
active U63 X -> U63 active X,
active U63 tt() -> mark tt(),
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark U71(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L),
active length nil() -> mark 0(),
active U71(X1, X2) -> U71(active X1, X2),
active U71(tt(), L) -> mark s length L,
active U81 X -> U81 active X,
active U81 tt() -> mark nil(),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark U81 and(isNatIList IL, isNatIListKind IL),
active take(s M, cons(N, IL)) -> mark U91(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N),
active U91(X1, X2, X3, X4) -> U91(active X1, X2, X3, X4),
active U91(tt(), IL, M, N) -> mark cons(N, take(M, IL)),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), X) -> mark X,
active isNatIListKind cons(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatIListKind zeros() -> mark tt(),
active isNatIListKind nil() -> mark tt(),
active isNatIListKind take(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatKind 0() -> mark tt(),
active isNatKind s V1 -> mark isNatKind V1,
active isNatKind length V1 -> mark isNatIListKind V1,
U12 mark X -> mark U12 X,
U12 ok X -> ok U12 X,
isNatList ok X -> ok isNatList X,
U11(mark X1, X2) -> mark U11(X1, X2),
U11(ok X1, ok X2) -> ok U11(X1, X2),
U22 mark X -> mark U22 X,
U22 ok X -> ok U22 X,
isNat ok X -> ok isNat X,
U21(mark X1, X2) -> mark U21(X1, X2),
U21(ok X1, ok X2) -> ok U21(X1, X2),
U32 mark X -> mark U32 X,
U32 ok X -> ok U32 X,
U31(mark X1, X2) -> mark U31(X1, X2),
U31(ok X1, ok X2) -> ok U31(X1, X2),
U42(mark X1, X2) -> mark U42(X1, X2),
U42(ok X1, ok X2) -> ok U42(X1, X2),
U41(mark X1, X2, X3) -> mark U41(X1, X2, X3),
U41(ok X1, ok X2, ok X3) -> ok U41(X1, X2, X3),
U43 mark X -> mark U43 X,
U43 ok X -> ok U43 X,
isNatIList ok X -> ok isNatIList X,
U52(mark X1, X2) -> mark U52(X1, X2),
U52(ok X1, ok X2) -> ok U52(X1, X2),
U51(mark X1, X2, X3) -> mark U51(X1, X2, X3),
U51(ok X1, ok X2, ok X3) -> ok U51(X1, X2, X3),
U53 mark X -> mark U53 X,
U53 ok X -> ok U53 X,
U62(mark X1, X2) -> mark U62(X1, X2),
U62(ok X1, ok X2) -> ok U62(X1, X2),
U61(mark X1, X2, X3) -> mark U61(X1, X2, X3),
U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3),
U63 mark X -> mark U63 X,
U63 ok X -> ok U63 X,
s mark X -> mark s X,
s ok X -> ok s X,
length mark X -> mark length X,
length ok X -> ok length X,
U71(mark X1, X2) -> mark U71(X1, X2),
U71(ok X1, ok X2) -> ok U71(X1, X2),
U81 mark X -> mark U81 X,
U81 ok X -> ok U81 X,
take(X1, mark X2) -> mark take(X1, X2),
take(mark X1, X2) -> mark take(X1, X2),
take(ok X1, ok X2) -> ok take(X1, X2),
U91(mark X1, X2, X3, X4) -> mark U91(X1, X2, X3, X4),
U91(ok X1, ok X2, ok X3, ok X4) -> ok U91(X1, X2, X3, X4),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatIListKind ok X -> ok isNatIListKind X,
isNatKind ok X -> ok isNatKind X,
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper 0() -> ok 0(),
proper zeros() -> ok zeros(),
proper U12 X -> U12 proper X,
proper isNatList X -> isNatList proper X,
proper U11(X1, X2) -> U11(proper X1, proper X2),
proper tt() -> ok tt(),
proper U22 X -> U22 proper X,
proper isNat X -> isNat proper X,
proper U21(X1, X2) -> U21(proper X1, proper X2),
proper U32 X -> U32 proper X,
proper U31(X1, X2) -> U31(proper X1, proper X2),
proper U42(X1, X2) -> U42(proper X1, proper X2),
proper U41(X1, X2, X3) -> U41(proper X1, proper X2, proper X3),
proper U43 X -> U43 proper X,
proper isNatIList X -> isNatIList proper X,
proper U52(X1, X2) -> U52(proper X1, proper X2),
proper U51(X1, X2, X3) -> U51(proper X1, proper X2, proper X3),
proper U53 X -> U53 proper X,
proper U62(X1, X2) -> U62(proper X1, proper X2),
proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3),
proper U63 X -> U63 proper X,
proper s X -> s proper X,
proper length X -> length proper X,
proper U71(X1, X2) -> U71(proper X1, proper X2),
proper nil() -> ok nil(),
proper U81 X -> U81 proper X,
proper take(X1, X2) -> take(proper X1, proper X2),
proper U91(X1, X2, X3, X4) -> U91(proper X1, proper X2, proper X3, proper X4),
proper and(X1, X2) -> and(proper X1, proper X2),
proper isNatIListKind X -> isNatIListKind proper X,
proper isNatKind X -> isNatKind proper X,
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (2):
Strict:
{U81# mark X -> U81# X,
U81# ok X -> U81# X}
Weak:
{ cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
active cons(X1, X2) -> cons(active X1, X2),
active zeros() -> mark cons(0(), zeros()),
active U12 X -> U12 active X,
active U12 tt() -> mark tt(),
active isNatList cons(V1, V2) -> mark U51(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatList nil() -> mark tt(),
active isNatList take(V1, V2) -> mark U61(and(isNatKind V1, isNatIListKind V2), V1, V2),
active U11(X1, X2) -> U11(active X1, X2),
active U11(tt(), V1) -> mark U12 isNatList V1,
active U22 X -> U22 active X,
active U22 tt() -> mark tt(),
active isNat 0() -> mark tt(),
active isNat s V1 -> mark U21(isNatKind V1, V1),
active isNat length V1 -> mark U11(isNatIListKind V1, V1),
active U21(X1, X2) -> U21(active X1, X2),
active U21(tt(), V1) -> mark U22 isNat V1,
active U32 X -> U32 active X,
active U32 tt() -> mark tt(),
active U31(X1, X2) -> U31(active X1, X2),
active U31(tt(), V) -> mark U32 isNatList V,
active U42(X1, X2) -> U42(active X1, X2),
active U42(tt(), V2) -> mark U43 isNatIList V2,
active U41(X1, X2, X3) -> U41(active X1, X2, X3),
active U41(tt(), V1, V2) -> mark U42(isNat V1, V2),
active U43 X -> U43 active X,
active U43 tt() -> mark tt(),
active isNatIList V -> mark U31(isNatIListKind V, V),
active isNatIList cons(V1, V2) -> mark U41(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatIList zeros() -> mark tt(),
active U52(X1, X2) -> U52(active X1, X2),
active U52(tt(), V2) -> mark U53 isNatList V2,
active U51(X1, X2, X3) -> U51(active X1, X2, X3),
active U51(tt(), V1, V2) -> mark U52(isNat V1, V2),
active U53 X -> U53 active X,
active U53 tt() -> mark tt(),
active U62(X1, X2) -> U62(active X1, X2),
active U62(tt(), V2) -> mark U63 isNatIList V2,
active U61(X1, X2, X3) -> U61(active X1, X2, X3),
active U61(tt(), V1, V2) -> mark U62(isNat V1, V2),
active U63 X -> U63 active X,
active U63 tt() -> mark tt(),
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark U71(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L),
active length nil() -> mark 0(),
active U71(X1, X2) -> U71(active X1, X2),
active U71(tt(), L) -> mark s length L,
active U81 X -> U81 active X,
active U81 tt() -> mark nil(),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark U81 and(isNatIList IL, isNatIListKind IL),
active take(s M, cons(N, IL)) -> mark U91(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N),
active U91(X1, X2, X3, X4) -> U91(active X1, X2, X3, X4),
active U91(tt(), IL, M, N) -> mark cons(N, take(M, IL)),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), X) -> mark X,
active isNatIListKind cons(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatIListKind zeros() -> mark tt(),
active isNatIListKind nil() -> mark tt(),
active isNatIListKind take(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatKind 0() -> mark tt(),
active isNatKind s V1 -> mark isNatKind V1,
active isNatKind length V1 -> mark isNatIListKind V1,
U12 mark X -> mark U12 X,
U12 ok X -> ok U12 X,
isNatList ok X -> ok isNatList X,
U11(mark X1, X2) -> mark U11(X1, X2),
U11(ok X1, ok X2) -> ok U11(X1, X2),
U22 mark X -> mark U22 X,
U22 ok X -> ok U22 X,
isNat ok X -> ok isNat X,
U21(mark X1, X2) -> mark U21(X1, X2),
U21(ok X1, ok X2) -> ok U21(X1, X2),
U32 mark X -> mark U32 X,
U32 ok X -> ok U32 X,
U31(mark X1, X2) -> mark U31(X1, X2),
U31(ok X1, ok X2) -> ok U31(X1, X2),
U42(mark X1, X2) -> mark U42(X1, X2),
U42(ok X1, ok X2) -> ok U42(X1, X2),
U41(mark X1, X2, X3) -> mark U41(X1, X2, X3),
U41(ok X1, ok X2, ok X3) -> ok U41(X1, X2, X3),
U43 mark X -> mark U43 X,
U43 ok X -> ok U43 X,
isNatIList ok X -> ok isNatIList X,
U52(mark X1, X2) -> mark U52(X1, X2),
U52(ok X1, ok X2) -> ok U52(X1, X2),
U51(mark X1, X2, X3) -> mark U51(X1, X2, X3),
U51(ok X1, ok X2, ok X3) -> ok U51(X1, X2, X3),
U53 mark X -> mark U53 X,
U53 ok X -> ok U53 X,
U62(mark X1, X2) -> mark U62(X1, X2),
U62(ok X1, ok X2) -> ok U62(X1, X2),
U61(mark X1, X2, X3) -> mark U61(X1, X2, X3),
U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3),
U63 mark X -> mark U63 X,
U63 ok X -> ok U63 X,
s mark X -> mark s X,
s ok X -> ok s X,
length mark X -> mark length X,
length ok X -> ok length X,
U71(mark X1, X2) -> mark U71(X1, X2),
U71(ok X1, ok X2) -> ok U71(X1, X2),
U81 mark X -> mark U81 X,
U81 ok X -> ok U81 X,
take(X1, mark X2) -> mark take(X1, X2),
take(mark X1, X2) -> mark take(X1, X2),
take(ok X1, ok X2) -> ok take(X1, X2),
U91(mark X1, X2, X3, X4) -> mark U91(X1, X2, X3, X4),
U91(ok X1, ok X2, ok X3, ok X4) -> ok U91(X1, X2, X3, X4),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatIListKind ok X -> ok isNatIListKind X,
isNatKind ok X -> ok isNatKind X,
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper 0() -> ok 0(),
proper zeros() -> ok zeros(),
proper U12 X -> U12 proper X,
proper isNatList X -> isNatList proper X,
proper U11(X1, X2) -> U11(proper X1, proper X2),
proper tt() -> ok tt(),
proper U22 X -> U22 proper X,
proper isNat X -> isNat proper X,
proper U21(X1, X2) -> U21(proper X1, proper X2),
proper U32 X -> U32 proper X,
proper U31(X1, X2) -> U31(proper X1, proper X2),
proper U42(X1, X2) -> U42(proper X1, proper X2),
proper U41(X1, X2, X3) -> U41(proper X1, proper X2, proper X3),
proper U43 X -> U43 proper X,
proper isNatIList X -> isNatIList proper X,
proper U52(X1, X2) -> U52(proper X1, proper X2),
proper U51(X1, X2, X3) -> U51(proper X1, proper X2, proper X3),
proper U53 X -> U53 proper X,
proper U62(X1, X2) -> U62(proper X1, proper X2),
proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3),
proper U63 X -> U63 proper X,
proper s X -> s proper X,
proper length X -> length proper X,
proper U71(X1, X2) -> U71(proper X1, proper X2),
proper nil() -> ok nil(),
proper U81 X -> U81 proper X,
proper take(X1, X2) -> take(proper X1, proper X2),
proper U91(X1, X2, X3, X4) -> U91(proper X1, proper X2, proper X3, proper X4),
proper and(X1, X2) -> and(proper X1, proper X2),
proper isNatIListKind X -> isNatIListKind proper X,
proper isNatKind X -> isNatKind proper X,
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (2):
Strict:
{ U71#(mark X1, X2) -> U71#(X1, X2),
U71#(ok X1, ok X2) -> U71#(X1, X2)}
Weak:
{ cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
active cons(X1, X2) -> cons(active X1, X2),
active zeros() -> mark cons(0(), zeros()),
active U12 X -> U12 active X,
active U12 tt() -> mark tt(),
active isNatList cons(V1, V2) -> mark U51(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatList nil() -> mark tt(),
active isNatList take(V1, V2) -> mark U61(and(isNatKind V1, isNatIListKind V2), V1, V2),
active U11(X1, X2) -> U11(active X1, X2),
active U11(tt(), V1) -> mark U12 isNatList V1,
active U22 X -> U22 active X,
active U22 tt() -> mark tt(),
active isNat 0() -> mark tt(),
active isNat s V1 -> mark U21(isNatKind V1, V1),
active isNat length V1 -> mark U11(isNatIListKind V1, V1),
active U21(X1, X2) -> U21(active X1, X2),
active U21(tt(), V1) -> mark U22 isNat V1,
active U32 X -> U32 active X,
active U32 tt() -> mark tt(),
active U31(X1, X2) -> U31(active X1, X2),
active U31(tt(), V) -> mark U32 isNatList V,
active U42(X1, X2) -> U42(active X1, X2),
active U42(tt(), V2) -> mark U43 isNatIList V2,
active U41(X1, X2, X3) -> U41(active X1, X2, X3),
active U41(tt(), V1, V2) -> mark U42(isNat V1, V2),
active U43 X -> U43 active X,
active U43 tt() -> mark tt(),
active isNatIList V -> mark U31(isNatIListKind V, V),
active isNatIList cons(V1, V2) -> mark U41(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatIList zeros() -> mark tt(),
active U52(X1, X2) -> U52(active X1, X2),
active U52(tt(), V2) -> mark U53 isNatList V2,
active U51(X1, X2, X3) -> U51(active X1, X2, X3),
active U51(tt(), V1, V2) -> mark U52(isNat V1, V2),
active U53 X -> U53 active X,
active U53 tt() -> mark tt(),
active U62(X1, X2) -> U62(active X1, X2),
active U62(tt(), V2) -> mark U63 isNatIList V2,
active U61(X1, X2, X3) -> U61(active X1, X2, X3),
active U61(tt(), V1, V2) -> mark U62(isNat V1, V2),
active U63 X -> U63 active X,
active U63 tt() -> mark tt(),
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark U71(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L),
active length nil() -> mark 0(),
active U71(X1, X2) -> U71(active X1, X2),
active U71(tt(), L) -> mark s length L,
active U81 X -> U81 active X,
active U81 tt() -> mark nil(),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark U81 and(isNatIList IL, isNatIListKind IL),
active take(s M, cons(N, IL)) -> mark U91(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N),
active U91(X1, X2, X3, X4) -> U91(active X1, X2, X3, X4),
active U91(tt(), IL, M, N) -> mark cons(N, take(M, IL)),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), X) -> mark X,
active isNatIListKind cons(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatIListKind zeros() -> mark tt(),
active isNatIListKind nil() -> mark tt(),
active isNatIListKind take(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatKind 0() -> mark tt(),
active isNatKind s V1 -> mark isNatKind V1,
active isNatKind length V1 -> mark isNatIListKind V1,
U12 mark X -> mark U12 X,
U12 ok X -> ok U12 X,
isNatList ok X -> ok isNatList X,
U11(mark X1, X2) -> mark U11(X1, X2),
U11(ok X1, ok X2) -> ok U11(X1, X2),
U22 mark X -> mark U22 X,
U22 ok X -> ok U22 X,
isNat ok X -> ok isNat X,
U21(mark X1, X2) -> mark U21(X1, X2),
U21(ok X1, ok X2) -> ok U21(X1, X2),
U32 mark X -> mark U32 X,
U32 ok X -> ok U32 X,
U31(mark X1, X2) -> mark U31(X1, X2),
U31(ok X1, ok X2) -> ok U31(X1, X2),
U42(mark X1, X2) -> mark U42(X1, X2),
U42(ok X1, ok X2) -> ok U42(X1, X2),
U41(mark X1, X2, X3) -> mark U41(X1, X2, X3),
U41(ok X1, ok X2, ok X3) -> ok U41(X1, X2, X3),
U43 mark X -> mark U43 X,
U43 ok X -> ok U43 X,
isNatIList ok X -> ok isNatIList X,
U52(mark X1, X2) -> mark U52(X1, X2),
U52(ok X1, ok X2) -> ok U52(X1, X2),
U51(mark X1, X2, X3) -> mark U51(X1, X2, X3),
U51(ok X1, ok X2, ok X3) -> ok U51(X1, X2, X3),
U53 mark X -> mark U53 X,
U53 ok X -> ok U53 X,
U62(mark X1, X2) -> mark U62(X1, X2),
U62(ok X1, ok X2) -> ok U62(X1, X2),
U61(mark X1, X2, X3) -> mark U61(X1, X2, X3),
U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3),
U63 mark X -> mark U63 X,
U63 ok X -> ok U63 X,
s mark X -> mark s X,
s ok X -> ok s X,
length mark X -> mark length X,
length ok X -> ok length X,
U71(mark X1, X2) -> mark U71(X1, X2),
U71(ok X1, ok X2) -> ok U71(X1, X2),
U81 mark X -> mark U81 X,
U81 ok X -> ok U81 X,
take(X1, mark X2) -> mark take(X1, X2),
take(mark X1, X2) -> mark take(X1, X2),
take(ok X1, ok X2) -> ok take(X1, X2),
U91(mark X1, X2, X3, X4) -> mark U91(X1, X2, X3, X4),
U91(ok X1, ok X2, ok X3, ok X4) -> ok U91(X1, X2, X3, X4),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatIListKind ok X -> ok isNatIListKind X,
isNatKind ok X -> ok isNatKind X,
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper 0() -> ok 0(),
proper zeros() -> ok zeros(),
proper U12 X -> U12 proper X,
proper isNatList X -> isNatList proper X,
proper U11(X1, X2) -> U11(proper X1, proper X2),
proper tt() -> ok tt(),
proper U22 X -> U22 proper X,
proper isNat X -> isNat proper X,
proper U21(X1, X2) -> U21(proper X1, proper X2),
proper U32 X -> U32 proper X,
proper U31(X1, X2) -> U31(proper X1, proper X2),
proper U42(X1, X2) -> U42(proper X1, proper X2),
proper U41(X1, X2, X3) -> U41(proper X1, proper X2, proper X3),
proper U43 X -> U43 proper X,
proper isNatIList X -> isNatIList proper X,
proper U52(X1, X2) -> U52(proper X1, proper X2),
proper U51(X1, X2, X3) -> U51(proper X1, proper X2, proper X3),
proper U53 X -> U53 proper X,
proper U62(X1, X2) -> U62(proper X1, proper X2),
proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3),
proper U63 X -> U63 proper X,
proper s X -> s proper X,
proper length X -> length proper X,
proper U71(X1, X2) -> U71(proper X1, proper X2),
proper nil() -> ok nil(),
proper U81 X -> U81 proper X,
proper take(X1, X2) -> take(proper X1, proper X2),
proper U91(X1, X2, X3, X4) -> U91(proper X1, proper X2, proper X3, proper X4),
proper and(X1, X2) -> and(proper X1, proper X2),
proper isNatIListKind X -> isNatIListKind proper X,
proper isNatKind X -> isNatKind proper X,
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (2):
Strict:
{length# mark X -> length# X,
length# ok X -> length# X}
Weak:
{ cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
active cons(X1, X2) -> cons(active X1, X2),
active zeros() -> mark cons(0(), zeros()),
active U12 X -> U12 active X,
active U12 tt() -> mark tt(),
active isNatList cons(V1, V2) -> mark U51(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatList nil() -> mark tt(),
active isNatList take(V1, V2) -> mark U61(and(isNatKind V1, isNatIListKind V2), V1, V2),
active U11(X1, X2) -> U11(active X1, X2),
active U11(tt(), V1) -> mark U12 isNatList V1,
active U22 X -> U22 active X,
active U22 tt() -> mark tt(),
active isNat 0() -> mark tt(),
active isNat s V1 -> mark U21(isNatKind V1, V1),
active isNat length V1 -> mark U11(isNatIListKind V1, V1),
active U21(X1, X2) -> U21(active X1, X2),
active U21(tt(), V1) -> mark U22 isNat V1,
active U32 X -> U32 active X,
active U32 tt() -> mark tt(),
active U31(X1, X2) -> U31(active X1, X2),
active U31(tt(), V) -> mark U32 isNatList V,
active U42(X1, X2) -> U42(active X1, X2),
active U42(tt(), V2) -> mark U43 isNatIList V2,
active U41(X1, X2, X3) -> U41(active X1, X2, X3),
active U41(tt(), V1, V2) -> mark U42(isNat V1, V2),
active U43 X -> U43 active X,
active U43 tt() -> mark tt(),
active isNatIList V -> mark U31(isNatIListKind V, V),
active isNatIList cons(V1, V2) -> mark U41(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatIList zeros() -> mark tt(),
active U52(X1, X2) -> U52(active X1, X2),
active U52(tt(), V2) -> mark U53 isNatList V2,
active U51(X1, X2, X3) -> U51(active X1, X2, X3),
active U51(tt(), V1, V2) -> mark U52(isNat V1, V2),
active U53 X -> U53 active X,
active U53 tt() -> mark tt(),
active U62(X1, X2) -> U62(active X1, X2),
active U62(tt(), V2) -> mark U63 isNatIList V2,
active U61(X1, X2, X3) -> U61(active X1, X2, X3),
active U61(tt(), V1, V2) -> mark U62(isNat V1, V2),
active U63 X -> U63 active X,
active U63 tt() -> mark tt(),
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark U71(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L),
active length nil() -> mark 0(),
active U71(X1, X2) -> U71(active X1, X2),
active U71(tt(), L) -> mark s length L,
active U81 X -> U81 active X,
active U81 tt() -> mark nil(),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark U81 and(isNatIList IL, isNatIListKind IL),
active take(s M, cons(N, IL)) -> mark U91(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N),
active U91(X1, X2, X3, X4) -> U91(active X1, X2, X3, X4),
active U91(tt(), IL, M, N) -> mark cons(N, take(M, IL)),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), X) -> mark X,
active isNatIListKind cons(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatIListKind zeros() -> mark tt(),
active isNatIListKind nil() -> mark tt(),
active isNatIListKind take(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatKind 0() -> mark tt(),
active isNatKind s V1 -> mark isNatKind V1,
active isNatKind length V1 -> mark isNatIListKind V1,
U12 mark X -> mark U12 X,
U12 ok X -> ok U12 X,
isNatList ok X -> ok isNatList X,
U11(mark X1, X2) -> mark U11(X1, X2),
U11(ok X1, ok X2) -> ok U11(X1, X2),
U22 mark X -> mark U22 X,
U22 ok X -> ok U22 X,
isNat ok X -> ok isNat X,
U21(mark X1, X2) -> mark U21(X1, X2),
U21(ok X1, ok X2) -> ok U21(X1, X2),
U32 mark X -> mark U32 X,
U32 ok X -> ok U32 X,
U31(mark X1, X2) -> mark U31(X1, X2),
U31(ok X1, ok X2) -> ok U31(X1, X2),
U42(mark X1, X2) -> mark U42(X1, X2),
U42(ok X1, ok X2) -> ok U42(X1, X2),
U41(mark X1, X2, X3) -> mark U41(X1, X2, X3),
U41(ok X1, ok X2, ok X3) -> ok U41(X1, X2, X3),
U43 mark X -> mark U43 X,
U43 ok X -> ok U43 X,
isNatIList ok X -> ok isNatIList X,
U52(mark X1, X2) -> mark U52(X1, X2),
U52(ok X1, ok X2) -> ok U52(X1, X2),
U51(mark X1, X2, X3) -> mark U51(X1, X2, X3),
U51(ok X1, ok X2, ok X3) -> ok U51(X1, X2, X3),
U53 mark X -> mark U53 X,
U53 ok X -> ok U53 X,
U62(mark X1, X2) -> mark U62(X1, X2),
U62(ok X1, ok X2) -> ok U62(X1, X2),
U61(mark X1, X2, X3) -> mark U61(X1, X2, X3),
U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3),
U63 mark X -> mark U63 X,
U63 ok X -> ok U63 X,
s mark X -> mark s X,
s ok X -> ok s X,
length mark X -> mark length X,
length ok X -> ok length X,
U71(mark X1, X2) -> mark U71(X1, X2),
U71(ok X1, ok X2) -> ok U71(X1, X2),
U81 mark X -> mark U81 X,
U81 ok X -> ok U81 X,
take(X1, mark X2) -> mark take(X1, X2),
take(mark X1, X2) -> mark take(X1, X2),
take(ok X1, ok X2) -> ok take(X1, X2),
U91(mark X1, X2, X3, X4) -> mark U91(X1, X2, X3, X4),
U91(ok X1, ok X2, ok X3, ok X4) -> ok U91(X1, X2, X3, X4),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatIListKind ok X -> ok isNatIListKind X,
isNatKind ok X -> ok isNatKind X,
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper 0() -> ok 0(),
proper zeros() -> ok zeros(),
proper U12 X -> U12 proper X,
proper isNatList X -> isNatList proper X,
proper U11(X1, X2) -> U11(proper X1, proper X2),
proper tt() -> ok tt(),
proper U22 X -> U22 proper X,
proper isNat X -> isNat proper X,
proper U21(X1, X2) -> U21(proper X1, proper X2),
proper U32 X -> U32 proper X,
proper U31(X1, X2) -> U31(proper X1, proper X2),
proper U42(X1, X2) -> U42(proper X1, proper X2),
proper U41(X1, X2, X3) -> U41(proper X1, proper X2, proper X3),
proper U43 X -> U43 proper X,
proper isNatIList X -> isNatIList proper X,
proper U52(X1, X2) -> U52(proper X1, proper X2),
proper U51(X1, X2, X3) -> U51(proper X1, proper X2, proper X3),
proper U53 X -> U53 proper X,
proper U62(X1, X2) -> U62(proper X1, proper X2),
proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3),
proper U63 X -> U63 proper X,
proper s X -> s proper X,
proper length X -> length proper X,
proper U71(X1, X2) -> U71(proper X1, proper X2),
proper nil() -> ok nil(),
proper U81 X -> U81 proper X,
proper take(X1, X2) -> take(proper X1, proper X2),
proper U91(X1, X2, X3, X4) -> U91(proper X1, proper X2, proper X3, proper X4),
proper and(X1, X2) -> and(proper X1, proper X2),
proper isNatIListKind X -> isNatIListKind proper X,
proper isNatKind X -> isNatKind proper X,
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (2):
Strict:
{s# mark X -> s# X,
s# ok X -> s# X}
Weak:
{ cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
active cons(X1, X2) -> cons(active X1, X2),
active zeros() -> mark cons(0(), zeros()),
active U12 X -> U12 active X,
active U12 tt() -> mark tt(),
active isNatList cons(V1, V2) -> mark U51(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatList nil() -> mark tt(),
active isNatList take(V1, V2) -> mark U61(and(isNatKind V1, isNatIListKind V2), V1, V2),
active U11(X1, X2) -> U11(active X1, X2),
active U11(tt(), V1) -> mark U12 isNatList V1,
active U22 X -> U22 active X,
active U22 tt() -> mark tt(),
active isNat 0() -> mark tt(),
active isNat s V1 -> mark U21(isNatKind V1, V1),
active isNat length V1 -> mark U11(isNatIListKind V1, V1),
active U21(X1, X2) -> U21(active X1, X2),
active U21(tt(), V1) -> mark U22 isNat V1,
active U32 X -> U32 active X,
active U32 tt() -> mark tt(),
active U31(X1, X2) -> U31(active X1, X2),
active U31(tt(), V) -> mark U32 isNatList V,
active U42(X1, X2) -> U42(active X1, X2),
active U42(tt(), V2) -> mark U43 isNatIList V2,
active U41(X1, X2, X3) -> U41(active X1, X2, X3),
active U41(tt(), V1, V2) -> mark U42(isNat V1, V2),
active U43 X -> U43 active X,
active U43 tt() -> mark tt(),
active isNatIList V -> mark U31(isNatIListKind V, V),
active isNatIList cons(V1, V2) -> mark U41(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatIList zeros() -> mark tt(),
active U52(X1, X2) -> U52(active X1, X2),
active U52(tt(), V2) -> mark U53 isNatList V2,
active U51(X1, X2, X3) -> U51(active X1, X2, X3),
active U51(tt(), V1, V2) -> mark U52(isNat V1, V2),
active U53 X -> U53 active X,
active U53 tt() -> mark tt(),
active U62(X1, X2) -> U62(active X1, X2),
active U62(tt(), V2) -> mark U63 isNatIList V2,
active U61(X1, X2, X3) -> U61(active X1, X2, X3),
active U61(tt(), V1, V2) -> mark U62(isNat V1, V2),
active U63 X -> U63 active X,
active U63 tt() -> mark tt(),
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark U71(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L),
active length nil() -> mark 0(),
active U71(X1, X2) -> U71(active X1, X2),
active U71(tt(), L) -> mark s length L,
active U81 X -> U81 active X,
active U81 tt() -> mark nil(),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark U81 and(isNatIList IL, isNatIListKind IL),
active take(s M, cons(N, IL)) -> mark U91(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N),
active U91(X1, X2, X3, X4) -> U91(active X1, X2, X3, X4),
active U91(tt(), IL, M, N) -> mark cons(N, take(M, IL)),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), X) -> mark X,
active isNatIListKind cons(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatIListKind zeros() -> mark tt(),
active isNatIListKind nil() -> mark tt(),
active isNatIListKind take(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatKind 0() -> mark tt(),
active isNatKind s V1 -> mark isNatKind V1,
active isNatKind length V1 -> mark isNatIListKind V1,
U12 mark X -> mark U12 X,
U12 ok X -> ok U12 X,
isNatList ok X -> ok isNatList X,
U11(mark X1, X2) -> mark U11(X1, X2),
U11(ok X1, ok X2) -> ok U11(X1, X2),
U22 mark X -> mark U22 X,
U22 ok X -> ok U22 X,
isNat ok X -> ok isNat X,
U21(mark X1, X2) -> mark U21(X1, X2),
U21(ok X1, ok X2) -> ok U21(X1, X2),
U32 mark X -> mark U32 X,
U32 ok X -> ok U32 X,
U31(mark X1, X2) -> mark U31(X1, X2),
U31(ok X1, ok X2) -> ok U31(X1, X2),
U42(mark X1, X2) -> mark U42(X1, X2),
U42(ok X1, ok X2) -> ok U42(X1, X2),
U41(mark X1, X2, X3) -> mark U41(X1, X2, X3),
U41(ok X1, ok X2, ok X3) -> ok U41(X1, X2, X3),
U43 mark X -> mark U43 X,
U43 ok X -> ok U43 X,
isNatIList ok X -> ok isNatIList X,
U52(mark X1, X2) -> mark U52(X1, X2),
U52(ok X1, ok X2) -> ok U52(X1, X2),
U51(mark X1, X2, X3) -> mark U51(X1, X2, X3),
U51(ok X1, ok X2, ok X3) -> ok U51(X1, X2, X3),
U53 mark X -> mark U53 X,
U53 ok X -> ok U53 X,
U62(mark X1, X2) -> mark U62(X1, X2),
U62(ok X1, ok X2) -> ok U62(X1, X2),
U61(mark X1, X2, X3) -> mark U61(X1, X2, X3),
U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3),
U63 mark X -> mark U63 X,
U63 ok X -> ok U63 X,
s mark X -> mark s X,
s ok X -> ok s X,
length mark X -> mark length X,
length ok X -> ok length X,
U71(mark X1, X2) -> mark U71(X1, X2),
U71(ok X1, ok X2) -> ok U71(X1, X2),
U81 mark X -> mark U81 X,
U81 ok X -> ok U81 X,
take(X1, mark X2) -> mark take(X1, X2),
take(mark X1, X2) -> mark take(X1, X2),
take(ok X1, ok X2) -> ok take(X1, X2),
U91(mark X1, X2, X3, X4) -> mark U91(X1, X2, X3, X4),
U91(ok X1, ok X2, ok X3, ok X4) -> ok U91(X1, X2, X3, X4),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatIListKind ok X -> ok isNatIListKind X,
isNatKind ok X -> ok isNatKind X,
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper 0() -> ok 0(),
proper zeros() -> ok zeros(),
proper U12 X -> U12 proper X,
proper isNatList X -> isNatList proper X,
proper U11(X1, X2) -> U11(proper X1, proper X2),
proper tt() -> ok tt(),
proper U22 X -> U22 proper X,
proper isNat X -> isNat proper X,
proper U21(X1, X2) -> U21(proper X1, proper X2),
proper U32 X -> U32 proper X,
proper U31(X1, X2) -> U31(proper X1, proper X2),
proper U42(X1, X2) -> U42(proper X1, proper X2),
proper U41(X1, X2, X3) -> U41(proper X1, proper X2, proper X3),
proper U43 X -> U43 proper X,
proper isNatIList X -> isNatIList proper X,
proper U52(X1, X2) -> U52(proper X1, proper X2),
proper U51(X1, X2, X3) -> U51(proper X1, proper X2, proper X3),
proper U53 X -> U53 proper X,
proper U62(X1, X2) -> U62(proper X1, proper X2),
proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3),
proper U63 X -> U63 proper X,
proper s X -> s proper X,
proper length X -> length proper X,
proper U71(X1, X2) -> U71(proper X1, proper X2),
proper nil() -> ok nil(),
proper U81 X -> U81 proper X,
proper take(X1, X2) -> take(proper X1, proper X2),
proper U91(X1, X2, X3, X4) -> U91(proper X1, proper X2, proper X3, proper X4),
proper and(X1, X2) -> and(proper X1, proper X2),
proper isNatIListKind X -> isNatIListKind proper X,
proper isNatKind X -> isNatKind proper X,
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (2):
Strict:
{U63# mark X -> U63# X,
U63# ok X -> U63# X}
Weak:
{ cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
active cons(X1, X2) -> cons(active X1, X2),
active zeros() -> mark cons(0(), zeros()),
active U12 X -> U12 active X,
active U12 tt() -> mark tt(),
active isNatList cons(V1, V2) -> mark U51(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatList nil() -> mark tt(),
active isNatList take(V1, V2) -> mark U61(and(isNatKind V1, isNatIListKind V2), V1, V2),
active U11(X1, X2) -> U11(active X1, X2),
active U11(tt(), V1) -> mark U12 isNatList V1,
active U22 X -> U22 active X,
active U22 tt() -> mark tt(),
active isNat 0() -> mark tt(),
active isNat s V1 -> mark U21(isNatKind V1, V1),
active isNat length V1 -> mark U11(isNatIListKind V1, V1),
active U21(X1, X2) -> U21(active X1, X2),
active U21(tt(), V1) -> mark U22 isNat V1,
active U32 X -> U32 active X,
active U32 tt() -> mark tt(),
active U31(X1, X2) -> U31(active X1, X2),
active U31(tt(), V) -> mark U32 isNatList V,
active U42(X1, X2) -> U42(active X1, X2),
active U42(tt(), V2) -> mark U43 isNatIList V2,
active U41(X1, X2, X3) -> U41(active X1, X2, X3),
active U41(tt(), V1, V2) -> mark U42(isNat V1, V2),
active U43 X -> U43 active X,
active U43 tt() -> mark tt(),
active isNatIList V -> mark U31(isNatIListKind V, V),
active isNatIList cons(V1, V2) -> mark U41(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatIList zeros() -> mark tt(),
active U52(X1, X2) -> U52(active X1, X2),
active U52(tt(), V2) -> mark U53 isNatList V2,
active U51(X1, X2, X3) -> U51(active X1, X2, X3),
active U51(tt(), V1, V2) -> mark U52(isNat V1, V2),
active U53 X -> U53 active X,
active U53 tt() -> mark tt(),
active U62(X1, X2) -> U62(active X1, X2),
active U62(tt(), V2) -> mark U63 isNatIList V2,
active U61(X1, X2, X3) -> U61(active X1, X2, X3),
active U61(tt(), V1, V2) -> mark U62(isNat V1, V2),
active U63 X -> U63 active X,
active U63 tt() -> mark tt(),
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark U71(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L),
active length nil() -> mark 0(),
active U71(X1, X2) -> U71(active X1, X2),
active U71(tt(), L) -> mark s length L,
active U81 X -> U81 active X,
active U81 tt() -> mark nil(),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark U81 and(isNatIList IL, isNatIListKind IL),
active take(s M, cons(N, IL)) -> mark U91(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N),
active U91(X1, X2, X3, X4) -> U91(active X1, X2, X3, X4),
active U91(tt(), IL, M, N) -> mark cons(N, take(M, IL)),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), X) -> mark X,
active isNatIListKind cons(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatIListKind zeros() -> mark tt(),
active isNatIListKind nil() -> mark tt(),
active isNatIListKind take(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatKind 0() -> mark tt(),
active isNatKind s V1 -> mark isNatKind V1,
active isNatKind length V1 -> mark isNatIListKind V1,
U12 mark X -> mark U12 X,
U12 ok X -> ok U12 X,
isNatList ok X -> ok isNatList X,
U11(mark X1, X2) -> mark U11(X1, X2),
U11(ok X1, ok X2) -> ok U11(X1, X2),
U22 mark X -> mark U22 X,
U22 ok X -> ok U22 X,
isNat ok X -> ok isNat X,
U21(mark X1, X2) -> mark U21(X1, X2),
U21(ok X1, ok X2) -> ok U21(X1, X2),
U32 mark X -> mark U32 X,
U32 ok X -> ok U32 X,
U31(mark X1, X2) -> mark U31(X1, X2),
U31(ok X1, ok X2) -> ok U31(X1, X2),
U42(mark X1, X2) -> mark U42(X1, X2),
U42(ok X1, ok X2) -> ok U42(X1, X2),
U41(mark X1, X2, X3) -> mark U41(X1, X2, X3),
U41(ok X1, ok X2, ok X3) -> ok U41(X1, X2, X3),
U43 mark X -> mark U43 X,
U43 ok X -> ok U43 X,
isNatIList ok X -> ok isNatIList X,
U52(mark X1, X2) -> mark U52(X1, X2),
U52(ok X1, ok X2) -> ok U52(X1, X2),
U51(mark X1, X2, X3) -> mark U51(X1, X2, X3),
U51(ok X1, ok X2, ok X3) -> ok U51(X1, X2, X3),
U53 mark X -> mark U53 X,
U53 ok X -> ok U53 X,
U62(mark X1, X2) -> mark U62(X1, X2),
U62(ok X1, ok X2) -> ok U62(X1, X2),
U61(mark X1, X2, X3) -> mark U61(X1, X2, X3),
U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3),
U63 mark X -> mark U63 X,
U63 ok X -> ok U63 X,
s mark X -> mark s X,
s ok X -> ok s X,
length mark X -> mark length X,
length ok X -> ok length X,
U71(mark X1, X2) -> mark U71(X1, X2),
U71(ok X1, ok X2) -> ok U71(X1, X2),
U81 mark X -> mark U81 X,
U81 ok X -> ok U81 X,
take(X1, mark X2) -> mark take(X1, X2),
take(mark X1, X2) -> mark take(X1, X2),
take(ok X1, ok X2) -> ok take(X1, X2),
U91(mark X1, X2, X3, X4) -> mark U91(X1, X2, X3, X4),
U91(ok X1, ok X2, ok X3, ok X4) -> ok U91(X1, X2, X3, X4),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatIListKind ok X -> ok isNatIListKind X,
isNatKind ok X -> ok isNatKind X,
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper 0() -> ok 0(),
proper zeros() -> ok zeros(),
proper U12 X -> U12 proper X,
proper isNatList X -> isNatList proper X,
proper U11(X1, X2) -> U11(proper X1, proper X2),
proper tt() -> ok tt(),
proper U22 X -> U22 proper X,
proper isNat X -> isNat proper X,
proper U21(X1, X2) -> U21(proper X1, proper X2),
proper U32 X -> U32 proper X,
proper U31(X1, X2) -> U31(proper X1, proper X2),
proper U42(X1, X2) -> U42(proper X1, proper X2),
proper U41(X1, X2, X3) -> U41(proper X1, proper X2, proper X3),
proper U43 X -> U43 proper X,
proper isNatIList X -> isNatIList proper X,
proper U52(X1, X2) -> U52(proper X1, proper X2),
proper U51(X1, X2, X3) -> U51(proper X1, proper X2, proper X3),
proper U53 X -> U53 proper X,
proper U62(X1, X2) -> U62(proper X1, proper X2),
proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3),
proper U63 X -> U63 proper X,
proper s X -> s proper X,
proper length X -> length proper X,
proper U71(X1, X2) -> U71(proper X1, proper X2),
proper nil() -> ok nil(),
proper U81 X -> U81 proper X,
proper take(X1, X2) -> take(proper X1, proper X2),
proper U91(X1, X2, X3, X4) -> U91(proper X1, proper X2, proper X3, proper X4),
proper and(X1, X2) -> and(proper X1, proper X2),
proper isNatIListKind X -> isNatIListKind proper X,
proper isNatKind X -> isNatKind proper X,
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (2):
Strict:
{ U62#(mark X1, X2) -> U62#(X1, X2),
U62#(ok X1, ok X2) -> U62#(X1, X2)}
Weak:
{ cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
active cons(X1, X2) -> cons(active X1, X2),
active zeros() -> mark cons(0(), zeros()),
active U12 X -> U12 active X,
active U12 tt() -> mark tt(),
active isNatList cons(V1, V2) -> mark U51(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatList nil() -> mark tt(),
active isNatList take(V1, V2) -> mark U61(and(isNatKind V1, isNatIListKind V2), V1, V2),
active U11(X1, X2) -> U11(active X1, X2),
active U11(tt(), V1) -> mark U12 isNatList V1,
active U22 X -> U22 active X,
active U22 tt() -> mark tt(),
active isNat 0() -> mark tt(),
active isNat s V1 -> mark U21(isNatKind V1, V1),
active isNat length V1 -> mark U11(isNatIListKind V1, V1),
active U21(X1, X2) -> U21(active X1, X2),
active U21(tt(), V1) -> mark U22 isNat V1,
active U32 X -> U32 active X,
active U32 tt() -> mark tt(),
active U31(X1, X2) -> U31(active X1, X2),
active U31(tt(), V) -> mark U32 isNatList V,
active U42(X1, X2) -> U42(active X1, X2),
active U42(tt(), V2) -> mark U43 isNatIList V2,
active U41(X1, X2, X3) -> U41(active X1, X2, X3),
active U41(tt(), V1, V2) -> mark U42(isNat V1, V2),
active U43 X -> U43 active X,
active U43 tt() -> mark tt(),
active isNatIList V -> mark U31(isNatIListKind V, V),
active isNatIList cons(V1, V2) -> mark U41(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatIList zeros() -> mark tt(),
active U52(X1, X2) -> U52(active X1, X2),
active U52(tt(), V2) -> mark U53 isNatList V2,
active U51(X1, X2, X3) -> U51(active X1, X2, X3),
active U51(tt(), V1, V2) -> mark U52(isNat V1, V2),
active U53 X -> U53 active X,
active U53 tt() -> mark tt(),
active U62(X1, X2) -> U62(active X1, X2),
active U62(tt(), V2) -> mark U63 isNatIList V2,
active U61(X1, X2, X3) -> U61(active X1, X2, X3),
active U61(tt(), V1, V2) -> mark U62(isNat V1, V2),
active U63 X -> U63 active X,
active U63 tt() -> mark tt(),
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark U71(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L),
active length nil() -> mark 0(),
active U71(X1, X2) -> U71(active X1, X2),
active U71(tt(), L) -> mark s length L,
active U81 X -> U81 active X,
active U81 tt() -> mark nil(),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark U81 and(isNatIList IL, isNatIListKind IL),
active take(s M, cons(N, IL)) -> mark U91(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N),
active U91(X1, X2, X3, X4) -> U91(active X1, X2, X3, X4),
active U91(tt(), IL, M, N) -> mark cons(N, take(M, IL)),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), X) -> mark X,
active isNatIListKind cons(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatIListKind zeros() -> mark tt(),
active isNatIListKind nil() -> mark tt(),
active isNatIListKind take(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatKind 0() -> mark tt(),
active isNatKind s V1 -> mark isNatKind V1,
active isNatKind length V1 -> mark isNatIListKind V1,
U12 mark X -> mark U12 X,
U12 ok X -> ok U12 X,
isNatList ok X -> ok isNatList X,
U11(mark X1, X2) -> mark U11(X1, X2),
U11(ok X1, ok X2) -> ok U11(X1, X2),
U22 mark X -> mark U22 X,
U22 ok X -> ok U22 X,
isNat ok X -> ok isNat X,
U21(mark X1, X2) -> mark U21(X1, X2),
U21(ok X1, ok X2) -> ok U21(X1, X2),
U32 mark X -> mark U32 X,
U32 ok X -> ok U32 X,
U31(mark X1, X2) -> mark U31(X1, X2),
U31(ok X1, ok X2) -> ok U31(X1, X2),
U42(mark X1, X2) -> mark U42(X1, X2),
U42(ok X1, ok X2) -> ok U42(X1, X2),
U41(mark X1, X2, X3) -> mark U41(X1, X2, X3),
U41(ok X1, ok X2, ok X3) -> ok U41(X1, X2, X3),
U43 mark X -> mark U43 X,
U43 ok X -> ok U43 X,
isNatIList ok X -> ok isNatIList X,
U52(mark X1, X2) -> mark U52(X1, X2),
U52(ok X1, ok X2) -> ok U52(X1, X2),
U51(mark X1, X2, X3) -> mark U51(X1, X2, X3),
U51(ok X1, ok X2, ok X3) -> ok U51(X1, X2, X3),
U53 mark X -> mark U53 X,
U53 ok X -> ok U53 X,
U62(mark X1, X2) -> mark U62(X1, X2),
U62(ok X1, ok X2) -> ok U62(X1, X2),
U61(mark X1, X2, X3) -> mark U61(X1, X2, X3),
U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3),
U63 mark X -> mark U63 X,
U63 ok X -> ok U63 X,
s mark X -> mark s X,
s ok X -> ok s X,
length mark X -> mark length X,
length ok X -> ok length X,
U71(mark X1, X2) -> mark U71(X1, X2),
U71(ok X1, ok X2) -> ok U71(X1, X2),
U81 mark X -> mark U81 X,
U81 ok X -> ok U81 X,
take(X1, mark X2) -> mark take(X1, X2),
take(mark X1, X2) -> mark take(X1, X2),
take(ok X1, ok X2) -> ok take(X1, X2),
U91(mark X1, X2, X3, X4) -> mark U91(X1, X2, X3, X4),
U91(ok X1, ok X2, ok X3, ok X4) -> ok U91(X1, X2, X3, X4),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatIListKind ok X -> ok isNatIListKind X,
isNatKind ok X -> ok isNatKind X,
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper 0() -> ok 0(),
proper zeros() -> ok zeros(),
proper U12 X -> U12 proper X,
proper isNatList X -> isNatList proper X,
proper U11(X1, X2) -> U11(proper X1, proper X2),
proper tt() -> ok tt(),
proper U22 X -> U22 proper X,
proper isNat X -> isNat proper X,
proper U21(X1, X2) -> U21(proper X1, proper X2),
proper U32 X -> U32 proper X,
proper U31(X1, X2) -> U31(proper X1, proper X2),
proper U42(X1, X2) -> U42(proper X1, proper X2),
proper U41(X1, X2, X3) -> U41(proper X1, proper X2, proper X3),
proper U43 X -> U43 proper X,
proper isNatIList X -> isNatIList proper X,
proper U52(X1, X2) -> U52(proper X1, proper X2),
proper U51(X1, X2, X3) -> U51(proper X1, proper X2, proper X3),
proper U53 X -> U53 proper X,
proper U62(X1, X2) -> U62(proper X1, proper X2),
proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3),
proper U63 X -> U63 proper X,
proper s X -> s proper X,
proper length X -> length proper X,
proper U71(X1, X2) -> U71(proper X1, proper X2),
proper nil() -> ok nil(),
proper U81 X -> U81 proper X,
proper take(X1, X2) -> take(proper X1, proper X2),
proper U91(X1, X2, X3, X4) -> U91(proper X1, proper X2, proper X3, proper X4),
proper and(X1, X2) -> and(proper X1, proper X2),
proper isNatIListKind X -> isNatIListKind proper X,
proper isNatKind X -> isNatKind proper X,
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (2):
Strict:
{U53# mark X -> U53# X,
U53# ok X -> U53# X}
Weak:
{ cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
active cons(X1, X2) -> cons(active X1, X2),
active zeros() -> mark cons(0(), zeros()),
active U12 X -> U12 active X,
active U12 tt() -> mark tt(),
active isNatList cons(V1, V2) -> mark U51(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatList nil() -> mark tt(),
active isNatList take(V1, V2) -> mark U61(and(isNatKind V1, isNatIListKind V2), V1, V2),
active U11(X1, X2) -> U11(active X1, X2),
active U11(tt(), V1) -> mark U12 isNatList V1,
active U22 X -> U22 active X,
active U22 tt() -> mark tt(),
active isNat 0() -> mark tt(),
active isNat s V1 -> mark U21(isNatKind V1, V1),
active isNat length V1 -> mark U11(isNatIListKind V1, V1),
active U21(X1, X2) -> U21(active X1, X2),
active U21(tt(), V1) -> mark U22 isNat V1,
active U32 X -> U32 active X,
active U32 tt() -> mark tt(),
active U31(X1, X2) -> U31(active X1, X2),
active U31(tt(), V) -> mark U32 isNatList V,
active U42(X1, X2) -> U42(active X1, X2),
active U42(tt(), V2) -> mark U43 isNatIList V2,
active U41(X1, X2, X3) -> U41(active X1, X2, X3),
active U41(tt(), V1, V2) -> mark U42(isNat V1, V2),
active U43 X -> U43 active X,
active U43 tt() -> mark tt(),
active isNatIList V -> mark U31(isNatIListKind V, V),
active isNatIList cons(V1, V2) -> mark U41(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatIList zeros() -> mark tt(),
active U52(X1, X2) -> U52(active X1, X2),
active U52(tt(), V2) -> mark U53 isNatList V2,
active U51(X1, X2, X3) -> U51(active X1, X2, X3),
active U51(tt(), V1, V2) -> mark U52(isNat V1, V2),
active U53 X -> U53 active X,
active U53 tt() -> mark tt(),
active U62(X1, X2) -> U62(active X1, X2),
active U62(tt(), V2) -> mark U63 isNatIList V2,
active U61(X1, X2, X3) -> U61(active X1, X2, X3),
active U61(tt(), V1, V2) -> mark U62(isNat V1, V2),
active U63 X -> U63 active X,
active U63 tt() -> mark tt(),
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark U71(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L),
active length nil() -> mark 0(),
active U71(X1, X2) -> U71(active X1, X2),
active U71(tt(), L) -> mark s length L,
active U81 X -> U81 active X,
active U81 tt() -> mark nil(),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark U81 and(isNatIList IL, isNatIListKind IL),
active take(s M, cons(N, IL)) -> mark U91(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N),
active U91(X1, X2, X3, X4) -> U91(active X1, X2, X3, X4),
active U91(tt(), IL, M, N) -> mark cons(N, take(M, IL)),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), X) -> mark X,
active isNatIListKind cons(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatIListKind zeros() -> mark tt(),
active isNatIListKind nil() -> mark tt(),
active isNatIListKind take(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatKind 0() -> mark tt(),
active isNatKind s V1 -> mark isNatKind V1,
active isNatKind length V1 -> mark isNatIListKind V1,
U12 mark X -> mark U12 X,
U12 ok X -> ok U12 X,
isNatList ok X -> ok isNatList X,
U11(mark X1, X2) -> mark U11(X1, X2),
U11(ok X1, ok X2) -> ok U11(X1, X2),
U22 mark X -> mark U22 X,
U22 ok X -> ok U22 X,
isNat ok X -> ok isNat X,
U21(mark X1, X2) -> mark U21(X1, X2),
U21(ok X1, ok X2) -> ok U21(X1, X2),
U32 mark X -> mark U32 X,
U32 ok X -> ok U32 X,
U31(mark X1, X2) -> mark U31(X1, X2),
U31(ok X1, ok X2) -> ok U31(X1, X2),
U42(mark X1, X2) -> mark U42(X1, X2),
U42(ok X1, ok X2) -> ok U42(X1, X2),
U41(mark X1, X2, X3) -> mark U41(X1, X2, X3),
U41(ok X1, ok X2, ok X3) -> ok U41(X1, X2, X3),
U43 mark X -> mark U43 X,
U43 ok X -> ok U43 X,
isNatIList ok X -> ok isNatIList X,
U52(mark X1, X2) -> mark U52(X1, X2),
U52(ok X1, ok X2) -> ok U52(X1, X2),
U51(mark X1, X2, X3) -> mark U51(X1, X2, X3),
U51(ok X1, ok X2, ok X3) -> ok U51(X1, X2, X3),
U53 mark X -> mark U53 X,
U53 ok X -> ok U53 X,
U62(mark X1, X2) -> mark U62(X1, X2),
U62(ok X1, ok X2) -> ok U62(X1, X2),
U61(mark X1, X2, X3) -> mark U61(X1, X2, X3),
U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3),
U63 mark X -> mark U63 X,
U63 ok X -> ok U63 X,
s mark X -> mark s X,
s ok X -> ok s X,
length mark X -> mark length X,
length ok X -> ok length X,
U71(mark X1, X2) -> mark U71(X1, X2),
U71(ok X1, ok X2) -> ok U71(X1, X2),
U81 mark X -> mark U81 X,
U81 ok X -> ok U81 X,
take(X1, mark X2) -> mark take(X1, X2),
take(mark X1, X2) -> mark take(X1, X2),
take(ok X1, ok X2) -> ok take(X1, X2),
U91(mark X1, X2, X3, X4) -> mark U91(X1, X2, X3, X4),
U91(ok X1, ok X2, ok X3, ok X4) -> ok U91(X1, X2, X3, X4),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatIListKind ok X -> ok isNatIListKind X,
isNatKind ok X -> ok isNatKind X,
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper 0() -> ok 0(),
proper zeros() -> ok zeros(),
proper U12 X -> U12 proper X,
proper isNatList X -> isNatList proper X,
proper U11(X1, X2) -> U11(proper X1, proper X2),
proper tt() -> ok tt(),
proper U22 X -> U22 proper X,
proper isNat X -> isNat proper X,
proper U21(X1, X2) -> U21(proper X1, proper X2),
proper U32 X -> U32 proper X,
proper U31(X1, X2) -> U31(proper X1, proper X2),
proper U42(X1, X2) -> U42(proper X1, proper X2),
proper U41(X1, X2, X3) -> U41(proper X1, proper X2, proper X3),
proper U43 X -> U43 proper X,
proper isNatIList X -> isNatIList proper X,
proper U52(X1, X2) -> U52(proper X1, proper X2),
proper U51(X1, X2, X3) -> U51(proper X1, proper X2, proper X3),
proper U53 X -> U53 proper X,
proper U62(X1, X2) -> U62(proper X1, proper X2),
proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3),
proper U63 X -> U63 proper X,
proper s X -> s proper X,
proper length X -> length proper X,
proper U71(X1, X2) -> U71(proper X1, proper X2),
proper nil() -> ok nil(),
proper U81 X -> U81 proper X,
proper take(X1, X2) -> take(proper X1, proper X2),
proper U91(X1, X2, X3, X4) -> U91(proper X1, proper X2, proper X3, proper X4),
proper and(X1, X2) -> and(proper X1, proper X2),
proper isNatIListKind X -> isNatIListKind proper X,
proper isNatKind X -> isNatKind proper X,
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (2):
Strict:
{ U52#(mark X1, X2) -> U52#(X1, X2),
U52#(ok X1, ok X2) -> U52#(X1, X2)}
Weak:
{ cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
active cons(X1, X2) -> cons(active X1, X2),
active zeros() -> mark cons(0(), zeros()),
active U12 X -> U12 active X,
active U12 tt() -> mark tt(),
active isNatList cons(V1, V2) -> mark U51(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatList nil() -> mark tt(),
active isNatList take(V1, V2) -> mark U61(and(isNatKind V1, isNatIListKind V2), V1, V2),
active U11(X1, X2) -> U11(active X1, X2),
active U11(tt(), V1) -> mark U12 isNatList V1,
active U22 X -> U22 active X,
active U22 tt() -> mark tt(),
active isNat 0() -> mark tt(),
active isNat s V1 -> mark U21(isNatKind V1, V1),
active isNat length V1 -> mark U11(isNatIListKind V1, V1),
active U21(X1, X2) -> U21(active X1, X2),
active U21(tt(), V1) -> mark U22 isNat V1,
active U32 X -> U32 active X,
active U32 tt() -> mark tt(),
active U31(X1, X2) -> U31(active X1, X2),
active U31(tt(), V) -> mark U32 isNatList V,
active U42(X1, X2) -> U42(active X1, X2),
active U42(tt(), V2) -> mark U43 isNatIList V2,
active U41(X1, X2, X3) -> U41(active X1, X2, X3),
active U41(tt(), V1, V2) -> mark U42(isNat V1, V2),
active U43 X -> U43 active X,
active U43 tt() -> mark tt(),
active isNatIList V -> mark U31(isNatIListKind V, V),
active isNatIList cons(V1, V2) -> mark U41(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatIList zeros() -> mark tt(),
active U52(X1, X2) -> U52(active X1, X2),
active U52(tt(), V2) -> mark U53 isNatList V2,
active U51(X1, X2, X3) -> U51(active X1, X2, X3),
active U51(tt(), V1, V2) -> mark U52(isNat V1, V2),
active U53 X -> U53 active X,
active U53 tt() -> mark tt(),
active U62(X1, X2) -> U62(active X1, X2),
active U62(tt(), V2) -> mark U63 isNatIList V2,
active U61(X1, X2, X3) -> U61(active X1, X2, X3),
active U61(tt(), V1, V2) -> mark U62(isNat V1, V2),
active U63 X -> U63 active X,
active U63 tt() -> mark tt(),
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark U71(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L),
active length nil() -> mark 0(),
active U71(X1, X2) -> U71(active X1, X2),
active U71(tt(), L) -> mark s length L,
active U81 X -> U81 active X,
active U81 tt() -> mark nil(),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark U81 and(isNatIList IL, isNatIListKind IL),
active take(s M, cons(N, IL)) -> mark U91(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N),
active U91(X1, X2, X3, X4) -> U91(active X1, X2, X3, X4),
active U91(tt(), IL, M, N) -> mark cons(N, take(M, IL)),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), X) -> mark X,
active isNatIListKind cons(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatIListKind zeros() -> mark tt(),
active isNatIListKind nil() -> mark tt(),
active isNatIListKind take(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatKind 0() -> mark tt(),
active isNatKind s V1 -> mark isNatKind V1,
active isNatKind length V1 -> mark isNatIListKind V1,
U12 mark X -> mark U12 X,
U12 ok X -> ok U12 X,
isNatList ok X -> ok isNatList X,
U11(mark X1, X2) -> mark U11(X1, X2),
U11(ok X1, ok X2) -> ok U11(X1, X2),
U22 mark X -> mark U22 X,
U22 ok X -> ok U22 X,
isNat ok X -> ok isNat X,
U21(mark X1, X2) -> mark U21(X1, X2),
U21(ok X1, ok X2) -> ok U21(X1, X2),
U32 mark X -> mark U32 X,
U32 ok X -> ok U32 X,
U31(mark X1, X2) -> mark U31(X1, X2),
U31(ok X1, ok X2) -> ok U31(X1, X2),
U42(mark X1, X2) -> mark U42(X1, X2),
U42(ok X1, ok X2) -> ok U42(X1, X2),
U41(mark X1, X2, X3) -> mark U41(X1, X2, X3),
U41(ok X1, ok X2, ok X3) -> ok U41(X1, X2, X3),
U43 mark X -> mark U43 X,
U43 ok X -> ok U43 X,
isNatIList ok X -> ok isNatIList X,
U52(mark X1, X2) -> mark U52(X1, X2),
U52(ok X1, ok X2) -> ok U52(X1, X2),
U51(mark X1, X2, X3) -> mark U51(X1, X2, X3),
U51(ok X1, ok X2, ok X3) -> ok U51(X1, X2, X3),
U53 mark X -> mark U53 X,
U53 ok X -> ok U53 X,
U62(mark X1, X2) -> mark U62(X1, X2),
U62(ok X1, ok X2) -> ok U62(X1, X2),
U61(mark X1, X2, X3) -> mark U61(X1, X2, X3),
U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3),
U63 mark X -> mark U63 X,
U63 ok X -> ok U63 X,
s mark X -> mark s X,
s ok X -> ok s X,
length mark X -> mark length X,
length ok X -> ok length X,
U71(mark X1, X2) -> mark U71(X1, X2),
U71(ok X1, ok X2) -> ok U71(X1, X2),
U81 mark X -> mark U81 X,
U81 ok X -> ok U81 X,
take(X1, mark X2) -> mark take(X1, X2),
take(mark X1, X2) -> mark take(X1, X2),
take(ok X1, ok X2) -> ok take(X1, X2),
U91(mark X1, X2, X3, X4) -> mark U91(X1, X2, X3, X4),
U91(ok X1, ok X2, ok X3, ok X4) -> ok U91(X1, X2, X3, X4),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatIListKind ok X -> ok isNatIListKind X,
isNatKind ok X -> ok isNatKind X,
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper 0() -> ok 0(),
proper zeros() -> ok zeros(),
proper U12 X -> U12 proper X,
proper isNatList X -> isNatList proper X,
proper U11(X1, X2) -> U11(proper X1, proper X2),
proper tt() -> ok tt(),
proper U22 X -> U22 proper X,
proper isNat X -> isNat proper X,
proper U21(X1, X2) -> U21(proper X1, proper X2),
proper U32 X -> U32 proper X,
proper U31(X1, X2) -> U31(proper X1, proper X2),
proper U42(X1, X2) -> U42(proper X1, proper X2),
proper U41(X1, X2, X3) -> U41(proper X1, proper X2, proper X3),
proper U43 X -> U43 proper X,
proper isNatIList X -> isNatIList proper X,
proper U52(X1, X2) -> U52(proper X1, proper X2),
proper U51(X1, X2, X3) -> U51(proper X1, proper X2, proper X3),
proper U53 X -> U53 proper X,
proper U62(X1, X2) -> U62(proper X1, proper X2),
proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3),
proper U63 X -> U63 proper X,
proper s X -> s proper X,
proper length X -> length proper X,
proper U71(X1, X2) -> U71(proper X1, proper X2),
proper nil() -> ok nil(),
proper U81 X -> U81 proper X,
proper take(X1, X2) -> take(proper X1, proper X2),
proper U91(X1, X2, X3, X4) -> U91(proper X1, proper X2, proper X3, proper X4),
proper and(X1, X2) -> and(proper X1, proper X2),
proper isNatIListKind X -> isNatIListKind proper X,
proper isNatKind X -> isNatKind proper X,
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (1):
Strict:
{isNatIList# ok X -> isNatIList# X}
Weak:
{ cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
active cons(X1, X2) -> cons(active X1, X2),
active zeros() -> mark cons(0(), zeros()),
active U12 X -> U12 active X,
active U12 tt() -> mark tt(),
active isNatList cons(V1, V2) -> mark U51(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatList nil() -> mark tt(),
active isNatList take(V1, V2) -> mark U61(and(isNatKind V1, isNatIListKind V2), V1, V2),
active U11(X1, X2) -> U11(active X1, X2),
active U11(tt(), V1) -> mark U12 isNatList V1,
active U22 X -> U22 active X,
active U22 tt() -> mark tt(),
active isNat 0() -> mark tt(),
active isNat s V1 -> mark U21(isNatKind V1, V1),
active isNat length V1 -> mark U11(isNatIListKind V1, V1),
active U21(X1, X2) -> U21(active X1, X2),
active U21(tt(), V1) -> mark U22 isNat V1,
active U32 X -> U32 active X,
active U32 tt() -> mark tt(),
active U31(X1, X2) -> U31(active X1, X2),
active U31(tt(), V) -> mark U32 isNatList V,
active U42(X1, X2) -> U42(active X1, X2),
active U42(tt(), V2) -> mark U43 isNatIList V2,
active U41(X1, X2, X3) -> U41(active X1, X2, X3),
active U41(tt(), V1, V2) -> mark U42(isNat V1, V2),
active U43 X -> U43 active X,
active U43 tt() -> mark tt(),
active isNatIList V -> mark U31(isNatIListKind V, V),
active isNatIList cons(V1, V2) -> mark U41(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatIList zeros() -> mark tt(),
active U52(X1, X2) -> U52(active X1, X2),
active U52(tt(), V2) -> mark U53 isNatList V2,
active U51(X1, X2, X3) -> U51(active X1, X2, X3),
active U51(tt(), V1, V2) -> mark U52(isNat V1, V2),
active U53 X -> U53 active X,
active U53 tt() -> mark tt(),
active U62(X1, X2) -> U62(active X1, X2),
active U62(tt(), V2) -> mark U63 isNatIList V2,
active U61(X1, X2, X3) -> U61(active X1, X2, X3),
active U61(tt(), V1, V2) -> mark U62(isNat V1, V2),
active U63 X -> U63 active X,
active U63 tt() -> mark tt(),
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark U71(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L),
active length nil() -> mark 0(),
active U71(X1, X2) -> U71(active X1, X2),
active U71(tt(), L) -> mark s length L,
active U81 X -> U81 active X,
active U81 tt() -> mark nil(),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark U81 and(isNatIList IL, isNatIListKind IL),
active take(s M, cons(N, IL)) -> mark U91(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N),
active U91(X1, X2, X3, X4) -> U91(active X1, X2, X3, X4),
active U91(tt(), IL, M, N) -> mark cons(N, take(M, IL)),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), X) -> mark X,
active isNatIListKind cons(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatIListKind zeros() -> mark tt(),
active isNatIListKind nil() -> mark tt(),
active isNatIListKind take(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatKind 0() -> mark tt(),
active isNatKind s V1 -> mark isNatKind V1,
active isNatKind length V1 -> mark isNatIListKind V1,
U12 mark X -> mark U12 X,
U12 ok X -> ok U12 X,
isNatList ok X -> ok isNatList X,
U11(mark X1, X2) -> mark U11(X1, X2),
U11(ok X1, ok X2) -> ok U11(X1, X2),
U22 mark X -> mark U22 X,
U22 ok X -> ok U22 X,
isNat ok X -> ok isNat X,
U21(mark X1, X2) -> mark U21(X1, X2),
U21(ok X1, ok X2) -> ok U21(X1, X2),
U32 mark X -> mark U32 X,
U32 ok X -> ok U32 X,
U31(mark X1, X2) -> mark U31(X1, X2),
U31(ok X1, ok X2) -> ok U31(X1, X2),
U42(mark X1, X2) -> mark U42(X1, X2),
U42(ok X1, ok X2) -> ok U42(X1, X2),
U41(mark X1, X2, X3) -> mark U41(X1, X2, X3),
U41(ok X1, ok X2, ok X3) -> ok U41(X1, X2, X3),
U43 mark X -> mark U43 X,
U43 ok X -> ok U43 X,
isNatIList ok X -> ok isNatIList X,
U52(mark X1, X2) -> mark U52(X1, X2),
U52(ok X1, ok X2) -> ok U52(X1, X2),
U51(mark X1, X2, X3) -> mark U51(X1, X2, X3),
U51(ok X1, ok X2, ok X3) -> ok U51(X1, X2, X3),
U53 mark X -> mark U53 X,
U53 ok X -> ok U53 X,
U62(mark X1, X2) -> mark U62(X1, X2),
U62(ok X1, ok X2) -> ok U62(X1, X2),
U61(mark X1, X2, X3) -> mark U61(X1, X2, X3),
U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3),
U63 mark X -> mark U63 X,
U63 ok X -> ok U63 X,
s mark X -> mark s X,
s ok X -> ok s X,
length mark X -> mark length X,
length ok X -> ok length X,
U71(mark X1, X2) -> mark U71(X1, X2),
U71(ok X1, ok X2) -> ok U71(X1, X2),
U81 mark X -> mark U81 X,
U81 ok X -> ok U81 X,
take(X1, mark X2) -> mark take(X1, X2),
take(mark X1, X2) -> mark take(X1, X2),
take(ok X1, ok X2) -> ok take(X1, X2),
U91(mark X1, X2, X3, X4) -> mark U91(X1, X2, X3, X4),
U91(ok X1, ok X2, ok X3, ok X4) -> ok U91(X1, X2, X3, X4),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatIListKind ok X -> ok isNatIListKind X,
isNatKind ok X -> ok isNatKind X,
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper 0() -> ok 0(),
proper zeros() -> ok zeros(),
proper U12 X -> U12 proper X,
proper isNatList X -> isNatList proper X,
proper U11(X1, X2) -> U11(proper X1, proper X2),
proper tt() -> ok tt(),
proper U22 X -> U22 proper X,
proper isNat X -> isNat proper X,
proper U21(X1, X2) -> U21(proper X1, proper X2),
proper U32 X -> U32 proper X,
proper U31(X1, X2) -> U31(proper X1, proper X2),
proper U42(X1, X2) -> U42(proper X1, proper X2),
proper U41(X1, X2, X3) -> U41(proper X1, proper X2, proper X3),
proper U43 X -> U43 proper X,
proper isNatIList X -> isNatIList proper X,
proper U52(X1, X2) -> U52(proper X1, proper X2),
proper U51(X1, X2, X3) -> U51(proper X1, proper X2, proper X3),
proper U53 X -> U53 proper X,
proper U62(X1, X2) -> U62(proper X1, proper X2),
proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3),
proper U63 X -> U63 proper X,
proper s X -> s proper X,
proper length X -> length proper X,
proper U71(X1, X2) -> U71(proper X1, proper X2),
proper nil() -> ok nil(),
proper U81 X -> U81 proper X,
proper take(X1, X2) -> take(proper X1, proper X2),
proper U91(X1, X2, X3, X4) -> U91(proper X1, proper X2, proper X3, proper X4),
proper and(X1, X2) -> and(proper X1, proper X2),
proper isNatIListKind X -> isNatIListKind proper X,
proper isNatKind X -> isNatKind proper X,
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (2):
Strict:
{U43# mark X -> U43# X,
U43# ok X -> U43# X}
Weak:
{ cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
active cons(X1, X2) -> cons(active X1, X2),
active zeros() -> mark cons(0(), zeros()),
active U12 X -> U12 active X,
active U12 tt() -> mark tt(),
active isNatList cons(V1, V2) -> mark U51(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatList nil() -> mark tt(),
active isNatList take(V1, V2) -> mark U61(and(isNatKind V1, isNatIListKind V2), V1, V2),
active U11(X1, X2) -> U11(active X1, X2),
active U11(tt(), V1) -> mark U12 isNatList V1,
active U22 X -> U22 active X,
active U22 tt() -> mark tt(),
active isNat 0() -> mark tt(),
active isNat s V1 -> mark U21(isNatKind V1, V1),
active isNat length V1 -> mark U11(isNatIListKind V1, V1),
active U21(X1, X2) -> U21(active X1, X2),
active U21(tt(), V1) -> mark U22 isNat V1,
active U32 X -> U32 active X,
active U32 tt() -> mark tt(),
active U31(X1, X2) -> U31(active X1, X2),
active U31(tt(), V) -> mark U32 isNatList V,
active U42(X1, X2) -> U42(active X1, X2),
active U42(tt(), V2) -> mark U43 isNatIList V2,
active U41(X1, X2, X3) -> U41(active X1, X2, X3),
active U41(tt(), V1, V2) -> mark U42(isNat V1, V2),
active U43 X -> U43 active X,
active U43 tt() -> mark tt(),
active isNatIList V -> mark U31(isNatIListKind V, V),
active isNatIList cons(V1, V2) -> mark U41(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatIList zeros() -> mark tt(),
active U52(X1, X2) -> U52(active X1, X2),
active U52(tt(), V2) -> mark U53 isNatList V2,
active U51(X1, X2, X3) -> U51(active X1, X2, X3),
active U51(tt(), V1, V2) -> mark U52(isNat V1, V2),
active U53 X -> U53 active X,
active U53 tt() -> mark tt(),
active U62(X1, X2) -> U62(active X1, X2),
active U62(tt(), V2) -> mark U63 isNatIList V2,
active U61(X1, X2, X3) -> U61(active X1, X2, X3),
active U61(tt(), V1, V2) -> mark U62(isNat V1, V2),
active U63 X -> U63 active X,
active U63 tt() -> mark tt(),
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark U71(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L),
active length nil() -> mark 0(),
active U71(X1, X2) -> U71(active X1, X2),
active U71(tt(), L) -> mark s length L,
active U81 X -> U81 active X,
active U81 tt() -> mark nil(),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark U81 and(isNatIList IL, isNatIListKind IL),
active take(s M, cons(N, IL)) -> mark U91(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N),
active U91(X1, X2, X3, X4) -> U91(active X1, X2, X3, X4),
active U91(tt(), IL, M, N) -> mark cons(N, take(M, IL)),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), X) -> mark X,
active isNatIListKind cons(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatIListKind zeros() -> mark tt(),
active isNatIListKind nil() -> mark tt(),
active isNatIListKind take(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatKind 0() -> mark tt(),
active isNatKind s V1 -> mark isNatKind V1,
active isNatKind length V1 -> mark isNatIListKind V1,
U12 mark X -> mark U12 X,
U12 ok X -> ok U12 X,
isNatList ok X -> ok isNatList X,
U11(mark X1, X2) -> mark U11(X1, X2),
U11(ok X1, ok X2) -> ok U11(X1, X2),
U22 mark X -> mark U22 X,
U22 ok X -> ok U22 X,
isNat ok X -> ok isNat X,
U21(mark X1, X2) -> mark U21(X1, X2),
U21(ok X1, ok X2) -> ok U21(X1, X2),
U32 mark X -> mark U32 X,
U32 ok X -> ok U32 X,
U31(mark X1, X2) -> mark U31(X1, X2),
U31(ok X1, ok X2) -> ok U31(X1, X2),
U42(mark X1, X2) -> mark U42(X1, X2),
U42(ok X1, ok X2) -> ok U42(X1, X2),
U41(mark X1, X2, X3) -> mark U41(X1, X2, X3),
U41(ok X1, ok X2, ok X3) -> ok U41(X1, X2, X3),
U43 mark X -> mark U43 X,
U43 ok X -> ok U43 X,
isNatIList ok X -> ok isNatIList X,
U52(mark X1, X2) -> mark U52(X1, X2),
U52(ok X1, ok X2) -> ok U52(X1, X2),
U51(mark X1, X2, X3) -> mark U51(X1, X2, X3),
U51(ok X1, ok X2, ok X3) -> ok U51(X1, X2, X3),
U53 mark X -> mark U53 X,
U53 ok X -> ok U53 X,
U62(mark X1, X2) -> mark U62(X1, X2),
U62(ok X1, ok X2) -> ok U62(X1, X2),
U61(mark X1, X2, X3) -> mark U61(X1, X2, X3),
U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3),
U63 mark X -> mark U63 X,
U63 ok X -> ok U63 X,
s mark X -> mark s X,
s ok X -> ok s X,
length mark X -> mark length X,
length ok X -> ok length X,
U71(mark X1, X2) -> mark U71(X1, X2),
U71(ok X1, ok X2) -> ok U71(X1, X2),
U81 mark X -> mark U81 X,
U81 ok X -> ok U81 X,
take(X1, mark X2) -> mark take(X1, X2),
take(mark X1, X2) -> mark take(X1, X2),
take(ok X1, ok X2) -> ok take(X1, X2),
U91(mark X1, X2, X3, X4) -> mark U91(X1, X2, X3, X4),
U91(ok X1, ok X2, ok X3, ok X4) -> ok U91(X1, X2, X3, X4),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatIListKind ok X -> ok isNatIListKind X,
isNatKind ok X -> ok isNatKind X,
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper 0() -> ok 0(),
proper zeros() -> ok zeros(),
proper U12 X -> U12 proper X,
proper isNatList X -> isNatList proper X,
proper U11(X1, X2) -> U11(proper X1, proper X2),
proper tt() -> ok tt(),
proper U22 X -> U22 proper X,
proper isNat X -> isNat proper X,
proper U21(X1, X2) -> U21(proper X1, proper X2),
proper U32 X -> U32 proper X,
proper U31(X1, X2) -> U31(proper X1, proper X2),
proper U42(X1, X2) -> U42(proper X1, proper X2),
proper U41(X1, X2, X3) -> U41(proper X1, proper X2, proper X3),
proper U43 X -> U43 proper X,
proper isNatIList X -> isNatIList proper X,
proper U52(X1, X2) -> U52(proper X1, proper X2),
proper U51(X1, X2, X3) -> U51(proper X1, proper X2, proper X3),
proper U53 X -> U53 proper X,
proper U62(X1, X2) -> U62(proper X1, proper X2),
proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3),
proper U63 X -> U63 proper X,
proper s X -> s proper X,
proper length X -> length proper X,
proper U71(X1, X2) -> U71(proper X1, proper X2),
proper nil() -> ok nil(),
proper U81 X -> U81 proper X,
proper take(X1, X2) -> take(proper X1, proper X2),
proper U91(X1, X2, X3, X4) -> U91(proper X1, proper X2, proper X3, proper X4),
proper and(X1, X2) -> and(proper X1, proper X2),
proper isNatIListKind X -> isNatIListKind proper X,
proper isNatKind X -> isNatKind proper X,
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (2):
Strict:
{ U42#(mark X1, X2) -> U42#(X1, X2),
U42#(ok X1, ok X2) -> U42#(X1, X2)}
Weak:
{ cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
active cons(X1, X2) -> cons(active X1, X2),
active zeros() -> mark cons(0(), zeros()),
active U12 X -> U12 active X,
active U12 tt() -> mark tt(),
active isNatList cons(V1, V2) -> mark U51(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatList nil() -> mark tt(),
active isNatList take(V1, V2) -> mark U61(and(isNatKind V1, isNatIListKind V2), V1, V2),
active U11(X1, X2) -> U11(active X1, X2),
active U11(tt(), V1) -> mark U12 isNatList V1,
active U22 X -> U22 active X,
active U22 tt() -> mark tt(),
active isNat 0() -> mark tt(),
active isNat s V1 -> mark U21(isNatKind V1, V1),
active isNat length V1 -> mark U11(isNatIListKind V1, V1),
active U21(X1, X2) -> U21(active X1, X2),
active U21(tt(), V1) -> mark U22 isNat V1,
active U32 X -> U32 active X,
active U32 tt() -> mark tt(),
active U31(X1, X2) -> U31(active X1, X2),
active U31(tt(), V) -> mark U32 isNatList V,
active U42(X1, X2) -> U42(active X1, X2),
active U42(tt(), V2) -> mark U43 isNatIList V2,
active U41(X1, X2, X3) -> U41(active X1, X2, X3),
active U41(tt(), V1, V2) -> mark U42(isNat V1, V2),
active U43 X -> U43 active X,
active U43 tt() -> mark tt(),
active isNatIList V -> mark U31(isNatIListKind V, V),
active isNatIList cons(V1, V2) -> mark U41(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatIList zeros() -> mark tt(),
active U52(X1, X2) -> U52(active X1, X2),
active U52(tt(), V2) -> mark U53 isNatList V2,
active U51(X1, X2, X3) -> U51(active X1, X2, X3),
active U51(tt(), V1, V2) -> mark U52(isNat V1, V2),
active U53 X -> U53 active X,
active U53 tt() -> mark tt(),
active U62(X1, X2) -> U62(active X1, X2),
active U62(tt(), V2) -> mark U63 isNatIList V2,
active U61(X1, X2, X3) -> U61(active X1, X2, X3),
active U61(tt(), V1, V2) -> mark U62(isNat V1, V2),
active U63 X -> U63 active X,
active U63 tt() -> mark tt(),
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark U71(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L),
active length nil() -> mark 0(),
active U71(X1, X2) -> U71(active X1, X2),
active U71(tt(), L) -> mark s length L,
active U81 X -> U81 active X,
active U81 tt() -> mark nil(),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark U81 and(isNatIList IL, isNatIListKind IL),
active take(s M, cons(N, IL)) -> mark U91(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N),
active U91(X1, X2, X3, X4) -> U91(active X1, X2, X3, X4),
active U91(tt(), IL, M, N) -> mark cons(N, take(M, IL)),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), X) -> mark X,
active isNatIListKind cons(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatIListKind zeros() -> mark tt(),
active isNatIListKind nil() -> mark tt(),
active isNatIListKind take(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatKind 0() -> mark tt(),
active isNatKind s V1 -> mark isNatKind V1,
active isNatKind length V1 -> mark isNatIListKind V1,
U12 mark X -> mark U12 X,
U12 ok X -> ok U12 X,
isNatList ok X -> ok isNatList X,
U11(mark X1, X2) -> mark U11(X1, X2),
U11(ok X1, ok X2) -> ok U11(X1, X2),
U22 mark X -> mark U22 X,
U22 ok X -> ok U22 X,
isNat ok X -> ok isNat X,
U21(mark X1, X2) -> mark U21(X1, X2),
U21(ok X1, ok X2) -> ok U21(X1, X2),
U32 mark X -> mark U32 X,
U32 ok X -> ok U32 X,
U31(mark X1, X2) -> mark U31(X1, X2),
U31(ok X1, ok X2) -> ok U31(X1, X2),
U42(mark X1, X2) -> mark U42(X1, X2),
U42(ok X1, ok X2) -> ok U42(X1, X2),
U41(mark X1, X2, X3) -> mark U41(X1, X2, X3),
U41(ok X1, ok X2, ok X3) -> ok U41(X1, X2, X3),
U43 mark X -> mark U43 X,
U43 ok X -> ok U43 X,
isNatIList ok X -> ok isNatIList X,
U52(mark X1, X2) -> mark U52(X1, X2),
U52(ok X1, ok X2) -> ok U52(X1, X2),
U51(mark X1, X2, X3) -> mark U51(X1, X2, X3),
U51(ok X1, ok X2, ok X3) -> ok U51(X1, X2, X3),
U53 mark X -> mark U53 X,
U53 ok X -> ok U53 X,
U62(mark X1, X2) -> mark U62(X1, X2),
U62(ok X1, ok X2) -> ok U62(X1, X2),
U61(mark X1, X2, X3) -> mark U61(X1, X2, X3),
U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3),
U63 mark X -> mark U63 X,
U63 ok X -> ok U63 X,
s mark X -> mark s X,
s ok X -> ok s X,
length mark X -> mark length X,
length ok X -> ok length X,
U71(mark X1, X2) -> mark U71(X1, X2),
U71(ok X1, ok X2) -> ok U71(X1, X2),
U81 mark X -> mark U81 X,
U81 ok X -> ok U81 X,
take(X1, mark X2) -> mark take(X1, X2),
take(mark X1, X2) -> mark take(X1, X2),
take(ok X1, ok X2) -> ok take(X1, X2),
U91(mark X1, X2, X3, X4) -> mark U91(X1, X2, X3, X4),
U91(ok X1, ok X2, ok X3, ok X4) -> ok U91(X1, X2, X3, X4),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatIListKind ok X -> ok isNatIListKind X,
isNatKind ok X -> ok isNatKind X,
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper 0() -> ok 0(),
proper zeros() -> ok zeros(),
proper U12 X -> U12 proper X,
proper isNatList X -> isNatList proper X,
proper U11(X1, X2) -> U11(proper X1, proper X2),
proper tt() -> ok tt(),
proper U22 X -> U22 proper X,
proper isNat X -> isNat proper X,
proper U21(X1, X2) -> U21(proper X1, proper X2),
proper U32 X -> U32 proper X,
proper U31(X1, X2) -> U31(proper X1, proper X2),
proper U42(X1, X2) -> U42(proper X1, proper X2),
proper U41(X1, X2, X3) -> U41(proper X1, proper X2, proper X3),
proper U43 X -> U43 proper X,
proper isNatIList X -> isNatIList proper X,
proper U52(X1, X2) -> U52(proper X1, proper X2),
proper U51(X1, X2, X3) -> U51(proper X1, proper X2, proper X3),
proper U53 X -> U53 proper X,
proper U62(X1, X2) -> U62(proper X1, proper X2),
proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3),
proper U63 X -> U63 proper X,
proper s X -> s proper X,
proper length X -> length proper X,
proper U71(X1, X2) -> U71(proper X1, proper X2),
proper nil() -> ok nil(),
proper U81 X -> U81 proper X,
proper take(X1, X2) -> take(proper X1, proper X2),
proper U91(X1, X2, X3, X4) -> U91(proper X1, proper X2, proper X3, proper X4),
proper and(X1, X2) -> and(proper X1, proper X2),
proper isNatIListKind X -> isNatIListKind proper X,
proper isNatKind X -> isNatKind proper X,
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (2):
Strict:
{U32# mark X -> U32# X,
U32# ok X -> U32# X}
Weak:
{ cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
active cons(X1, X2) -> cons(active X1, X2),
active zeros() -> mark cons(0(), zeros()),
active U12 X -> U12 active X,
active U12 tt() -> mark tt(),
active isNatList cons(V1, V2) -> mark U51(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatList nil() -> mark tt(),
active isNatList take(V1, V2) -> mark U61(and(isNatKind V1, isNatIListKind V2), V1, V2),
active U11(X1, X2) -> U11(active X1, X2),
active U11(tt(), V1) -> mark U12 isNatList V1,
active U22 X -> U22 active X,
active U22 tt() -> mark tt(),
active isNat 0() -> mark tt(),
active isNat s V1 -> mark U21(isNatKind V1, V1),
active isNat length V1 -> mark U11(isNatIListKind V1, V1),
active U21(X1, X2) -> U21(active X1, X2),
active U21(tt(), V1) -> mark U22 isNat V1,
active U32 X -> U32 active X,
active U32 tt() -> mark tt(),
active U31(X1, X2) -> U31(active X1, X2),
active U31(tt(), V) -> mark U32 isNatList V,
active U42(X1, X2) -> U42(active X1, X2),
active U42(tt(), V2) -> mark U43 isNatIList V2,
active U41(X1, X2, X3) -> U41(active X1, X2, X3),
active U41(tt(), V1, V2) -> mark U42(isNat V1, V2),
active U43 X -> U43 active X,
active U43 tt() -> mark tt(),
active isNatIList V -> mark U31(isNatIListKind V, V),
active isNatIList cons(V1, V2) -> mark U41(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatIList zeros() -> mark tt(),
active U52(X1, X2) -> U52(active X1, X2),
active U52(tt(), V2) -> mark U53 isNatList V2,
active U51(X1, X2, X3) -> U51(active X1, X2, X3),
active U51(tt(), V1, V2) -> mark U52(isNat V1, V2),
active U53 X -> U53 active X,
active U53 tt() -> mark tt(),
active U62(X1, X2) -> U62(active X1, X2),
active U62(tt(), V2) -> mark U63 isNatIList V2,
active U61(X1, X2, X3) -> U61(active X1, X2, X3),
active U61(tt(), V1, V2) -> mark U62(isNat V1, V2),
active U63 X -> U63 active X,
active U63 tt() -> mark tt(),
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark U71(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L),
active length nil() -> mark 0(),
active U71(X1, X2) -> U71(active X1, X2),
active U71(tt(), L) -> mark s length L,
active U81 X -> U81 active X,
active U81 tt() -> mark nil(),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark U81 and(isNatIList IL, isNatIListKind IL),
active take(s M, cons(N, IL)) -> mark U91(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N),
active U91(X1, X2, X3, X4) -> U91(active X1, X2, X3, X4),
active U91(tt(), IL, M, N) -> mark cons(N, take(M, IL)),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), X) -> mark X,
active isNatIListKind cons(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatIListKind zeros() -> mark tt(),
active isNatIListKind nil() -> mark tt(),
active isNatIListKind take(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatKind 0() -> mark tt(),
active isNatKind s V1 -> mark isNatKind V1,
active isNatKind length V1 -> mark isNatIListKind V1,
U12 mark X -> mark U12 X,
U12 ok X -> ok U12 X,
isNatList ok X -> ok isNatList X,
U11(mark X1, X2) -> mark U11(X1, X2),
U11(ok X1, ok X2) -> ok U11(X1, X2),
U22 mark X -> mark U22 X,
U22 ok X -> ok U22 X,
isNat ok X -> ok isNat X,
U21(mark X1, X2) -> mark U21(X1, X2),
U21(ok X1, ok X2) -> ok U21(X1, X2),
U32 mark X -> mark U32 X,
U32 ok X -> ok U32 X,
U31(mark X1, X2) -> mark U31(X1, X2),
U31(ok X1, ok X2) -> ok U31(X1, X2),
U42(mark X1, X2) -> mark U42(X1, X2),
U42(ok X1, ok X2) -> ok U42(X1, X2),
U41(mark X1, X2, X3) -> mark U41(X1, X2, X3),
U41(ok X1, ok X2, ok X3) -> ok U41(X1, X2, X3),
U43 mark X -> mark U43 X,
U43 ok X -> ok U43 X,
isNatIList ok X -> ok isNatIList X,
U52(mark X1, X2) -> mark U52(X1, X2),
U52(ok X1, ok X2) -> ok U52(X1, X2),
U51(mark X1, X2, X3) -> mark U51(X1, X2, X3),
U51(ok X1, ok X2, ok X3) -> ok U51(X1, X2, X3),
U53 mark X -> mark U53 X,
U53 ok X -> ok U53 X,
U62(mark X1, X2) -> mark U62(X1, X2),
U62(ok X1, ok X2) -> ok U62(X1, X2),
U61(mark X1, X2, X3) -> mark U61(X1, X2, X3),
U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3),
U63 mark X -> mark U63 X,
U63 ok X -> ok U63 X,
s mark X -> mark s X,
s ok X -> ok s X,
length mark X -> mark length X,
length ok X -> ok length X,
U71(mark X1, X2) -> mark U71(X1, X2),
U71(ok X1, ok X2) -> ok U71(X1, X2),
U81 mark X -> mark U81 X,
U81 ok X -> ok U81 X,
take(X1, mark X2) -> mark take(X1, X2),
take(mark X1, X2) -> mark take(X1, X2),
take(ok X1, ok X2) -> ok take(X1, X2),
U91(mark X1, X2, X3, X4) -> mark U91(X1, X2, X3, X4),
U91(ok X1, ok X2, ok X3, ok X4) -> ok U91(X1, X2, X3, X4),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatIListKind ok X -> ok isNatIListKind X,
isNatKind ok X -> ok isNatKind X,
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper 0() -> ok 0(),
proper zeros() -> ok zeros(),
proper U12 X -> U12 proper X,
proper isNatList X -> isNatList proper X,
proper U11(X1, X2) -> U11(proper X1, proper X2),
proper tt() -> ok tt(),
proper U22 X -> U22 proper X,
proper isNat X -> isNat proper X,
proper U21(X1, X2) -> U21(proper X1, proper X2),
proper U32 X -> U32 proper X,
proper U31(X1, X2) -> U31(proper X1, proper X2),
proper U42(X1, X2) -> U42(proper X1, proper X2),
proper U41(X1, X2, X3) -> U41(proper X1, proper X2, proper X3),
proper U43 X -> U43 proper X,
proper isNatIList X -> isNatIList proper X,
proper U52(X1, X2) -> U52(proper X1, proper X2),
proper U51(X1, X2, X3) -> U51(proper X1, proper X2, proper X3),
proper U53 X -> U53 proper X,
proper U62(X1, X2) -> U62(proper X1, proper X2),
proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3),
proper U63 X -> U63 proper X,
proper s X -> s proper X,
proper length X -> length proper X,
proper U71(X1, X2) -> U71(proper X1, proper X2),
proper nil() -> ok nil(),
proper U81 X -> U81 proper X,
proper take(X1, X2) -> take(proper X1, proper X2),
proper U91(X1, X2, X3, X4) -> U91(proper X1, proper X2, proper X3, proper X4),
proper and(X1, X2) -> and(proper X1, proper X2),
proper isNatIListKind X -> isNatIListKind proper X,
proper isNatKind X -> isNatKind proper X,
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (2):
Strict:
{ U21#(mark X1, X2) -> U21#(X1, X2),
U21#(ok X1, ok X2) -> U21#(X1, X2)}
Weak:
{ cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
active cons(X1, X2) -> cons(active X1, X2),
active zeros() -> mark cons(0(), zeros()),
active U12 X -> U12 active X,
active U12 tt() -> mark tt(),
active isNatList cons(V1, V2) -> mark U51(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatList nil() -> mark tt(),
active isNatList take(V1, V2) -> mark U61(and(isNatKind V1, isNatIListKind V2), V1, V2),
active U11(X1, X2) -> U11(active X1, X2),
active U11(tt(), V1) -> mark U12 isNatList V1,
active U22 X -> U22 active X,
active U22 tt() -> mark tt(),
active isNat 0() -> mark tt(),
active isNat s V1 -> mark U21(isNatKind V1, V1),
active isNat length V1 -> mark U11(isNatIListKind V1, V1),
active U21(X1, X2) -> U21(active X1, X2),
active U21(tt(), V1) -> mark U22 isNat V1,
active U32 X -> U32 active X,
active U32 tt() -> mark tt(),
active U31(X1, X2) -> U31(active X1, X2),
active U31(tt(), V) -> mark U32 isNatList V,
active U42(X1, X2) -> U42(active X1, X2),
active U42(tt(), V2) -> mark U43 isNatIList V2,
active U41(X1, X2, X3) -> U41(active X1, X2, X3),
active U41(tt(), V1, V2) -> mark U42(isNat V1, V2),
active U43 X -> U43 active X,
active U43 tt() -> mark tt(),
active isNatIList V -> mark U31(isNatIListKind V, V),
active isNatIList cons(V1, V2) -> mark U41(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatIList zeros() -> mark tt(),
active U52(X1, X2) -> U52(active X1, X2),
active U52(tt(), V2) -> mark U53 isNatList V2,
active U51(X1, X2, X3) -> U51(active X1, X2, X3),
active U51(tt(), V1, V2) -> mark U52(isNat V1, V2),
active U53 X -> U53 active X,
active U53 tt() -> mark tt(),
active U62(X1, X2) -> U62(active X1, X2),
active U62(tt(), V2) -> mark U63 isNatIList V2,
active U61(X1, X2, X3) -> U61(active X1, X2, X3),
active U61(tt(), V1, V2) -> mark U62(isNat V1, V2),
active U63 X -> U63 active X,
active U63 tt() -> mark tt(),
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark U71(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L),
active length nil() -> mark 0(),
active U71(X1, X2) -> U71(active X1, X2),
active U71(tt(), L) -> mark s length L,
active U81 X -> U81 active X,
active U81 tt() -> mark nil(),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark U81 and(isNatIList IL, isNatIListKind IL),
active take(s M, cons(N, IL)) -> mark U91(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N),
active U91(X1, X2, X3, X4) -> U91(active X1, X2, X3, X4),
active U91(tt(), IL, M, N) -> mark cons(N, take(M, IL)),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), X) -> mark X,
active isNatIListKind cons(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatIListKind zeros() -> mark tt(),
active isNatIListKind nil() -> mark tt(),
active isNatIListKind take(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatKind 0() -> mark tt(),
active isNatKind s V1 -> mark isNatKind V1,
active isNatKind length V1 -> mark isNatIListKind V1,
U12 mark X -> mark U12 X,
U12 ok X -> ok U12 X,
isNatList ok X -> ok isNatList X,
U11(mark X1, X2) -> mark U11(X1, X2),
U11(ok X1, ok X2) -> ok U11(X1, X2),
U22 mark X -> mark U22 X,
U22 ok X -> ok U22 X,
isNat ok X -> ok isNat X,
U21(mark X1, X2) -> mark U21(X1, X2),
U21(ok X1, ok X2) -> ok U21(X1, X2),
U32 mark X -> mark U32 X,
U32 ok X -> ok U32 X,
U31(mark X1, X2) -> mark U31(X1, X2),
U31(ok X1, ok X2) -> ok U31(X1, X2),
U42(mark X1, X2) -> mark U42(X1, X2),
U42(ok X1, ok X2) -> ok U42(X1, X2),
U41(mark X1, X2, X3) -> mark U41(X1, X2, X3),
U41(ok X1, ok X2, ok X3) -> ok U41(X1, X2, X3),
U43 mark X -> mark U43 X,
U43 ok X -> ok U43 X,
isNatIList ok X -> ok isNatIList X,
U52(mark X1, X2) -> mark U52(X1, X2),
U52(ok X1, ok X2) -> ok U52(X1, X2),
U51(mark X1, X2, X3) -> mark U51(X1, X2, X3),
U51(ok X1, ok X2, ok X3) -> ok U51(X1, X2, X3),
U53 mark X -> mark U53 X,
U53 ok X -> ok U53 X,
U62(mark X1, X2) -> mark U62(X1, X2),
U62(ok X1, ok X2) -> ok U62(X1, X2),
U61(mark X1, X2, X3) -> mark U61(X1, X2, X3),
U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3),
U63 mark X -> mark U63 X,
U63 ok X -> ok U63 X,
s mark X -> mark s X,
s ok X -> ok s X,
length mark X -> mark length X,
length ok X -> ok length X,
U71(mark X1, X2) -> mark U71(X1, X2),
U71(ok X1, ok X2) -> ok U71(X1, X2),
U81 mark X -> mark U81 X,
U81 ok X -> ok U81 X,
take(X1, mark X2) -> mark take(X1, X2),
take(mark X1, X2) -> mark take(X1, X2),
take(ok X1, ok X2) -> ok take(X1, X2),
U91(mark X1, X2, X3, X4) -> mark U91(X1, X2, X3, X4),
U91(ok X1, ok X2, ok X3, ok X4) -> ok U91(X1, X2, X3, X4),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatIListKind ok X -> ok isNatIListKind X,
isNatKind ok X -> ok isNatKind X,
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper 0() -> ok 0(),
proper zeros() -> ok zeros(),
proper U12 X -> U12 proper X,
proper isNatList X -> isNatList proper X,
proper U11(X1, X2) -> U11(proper X1, proper X2),
proper tt() -> ok tt(),
proper U22 X -> U22 proper X,
proper isNat X -> isNat proper X,
proper U21(X1, X2) -> U21(proper X1, proper X2),
proper U32 X -> U32 proper X,
proper U31(X1, X2) -> U31(proper X1, proper X2),
proper U42(X1, X2) -> U42(proper X1, proper X2),
proper U41(X1, X2, X3) -> U41(proper X1, proper X2, proper X3),
proper U43 X -> U43 proper X,
proper isNatIList X -> isNatIList proper X,
proper U52(X1, X2) -> U52(proper X1, proper X2),
proper U51(X1, X2, X3) -> U51(proper X1, proper X2, proper X3),
proper U53 X -> U53 proper X,
proper U62(X1, X2) -> U62(proper X1, proper X2),
proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3),
proper U63 X -> U63 proper X,
proper s X -> s proper X,
proper length X -> length proper X,
proper U71(X1, X2) -> U71(proper X1, proper X2),
proper nil() -> ok nil(),
proper U81 X -> U81 proper X,
proper take(X1, X2) -> take(proper X1, proper X2),
proper U91(X1, X2, X3, X4) -> U91(proper X1, proper X2, proper X3, proper X4),
proper and(X1, X2) -> and(proper X1, proper X2),
proper isNatIListKind X -> isNatIListKind proper X,
proper isNatKind X -> isNatKind proper X,
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (2):
Strict:
{U22# mark X -> U22# X,
U22# ok X -> U22# X}
Weak:
{ cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
active cons(X1, X2) -> cons(active X1, X2),
active zeros() -> mark cons(0(), zeros()),
active U12 X -> U12 active X,
active U12 tt() -> mark tt(),
active isNatList cons(V1, V2) -> mark U51(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatList nil() -> mark tt(),
active isNatList take(V1, V2) -> mark U61(and(isNatKind V1, isNatIListKind V2), V1, V2),
active U11(X1, X2) -> U11(active X1, X2),
active U11(tt(), V1) -> mark U12 isNatList V1,
active U22 X -> U22 active X,
active U22 tt() -> mark tt(),
active isNat 0() -> mark tt(),
active isNat s V1 -> mark U21(isNatKind V1, V1),
active isNat length V1 -> mark U11(isNatIListKind V1, V1),
active U21(X1, X2) -> U21(active X1, X2),
active U21(tt(), V1) -> mark U22 isNat V1,
active U32 X -> U32 active X,
active U32 tt() -> mark tt(),
active U31(X1, X2) -> U31(active X1, X2),
active U31(tt(), V) -> mark U32 isNatList V,
active U42(X1, X2) -> U42(active X1, X2),
active U42(tt(), V2) -> mark U43 isNatIList V2,
active U41(X1, X2, X3) -> U41(active X1, X2, X3),
active U41(tt(), V1, V2) -> mark U42(isNat V1, V2),
active U43 X -> U43 active X,
active U43 tt() -> mark tt(),
active isNatIList V -> mark U31(isNatIListKind V, V),
active isNatIList cons(V1, V2) -> mark U41(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatIList zeros() -> mark tt(),
active U52(X1, X2) -> U52(active X1, X2),
active U52(tt(), V2) -> mark U53 isNatList V2,
active U51(X1, X2, X3) -> U51(active X1, X2, X3),
active U51(tt(), V1, V2) -> mark U52(isNat V1, V2),
active U53 X -> U53 active X,
active U53 tt() -> mark tt(),
active U62(X1, X2) -> U62(active X1, X2),
active U62(tt(), V2) -> mark U63 isNatIList V2,
active U61(X1, X2, X3) -> U61(active X1, X2, X3),
active U61(tt(), V1, V2) -> mark U62(isNat V1, V2),
active U63 X -> U63 active X,
active U63 tt() -> mark tt(),
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark U71(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L),
active length nil() -> mark 0(),
active U71(X1, X2) -> U71(active X1, X2),
active U71(tt(), L) -> mark s length L,
active U81 X -> U81 active X,
active U81 tt() -> mark nil(),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark U81 and(isNatIList IL, isNatIListKind IL),
active take(s M, cons(N, IL)) -> mark U91(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N),
active U91(X1, X2, X3, X4) -> U91(active X1, X2, X3, X4),
active U91(tt(), IL, M, N) -> mark cons(N, take(M, IL)),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), X) -> mark X,
active isNatIListKind cons(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatIListKind zeros() -> mark tt(),
active isNatIListKind nil() -> mark tt(),
active isNatIListKind take(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatKind 0() -> mark tt(),
active isNatKind s V1 -> mark isNatKind V1,
active isNatKind length V1 -> mark isNatIListKind V1,
U12 mark X -> mark U12 X,
U12 ok X -> ok U12 X,
isNatList ok X -> ok isNatList X,
U11(mark X1, X2) -> mark U11(X1, X2),
U11(ok X1, ok X2) -> ok U11(X1, X2),
U22 mark X -> mark U22 X,
U22 ok X -> ok U22 X,
isNat ok X -> ok isNat X,
U21(mark X1, X2) -> mark U21(X1, X2),
U21(ok X1, ok X2) -> ok U21(X1, X2),
U32 mark X -> mark U32 X,
U32 ok X -> ok U32 X,
U31(mark X1, X2) -> mark U31(X1, X2),
U31(ok X1, ok X2) -> ok U31(X1, X2),
U42(mark X1, X2) -> mark U42(X1, X2),
U42(ok X1, ok X2) -> ok U42(X1, X2),
U41(mark X1, X2, X3) -> mark U41(X1, X2, X3),
U41(ok X1, ok X2, ok X3) -> ok U41(X1, X2, X3),
U43 mark X -> mark U43 X,
U43 ok X -> ok U43 X,
isNatIList ok X -> ok isNatIList X,
U52(mark X1, X2) -> mark U52(X1, X2),
U52(ok X1, ok X2) -> ok U52(X1, X2),
U51(mark X1, X2, X3) -> mark U51(X1, X2, X3),
U51(ok X1, ok X2, ok X3) -> ok U51(X1, X2, X3),
U53 mark X -> mark U53 X,
U53 ok X -> ok U53 X,
U62(mark X1, X2) -> mark U62(X1, X2),
U62(ok X1, ok X2) -> ok U62(X1, X2),
U61(mark X1, X2, X3) -> mark U61(X1, X2, X3),
U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3),
U63 mark X -> mark U63 X,
U63 ok X -> ok U63 X,
s mark X -> mark s X,
s ok X -> ok s X,
length mark X -> mark length X,
length ok X -> ok length X,
U71(mark X1, X2) -> mark U71(X1, X2),
U71(ok X1, ok X2) -> ok U71(X1, X2),
U81 mark X -> mark U81 X,
U81 ok X -> ok U81 X,
take(X1, mark X2) -> mark take(X1, X2),
take(mark X1, X2) -> mark take(X1, X2),
take(ok X1, ok X2) -> ok take(X1, X2),
U91(mark X1, X2, X3, X4) -> mark U91(X1, X2, X3, X4),
U91(ok X1, ok X2, ok X3, ok X4) -> ok U91(X1, X2, X3, X4),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatIListKind ok X -> ok isNatIListKind X,
isNatKind ok X -> ok isNatKind X,
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper 0() -> ok 0(),
proper zeros() -> ok zeros(),
proper U12 X -> U12 proper X,
proper isNatList X -> isNatList proper X,
proper U11(X1, X2) -> U11(proper X1, proper X2),
proper tt() -> ok tt(),
proper U22 X -> U22 proper X,
proper isNat X -> isNat proper X,
proper U21(X1, X2) -> U21(proper X1, proper X2),
proper U32 X -> U32 proper X,
proper U31(X1, X2) -> U31(proper X1, proper X2),
proper U42(X1, X2) -> U42(proper X1, proper X2),
proper U41(X1, X2, X3) -> U41(proper X1, proper X2, proper X3),
proper U43 X -> U43 proper X,
proper isNatIList X -> isNatIList proper X,
proper U52(X1, X2) -> U52(proper X1, proper X2),
proper U51(X1, X2, X3) -> U51(proper X1, proper X2, proper X3),
proper U53 X -> U53 proper X,
proper U62(X1, X2) -> U62(proper X1, proper X2),
proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3),
proper U63 X -> U63 proper X,
proper s X -> s proper X,
proper length X -> length proper X,
proper U71(X1, X2) -> U71(proper X1, proper X2),
proper nil() -> ok nil(),
proper U81 X -> U81 proper X,
proper take(X1, X2) -> take(proper X1, proper X2),
proper U91(X1, X2, X3, X4) -> U91(proper X1, proper X2, proper X3, proper X4),
proper and(X1, X2) -> and(proper X1, proper X2),
proper isNatIListKind X -> isNatIListKind proper X,
proper isNatKind X -> isNatKind proper X,
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (2):
Strict:
{ U11#(mark X1, X2) -> U11#(X1, X2),
U11#(ok X1, ok X2) -> U11#(X1, X2)}
Weak:
{ cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
active cons(X1, X2) -> cons(active X1, X2),
active zeros() -> mark cons(0(), zeros()),
active U12 X -> U12 active X,
active U12 tt() -> mark tt(),
active isNatList cons(V1, V2) -> mark U51(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatList nil() -> mark tt(),
active isNatList take(V1, V2) -> mark U61(and(isNatKind V1, isNatIListKind V2), V1, V2),
active U11(X1, X2) -> U11(active X1, X2),
active U11(tt(), V1) -> mark U12 isNatList V1,
active U22 X -> U22 active X,
active U22 tt() -> mark tt(),
active isNat 0() -> mark tt(),
active isNat s V1 -> mark U21(isNatKind V1, V1),
active isNat length V1 -> mark U11(isNatIListKind V1, V1),
active U21(X1, X2) -> U21(active X1, X2),
active U21(tt(), V1) -> mark U22 isNat V1,
active U32 X -> U32 active X,
active U32 tt() -> mark tt(),
active U31(X1, X2) -> U31(active X1, X2),
active U31(tt(), V) -> mark U32 isNatList V,
active U42(X1, X2) -> U42(active X1, X2),
active U42(tt(), V2) -> mark U43 isNatIList V2,
active U41(X1, X2, X3) -> U41(active X1, X2, X3),
active U41(tt(), V1, V2) -> mark U42(isNat V1, V2),
active U43 X -> U43 active X,
active U43 tt() -> mark tt(),
active isNatIList V -> mark U31(isNatIListKind V, V),
active isNatIList cons(V1, V2) -> mark U41(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatIList zeros() -> mark tt(),
active U52(X1, X2) -> U52(active X1, X2),
active U52(tt(), V2) -> mark U53 isNatList V2,
active U51(X1, X2, X3) -> U51(active X1, X2, X3),
active U51(tt(), V1, V2) -> mark U52(isNat V1, V2),
active U53 X -> U53 active X,
active U53 tt() -> mark tt(),
active U62(X1, X2) -> U62(active X1, X2),
active U62(tt(), V2) -> mark U63 isNatIList V2,
active U61(X1, X2, X3) -> U61(active X1, X2, X3),
active U61(tt(), V1, V2) -> mark U62(isNat V1, V2),
active U63 X -> U63 active X,
active U63 tt() -> mark tt(),
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark U71(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L),
active length nil() -> mark 0(),
active U71(X1, X2) -> U71(active X1, X2),
active U71(tt(), L) -> mark s length L,
active U81 X -> U81 active X,
active U81 tt() -> mark nil(),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark U81 and(isNatIList IL, isNatIListKind IL),
active take(s M, cons(N, IL)) -> mark U91(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N),
active U91(X1, X2, X3, X4) -> U91(active X1, X2, X3, X4),
active U91(tt(), IL, M, N) -> mark cons(N, take(M, IL)),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), X) -> mark X,
active isNatIListKind cons(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatIListKind zeros() -> mark tt(),
active isNatIListKind nil() -> mark tt(),
active isNatIListKind take(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatKind 0() -> mark tt(),
active isNatKind s V1 -> mark isNatKind V1,
active isNatKind length V1 -> mark isNatIListKind V1,
U12 mark X -> mark U12 X,
U12 ok X -> ok U12 X,
isNatList ok X -> ok isNatList X,
U11(mark X1, X2) -> mark U11(X1, X2),
U11(ok X1, ok X2) -> ok U11(X1, X2),
U22 mark X -> mark U22 X,
U22 ok X -> ok U22 X,
isNat ok X -> ok isNat X,
U21(mark X1, X2) -> mark U21(X1, X2),
U21(ok X1, ok X2) -> ok U21(X1, X2),
U32 mark X -> mark U32 X,
U32 ok X -> ok U32 X,
U31(mark X1, X2) -> mark U31(X1, X2),
U31(ok X1, ok X2) -> ok U31(X1, X2),
U42(mark X1, X2) -> mark U42(X1, X2),
U42(ok X1, ok X2) -> ok U42(X1, X2),
U41(mark X1, X2, X3) -> mark U41(X1, X2, X3),
U41(ok X1, ok X2, ok X3) -> ok U41(X1, X2, X3),
U43 mark X -> mark U43 X,
U43 ok X -> ok U43 X,
isNatIList ok X -> ok isNatIList X,
U52(mark X1, X2) -> mark U52(X1, X2),
U52(ok X1, ok X2) -> ok U52(X1, X2),
U51(mark X1, X2, X3) -> mark U51(X1, X2, X3),
U51(ok X1, ok X2, ok X3) -> ok U51(X1, X2, X3),
U53 mark X -> mark U53 X,
U53 ok X -> ok U53 X,
U62(mark X1, X2) -> mark U62(X1, X2),
U62(ok X1, ok X2) -> ok U62(X1, X2),
U61(mark X1, X2, X3) -> mark U61(X1, X2, X3),
U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3),
U63 mark X -> mark U63 X,
U63 ok X -> ok U63 X,
s mark X -> mark s X,
s ok X -> ok s X,
length mark X -> mark length X,
length ok X -> ok length X,
U71(mark X1, X2) -> mark U71(X1, X2),
U71(ok X1, ok X2) -> ok U71(X1, X2),
U81 mark X -> mark U81 X,
U81 ok X -> ok U81 X,
take(X1, mark X2) -> mark take(X1, X2),
take(mark X1, X2) -> mark take(X1, X2),
take(ok X1, ok X2) -> ok take(X1, X2),
U91(mark X1, X2, X3, X4) -> mark U91(X1, X2, X3, X4),
U91(ok X1, ok X2, ok X3, ok X4) -> ok U91(X1, X2, X3, X4),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatIListKind ok X -> ok isNatIListKind X,
isNatKind ok X -> ok isNatKind X,
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper 0() -> ok 0(),
proper zeros() -> ok zeros(),
proper U12 X -> U12 proper X,
proper isNatList X -> isNatList proper X,
proper U11(X1, X2) -> U11(proper X1, proper X2),
proper tt() -> ok tt(),
proper U22 X -> U22 proper X,
proper isNat X -> isNat proper X,
proper U21(X1, X2) -> U21(proper X1, proper X2),
proper U32 X -> U32 proper X,
proper U31(X1, X2) -> U31(proper X1, proper X2),
proper U42(X1, X2) -> U42(proper X1, proper X2),
proper U41(X1, X2, X3) -> U41(proper X1, proper X2, proper X3),
proper U43 X -> U43 proper X,
proper isNatIList X -> isNatIList proper X,
proper U52(X1, X2) -> U52(proper X1, proper X2),
proper U51(X1, X2, X3) -> U51(proper X1, proper X2, proper X3),
proper U53 X -> U53 proper X,
proper U62(X1, X2) -> U62(proper X1, proper X2),
proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3),
proper U63 X -> U63 proper X,
proper s X -> s proper X,
proper length X -> length proper X,
proper U71(X1, X2) -> U71(proper X1, proper X2),
proper nil() -> ok nil(),
proper U81 X -> U81 proper X,
proper take(X1, X2) -> take(proper X1, proper X2),
proper U91(X1, X2, X3, X4) -> U91(proper X1, proper X2, proper X3, proper X4),
proper and(X1, X2) -> and(proper X1, proper X2),
proper isNatIListKind X -> isNatIListKind proper X,
proper isNatKind X -> isNatKind proper X,
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (2):
Strict:
{U12# mark X -> U12# X,
U12# ok X -> U12# X}
Weak:
{ cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
active cons(X1, X2) -> cons(active X1, X2),
active zeros() -> mark cons(0(), zeros()),
active U12 X -> U12 active X,
active U12 tt() -> mark tt(),
active isNatList cons(V1, V2) -> mark U51(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatList nil() -> mark tt(),
active isNatList take(V1, V2) -> mark U61(and(isNatKind V1, isNatIListKind V2), V1, V2),
active U11(X1, X2) -> U11(active X1, X2),
active U11(tt(), V1) -> mark U12 isNatList V1,
active U22 X -> U22 active X,
active U22 tt() -> mark tt(),
active isNat 0() -> mark tt(),
active isNat s V1 -> mark U21(isNatKind V1, V1),
active isNat length V1 -> mark U11(isNatIListKind V1, V1),
active U21(X1, X2) -> U21(active X1, X2),
active U21(tt(), V1) -> mark U22 isNat V1,
active U32 X -> U32 active X,
active U32 tt() -> mark tt(),
active U31(X1, X2) -> U31(active X1, X2),
active U31(tt(), V) -> mark U32 isNatList V,
active U42(X1, X2) -> U42(active X1, X2),
active U42(tt(), V2) -> mark U43 isNatIList V2,
active U41(X1, X2, X3) -> U41(active X1, X2, X3),
active U41(tt(), V1, V2) -> mark U42(isNat V1, V2),
active U43 X -> U43 active X,
active U43 tt() -> mark tt(),
active isNatIList V -> mark U31(isNatIListKind V, V),
active isNatIList cons(V1, V2) -> mark U41(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatIList zeros() -> mark tt(),
active U52(X1, X2) -> U52(active X1, X2),
active U52(tt(), V2) -> mark U53 isNatList V2,
active U51(X1, X2, X3) -> U51(active X1, X2, X3),
active U51(tt(), V1, V2) -> mark U52(isNat V1, V2),
active U53 X -> U53 active X,
active U53 tt() -> mark tt(),
active U62(X1, X2) -> U62(active X1, X2),
active U62(tt(), V2) -> mark U63 isNatIList V2,
active U61(X1, X2, X3) -> U61(active X1, X2, X3),
active U61(tt(), V1, V2) -> mark U62(isNat V1, V2),
active U63 X -> U63 active X,
active U63 tt() -> mark tt(),
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark U71(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L),
active length nil() -> mark 0(),
active U71(X1, X2) -> U71(active X1, X2),
active U71(tt(), L) -> mark s length L,
active U81 X -> U81 active X,
active U81 tt() -> mark nil(),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark U81 and(isNatIList IL, isNatIListKind IL),
active take(s M, cons(N, IL)) -> mark U91(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N),
active U91(X1, X2, X3, X4) -> U91(active X1, X2, X3, X4),
active U91(tt(), IL, M, N) -> mark cons(N, take(M, IL)),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), X) -> mark X,
active isNatIListKind cons(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatIListKind zeros() -> mark tt(),
active isNatIListKind nil() -> mark tt(),
active isNatIListKind take(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatKind 0() -> mark tt(),
active isNatKind s V1 -> mark isNatKind V1,
active isNatKind length V1 -> mark isNatIListKind V1,
U12 mark X -> mark U12 X,
U12 ok X -> ok U12 X,
isNatList ok X -> ok isNatList X,
U11(mark X1, X2) -> mark U11(X1, X2),
U11(ok X1, ok X2) -> ok U11(X1, X2),
U22 mark X -> mark U22 X,
U22 ok X -> ok U22 X,
isNat ok X -> ok isNat X,
U21(mark X1, X2) -> mark U21(X1, X2),
U21(ok X1, ok X2) -> ok U21(X1, X2),
U32 mark X -> mark U32 X,
U32 ok X -> ok U32 X,
U31(mark X1, X2) -> mark U31(X1, X2),
U31(ok X1, ok X2) -> ok U31(X1, X2),
U42(mark X1, X2) -> mark U42(X1, X2),
U42(ok X1, ok X2) -> ok U42(X1, X2),
U41(mark X1, X2, X3) -> mark U41(X1, X2, X3),
U41(ok X1, ok X2, ok X3) -> ok U41(X1, X2, X3),
U43 mark X -> mark U43 X,
U43 ok X -> ok U43 X,
isNatIList ok X -> ok isNatIList X,
U52(mark X1, X2) -> mark U52(X1, X2),
U52(ok X1, ok X2) -> ok U52(X1, X2),
U51(mark X1, X2, X3) -> mark U51(X1, X2, X3),
U51(ok X1, ok X2, ok X3) -> ok U51(X1, X2, X3),
U53 mark X -> mark U53 X,
U53 ok X -> ok U53 X,
U62(mark X1, X2) -> mark U62(X1, X2),
U62(ok X1, ok X2) -> ok U62(X1, X2),
U61(mark X1, X2, X3) -> mark U61(X1, X2, X3),
U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3),
U63 mark X -> mark U63 X,
U63 ok X -> ok U63 X,
s mark X -> mark s X,
s ok X -> ok s X,
length mark X -> mark length X,
length ok X -> ok length X,
U71(mark X1, X2) -> mark U71(X1, X2),
U71(ok X1, ok X2) -> ok U71(X1, X2),
U81 mark X -> mark U81 X,
U81 ok X -> ok U81 X,
take(X1, mark X2) -> mark take(X1, X2),
take(mark X1, X2) -> mark take(X1, X2),
take(ok X1, ok X2) -> ok take(X1, X2),
U91(mark X1, X2, X3, X4) -> mark U91(X1, X2, X3, X4),
U91(ok X1, ok X2, ok X3, ok X4) -> ok U91(X1, X2, X3, X4),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatIListKind ok X -> ok isNatIListKind X,
isNatKind ok X -> ok isNatKind X,
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper 0() -> ok 0(),
proper zeros() -> ok zeros(),
proper U12 X -> U12 proper X,
proper isNatList X -> isNatList proper X,
proper U11(X1, X2) -> U11(proper X1, proper X2),
proper tt() -> ok tt(),
proper U22 X -> U22 proper X,
proper isNat X -> isNat proper X,
proper U21(X1, X2) -> U21(proper X1, proper X2),
proper U32 X -> U32 proper X,
proper U31(X1, X2) -> U31(proper X1, proper X2),
proper U42(X1, X2) -> U42(proper X1, proper X2),
proper U41(X1, X2, X3) -> U41(proper X1, proper X2, proper X3),
proper U43 X -> U43 proper X,
proper isNatIList X -> isNatIList proper X,
proper U52(X1, X2) -> U52(proper X1, proper X2),
proper U51(X1, X2, X3) -> U51(proper X1, proper X2, proper X3),
proper U53 X -> U53 proper X,
proper U62(X1, X2) -> U62(proper X1, proper X2),
proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3),
proper U63 X -> U63 proper X,
proper s X -> s proper X,
proper length X -> length proper X,
proper U71(X1, X2) -> U71(proper X1, proper X2),
proper nil() -> ok nil(),
proper U81 X -> U81 proper X,
proper take(X1, X2) -> take(proper X1, proper X2),
proper U91(X1, X2, X3, X4) -> U91(proper X1, proper X2, proper X3, proper X4),
proper and(X1, X2) -> and(proper X1, proper X2),
proper isNatIListKind X -> isNatIListKind proper X,
proper isNatKind X -> isNatKind proper X,
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (2):
Strict:
{ cons#(mark X1, X2) -> cons#(X1, X2),
cons#(ok X1, ok X2) -> cons#(X1, X2)}
Weak:
{ cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
active cons(X1, X2) -> cons(active X1, X2),
active zeros() -> mark cons(0(), zeros()),
active U12 X -> U12 active X,
active U12 tt() -> mark tt(),
active isNatList cons(V1, V2) -> mark U51(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatList nil() -> mark tt(),
active isNatList take(V1, V2) -> mark U61(and(isNatKind V1, isNatIListKind V2), V1, V2),
active U11(X1, X2) -> U11(active X1, X2),
active U11(tt(), V1) -> mark U12 isNatList V1,
active U22 X -> U22 active X,
active U22 tt() -> mark tt(),
active isNat 0() -> mark tt(),
active isNat s V1 -> mark U21(isNatKind V1, V1),
active isNat length V1 -> mark U11(isNatIListKind V1, V1),
active U21(X1, X2) -> U21(active X1, X2),
active U21(tt(), V1) -> mark U22 isNat V1,
active U32 X -> U32 active X,
active U32 tt() -> mark tt(),
active U31(X1, X2) -> U31(active X1, X2),
active U31(tt(), V) -> mark U32 isNatList V,
active U42(X1, X2) -> U42(active X1, X2),
active U42(tt(), V2) -> mark U43 isNatIList V2,
active U41(X1, X2, X3) -> U41(active X1, X2, X3),
active U41(tt(), V1, V2) -> mark U42(isNat V1, V2),
active U43 X -> U43 active X,
active U43 tt() -> mark tt(),
active isNatIList V -> mark U31(isNatIListKind V, V),
active isNatIList cons(V1, V2) -> mark U41(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatIList zeros() -> mark tt(),
active U52(X1, X2) -> U52(active X1, X2),
active U52(tt(), V2) -> mark U53 isNatList V2,
active U51(X1, X2, X3) -> U51(active X1, X2, X3),
active U51(tt(), V1, V2) -> mark U52(isNat V1, V2),
active U53 X -> U53 active X,
active U53 tt() -> mark tt(),
active U62(X1, X2) -> U62(active X1, X2),
active U62(tt(), V2) -> mark U63 isNatIList V2,
active U61(X1, X2, X3) -> U61(active X1, X2, X3),
active U61(tt(), V1, V2) -> mark U62(isNat V1, V2),
active U63 X -> U63 active X,
active U63 tt() -> mark tt(),
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark U71(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L),
active length nil() -> mark 0(),
active U71(X1, X2) -> U71(active X1, X2),
active U71(tt(), L) -> mark s length L,
active U81 X -> U81 active X,
active U81 tt() -> mark nil(),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark U81 and(isNatIList IL, isNatIListKind IL),
active take(s M, cons(N, IL)) -> mark U91(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N),
active U91(X1, X2, X3, X4) -> U91(active X1, X2, X3, X4),
active U91(tt(), IL, M, N) -> mark cons(N, take(M, IL)),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), X) -> mark X,
active isNatIListKind cons(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatIListKind zeros() -> mark tt(),
active isNatIListKind nil() -> mark tt(),
active isNatIListKind take(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatKind 0() -> mark tt(),
active isNatKind s V1 -> mark isNatKind V1,
active isNatKind length V1 -> mark isNatIListKind V1,
U12 mark X -> mark U12 X,
U12 ok X -> ok U12 X,
isNatList ok X -> ok isNatList X,
U11(mark X1, X2) -> mark U11(X1, X2),
U11(ok X1, ok X2) -> ok U11(X1, X2),
U22 mark X -> mark U22 X,
U22 ok X -> ok U22 X,
isNat ok X -> ok isNat X,
U21(mark X1, X2) -> mark U21(X1, X2),
U21(ok X1, ok X2) -> ok U21(X1, X2),
U32 mark X -> mark U32 X,
U32 ok X -> ok U32 X,
U31(mark X1, X2) -> mark U31(X1, X2),
U31(ok X1, ok X2) -> ok U31(X1, X2),
U42(mark X1, X2) -> mark U42(X1, X2),
U42(ok X1, ok X2) -> ok U42(X1, X2),
U41(mark X1, X2, X3) -> mark U41(X1, X2, X3),
U41(ok X1, ok X2, ok X3) -> ok U41(X1, X2, X3),
U43 mark X -> mark U43 X,
U43 ok X -> ok U43 X,
isNatIList ok X -> ok isNatIList X,
U52(mark X1, X2) -> mark U52(X1, X2),
U52(ok X1, ok X2) -> ok U52(X1, X2),
U51(mark X1, X2, X3) -> mark U51(X1, X2, X3),
U51(ok X1, ok X2, ok X3) -> ok U51(X1, X2, X3),
U53 mark X -> mark U53 X,
U53 ok X -> ok U53 X,
U62(mark X1, X2) -> mark U62(X1, X2),
U62(ok X1, ok X2) -> ok U62(X1, X2),
U61(mark X1, X2, X3) -> mark U61(X1, X2, X3),
U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3),
U63 mark X -> mark U63 X,
U63 ok X -> ok U63 X,
s mark X -> mark s X,
s ok X -> ok s X,
length mark X -> mark length X,
length ok X -> ok length X,
U71(mark X1, X2) -> mark U71(X1, X2),
U71(ok X1, ok X2) -> ok U71(X1, X2),
U81 mark X -> mark U81 X,
U81 ok X -> ok U81 X,
take(X1, mark X2) -> mark take(X1, X2),
take(mark X1, X2) -> mark take(X1, X2),
take(ok X1, ok X2) -> ok take(X1, X2),
U91(mark X1, X2, X3, X4) -> mark U91(X1, X2, X3, X4),
U91(ok X1, ok X2, ok X3, ok X4) -> ok U91(X1, X2, X3, X4),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatIListKind ok X -> ok isNatIListKind X,
isNatKind ok X -> ok isNatKind X,
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper 0() -> ok 0(),
proper zeros() -> ok zeros(),
proper U12 X -> U12 proper X,
proper isNatList X -> isNatList proper X,
proper U11(X1, X2) -> U11(proper X1, proper X2),
proper tt() -> ok tt(),
proper U22 X -> U22 proper X,
proper isNat X -> isNat proper X,
proper U21(X1, X2) -> U21(proper X1, proper X2),
proper U32 X -> U32 proper X,
proper U31(X1, X2) -> U31(proper X1, proper X2),
proper U42(X1, X2) -> U42(proper X1, proper X2),
proper U41(X1, X2, X3) -> U41(proper X1, proper X2, proper X3),
proper U43 X -> U43 proper X,
proper isNatIList X -> isNatIList proper X,
proper U52(X1, X2) -> U52(proper X1, proper X2),
proper U51(X1, X2, X3) -> U51(proper X1, proper X2, proper X3),
proper U53 X -> U53 proper X,
proper U62(X1, X2) -> U62(proper X1, proper X2),
proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3),
proper U63 X -> U63 proper X,
proper s X -> s proper X,
proper length X -> length proper X,
proper U71(X1, X2) -> U71(proper X1, proper X2),
proper nil() -> ok nil(),
proper U81 X -> U81 proper X,
proper take(X1, X2) -> take(proper X1, proper X2),
proper U91(X1, X2, X3, X4) -> U91(proper X1, proper X2, proper X3, proper X4),
proper and(X1, X2) -> and(proper X1, proper X2),
proper isNatIListKind X -> isNatIListKind proper X,
proper isNatKind X -> isNatKind proper X,
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (2):
Strict:
{ U61#(mark X1, X2, X3) -> U61#(X1, X2, X3),
U61#(ok X1, ok X2, ok X3) -> U61#(X1, X2, X3)}
Weak:
{ cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
active cons(X1, X2) -> cons(active X1, X2),
active zeros() -> mark cons(0(), zeros()),
active U12 X -> U12 active X,
active U12 tt() -> mark tt(),
active isNatList cons(V1, V2) -> mark U51(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatList nil() -> mark tt(),
active isNatList take(V1, V2) -> mark U61(and(isNatKind V1, isNatIListKind V2), V1, V2),
active U11(X1, X2) -> U11(active X1, X2),
active U11(tt(), V1) -> mark U12 isNatList V1,
active U22 X -> U22 active X,
active U22 tt() -> mark tt(),
active isNat 0() -> mark tt(),
active isNat s V1 -> mark U21(isNatKind V1, V1),
active isNat length V1 -> mark U11(isNatIListKind V1, V1),
active U21(X1, X2) -> U21(active X1, X2),
active U21(tt(), V1) -> mark U22 isNat V1,
active U32 X -> U32 active X,
active U32 tt() -> mark tt(),
active U31(X1, X2) -> U31(active X1, X2),
active U31(tt(), V) -> mark U32 isNatList V,
active U42(X1, X2) -> U42(active X1, X2),
active U42(tt(), V2) -> mark U43 isNatIList V2,
active U41(X1, X2, X3) -> U41(active X1, X2, X3),
active U41(tt(), V1, V2) -> mark U42(isNat V1, V2),
active U43 X -> U43 active X,
active U43 tt() -> mark tt(),
active isNatIList V -> mark U31(isNatIListKind V, V),
active isNatIList cons(V1, V2) -> mark U41(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatIList zeros() -> mark tt(),
active U52(X1, X2) -> U52(active X1, X2),
active U52(tt(), V2) -> mark U53 isNatList V2,
active U51(X1, X2, X3) -> U51(active X1, X2, X3),
active U51(tt(), V1, V2) -> mark U52(isNat V1, V2),
active U53 X -> U53 active X,
active U53 tt() -> mark tt(),
active U62(X1, X2) -> U62(active X1, X2),
active U62(tt(), V2) -> mark U63 isNatIList V2,
active U61(X1, X2, X3) -> U61(active X1, X2, X3),
active U61(tt(), V1, V2) -> mark U62(isNat V1, V2),
active U63 X -> U63 active X,
active U63 tt() -> mark tt(),
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark U71(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L),
active length nil() -> mark 0(),
active U71(X1, X2) -> U71(active X1, X2),
active U71(tt(), L) -> mark s length L,
active U81 X -> U81 active X,
active U81 tt() -> mark nil(),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark U81 and(isNatIList IL, isNatIListKind IL),
active take(s M, cons(N, IL)) -> mark U91(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N),
active U91(X1, X2, X3, X4) -> U91(active X1, X2, X3, X4),
active U91(tt(), IL, M, N) -> mark cons(N, take(M, IL)),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), X) -> mark X,
active isNatIListKind cons(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatIListKind zeros() -> mark tt(),
active isNatIListKind nil() -> mark tt(),
active isNatIListKind take(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatKind 0() -> mark tt(),
active isNatKind s V1 -> mark isNatKind V1,
active isNatKind length V1 -> mark isNatIListKind V1,
U12 mark X -> mark U12 X,
U12 ok X -> ok U12 X,
isNatList ok X -> ok isNatList X,
U11(mark X1, X2) -> mark U11(X1, X2),
U11(ok X1, ok X2) -> ok U11(X1, X2),
U22 mark X -> mark U22 X,
U22 ok X -> ok U22 X,
isNat ok X -> ok isNat X,
U21(mark X1, X2) -> mark U21(X1, X2),
U21(ok X1, ok X2) -> ok U21(X1, X2),
U32 mark X -> mark U32 X,
U32 ok X -> ok U32 X,
U31(mark X1, X2) -> mark U31(X1, X2),
U31(ok X1, ok X2) -> ok U31(X1, X2),
U42(mark X1, X2) -> mark U42(X1, X2),
U42(ok X1, ok X2) -> ok U42(X1, X2),
U41(mark X1, X2, X3) -> mark U41(X1, X2, X3),
U41(ok X1, ok X2, ok X3) -> ok U41(X1, X2, X3),
U43 mark X -> mark U43 X,
U43 ok X -> ok U43 X,
isNatIList ok X -> ok isNatIList X,
U52(mark X1, X2) -> mark U52(X1, X2),
U52(ok X1, ok X2) -> ok U52(X1, X2),
U51(mark X1, X2, X3) -> mark U51(X1, X2, X3),
U51(ok X1, ok X2, ok X3) -> ok U51(X1, X2, X3),
U53 mark X -> mark U53 X,
U53 ok X -> ok U53 X,
U62(mark X1, X2) -> mark U62(X1, X2),
U62(ok X1, ok X2) -> ok U62(X1, X2),
U61(mark X1, X2, X3) -> mark U61(X1, X2, X3),
U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3),
U63 mark X -> mark U63 X,
U63 ok X -> ok U63 X,
s mark X -> mark s X,
s ok X -> ok s X,
length mark X -> mark length X,
length ok X -> ok length X,
U71(mark X1, X2) -> mark U71(X1, X2),
U71(ok X1, ok X2) -> ok U71(X1, X2),
U81 mark X -> mark U81 X,
U81 ok X -> ok U81 X,
take(X1, mark X2) -> mark take(X1, X2),
take(mark X1, X2) -> mark take(X1, X2),
take(ok X1, ok X2) -> ok take(X1, X2),
U91(mark X1, X2, X3, X4) -> mark U91(X1, X2, X3, X4),
U91(ok X1, ok X2, ok X3, ok X4) -> ok U91(X1, X2, X3, X4),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatIListKind ok X -> ok isNatIListKind X,
isNatKind ok X -> ok isNatKind X,
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper 0() -> ok 0(),
proper zeros() -> ok zeros(),
proper U12 X -> U12 proper X,
proper isNatList X -> isNatList proper X,
proper U11(X1, X2) -> U11(proper X1, proper X2),
proper tt() -> ok tt(),
proper U22 X -> U22 proper X,
proper isNat X -> isNat proper X,
proper U21(X1, X2) -> U21(proper X1, proper X2),
proper U32 X -> U32 proper X,
proper U31(X1, X2) -> U31(proper X1, proper X2),
proper U42(X1, X2) -> U42(proper X1, proper X2),
proper U41(X1, X2, X3) -> U41(proper X1, proper X2, proper X3),
proper U43 X -> U43 proper X,
proper isNatIList X -> isNatIList proper X,
proper U52(X1, X2) -> U52(proper X1, proper X2),
proper U51(X1, X2, X3) -> U51(proper X1, proper X2, proper X3),
proper U53 X -> U53 proper X,
proper U62(X1, X2) -> U62(proper X1, proper X2),
proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3),
proper U63 X -> U63 proper X,
proper s X -> s proper X,
proper length X -> length proper X,
proper U71(X1, X2) -> U71(proper X1, proper X2),
proper nil() -> ok nil(),
proper U81 X -> U81 proper X,
proper take(X1, X2) -> take(proper X1, proper X2),
proper U91(X1, X2, X3, X4) -> U91(proper X1, proper X2, proper X3, proper X4),
proper and(X1, X2) -> and(proper X1, proper X2),
proper isNatIListKind X -> isNatIListKind proper X,
proper isNatKind X -> isNatKind proper X,
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (2):
Strict:
{ U51#(mark X1, X2, X3) -> U51#(X1, X2, X3),
U51#(ok X1, ok X2, ok X3) -> U51#(X1, X2, X3)}
Weak:
{ cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
active cons(X1, X2) -> cons(active X1, X2),
active zeros() -> mark cons(0(), zeros()),
active U12 X -> U12 active X,
active U12 tt() -> mark tt(),
active isNatList cons(V1, V2) -> mark U51(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatList nil() -> mark tt(),
active isNatList take(V1, V2) -> mark U61(and(isNatKind V1, isNatIListKind V2), V1, V2),
active U11(X1, X2) -> U11(active X1, X2),
active U11(tt(), V1) -> mark U12 isNatList V1,
active U22 X -> U22 active X,
active U22 tt() -> mark tt(),
active isNat 0() -> mark tt(),
active isNat s V1 -> mark U21(isNatKind V1, V1),
active isNat length V1 -> mark U11(isNatIListKind V1, V1),
active U21(X1, X2) -> U21(active X1, X2),
active U21(tt(), V1) -> mark U22 isNat V1,
active U32 X -> U32 active X,
active U32 tt() -> mark tt(),
active U31(X1, X2) -> U31(active X1, X2),
active U31(tt(), V) -> mark U32 isNatList V,
active U42(X1, X2) -> U42(active X1, X2),
active U42(tt(), V2) -> mark U43 isNatIList V2,
active U41(X1, X2, X3) -> U41(active X1, X2, X3),
active U41(tt(), V1, V2) -> mark U42(isNat V1, V2),
active U43 X -> U43 active X,
active U43 tt() -> mark tt(),
active isNatIList V -> mark U31(isNatIListKind V, V),
active isNatIList cons(V1, V2) -> mark U41(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatIList zeros() -> mark tt(),
active U52(X1, X2) -> U52(active X1, X2),
active U52(tt(), V2) -> mark U53 isNatList V2,
active U51(X1, X2, X3) -> U51(active X1, X2, X3),
active U51(tt(), V1, V2) -> mark U52(isNat V1, V2),
active U53 X -> U53 active X,
active U53 tt() -> mark tt(),
active U62(X1, X2) -> U62(active X1, X2),
active U62(tt(), V2) -> mark U63 isNatIList V2,
active U61(X1, X2, X3) -> U61(active X1, X2, X3),
active U61(tt(), V1, V2) -> mark U62(isNat V1, V2),
active U63 X -> U63 active X,
active U63 tt() -> mark tt(),
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark U71(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L),
active length nil() -> mark 0(),
active U71(X1, X2) -> U71(active X1, X2),
active U71(tt(), L) -> mark s length L,
active U81 X -> U81 active X,
active U81 tt() -> mark nil(),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark U81 and(isNatIList IL, isNatIListKind IL),
active take(s M, cons(N, IL)) -> mark U91(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N),
active U91(X1, X2, X3, X4) -> U91(active X1, X2, X3, X4),
active U91(tt(), IL, M, N) -> mark cons(N, take(M, IL)),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), X) -> mark X,
active isNatIListKind cons(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatIListKind zeros() -> mark tt(),
active isNatIListKind nil() -> mark tt(),
active isNatIListKind take(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatKind 0() -> mark tt(),
active isNatKind s V1 -> mark isNatKind V1,
active isNatKind length V1 -> mark isNatIListKind V1,
U12 mark X -> mark U12 X,
U12 ok X -> ok U12 X,
isNatList ok X -> ok isNatList X,
U11(mark X1, X2) -> mark U11(X1, X2),
U11(ok X1, ok X2) -> ok U11(X1, X2),
U22 mark X -> mark U22 X,
U22 ok X -> ok U22 X,
isNat ok X -> ok isNat X,
U21(mark X1, X2) -> mark U21(X1, X2),
U21(ok X1, ok X2) -> ok U21(X1, X2),
U32 mark X -> mark U32 X,
U32 ok X -> ok U32 X,
U31(mark X1, X2) -> mark U31(X1, X2),
U31(ok X1, ok X2) -> ok U31(X1, X2),
U42(mark X1, X2) -> mark U42(X1, X2),
U42(ok X1, ok X2) -> ok U42(X1, X2),
U41(mark X1, X2, X3) -> mark U41(X1, X2, X3),
U41(ok X1, ok X2, ok X3) -> ok U41(X1, X2, X3),
U43 mark X -> mark U43 X,
U43 ok X -> ok U43 X,
isNatIList ok X -> ok isNatIList X,
U52(mark X1, X2) -> mark U52(X1, X2),
U52(ok X1, ok X2) -> ok U52(X1, X2),
U51(mark X1, X2, X3) -> mark U51(X1, X2, X3),
U51(ok X1, ok X2, ok X3) -> ok U51(X1, X2, X3),
U53 mark X -> mark U53 X,
U53 ok X -> ok U53 X,
U62(mark X1, X2) -> mark U62(X1, X2),
U62(ok X1, ok X2) -> ok U62(X1, X2),
U61(mark X1, X2, X3) -> mark U61(X1, X2, X3),
U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3),
U63 mark X -> mark U63 X,
U63 ok X -> ok U63 X,
s mark X -> mark s X,
s ok X -> ok s X,
length mark X -> mark length X,
length ok X -> ok length X,
U71(mark X1, X2) -> mark U71(X1, X2),
U71(ok X1, ok X2) -> ok U71(X1, X2),
U81 mark X -> mark U81 X,
U81 ok X -> ok U81 X,
take(X1, mark X2) -> mark take(X1, X2),
take(mark X1, X2) -> mark take(X1, X2),
take(ok X1, ok X2) -> ok take(X1, X2),
U91(mark X1, X2, X3, X4) -> mark U91(X1, X2, X3, X4),
U91(ok X1, ok X2, ok X3, ok X4) -> ok U91(X1, X2, X3, X4),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatIListKind ok X -> ok isNatIListKind X,
isNatKind ok X -> ok isNatKind X,
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper 0() -> ok 0(),
proper zeros() -> ok zeros(),
proper U12 X -> U12 proper X,
proper isNatList X -> isNatList proper X,
proper U11(X1, X2) -> U11(proper X1, proper X2),
proper tt() -> ok tt(),
proper U22 X -> U22 proper X,
proper isNat X -> isNat proper X,
proper U21(X1, X2) -> U21(proper X1, proper X2),
proper U32 X -> U32 proper X,
proper U31(X1, X2) -> U31(proper X1, proper X2),
proper U42(X1, X2) -> U42(proper X1, proper X2),
proper U41(X1, X2, X3) -> U41(proper X1, proper X2, proper X3),
proper U43 X -> U43 proper X,
proper isNatIList X -> isNatIList proper X,
proper U52(X1, X2) -> U52(proper X1, proper X2),
proper U51(X1, X2, X3) -> U51(proper X1, proper X2, proper X3),
proper U53 X -> U53 proper X,
proper U62(X1, X2) -> U62(proper X1, proper X2),
proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3),
proper U63 X -> U63 proper X,
proper s X -> s proper X,
proper length X -> length proper X,
proper U71(X1, X2) -> U71(proper X1, proper X2),
proper nil() -> ok nil(),
proper U81 X -> U81 proper X,
proper take(X1, X2) -> take(proper X1, proper X2),
proper U91(X1, X2, X3, X4) -> U91(proper X1, proper X2, proper X3, proper X4),
proper and(X1, X2) -> and(proper X1, proper X2),
proper isNatIListKind X -> isNatIListKind proper X,
proper isNatKind X -> isNatKind proper X,
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (2):
Strict:
{ U41#(mark X1, X2, X3) -> U41#(X1, X2, X3),
U41#(ok X1, ok X2, ok X3) -> U41#(X1, X2, X3)}
Weak:
{ cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
active cons(X1, X2) -> cons(active X1, X2),
active zeros() -> mark cons(0(), zeros()),
active U12 X -> U12 active X,
active U12 tt() -> mark tt(),
active isNatList cons(V1, V2) -> mark U51(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatList nil() -> mark tt(),
active isNatList take(V1, V2) -> mark U61(and(isNatKind V1, isNatIListKind V2), V1, V2),
active U11(X1, X2) -> U11(active X1, X2),
active U11(tt(), V1) -> mark U12 isNatList V1,
active U22 X -> U22 active X,
active U22 tt() -> mark tt(),
active isNat 0() -> mark tt(),
active isNat s V1 -> mark U21(isNatKind V1, V1),
active isNat length V1 -> mark U11(isNatIListKind V1, V1),
active U21(X1, X2) -> U21(active X1, X2),
active U21(tt(), V1) -> mark U22 isNat V1,
active U32 X -> U32 active X,
active U32 tt() -> mark tt(),
active U31(X1, X2) -> U31(active X1, X2),
active U31(tt(), V) -> mark U32 isNatList V,
active U42(X1, X2) -> U42(active X1, X2),
active U42(tt(), V2) -> mark U43 isNatIList V2,
active U41(X1, X2, X3) -> U41(active X1, X2, X3),
active U41(tt(), V1, V2) -> mark U42(isNat V1, V2),
active U43 X -> U43 active X,
active U43 tt() -> mark tt(),
active isNatIList V -> mark U31(isNatIListKind V, V),
active isNatIList cons(V1, V2) -> mark U41(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatIList zeros() -> mark tt(),
active U52(X1, X2) -> U52(active X1, X2),
active U52(tt(), V2) -> mark U53 isNatList V2,
active U51(X1, X2, X3) -> U51(active X1, X2, X3),
active U51(tt(), V1, V2) -> mark U52(isNat V1, V2),
active U53 X -> U53 active X,
active U53 tt() -> mark tt(),
active U62(X1, X2) -> U62(active X1, X2),
active U62(tt(), V2) -> mark U63 isNatIList V2,
active U61(X1, X2, X3) -> U61(active X1, X2, X3),
active U61(tt(), V1, V2) -> mark U62(isNat V1, V2),
active U63 X -> U63 active X,
active U63 tt() -> mark tt(),
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark U71(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L),
active length nil() -> mark 0(),
active U71(X1, X2) -> U71(active X1, X2),
active U71(tt(), L) -> mark s length L,
active U81 X -> U81 active X,
active U81 tt() -> mark nil(),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark U81 and(isNatIList IL, isNatIListKind IL),
active take(s M, cons(N, IL)) -> mark U91(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N),
active U91(X1, X2, X3, X4) -> U91(active X1, X2, X3, X4),
active U91(tt(), IL, M, N) -> mark cons(N, take(M, IL)),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), X) -> mark X,
active isNatIListKind cons(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatIListKind zeros() -> mark tt(),
active isNatIListKind nil() -> mark tt(),
active isNatIListKind take(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatKind 0() -> mark tt(),
active isNatKind s V1 -> mark isNatKind V1,
active isNatKind length V1 -> mark isNatIListKind V1,
U12 mark X -> mark U12 X,
U12 ok X -> ok U12 X,
isNatList ok X -> ok isNatList X,
U11(mark X1, X2) -> mark U11(X1, X2),
U11(ok X1, ok X2) -> ok U11(X1, X2),
U22 mark X -> mark U22 X,
U22 ok X -> ok U22 X,
isNat ok X -> ok isNat X,
U21(mark X1, X2) -> mark U21(X1, X2),
U21(ok X1, ok X2) -> ok U21(X1, X2),
U32 mark X -> mark U32 X,
U32 ok X -> ok U32 X,
U31(mark X1, X2) -> mark U31(X1, X2),
U31(ok X1, ok X2) -> ok U31(X1, X2),
U42(mark X1, X2) -> mark U42(X1, X2),
U42(ok X1, ok X2) -> ok U42(X1, X2),
U41(mark X1, X2, X3) -> mark U41(X1, X2, X3),
U41(ok X1, ok X2, ok X3) -> ok U41(X1, X2, X3),
U43 mark X -> mark U43 X,
U43 ok X -> ok U43 X,
isNatIList ok X -> ok isNatIList X,
U52(mark X1, X2) -> mark U52(X1, X2),
U52(ok X1, ok X2) -> ok U52(X1, X2),
U51(mark X1, X2, X3) -> mark U51(X1, X2, X3),
U51(ok X1, ok X2, ok X3) -> ok U51(X1, X2, X3),
U53 mark X -> mark U53 X,
U53 ok X -> ok U53 X,
U62(mark X1, X2) -> mark U62(X1, X2),
U62(ok X1, ok X2) -> ok U62(X1, X2),
U61(mark X1, X2, X3) -> mark U61(X1, X2, X3),
U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3),
U63 mark X -> mark U63 X,
U63 ok X -> ok U63 X,
s mark X -> mark s X,
s ok X -> ok s X,
length mark X -> mark length X,
length ok X -> ok length X,
U71(mark X1, X2) -> mark U71(X1, X2),
U71(ok X1, ok X2) -> ok U71(X1, X2),
U81 mark X -> mark U81 X,
U81 ok X -> ok U81 X,
take(X1, mark X2) -> mark take(X1, X2),
take(mark X1, X2) -> mark take(X1, X2),
take(ok X1, ok X2) -> ok take(X1, X2),
U91(mark X1, X2, X3, X4) -> mark U91(X1, X2, X3, X4),
U91(ok X1, ok X2, ok X3, ok X4) -> ok U91(X1, X2, X3, X4),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatIListKind ok X -> ok isNatIListKind X,
isNatKind ok X -> ok isNatKind X,
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper 0() -> ok 0(),
proper zeros() -> ok zeros(),
proper U12 X -> U12 proper X,
proper isNatList X -> isNatList proper X,
proper U11(X1, X2) -> U11(proper X1, proper X2),
proper tt() -> ok tt(),
proper U22 X -> U22 proper X,
proper isNat X -> isNat proper X,
proper U21(X1, X2) -> U21(proper X1, proper X2),
proper U32 X -> U32 proper X,
proper U31(X1, X2) -> U31(proper X1, proper X2),
proper U42(X1, X2) -> U42(proper X1, proper X2),
proper U41(X1, X2, X3) -> U41(proper X1, proper X2, proper X3),
proper U43 X -> U43 proper X,
proper isNatIList X -> isNatIList proper X,
proper U52(X1, X2) -> U52(proper X1, proper X2),
proper U51(X1, X2, X3) -> U51(proper X1, proper X2, proper X3),
proper U53 X -> U53 proper X,
proper U62(X1, X2) -> U62(proper X1, proper X2),
proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3),
proper U63 X -> U63 proper X,
proper s X -> s proper X,
proper length X -> length proper X,
proper U71(X1, X2) -> U71(proper X1, proper X2),
proper nil() -> ok nil(),
proper U81 X -> U81 proper X,
proper take(X1, X2) -> take(proper X1, proper X2),
proper U91(X1, X2, X3, X4) -> U91(proper X1, proper X2, proper X3, proper X4),
proper and(X1, X2) -> and(proper X1, proper X2),
proper isNatIListKind X -> isNatIListKind proper X,
proper isNatKind X -> isNatKind proper X,
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (2):
Strict:
{ and#(mark X1, X2) -> and#(X1, X2),
and#(ok X1, ok X2) -> and#(X1, X2)}
Weak:
{ cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
active cons(X1, X2) -> cons(active X1, X2),
active zeros() -> mark cons(0(), zeros()),
active U12 X -> U12 active X,
active U12 tt() -> mark tt(),
active isNatList cons(V1, V2) -> mark U51(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatList nil() -> mark tt(),
active isNatList take(V1, V2) -> mark U61(and(isNatKind V1, isNatIListKind V2), V1, V2),
active U11(X1, X2) -> U11(active X1, X2),
active U11(tt(), V1) -> mark U12 isNatList V1,
active U22 X -> U22 active X,
active U22 tt() -> mark tt(),
active isNat 0() -> mark tt(),
active isNat s V1 -> mark U21(isNatKind V1, V1),
active isNat length V1 -> mark U11(isNatIListKind V1, V1),
active U21(X1, X2) -> U21(active X1, X2),
active U21(tt(), V1) -> mark U22 isNat V1,
active U32 X -> U32 active X,
active U32 tt() -> mark tt(),
active U31(X1, X2) -> U31(active X1, X2),
active U31(tt(), V) -> mark U32 isNatList V,
active U42(X1, X2) -> U42(active X1, X2),
active U42(tt(), V2) -> mark U43 isNatIList V2,
active U41(X1, X2, X3) -> U41(active X1, X2, X3),
active U41(tt(), V1, V2) -> mark U42(isNat V1, V2),
active U43 X -> U43 active X,
active U43 tt() -> mark tt(),
active isNatIList V -> mark U31(isNatIListKind V, V),
active isNatIList cons(V1, V2) -> mark U41(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatIList zeros() -> mark tt(),
active U52(X1, X2) -> U52(active X1, X2),
active U52(tt(), V2) -> mark U53 isNatList V2,
active U51(X1, X2, X3) -> U51(active X1, X2, X3),
active U51(tt(), V1, V2) -> mark U52(isNat V1, V2),
active U53 X -> U53 active X,
active U53 tt() -> mark tt(),
active U62(X1, X2) -> U62(active X1, X2),
active U62(tt(), V2) -> mark U63 isNatIList V2,
active U61(X1, X2, X3) -> U61(active X1, X2, X3),
active U61(tt(), V1, V2) -> mark U62(isNat V1, V2),
active U63 X -> U63 active X,
active U63 tt() -> mark tt(),
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark U71(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L),
active length nil() -> mark 0(),
active U71(X1, X2) -> U71(active X1, X2),
active U71(tt(), L) -> mark s length L,
active U81 X -> U81 active X,
active U81 tt() -> mark nil(),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark U81 and(isNatIList IL, isNatIListKind IL),
active take(s M, cons(N, IL)) -> mark U91(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N),
active U91(X1, X2, X3, X4) -> U91(active X1, X2, X3, X4),
active U91(tt(), IL, M, N) -> mark cons(N, take(M, IL)),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), X) -> mark X,
active isNatIListKind cons(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatIListKind zeros() -> mark tt(),
active isNatIListKind nil() -> mark tt(),
active isNatIListKind take(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatKind 0() -> mark tt(),
active isNatKind s V1 -> mark isNatKind V1,
active isNatKind length V1 -> mark isNatIListKind V1,
U12 mark X -> mark U12 X,
U12 ok X -> ok U12 X,
isNatList ok X -> ok isNatList X,
U11(mark X1, X2) -> mark U11(X1, X2),
U11(ok X1, ok X2) -> ok U11(X1, X2),
U22 mark X -> mark U22 X,
U22 ok X -> ok U22 X,
isNat ok X -> ok isNat X,
U21(mark X1, X2) -> mark U21(X1, X2),
U21(ok X1, ok X2) -> ok U21(X1, X2),
U32 mark X -> mark U32 X,
U32 ok X -> ok U32 X,
U31(mark X1, X2) -> mark U31(X1, X2),
U31(ok X1, ok X2) -> ok U31(X1, X2),
U42(mark X1, X2) -> mark U42(X1, X2),
U42(ok X1, ok X2) -> ok U42(X1, X2),
U41(mark X1, X2, X3) -> mark U41(X1, X2, X3),
U41(ok X1, ok X2, ok X3) -> ok U41(X1, X2, X3),
U43 mark X -> mark U43 X,
U43 ok X -> ok U43 X,
isNatIList ok X -> ok isNatIList X,
U52(mark X1, X2) -> mark U52(X1, X2),
U52(ok X1, ok X2) -> ok U52(X1, X2),
U51(mark X1, X2, X3) -> mark U51(X1, X2, X3),
U51(ok X1, ok X2, ok X3) -> ok U51(X1, X2, X3),
U53 mark X -> mark U53 X,
U53 ok X -> ok U53 X,
U62(mark X1, X2) -> mark U62(X1, X2),
U62(ok X1, ok X2) -> ok U62(X1, X2),
U61(mark X1, X2, X3) -> mark U61(X1, X2, X3),
U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3),
U63 mark X -> mark U63 X,
U63 ok X -> ok U63 X,
s mark X -> mark s X,
s ok X -> ok s X,
length mark X -> mark length X,
length ok X -> ok length X,
U71(mark X1, X2) -> mark U71(X1, X2),
U71(ok X1, ok X2) -> ok U71(X1, X2),
U81 mark X -> mark U81 X,
U81 ok X -> ok U81 X,
take(X1, mark X2) -> mark take(X1, X2),
take(mark X1, X2) -> mark take(X1, X2),
take(ok X1, ok X2) -> ok take(X1, X2),
U91(mark X1, X2, X3, X4) -> mark U91(X1, X2, X3, X4),
U91(ok X1, ok X2, ok X3, ok X4) -> ok U91(X1, X2, X3, X4),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatIListKind ok X -> ok isNatIListKind X,
isNatKind ok X -> ok isNatKind X,
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper 0() -> ok 0(),
proper zeros() -> ok zeros(),
proper U12 X -> U12 proper X,
proper isNatList X -> isNatList proper X,
proper U11(X1, X2) -> U11(proper X1, proper X2),
proper tt() -> ok tt(),
proper U22 X -> U22 proper X,
proper isNat X -> isNat proper X,
proper U21(X1, X2) -> U21(proper X1, proper X2),
proper U32 X -> U32 proper X,
proper U31(X1, X2) -> U31(proper X1, proper X2),
proper U42(X1, X2) -> U42(proper X1, proper X2),
proper U41(X1, X2, X3) -> U41(proper X1, proper X2, proper X3),
proper U43 X -> U43 proper X,
proper isNatIList X -> isNatIList proper X,
proper U52(X1, X2) -> U52(proper X1, proper X2),
proper U51(X1, X2, X3) -> U51(proper X1, proper X2, proper X3),
proper U53 X -> U53 proper X,
proper U62(X1, X2) -> U62(proper X1, proper X2),
proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3),
proper U63 X -> U63 proper X,
proper s X -> s proper X,
proper length X -> length proper X,
proper U71(X1, X2) -> U71(proper X1, proper X2),
proper nil() -> ok nil(),
proper U81 X -> U81 proper X,
proper take(X1, X2) -> take(proper X1, proper X2),
proper U91(X1, X2, X3, X4) -> U91(proper X1, proper X2, proper X3, proper X4),
proper and(X1, X2) -> and(proper X1, proper X2),
proper isNatIListKind X -> isNatIListKind proper X,
proper isNatKind X -> isNatKind proper X,
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (2):
Strict:
{ U31#(mark X1, X2) -> U31#(X1, X2),
U31#(ok X1, ok X2) -> U31#(X1, X2)}
Weak:
{ cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
active cons(X1, X2) -> cons(active X1, X2),
active zeros() -> mark cons(0(), zeros()),
active U12 X -> U12 active X,
active U12 tt() -> mark tt(),
active isNatList cons(V1, V2) -> mark U51(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatList nil() -> mark tt(),
active isNatList take(V1, V2) -> mark U61(and(isNatKind V1, isNatIListKind V2), V1, V2),
active U11(X1, X2) -> U11(active X1, X2),
active U11(tt(), V1) -> mark U12 isNatList V1,
active U22 X -> U22 active X,
active U22 tt() -> mark tt(),
active isNat 0() -> mark tt(),
active isNat s V1 -> mark U21(isNatKind V1, V1),
active isNat length V1 -> mark U11(isNatIListKind V1, V1),
active U21(X1, X2) -> U21(active X1, X2),
active U21(tt(), V1) -> mark U22 isNat V1,
active U32 X -> U32 active X,
active U32 tt() -> mark tt(),
active U31(X1, X2) -> U31(active X1, X2),
active U31(tt(), V) -> mark U32 isNatList V,
active U42(X1, X2) -> U42(active X1, X2),
active U42(tt(), V2) -> mark U43 isNatIList V2,
active U41(X1, X2, X3) -> U41(active X1, X2, X3),
active U41(tt(), V1, V2) -> mark U42(isNat V1, V2),
active U43 X -> U43 active X,
active U43 tt() -> mark tt(),
active isNatIList V -> mark U31(isNatIListKind V, V),
active isNatIList cons(V1, V2) -> mark U41(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatIList zeros() -> mark tt(),
active U52(X1, X2) -> U52(active X1, X2),
active U52(tt(), V2) -> mark U53 isNatList V2,
active U51(X1, X2, X3) -> U51(active X1, X2, X3),
active U51(tt(), V1, V2) -> mark U52(isNat V1, V2),
active U53 X -> U53 active X,
active U53 tt() -> mark tt(),
active U62(X1, X2) -> U62(active X1, X2),
active U62(tt(), V2) -> mark U63 isNatIList V2,
active U61(X1, X2, X3) -> U61(active X1, X2, X3),
active U61(tt(), V1, V2) -> mark U62(isNat V1, V2),
active U63 X -> U63 active X,
active U63 tt() -> mark tt(),
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark U71(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L),
active length nil() -> mark 0(),
active U71(X1, X2) -> U71(active X1, X2),
active U71(tt(), L) -> mark s length L,
active U81 X -> U81 active X,
active U81 tt() -> mark nil(),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark U81 and(isNatIList IL, isNatIListKind IL),
active take(s M, cons(N, IL)) -> mark U91(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N),
active U91(X1, X2, X3, X4) -> U91(active X1, X2, X3, X4),
active U91(tt(), IL, M, N) -> mark cons(N, take(M, IL)),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), X) -> mark X,
active isNatIListKind cons(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatIListKind zeros() -> mark tt(),
active isNatIListKind nil() -> mark tt(),
active isNatIListKind take(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatKind 0() -> mark tt(),
active isNatKind s V1 -> mark isNatKind V1,
active isNatKind length V1 -> mark isNatIListKind V1,
U12 mark X -> mark U12 X,
U12 ok X -> ok U12 X,
isNatList ok X -> ok isNatList X,
U11(mark X1, X2) -> mark U11(X1, X2),
U11(ok X1, ok X2) -> ok U11(X1, X2),
U22 mark X -> mark U22 X,
U22 ok X -> ok U22 X,
isNat ok X -> ok isNat X,
U21(mark X1, X2) -> mark U21(X1, X2),
U21(ok X1, ok X2) -> ok U21(X1, X2),
U32 mark X -> mark U32 X,
U32 ok X -> ok U32 X,
U31(mark X1, X2) -> mark U31(X1, X2),
U31(ok X1, ok X2) -> ok U31(X1, X2),
U42(mark X1, X2) -> mark U42(X1, X2),
U42(ok X1, ok X2) -> ok U42(X1, X2),
U41(mark X1, X2, X3) -> mark U41(X1, X2, X3),
U41(ok X1, ok X2, ok X3) -> ok U41(X1, X2, X3),
U43 mark X -> mark U43 X,
U43 ok X -> ok U43 X,
isNatIList ok X -> ok isNatIList X,
U52(mark X1, X2) -> mark U52(X1, X2),
U52(ok X1, ok X2) -> ok U52(X1, X2),
U51(mark X1, X2, X3) -> mark U51(X1, X2, X3),
U51(ok X1, ok X2, ok X3) -> ok U51(X1, X2, X3),
U53 mark X -> mark U53 X,
U53 ok X -> ok U53 X,
U62(mark X1, X2) -> mark U62(X1, X2),
U62(ok X1, ok X2) -> ok U62(X1, X2),
U61(mark X1, X2, X3) -> mark U61(X1, X2, X3),
U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3),
U63 mark X -> mark U63 X,
U63 ok X -> ok U63 X,
s mark X -> mark s X,
s ok X -> ok s X,
length mark X -> mark length X,
length ok X -> ok length X,
U71(mark X1, X2) -> mark U71(X1, X2),
U71(ok X1, ok X2) -> ok U71(X1, X2),
U81 mark X -> mark U81 X,
U81 ok X -> ok U81 X,
take(X1, mark X2) -> mark take(X1, X2),
take(mark X1, X2) -> mark take(X1, X2),
take(ok X1, ok X2) -> ok take(X1, X2),
U91(mark X1, X2, X3, X4) -> mark U91(X1, X2, X3, X4),
U91(ok X1, ok X2, ok X3, ok X4) -> ok U91(X1, X2, X3, X4),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatIListKind ok X -> ok isNatIListKind X,
isNatKind ok X -> ok isNatKind X,
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper 0() -> ok 0(),
proper zeros() -> ok zeros(),
proper U12 X -> U12 proper X,
proper isNatList X -> isNatList proper X,
proper U11(X1, X2) -> U11(proper X1, proper X2),
proper tt() -> ok tt(),
proper U22 X -> U22 proper X,
proper isNat X -> isNat proper X,
proper U21(X1, X2) -> U21(proper X1, proper X2),
proper U32 X -> U32 proper X,
proper U31(X1, X2) -> U31(proper X1, proper X2),
proper U42(X1, X2) -> U42(proper X1, proper X2),
proper U41(X1, X2, X3) -> U41(proper X1, proper X2, proper X3),
proper U43 X -> U43 proper X,
proper isNatIList X -> isNatIList proper X,
proper U52(X1, X2) -> U52(proper X1, proper X2),
proper U51(X1, X2, X3) -> U51(proper X1, proper X2, proper X3),
proper U53 X -> U53 proper X,
proper U62(X1, X2) -> U62(proper X1, proper X2),
proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3),
proper U63 X -> U63 proper X,
proper s X -> s proper X,
proper length X -> length proper X,
proper U71(X1, X2) -> U71(proper X1, proper X2),
proper nil() -> ok nil(),
proper U81 X -> U81 proper X,
proper take(X1, X2) -> take(proper X1, proper X2),
proper U91(X1, X2, X3, X4) -> U91(proper X1, proper X2, proper X3, proper X4),
proper and(X1, X2) -> and(proper X1, proper X2),
proper isNatIListKind X -> isNatIListKind proper X,
proper isNatKind X -> isNatKind proper X,
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (1):
Strict:
{isNat# ok X -> isNat# X}
Weak:
{ cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
active cons(X1, X2) -> cons(active X1, X2),
active zeros() -> mark cons(0(), zeros()),
active U12 X -> U12 active X,
active U12 tt() -> mark tt(),
active isNatList cons(V1, V2) -> mark U51(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatList nil() -> mark tt(),
active isNatList take(V1, V2) -> mark U61(and(isNatKind V1, isNatIListKind V2), V1, V2),
active U11(X1, X2) -> U11(active X1, X2),
active U11(tt(), V1) -> mark U12 isNatList V1,
active U22 X -> U22 active X,
active U22 tt() -> mark tt(),
active isNat 0() -> mark tt(),
active isNat s V1 -> mark U21(isNatKind V1, V1),
active isNat length V1 -> mark U11(isNatIListKind V1, V1),
active U21(X1, X2) -> U21(active X1, X2),
active U21(tt(), V1) -> mark U22 isNat V1,
active U32 X -> U32 active X,
active U32 tt() -> mark tt(),
active U31(X1, X2) -> U31(active X1, X2),
active U31(tt(), V) -> mark U32 isNatList V,
active U42(X1, X2) -> U42(active X1, X2),
active U42(tt(), V2) -> mark U43 isNatIList V2,
active U41(X1, X2, X3) -> U41(active X1, X2, X3),
active U41(tt(), V1, V2) -> mark U42(isNat V1, V2),
active U43 X -> U43 active X,
active U43 tt() -> mark tt(),
active isNatIList V -> mark U31(isNatIListKind V, V),
active isNatIList cons(V1, V2) -> mark U41(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatIList zeros() -> mark tt(),
active U52(X1, X2) -> U52(active X1, X2),
active U52(tt(), V2) -> mark U53 isNatList V2,
active U51(X1, X2, X3) -> U51(active X1, X2, X3),
active U51(tt(), V1, V2) -> mark U52(isNat V1, V2),
active U53 X -> U53 active X,
active U53 tt() -> mark tt(),
active U62(X1, X2) -> U62(active X1, X2),
active U62(tt(), V2) -> mark U63 isNatIList V2,
active U61(X1, X2, X3) -> U61(active X1, X2, X3),
active U61(tt(), V1, V2) -> mark U62(isNat V1, V2),
active U63 X -> U63 active X,
active U63 tt() -> mark tt(),
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark U71(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L),
active length nil() -> mark 0(),
active U71(X1, X2) -> U71(active X1, X2),
active U71(tt(), L) -> mark s length L,
active U81 X -> U81 active X,
active U81 tt() -> mark nil(),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark U81 and(isNatIList IL, isNatIListKind IL),
active take(s M, cons(N, IL)) -> mark U91(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N),
active U91(X1, X2, X3, X4) -> U91(active X1, X2, X3, X4),
active U91(tt(), IL, M, N) -> mark cons(N, take(M, IL)),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), X) -> mark X,
active isNatIListKind cons(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatIListKind zeros() -> mark tt(),
active isNatIListKind nil() -> mark tt(),
active isNatIListKind take(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatKind 0() -> mark tt(),
active isNatKind s V1 -> mark isNatKind V1,
active isNatKind length V1 -> mark isNatIListKind V1,
U12 mark X -> mark U12 X,
U12 ok X -> ok U12 X,
isNatList ok X -> ok isNatList X,
U11(mark X1, X2) -> mark U11(X1, X2),
U11(ok X1, ok X2) -> ok U11(X1, X2),
U22 mark X -> mark U22 X,
U22 ok X -> ok U22 X,
isNat ok X -> ok isNat X,
U21(mark X1, X2) -> mark U21(X1, X2),
U21(ok X1, ok X2) -> ok U21(X1, X2),
U32 mark X -> mark U32 X,
U32 ok X -> ok U32 X,
U31(mark X1, X2) -> mark U31(X1, X2),
U31(ok X1, ok X2) -> ok U31(X1, X2),
U42(mark X1, X2) -> mark U42(X1, X2),
U42(ok X1, ok X2) -> ok U42(X1, X2),
U41(mark X1, X2, X3) -> mark U41(X1, X2, X3),
U41(ok X1, ok X2, ok X3) -> ok U41(X1, X2, X3),
U43 mark X -> mark U43 X,
U43 ok X -> ok U43 X,
isNatIList ok X -> ok isNatIList X,
U52(mark X1, X2) -> mark U52(X1, X2),
U52(ok X1, ok X2) -> ok U52(X1, X2),
U51(mark X1, X2, X3) -> mark U51(X1, X2, X3),
U51(ok X1, ok X2, ok X3) -> ok U51(X1, X2, X3),
U53 mark X -> mark U53 X,
U53 ok X -> ok U53 X,
U62(mark X1, X2) -> mark U62(X1, X2),
U62(ok X1, ok X2) -> ok U62(X1, X2),
U61(mark X1, X2, X3) -> mark U61(X1, X2, X3),
U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3),
U63 mark X -> mark U63 X,
U63 ok X -> ok U63 X,
s mark X -> mark s X,
s ok X -> ok s X,
length mark X -> mark length X,
length ok X -> ok length X,
U71(mark X1, X2) -> mark U71(X1, X2),
U71(ok X1, ok X2) -> ok U71(X1, X2),
U81 mark X -> mark U81 X,
U81 ok X -> ok U81 X,
take(X1, mark X2) -> mark take(X1, X2),
take(mark X1, X2) -> mark take(X1, X2),
take(ok X1, ok X2) -> ok take(X1, X2),
U91(mark X1, X2, X3, X4) -> mark U91(X1, X2, X3, X4),
U91(ok X1, ok X2, ok X3, ok X4) -> ok U91(X1, X2, X3, X4),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatIListKind ok X -> ok isNatIListKind X,
isNatKind ok X -> ok isNatKind X,
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper 0() -> ok 0(),
proper zeros() -> ok zeros(),
proper U12 X -> U12 proper X,
proper isNatList X -> isNatList proper X,
proper U11(X1, X2) -> U11(proper X1, proper X2),
proper tt() -> ok tt(),
proper U22 X -> U22 proper X,
proper isNat X -> isNat proper X,
proper U21(X1, X2) -> U21(proper X1, proper X2),
proper U32 X -> U32 proper X,
proper U31(X1, X2) -> U31(proper X1, proper X2),
proper U42(X1, X2) -> U42(proper X1, proper X2),
proper U41(X1, X2, X3) -> U41(proper X1, proper X2, proper X3),
proper U43 X -> U43 proper X,
proper isNatIList X -> isNatIList proper X,
proper U52(X1, X2) -> U52(proper X1, proper X2),
proper U51(X1, X2, X3) -> U51(proper X1, proper X2, proper X3),
proper U53 X -> U53 proper X,
proper U62(X1, X2) -> U62(proper X1, proper X2),
proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3),
proper U63 X -> U63 proper X,
proper s X -> s proper X,
proper length X -> length proper X,
proper U71(X1, X2) -> U71(proper X1, proper X2),
proper nil() -> ok nil(),
proper U81 X -> U81 proper X,
proper take(X1, X2) -> take(proper X1, proper X2),
proper U91(X1, X2, X3, X4) -> U91(proper X1, proper X2, proper X3, proper X4),
proper and(X1, X2) -> and(proper X1, proper X2),
proper isNatIListKind X -> isNatIListKind proper X,
proper isNatKind X -> isNatKind proper X,
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (1):
Strict:
{isNatIListKind# ok X -> isNatIListKind# X}
Weak:
{ cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
active cons(X1, X2) -> cons(active X1, X2),
active zeros() -> mark cons(0(), zeros()),
active U12 X -> U12 active X,
active U12 tt() -> mark tt(),
active isNatList cons(V1, V2) -> mark U51(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatList nil() -> mark tt(),
active isNatList take(V1, V2) -> mark U61(and(isNatKind V1, isNatIListKind V2), V1, V2),
active U11(X1, X2) -> U11(active X1, X2),
active U11(tt(), V1) -> mark U12 isNatList V1,
active U22 X -> U22 active X,
active U22 tt() -> mark tt(),
active isNat 0() -> mark tt(),
active isNat s V1 -> mark U21(isNatKind V1, V1),
active isNat length V1 -> mark U11(isNatIListKind V1, V1),
active U21(X1, X2) -> U21(active X1, X2),
active U21(tt(), V1) -> mark U22 isNat V1,
active U32 X -> U32 active X,
active U32 tt() -> mark tt(),
active U31(X1, X2) -> U31(active X1, X2),
active U31(tt(), V) -> mark U32 isNatList V,
active U42(X1, X2) -> U42(active X1, X2),
active U42(tt(), V2) -> mark U43 isNatIList V2,
active U41(X1, X2, X3) -> U41(active X1, X2, X3),
active U41(tt(), V1, V2) -> mark U42(isNat V1, V2),
active U43 X -> U43 active X,
active U43 tt() -> mark tt(),
active isNatIList V -> mark U31(isNatIListKind V, V),
active isNatIList cons(V1, V2) -> mark U41(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatIList zeros() -> mark tt(),
active U52(X1, X2) -> U52(active X1, X2),
active U52(tt(), V2) -> mark U53 isNatList V2,
active U51(X1, X2, X3) -> U51(active X1, X2, X3),
active U51(tt(), V1, V2) -> mark U52(isNat V1, V2),
active U53 X -> U53 active X,
active U53 tt() -> mark tt(),
active U62(X1, X2) -> U62(active X1, X2),
active U62(tt(), V2) -> mark U63 isNatIList V2,
active U61(X1, X2, X3) -> U61(active X1, X2, X3),
active U61(tt(), V1, V2) -> mark U62(isNat V1, V2),
active U63 X -> U63 active X,
active U63 tt() -> mark tt(),
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark U71(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L),
active length nil() -> mark 0(),
active U71(X1, X2) -> U71(active X1, X2),
active U71(tt(), L) -> mark s length L,
active U81 X -> U81 active X,
active U81 tt() -> mark nil(),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark U81 and(isNatIList IL, isNatIListKind IL),
active take(s M, cons(N, IL)) -> mark U91(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N),
active U91(X1, X2, X3, X4) -> U91(active X1, X2, X3, X4),
active U91(tt(), IL, M, N) -> mark cons(N, take(M, IL)),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), X) -> mark X,
active isNatIListKind cons(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatIListKind zeros() -> mark tt(),
active isNatIListKind nil() -> mark tt(),
active isNatIListKind take(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatKind 0() -> mark tt(),
active isNatKind s V1 -> mark isNatKind V1,
active isNatKind length V1 -> mark isNatIListKind V1,
U12 mark X -> mark U12 X,
U12 ok X -> ok U12 X,
isNatList ok X -> ok isNatList X,
U11(mark X1, X2) -> mark U11(X1, X2),
U11(ok X1, ok X2) -> ok U11(X1, X2),
U22 mark X -> mark U22 X,
U22 ok X -> ok U22 X,
isNat ok X -> ok isNat X,
U21(mark X1, X2) -> mark U21(X1, X2),
U21(ok X1, ok X2) -> ok U21(X1, X2),
U32 mark X -> mark U32 X,
U32 ok X -> ok U32 X,
U31(mark X1, X2) -> mark U31(X1, X2),
U31(ok X1, ok X2) -> ok U31(X1, X2),
U42(mark X1, X2) -> mark U42(X1, X2),
U42(ok X1, ok X2) -> ok U42(X1, X2),
U41(mark X1, X2, X3) -> mark U41(X1, X2, X3),
U41(ok X1, ok X2, ok X3) -> ok U41(X1, X2, X3),
U43 mark X -> mark U43 X,
U43 ok X -> ok U43 X,
isNatIList ok X -> ok isNatIList X,
U52(mark X1, X2) -> mark U52(X1, X2),
U52(ok X1, ok X2) -> ok U52(X1, X2),
U51(mark X1, X2, X3) -> mark U51(X1, X2, X3),
U51(ok X1, ok X2, ok X3) -> ok U51(X1, X2, X3),
U53 mark X -> mark U53 X,
U53 ok X -> ok U53 X,
U62(mark X1, X2) -> mark U62(X1, X2),
U62(ok X1, ok X2) -> ok U62(X1, X2),
U61(mark X1, X2, X3) -> mark U61(X1, X2, X3),
U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3),
U63 mark X -> mark U63 X,
U63 ok X -> ok U63 X,
s mark X -> mark s X,
s ok X -> ok s X,
length mark X -> mark length X,
length ok X -> ok length X,
U71(mark X1, X2) -> mark U71(X1, X2),
U71(ok X1, ok X2) -> ok U71(X1, X2),
U81 mark X -> mark U81 X,
U81 ok X -> ok U81 X,
take(X1, mark X2) -> mark take(X1, X2),
take(mark X1, X2) -> mark take(X1, X2),
take(ok X1, ok X2) -> ok take(X1, X2),
U91(mark X1, X2, X3, X4) -> mark U91(X1, X2, X3, X4),
U91(ok X1, ok X2, ok X3, ok X4) -> ok U91(X1, X2, X3, X4),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatIListKind ok X -> ok isNatIListKind X,
isNatKind ok X -> ok isNatKind X,
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper 0() -> ok 0(),
proper zeros() -> ok zeros(),
proper U12 X -> U12 proper X,
proper isNatList X -> isNatList proper X,
proper U11(X1, X2) -> U11(proper X1, proper X2),
proper tt() -> ok tt(),
proper U22 X -> U22 proper X,
proper isNat X -> isNat proper X,
proper U21(X1, X2) -> U21(proper X1, proper X2),
proper U32 X -> U32 proper X,
proper U31(X1, X2) -> U31(proper X1, proper X2),
proper U42(X1, X2) -> U42(proper X1, proper X2),
proper U41(X1, X2, X3) -> U41(proper X1, proper X2, proper X3),
proper U43 X -> U43 proper X,
proper isNatIList X -> isNatIList proper X,
proper U52(X1, X2) -> U52(proper X1, proper X2),
proper U51(X1, X2, X3) -> U51(proper X1, proper X2, proper X3),
proper U53 X -> U53 proper X,
proper U62(X1, X2) -> U62(proper X1, proper X2),
proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3),
proper U63 X -> U63 proper X,
proper s X -> s proper X,
proper length X -> length proper X,
proper U71(X1, X2) -> U71(proper X1, proper X2),
proper nil() -> ok nil(),
proper U81 X -> U81 proper X,
proper take(X1, X2) -> take(proper X1, proper X2),
proper U91(X1, X2, X3, X4) -> U91(proper X1, proper X2, proper X3, proper X4),
proper and(X1, X2) -> and(proper X1, proper X2),
proper isNatIListKind X -> isNatIListKind proper X,
proper isNatKind X -> isNatKind proper X,
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (1):
Strict:
{isNatList# ok X -> isNatList# X}
Weak:
{ cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
active cons(X1, X2) -> cons(active X1, X2),
active zeros() -> mark cons(0(), zeros()),
active U12 X -> U12 active X,
active U12 tt() -> mark tt(),
active isNatList cons(V1, V2) -> mark U51(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatList nil() -> mark tt(),
active isNatList take(V1, V2) -> mark U61(and(isNatKind V1, isNatIListKind V2), V1, V2),
active U11(X1, X2) -> U11(active X1, X2),
active U11(tt(), V1) -> mark U12 isNatList V1,
active U22 X -> U22 active X,
active U22 tt() -> mark tt(),
active isNat 0() -> mark tt(),
active isNat s V1 -> mark U21(isNatKind V1, V1),
active isNat length V1 -> mark U11(isNatIListKind V1, V1),
active U21(X1, X2) -> U21(active X1, X2),
active U21(tt(), V1) -> mark U22 isNat V1,
active U32 X -> U32 active X,
active U32 tt() -> mark tt(),
active U31(X1, X2) -> U31(active X1, X2),
active U31(tt(), V) -> mark U32 isNatList V,
active U42(X1, X2) -> U42(active X1, X2),
active U42(tt(), V2) -> mark U43 isNatIList V2,
active U41(X1, X2, X3) -> U41(active X1, X2, X3),
active U41(tt(), V1, V2) -> mark U42(isNat V1, V2),
active U43 X -> U43 active X,
active U43 tt() -> mark tt(),
active isNatIList V -> mark U31(isNatIListKind V, V),
active isNatIList cons(V1, V2) -> mark U41(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatIList zeros() -> mark tt(),
active U52(X1, X2) -> U52(active X1, X2),
active U52(tt(), V2) -> mark U53 isNatList V2,
active U51(X1, X2, X3) -> U51(active X1, X2, X3),
active U51(tt(), V1, V2) -> mark U52(isNat V1, V2),
active U53 X -> U53 active X,
active U53 tt() -> mark tt(),
active U62(X1, X2) -> U62(active X1, X2),
active U62(tt(), V2) -> mark U63 isNatIList V2,
active U61(X1, X2, X3) -> U61(active X1, X2, X3),
active U61(tt(), V1, V2) -> mark U62(isNat V1, V2),
active U63 X -> U63 active X,
active U63 tt() -> mark tt(),
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark U71(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L),
active length nil() -> mark 0(),
active U71(X1, X2) -> U71(active X1, X2),
active U71(tt(), L) -> mark s length L,
active U81 X -> U81 active X,
active U81 tt() -> mark nil(),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark U81 and(isNatIList IL, isNatIListKind IL),
active take(s M, cons(N, IL)) -> mark U91(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N),
active U91(X1, X2, X3, X4) -> U91(active X1, X2, X3, X4),
active U91(tt(), IL, M, N) -> mark cons(N, take(M, IL)),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), X) -> mark X,
active isNatIListKind cons(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatIListKind zeros() -> mark tt(),
active isNatIListKind nil() -> mark tt(),
active isNatIListKind take(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatKind 0() -> mark tt(),
active isNatKind s V1 -> mark isNatKind V1,
active isNatKind length V1 -> mark isNatIListKind V1,
U12 mark X -> mark U12 X,
U12 ok X -> ok U12 X,
isNatList ok X -> ok isNatList X,
U11(mark X1, X2) -> mark U11(X1, X2),
U11(ok X1, ok X2) -> ok U11(X1, X2),
U22 mark X -> mark U22 X,
U22 ok X -> ok U22 X,
isNat ok X -> ok isNat X,
U21(mark X1, X2) -> mark U21(X1, X2),
U21(ok X1, ok X2) -> ok U21(X1, X2),
U32 mark X -> mark U32 X,
U32 ok X -> ok U32 X,
U31(mark X1, X2) -> mark U31(X1, X2),
U31(ok X1, ok X2) -> ok U31(X1, X2),
U42(mark X1, X2) -> mark U42(X1, X2),
U42(ok X1, ok X2) -> ok U42(X1, X2),
U41(mark X1, X2, X3) -> mark U41(X1, X2, X3),
U41(ok X1, ok X2, ok X3) -> ok U41(X1, X2, X3),
U43 mark X -> mark U43 X,
U43 ok X -> ok U43 X,
isNatIList ok X -> ok isNatIList X,
U52(mark X1, X2) -> mark U52(X1, X2),
U52(ok X1, ok X2) -> ok U52(X1, X2),
U51(mark X1, X2, X3) -> mark U51(X1, X2, X3),
U51(ok X1, ok X2, ok X3) -> ok U51(X1, X2, X3),
U53 mark X -> mark U53 X,
U53 ok X -> ok U53 X,
U62(mark X1, X2) -> mark U62(X1, X2),
U62(ok X1, ok X2) -> ok U62(X1, X2),
U61(mark X1, X2, X3) -> mark U61(X1, X2, X3),
U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3),
U63 mark X -> mark U63 X,
U63 ok X -> ok U63 X,
s mark X -> mark s X,
s ok X -> ok s X,
length mark X -> mark length X,
length ok X -> ok length X,
U71(mark X1, X2) -> mark U71(X1, X2),
U71(ok X1, ok X2) -> ok U71(X1, X2),
U81 mark X -> mark U81 X,
U81 ok X -> ok U81 X,
take(X1, mark X2) -> mark take(X1, X2),
take(mark X1, X2) -> mark take(X1, X2),
take(ok X1, ok X2) -> ok take(X1, X2),
U91(mark X1, X2, X3, X4) -> mark U91(X1, X2, X3, X4),
U91(ok X1, ok X2, ok X3, ok X4) -> ok U91(X1, X2, X3, X4),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatIListKind ok X -> ok isNatIListKind X,
isNatKind ok X -> ok isNatKind X,
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper 0() -> ok 0(),
proper zeros() -> ok zeros(),
proper U12 X -> U12 proper X,
proper isNatList X -> isNatList proper X,
proper U11(X1, X2) -> U11(proper X1, proper X2),
proper tt() -> ok tt(),
proper U22 X -> U22 proper X,
proper isNat X -> isNat proper X,
proper U21(X1, X2) -> U21(proper X1, proper X2),
proper U32 X -> U32 proper X,
proper U31(X1, X2) -> U31(proper X1, proper X2),
proper U42(X1, X2) -> U42(proper X1, proper X2),
proper U41(X1, X2, X3) -> U41(proper X1, proper X2, proper X3),
proper U43 X -> U43 proper X,
proper isNatIList X -> isNatIList proper X,
proper U52(X1, X2) -> U52(proper X1, proper X2),
proper U51(X1, X2, X3) -> U51(proper X1, proper X2, proper X3),
proper U53 X -> U53 proper X,
proper U62(X1, X2) -> U62(proper X1, proper X2),
proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3),
proper U63 X -> U63 proper X,
proper s X -> s proper X,
proper length X -> length proper X,
proper U71(X1, X2) -> U71(proper X1, proper X2),
proper nil() -> ok nil(),
proper U81 X -> U81 proper X,
proper take(X1, X2) -> take(proper X1, proper X2),
proper U91(X1, X2, X3, X4) -> U91(proper X1, proper X2, proper X3, proper X4),
proper and(X1, X2) -> and(proper X1, proper X2),
proper isNatIListKind X -> isNatIListKind proper X,
proper isNatKind X -> isNatKind proper X,
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (1):
Strict:
{isNatKind# ok X -> isNatKind# X}
Weak:
{ cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
active cons(X1, X2) -> cons(active X1, X2),
active zeros() -> mark cons(0(), zeros()),
active U12 X -> U12 active X,
active U12 tt() -> mark tt(),
active isNatList cons(V1, V2) -> mark U51(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatList nil() -> mark tt(),
active isNatList take(V1, V2) -> mark U61(and(isNatKind V1, isNatIListKind V2), V1, V2),
active U11(X1, X2) -> U11(active X1, X2),
active U11(tt(), V1) -> mark U12 isNatList V1,
active U22 X -> U22 active X,
active U22 tt() -> mark tt(),
active isNat 0() -> mark tt(),
active isNat s V1 -> mark U21(isNatKind V1, V1),
active isNat length V1 -> mark U11(isNatIListKind V1, V1),
active U21(X1, X2) -> U21(active X1, X2),
active U21(tt(), V1) -> mark U22 isNat V1,
active U32 X -> U32 active X,
active U32 tt() -> mark tt(),
active U31(X1, X2) -> U31(active X1, X2),
active U31(tt(), V) -> mark U32 isNatList V,
active U42(X1, X2) -> U42(active X1, X2),
active U42(tt(), V2) -> mark U43 isNatIList V2,
active U41(X1, X2, X3) -> U41(active X1, X2, X3),
active U41(tt(), V1, V2) -> mark U42(isNat V1, V2),
active U43 X -> U43 active X,
active U43 tt() -> mark tt(),
active isNatIList V -> mark U31(isNatIListKind V, V),
active isNatIList cons(V1, V2) -> mark U41(and(isNatKind V1, isNatIListKind V2), V1, V2),
active isNatIList zeros() -> mark tt(),
active U52(X1, X2) -> U52(active X1, X2),
active U52(tt(), V2) -> mark U53 isNatList V2,
active U51(X1, X2, X3) -> U51(active X1, X2, X3),
active U51(tt(), V1, V2) -> mark U52(isNat V1, V2),
active U53 X -> U53 active X,
active U53 tt() -> mark tt(),
active U62(X1, X2) -> U62(active X1, X2),
active U62(tt(), V2) -> mark U63 isNatIList V2,
active U61(X1, X2, X3) -> U61(active X1, X2, X3),
active U61(tt(), V1, V2) -> mark U62(isNat V1, V2),
active U63 X -> U63 active X,
active U63 tt() -> mark tt(),
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark U71(and(and(isNatList L, isNatIListKind L), and(isNat N, isNatKind N)), L),
active length nil() -> mark 0(),
active U71(X1, X2) -> U71(active X1, X2),
active U71(tt(), L) -> mark s length L,
active U81 X -> U81 active X,
active U81 tt() -> mark nil(),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark U81 and(isNatIList IL, isNatIListKind IL),
active take(s M, cons(N, IL)) -> mark U91(and(and(isNatIList IL, isNatIListKind IL), and(and(isNat M, isNatKind M), and(isNat N, isNatKind N))), IL, M, N),
active U91(X1, X2, X3, X4) -> U91(active X1, X2, X3, X4),
active U91(tt(), IL, M, N) -> mark cons(N, take(M, IL)),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), X) -> mark X,
active isNatIListKind cons(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatIListKind zeros() -> mark tt(),
active isNatIListKind nil() -> mark tt(),
active isNatIListKind take(V1, V2) -> mark and(isNatKind V1, isNatIListKind V2),
active isNatKind 0() -> mark tt(),
active isNatKind s V1 -> mark isNatKind V1,
active isNatKind length V1 -> mark isNatIListKind V1,
U12 mark X -> mark U12 X,
U12 ok X -> ok U12 X,
isNatList ok X -> ok isNatList X,
U11(mark X1, X2) -> mark U11(X1, X2),
U11(ok X1, ok X2) -> ok U11(X1, X2),
U22 mark X -> mark U22 X,
U22 ok X -> ok U22 X,
isNat ok X -> ok isNat X,
U21(mark X1, X2) -> mark U21(X1, X2),
U21(ok X1, ok X2) -> ok U21(X1, X2),
U32 mark X -> mark U32 X,
U32 ok X -> ok U32 X,
U31(mark X1, X2) -> mark U31(X1, X2),
U31(ok X1, ok X2) -> ok U31(X1, X2),
U42(mark X1, X2) -> mark U42(X1, X2),
U42(ok X1, ok X2) -> ok U42(X1, X2),
U41(mark X1, X2, X3) -> mark U41(X1, X2, X3),
U41(ok X1, ok X2, ok X3) -> ok U41(X1, X2, X3),
U43 mark X -> mark U43 X,
U43 ok X -> ok U43 X,
isNatIList ok X -> ok isNatIList X,
U52(mark X1, X2) -> mark U52(X1, X2),
U52(ok X1, ok X2) -> ok U52(X1, X2),
U51(mark X1, X2, X3) -> mark U51(X1, X2, X3),
U51(ok X1, ok X2, ok X3) -> ok U51(X1, X2, X3),
U53 mark X -> mark U53 X,
U53 ok X -> ok U53 X,
U62(mark X1, X2) -> mark U62(X1, X2),
U62(ok X1, ok X2) -> ok U62(X1, X2),
U61(mark X1, X2, X3) -> mark U61(X1, X2, X3),
U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3),
U63 mark X -> mark U63 X,
U63 ok X -> ok U63 X,
s mark X -> mark s X,
s ok X -> ok s X,
length mark X -> mark length X,
length ok X -> ok length X,
U71(mark X1, X2) -> mark U71(X1, X2),
U71(ok X1, ok X2) -> ok U71(X1, X2),
U81 mark X -> mark U81 X,
U81 ok X -> ok U81 X,
take(X1, mark X2) -> mark take(X1, X2),
take(mark X1, X2) -> mark take(X1, X2),
take(ok X1, ok X2) -> ok take(X1, X2),
U91(mark X1, X2, X3, X4) -> mark U91(X1, X2, X3, X4),
U91(ok X1, ok X2, ok X3, ok X4) -> ok U91(X1, X2, X3, X4),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatIListKind ok X -> ok isNatIListKind X,
isNatKind ok X -> ok isNatKind X,
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper 0() -> ok 0(),
proper zeros() -> ok zeros(),
proper U12 X -> U12 proper X,
proper isNatList X -> isNatList proper X,
proper U11(X1, X2) -> U11(proper X1, proper X2),
proper tt() -> ok tt(),
proper U22 X -> U22 proper X,
proper isNat X -> isNat proper X,
proper U21(X1, X2) -> U21(proper X1, proper X2),
proper U32 X -> U32 proper X,
proper U31(X1, X2) -> U31(proper X1, proper X2),
proper U42(X1, X2) -> U42(proper X1, proper X2),
proper U41(X1, X2, X3) -> U41(proper X1, proper X2, proper X3),
proper U43 X -> U43 proper X,
proper isNatIList X -> isNatIList proper X,
proper U52(X1, X2) -> U52(proper X1, proper X2),
proper U51(X1, X2, X3) -> U51(proper X1, proper X2, proper X3),
proper U53 X -> U53 proper X,
proper U62(X1, X2) -> U62(proper X1, proper X2),
proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3),
proper U63 X -> U63 proper X,
proper s X -> s proper X,
proper length X -> length proper X,
proper U71(X1, X2) -> U71(proper X1, proper X2),
proper nil() -> ok nil(),
proper U81 X -> U81 proper X,
proper take(X1, X2) -> take(proper X1, proper X2),
proper U91(X1, X2, X3, X4) -> U91(proper X1, proper X2, proper X3, proper X4),
proper and(X1, X2) -> and(proper X1, proper X2),
proper isNatIListKind X -> isNatIListKind proper X,
proper isNatKind X -> isNatKind proper X,
top mark X -> top proper X,
top ok X -> top active X}
Open