MAYBE
Time: 0.176345
TRS:
{ active and(X1, X2) -> and(X1, active X2),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), T) -> mark T,
active isNatList cons(N, L) -> mark and(isNat N, isNatList L),
active isNatList nil() -> mark tt(),
active isNatList take(N, IL) -> mark and(isNat N, isNatIList IL),
active isNatIList IL -> mark isNatList IL,
active isNatIList zeros() -> mark tt(),
active isNatIList cons(N, IL) -> mark and(isNat N, isNatIList IL),
active isNat 0() -> mark tt(),
active isNat s N -> mark isNat N,
active isNat length L -> mark isNatList L,
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark uLength(and(isNat N, isNatList L), L),
active zeros() -> mark cons(0(), zeros()),
active cons(X1, X2) -> cons(active X1, X2),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark uTake1 isNatIList IL,
active take(s M, cons(N, IL)) -> mark uTake2(and(isNat M, and(isNat N, isNatIList IL)), M, N, IL),
active uTake1 X -> uTake1 active X,
active uTake1 tt() -> mark nil(),
active uTake2(X1, X2, X3, X4) -> uTake2(active X1, X2, X3, X4),
active uTake2(tt(), M, N, IL) -> mark cons(N, take(M, IL)),
active uLength(X1, X2) -> uLength(active X1, X2),
active uLength(tt(), L) -> mark s length L,
and(X1, mark X2) -> mark and(X1, X2),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatList ok X -> ok isNatList X,
isNatIList ok X -> ok isNatIList X,
isNat ok X -> ok isNat 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,
cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
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),
uTake1 mark X -> mark uTake1 X,
uTake1 ok X -> ok uTake1 X,
uTake2(mark X1, X2, X3, X4) -> mark uTake2(X1, X2, X3, X4),
uTake2(ok X1, ok X2, ok X3, ok X4) -> ok uTake2(X1, X2, X3, X4),
uLength(mark X1, X2) -> mark uLength(X1, X2),
uLength(ok X1, ok X2) -> ok uLength(X1, X2),
proper and(X1, X2) -> and(proper X1, proper X2),
proper tt() -> ok tt(),
proper isNatList X -> isNatList proper X,
proper isNatIList X -> isNatIList proper X,
proper isNat X -> isNat proper X,
proper 0() -> ok 0(),
proper s X -> s proper X,
proper length X -> length proper X,
proper zeros() -> ok zeros(),
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper nil() -> ok nil(),
proper take(X1, X2) -> take(proper X1, proper X2),
proper uTake1 X -> uTake1 proper X,
proper uTake2(X1, X2, X3, X4) -> uTake2(proper X1, proper X2, proper X3, proper X4),
proper uLength(X1, X2) -> uLength(proper X1, proper X2),
top mark X -> top proper X,
top ok X -> top active X}
DP:
DP:
{ active# and(X1, X2) -> active# X1,
active# and(X1, X2) -> active# X2,
active# and(X1, X2) -> and#(X1, active X2),
active# and(X1, X2) -> and#(active X1, X2),
active# isNatList cons(N, L) -> and#(isNat N, isNatList L),
active# isNatList cons(N, L) -> isNatList# L,
active# isNatList cons(N, L) -> isNat# N,
active# isNatList take(N, IL) -> and#(isNat N, isNatIList IL),
active# isNatList take(N, IL) -> isNatIList# IL,
active# isNatList take(N, IL) -> isNat# N,
active# isNatIList IL -> isNatList# IL,
active# isNatIList cons(N, IL) -> and#(isNat N, isNatIList IL),
active# isNatIList cons(N, IL) -> isNatIList# IL,
active# isNatIList cons(N, IL) -> isNat# N,
active# isNat s N -> isNat# N,
active# isNat length L -> isNatList# L,
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) -> and#(isNat N, isNatList L),
active# length cons(N, L) -> isNatList# L,
active# length cons(N, L) -> isNat# N,
active# length cons(N, L) -> uLength#(and(isNat N, isNatList L), L),
active# zeros() -> cons#(0(), zeros()),
active# cons(X1, X2) -> active# X1,
active# cons(X1, X2) -> cons#(active X1, X2),
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) -> uTake1# isNatIList IL,
active# take(s M, cons(N, IL)) -> and#(isNat N, isNatIList IL),
active# take(s M, cons(N, IL)) -> and#(isNat M, and(isNat N, isNatIList IL)),
active# take(s M, cons(N, IL)) -> isNatIList# 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)) -> uTake2#(and(isNat M, and(isNat N, isNatIList IL)), M, N, IL),
active# uTake1 X -> active# X,
active# uTake1 X -> uTake1# active X,
active# uTake2(X1, X2, X3, X4) -> active# X1,
active# uTake2(X1, X2, X3, X4) -> uTake2#(active X1, X2, X3, X4),
active# uTake2(tt(), M, N, IL) -> cons#(N, take(M, IL)),
active# uTake2(tt(), M, N, IL) -> take#(M, IL),
active# uLength(X1, X2) -> active# X1,
active# uLength(X1, X2) -> uLength#(active X1, X2),
active# uLength(tt(), L) -> s# length L,
active# uLength(tt(), L) -> length# L,
and#(X1, mark X2) -> and#(X1, X2),
and#(mark X1, X2) -> and#(X1, X2),
and#(ok X1, ok X2) -> and#(X1, X2),
isNatList# ok X -> isNatList# X,
isNatIList# ok X -> isNatIList# X,
isNat# ok X -> isNat# X,
s# mark X -> s# X,
s# ok X -> s# X,
length# mark X -> length# X,
length# ok X -> length# X,
cons#(mark X1, X2) -> cons#(X1, X2),
cons#(ok X1, ok X2) -> cons#(X1, X2),
take#(X1, mark X2) -> take#(X1, X2),
take#(mark X1, X2) -> take#(X1, X2),
take#(ok X1, ok X2) -> take#(X1, X2),
uTake1# mark X -> uTake1# X,
uTake1# ok X -> uTake1# X,
uTake2#(mark X1, X2, X3, X4) -> uTake2#(X1, X2, X3, X4),
uTake2#(ok X1, ok X2, ok X3, ok X4) -> uTake2#(X1, X2, X3, X4),
uLength#(mark X1, X2) -> uLength#(X1, X2),
uLength#(ok X1, ok X2) -> uLength#(X1, X2),
proper# and(X1, X2) -> and#(proper X1, proper X2),
proper# and(X1, X2) -> proper# X1,
proper# and(X1, X2) -> proper# X2,
proper# isNatList X -> isNatList# proper X,
proper# isNatList X -> proper# X,
proper# isNatIList X -> isNatIList# proper X,
proper# isNatIList X -> proper# X,
proper# isNat X -> isNat# proper X,
proper# isNat 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# cons(X1, X2) -> cons#(proper X1, proper X2),
proper# cons(X1, X2) -> proper# X1,
proper# cons(X1, X2) -> proper# X2,
proper# take(X1, X2) -> take#(proper X1, proper X2),
proper# take(X1, X2) -> proper# X1,
proper# take(X1, X2) -> proper# X2,
proper# uTake1 X -> uTake1# proper X,
proper# uTake1 X -> proper# X,
proper# uTake2(X1, X2, X3, X4) -> uTake2#(proper X1, proper X2, proper X3, proper X4),
proper# uTake2(X1, X2, X3, X4) -> proper# X1,
proper# uTake2(X1, X2, X3, X4) -> proper# X2,
proper# uTake2(X1, X2, X3, X4) -> proper# X3,
proper# uTake2(X1, X2, X3, X4) -> proper# X4,
proper# uLength(X1, X2) -> uLength#(proper X1, proper X2),
proper# uLength(X1, X2) -> proper# X1,
proper# uLength(X1, X2) -> proper# X2,
top# mark X -> proper# X,
top# mark X -> top# proper X,
top# ok X -> active# X,
top# ok X -> top# active X}
TRS:
{ active and(X1, X2) -> and(X1, active X2),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), T) -> mark T,
active isNatList cons(N, L) -> mark and(isNat N, isNatList L),
active isNatList nil() -> mark tt(),
active isNatList take(N, IL) -> mark and(isNat N, isNatIList IL),
active isNatIList IL -> mark isNatList IL,
active isNatIList zeros() -> mark tt(),
active isNatIList cons(N, IL) -> mark and(isNat N, isNatIList IL),
active isNat 0() -> mark tt(),
active isNat s N -> mark isNat N,
active isNat length L -> mark isNatList L,
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark uLength(and(isNat N, isNatList L), L),
active zeros() -> mark cons(0(), zeros()),
active cons(X1, X2) -> cons(active X1, X2),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark uTake1 isNatIList IL,
active take(s M, cons(N, IL)) -> mark uTake2(and(isNat M, and(isNat N, isNatIList IL)), M, N, IL),
active uTake1 X -> uTake1 active X,
active uTake1 tt() -> mark nil(),
active uTake2(X1, X2, X3, X4) -> uTake2(active X1, X2, X3, X4),
active uTake2(tt(), M, N, IL) -> mark cons(N, take(M, IL)),
active uLength(X1, X2) -> uLength(active X1, X2),
active uLength(tt(), L) -> mark s length L,
and(X1, mark X2) -> mark and(X1, X2),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatList ok X -> ok isNatList X,
isNatIList ok X -> ok isNatIList X,
isNat ok X -> ok isNat 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,
cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
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),
uTake1 mark X -> mark uTake1 X,
uTake1 ok X -> ok uTake1 X,
uTake2(mark X1, X2, X3, X4) -> mark uTake2(X1, X2, X3, X4),
uTake2(ok X1, ok X2, ok X3, ok X4) -> ok uTake2(X1, X2, X3, X4),
uLength(mark X1, X2) -> mark uLength(X1, X2),
uLength(ok X1, ok X2) -> ok uLength(X1, X2),
proper and(X1, X2) -> and(proper X1, proper X2),
proper tt() -> ok tt(),
proper isNatList X -> isNatList proper X,
proper isNatIList X -> isNatIList proper X,
proper isNat X -> isNat proper X,
proper 0() -> ok 0(),
proper s X -> s proper X,
proper length X -> length proper X,
proper zeros() -> ok zeros(),
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper nil() -> ok nil(),
proper take(X1, X2) -> take(proper X1, proper X2),
proper uTake1 X -> uTake1 proper X,
proper uTake2(X1, X2, X3, X4) -> uTake2(proper X1, proper X2, proper X3, proper X4),
proper uLength(X1, X2) -> uLength(proper X1, proper X2),
top mark X -> top proper X,
top ok X -> top active X}
EDG:
{
(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# uLength(X1, X2) -> uLength#(active X1, X2), uLength#(ok X1, ok X2) -> uLength#(X1, X2))
(active# uLength(X1, X2) -> uLength#(active X1, X2), uLength#(mark X1, X2) -> uLength#(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))
(and#(mark X1, X2) -> and#(X1, X2), and#(X1, mark X2) -> and#(X1, X2))
(cons#(mark X1, X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2))
(cons#(mark X1, X2) -> cons#(X1, X2), cons#(mark X1, X2) -> cons#(X1, X2))
(take#(X1, mark X2) -> take#(X1, X2), take#(ok X1, ok 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#(X1, mark X2) -> take#(X1, X2))
(take#(ok X1, ok X2) -> take#(X1, X2), take#(ok X1, ok 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#(X1, mark X2) -> take#(X1, X2))
(uLength#(ok X1, ok X2) -> uLength#(X1, X2), uLength#(ok X1, ok X2) -> uLength#(X1, X2))
(uLength#(ok X1, ok X2) -> uLength#(X1, X2), uLength#(mark X1, X2) -> uLength#(X1, X2))
(active# take(s M, cons(N, IL)) -> and#(isNat M, and(isNat N, isNatIList IL)), and#(ok X1, ok X2) -> and#(X1, X2))
(active# isNatList take(N, IL) -> isNat# N, isNat# ok X -> isNat# X)
(active# isNat s N -> isNat# N, isNat# ok X -> isNat# X)
(active# take(s M, cons(N, IL)) -> isNat# N, isNat# ok X -> isNat# X)
(active# uTake2(tt(), M, N, IL) -> cons#(N, take(M, IL)), cons#(ok X1, ok X2) -> cons#(X1, X2))
(active# uTake2(tt(), M, N, IL) -> cons#(N, take(M, IL)), cons#(mark X1, X2) -> cons#(X1, X2))
(active# uTake2(X1, X2, X3, X4) -> uTake2#(active X1, X2, X3, X4), uTake2#(ok X1, ok X2, ok X3, ok X4) -> uTake2#(X1, X2, X3, X4))
(active# uTake2(X1, X2, X3, X4) -> uTake2#(active X1, X2, X3, X4), uTake2#(mark X1, X2, X3, X4) -> uTake2#(X1, X2, X3, X4))
(uTake2#(ok X1, ok X2, ok X3, ok X4) -> uTake2#(X1, X2, X3, X4), uTake2#(ok X1, ok X2, ok X3, ok X4) -> uTake2#(X1, X2, X3, X4))
(uTake2#(ok X1, ok X2, ok X3, ok X4) -> uTake2#(X1, X2, X3, X4), uTake2#(mark X1, X2, X3, X4) -> uTake2#(X1, X2, X3, X4))
(active# and(X1, X2) -> active# X2, active# uLength(tt(), L) -> length# L)
(active# and(X1, X2) -> active# X2, active# uLength(tt(), L) -> s# length L)
(active# and(X1, X2) -> active# X2, active# uLength(X1, X2) -> uLength#(active X1, X2))
(active# and(X1, X2) -> active# X2, active# uLength(X1, X2) -> active# X1)
(active# and(X1, X2) -> active# X2, active# uTake2(tt(), M, N, IL) -> take#(M, IL))
(active# and(X1, X2) -> active# X2, active# uTake2(tt(), M, N, IL) -> cons#(N, take(M, IL)))
(active# and(X1, X2) -> active# X2, active# uTake2(X1, X2, X3, X4) -> uTake2#(active X1, X2, X3, X4))
(active# and(X1, X2) -> active# X2, active# uTake2(X1, X2, X3, X4) -> active# X1)
(active# and(X1, X2) -> active# X2, active# uTake1 X -> uTake1# active X)
(active# and(X1, X2) -> active# X2, active# uTake1 X -> active# X)
(active# and(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> uTake2#(and(isNat M, and(isNat N, isNatIList IL)), M, N, IL))
(active# and(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> isNat# M)
(active# and(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> isNat# N)
(active# and(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> isNatIList# IL)
(active# and(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> and#(isNat M, and(isNat N, isNatIList IL)))
(active# and(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> and#(isNat N, isNatIList IL))
(active# and(X1, X2) -> active# X2, active# take(0(), IL) -> uTake1# isNatIList IL)
(active# and(X1, X2) -> active# X2, active# take(0(), IL) -> isNatIList# IL)
(active# and(X1, X2) -> active# X2, active# take(X1, X2) -> take#(active X1, X2))
(active# and(X1, X2) -> active# X2, active# take(X1, X2) -> take#(X1, active X2))
(active# and(X1, X2) -> active# X2, active# take(X1, X2) -> active# X2)
(active# and(X1, X2) -> active# X2, active# take(X1, X2) -> active# X1)
(active# and(X1, X2) -> active# X2, active# cons(X1, X2) -> cons#(active X1, X2))
(active# and(X1, X2) -> active# X2, active# cons(X1, X2) -> active# X1)
(active# and(X1, X2) -> active# X2, active# zeros() -> cons#(0(), zeros()))
(active# and(X1, X2) -> active# X2, active# length cons(N, L) -> uLength#(and(isNat N, isNatList L), L))
(active# and(X1, X2) -> active# X2, active# length cons(N, L) -> isNat# N)
(active# and(X1, X2) -> active# X2, active# length cons(N, L) -> isNatList# L)
(active# and(X1, X2) -> active# X2, active# length cons(N, L) -> and#(isNat N, isNatList L))
(active# and(X1, X2) -> active# X2, active# length X -> length# active X)
(active# and(X1, X2) -> active# X2, active# length X -> active# X)
(active# and(X1, X2) -> active# X2, active# s X -> s# active X)
(active# and(X1, X2) -> active# X2, active# s X -> active# X)
(active# and(X1, X2) -> active# X2, active# isNat length L -> isNatList# L)
(active# and(X1, X2) -> active# X2, active# isNat s N -> isNat# N)
(active# and(X1, X2) -> active# X2, active# isNatIList cons(N, IL) -> isNat# N)
(active# and(X1, X2) -> active# X2, active# isNatIList cons(N, IL) -> isNatIList# IL)
(active# and(X1, X2) -> active# X2, active# isNatIList cons(N, IL) -> and#(isNat N, isNatIList IL))
(active# and(X1, X2) -> active# X2, active# isNatIList IL -> isNatList# IL)
(active# and(X1, X2) -> active# X2, active# isNatList take(N, IL) -> isNat# N)
(active# and(X1, X2) -> active# X2, active# isNatList take(N, IL) -> isNatIList# IL)
(active# and(X1, X2) -> active# X2, active# isNatList take(N, IL) -> and#(isNat N, isNatIList IL))
(active# and(X1, X2) -> active# X2, active# isNatList cons(N, L) -> isNat# N)
(active# and(X1, X2) -> active# X2, active# isNatList cons(N, L) -> isNatList# L)
(active# and(X1, X2) -> active# X2, active# isNatList cons(N, L) -> and#(isNat N, isNatList L))
(active# and(X1, X2) -> active# X2, active# and(X1, X2) -> and#(active X1, X2))
(active# and(X1, X2) -> active# X2, active# and(X1, X2) -> and#(X1, active X2))
(active# and(X1, X2) -> active# X2, active# and(X1, X2) -> active# X2)
(active# and(X1, X2) -> active# X2, active# and(X1, X2) -> active# X1)
(proper# and(X1, X2) -> proper# X2, proper# uLength(X1, X2) -> proper# X2)
(proper# and(X1, X2) -> proper# X2, proper# uLength(X1, X2) -> proper# X1)
(proper# and(X1, X2) -> proper# X2, proper# uLength(X1, X2) -> uLength#(proper X1, proper X2))
(proper# and(X1, X2) -> proper# X2, proper# uTake2(X1, X2, X3, X4) -> proper# X4)
(proper# and(X1, X2) -> proper# X2, proper# uTake2(X1, X2, X3, X4) -> proper# X3)
(proper# and(X1, X2) -> proper# X2, proper# uTake2(X1, X2, X3, X4) -> proper# X2)
(proper# and(X1, X2) -> proper# X2, proper# uTake2(X1, X2, X3, X4) -> proper# X1)
(proper# and(X1, X2) -> proper# X2, proper# uTake2(X1, X2, X3, X4) -> uTake2#(proper X1, proper X2, proper X3, proper X4))
(proper# and(X1, X2) -> proper# X2, proper# uTake1 X -> proper# X)
(proper# and(X1, X2) -> proper# X2, proper# uTake1 X -> uTake1# proper X)
(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# 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))
(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# isNat X -> proper# X)
(proper# and(X1, X2) -> proper# X2, proper# isNat X -> isNat# proper X)
(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# isNatList X -> proper# X)
(proper# and(X1, X2) -> proper# X2, proper# isNatList X -> isNatList# 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# take(X1, X2) -> proper# X2, proper# uLength(X1, X2) -> proper# X2)
(proper# take(X1, X2) -> proper# X2, proper# uLength(X1, X2) -> proper# X1)
(proper# take(X1, X2) -> proper# X2, proper# uLength(X1, X2) -> uLength#(proper X1, proper X2))
(proper# take(X1, X2) -> proper# X2, proper# uTake2(X1, X2, X3, X4) -> proper# X4)
(proper# take(X1, X2) -> proper# X2, proper# uTake2(X1, X2, X3, X4) -> proper# X3)
(proper# take(X1, X2) -> proper# X2, proper# uTake2(X1, X2, X3, X4) -> proper# X2)
(proper# take(X1, X2) -> proper# X2, proper# uTake2(X1, X2, X3, X4) -> proper# X1)
(proper# take(X1, X2) -> proper# X2, proper# uTake2(X1, X2, X3, X4) -> uTake2#(proper X1, proper X2, proper X3, proper X4))
(proper# take(X1, X2) -> proper# X2, proper# uTake1 X -> proper# X)
(proper# take(X1, X2) -> proper# X2, proper# uTake1 X -> uTake1# proper X)
(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# 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# 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# isNat X -> proper# X)
(proper# take(X1, X2) -> proper# X2, proper# isNat X -> isNat# proper X)
(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# isNatList X -> proper# X)
(proper# take(X1, X2) -> proper# X2, proper# isNatList X -> isNatList# 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# uLength(X1, X2) -> proper# X2, proper# uLength(X1, X2) -> proper# X2)
(proper# uLength(X1, X2) -> proper# X2, proper# uLength(X1, X2) -> proper# X1)
(proper# uLength(X1, X2) -> proper# X2, proper# uLength(X1, X2) -> uLength#(proper X1, proper X2))
(proper# uLength(X1, X2) -> proper# X2, proper# uTake2(X1, X2, X3, X4) -> proper# X4)
(proper# uLength(X1, X2) -> proper# X2, proper# uTake2(X1, X2, X3, X4) -> proper# X3)
(proper# uLength(X1, X2) -> proper# X2, proper# uTake2(X1, X2, X3, X4) -> proper# X2)
(proper# uLength(X1, X2) -> proper# X2, proper# uTake2(X1, X2, X3, X4) -> proper# X1)
(proper# uLength(X1, X2) -> proper# X2, proper# uTake2(X1, X2, X3, X4) -> uTake2#(proper X1, proper X2, proper X3, proper X4))
(proper# uLength(X1, X2) -> proper# X2, proper# uTake1 X -> proper# X)
(proper# uLength(X1, X2) -> proper# X2, proper# uTake1 X -> uTake1# proper X)
(proper# uLength(X1, X2) -> proper# X2, proper# take(X1, X2) -> proper# X2)
(proper# uLength(X1, X2) -> proper# X2, proper# take(X1, X2) -> proper# X1)
(proper# uLength(X1, X2) -> proper# X2, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# uLength(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X2)
(proper# uLength(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1)
(proper# uLength(X1, X2) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# uLength(X1, X2) -> proper# X2, proper# length X -> proper# X)
(proper# uLength(X1, X2) -> proper# X2, proper# length X -> length# proper X)
(proper# uLength(X1, X2) -> proper# X2, proper# s X -> proper# X)
(proper# uLength(X1, X2) -> proper# X2, proper# s X -> s# proper X)
(proper# uLength(X1, X2) -> proper# X2, proper# isNat X -> proper# X)
(proper# uLength(X1, X2) -> proper# X2, proper# isNat X -> isNat# proper X)
(proper# uLength(X1, X2) -> proper# X2, proper# isNatIList X -> proper# X)
(proper# uLength(X1, X2) -> proper# X2, proper# isNatIList X -> isNatIList# proper X)
(proper# uLength(X1, X2) -> proper# X2, proper# isNatList X -> proper# X)
(proper# uLength(X1, X2) -> proper# X2, proper# isNatList X -> isNatList# proper X)
(proper# uLength(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X2)
(proper# uLength(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X1)
(proper# uLength(X1, X2) -> proper# X2, proper# and(X1, X2) -> and#(proper X1, proper X2))
(active# s X -> s# active X, s# ok X -> s# X)
(active# s X -> s# active X, s# mark X -> s# X)
(active# uTake1 X -> uTake1# active X, uTake1# ok X -> uTake1# X)
(active# uTake1 X -> uTake1# active X, uTake1# mark X -> uTake1# X)
(proper# isNatIList X -> isNatIList# proper X, isNatIList# ok X -> isNatIList# X)
(proper# s X -> s# proper X, s# ok X -> s# X)
(proper# s X -> s# proper X, s# mark X -> s# X)
(proper# uTake1 X -> uTake1# proper X, uTake1# ok X -> uTake1# X)
(proper# uTake1 X -> uTake1# proper X, uTake1# mark X -> uTake1# 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# take(0(), IL) -> uTake1# isNatIList IL, uTake1# ok X -> uTake1# X)
(active# isNatList take(N, IL) -> isNatIList# IL, isNatIList# ok X -> isNatIList# X)
(active# isNatIList cons(N, IL) -> isNatIList# IL, isNatIList# ok X -> isNatIList# X)
(active# take(s M, cons(N, IL)) -> isNatIList# IL, isNatIList# ok X -> isNatIList# X)
(active# isNat length L -> isNatList# L, isNatList# ok X -> isNatList# X)
(active# uLength(tt(), L) -> length# L, length# ok X -> length# X)
(active# uLength(tt(), L) -> length# L, length# mark X -> length# X)
(active# cons(X1, X2) -> active# X1, active# uLength(tt(), L) -> length# L)
(active# cons(X1, X2) -> active# X1, active# uLength(tt(), L) -> s# length L)
(active# cons(X1, X2) -> active# X1, active# uLength(X1, X2) -> uLength#(active X1, X2))
(active# cons(X1, X2) -> active# X1, active# uLength(X1, X2) -> active# X1)
(active# cons(X1, X2) -> active# X1, active# uTake2(tt(), M, N, IL) -> take#(M, IL))
(active# cons(X1, X2) -> active# X1, active# uTake2(tt(), M, N, IL) -> cons#(N, take(M, IL)))
(active# cons(X1, X2) -> active# X1, active# uTake2(X1, X2, X3, X4) -> uTake2#(active X1, X2, X3, X4))
(active# cons(X1, X2) -> active# X1, active# uTake2(X1, X2, X3, X4) -> active# X1)
(active# cons(X1, X2) -> active# X1, active# uTake1 X -> uTake1# active X)
(active# cons(X1, X2) -> active# X1, active# uTake1 X -> active# X)
(active# cons(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> uTake2#(and(isNat M, and(isNat N, isNatIList IL)), M, N, IL))
(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)) -> isNat# N)
(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)) -> and#(isNat M, and(isNat N, isNatIList IL)))
(active# cons(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat N, isNatIList IL))
(active# cons(X1, X2) -> active# X1, active# take(0(), IL) -> uTake1# isNatIList IL)
(active# cons(X1, X2) -> active# X1, active# take(0(), IL) -> isNatIList# IL)
(active# cons(X1, X2) -> active# X1, active# take(X1, X2) -> take#(active X1, 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) -> active# X2)
(active# cons(X1, X2) -> active# X1, active# take(X1, X2) -> active# X1)
(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# length cons(N, L) -> uLength#(and(isNat N, isNatList L), 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) -> isNatList# L)
(active# cons(X1, X2) -> active# X1, active# length cons(N, L) -> and#(isNat N, isNatList L))
(active# cons(X1, X2) -> active# X1, active# length X -> length# active X)
(active# cons(X1, X2) -> active# X1, active# length X -> active# X)
(active# cons(X1, X2) -> active# X1, active# s X -> s# active X)
(active# cons(X1, X2) -> active# X1, active# s X -> active# X)
(active# cons(X1, X2) -> active# X1, active# isNat length L -> isNatList# L)
(active# cons(X1, X2) -> active# X1, active# isNat s N -> isNat# N)
(active# cons(X1, X2) -> active# X1, active# isNatIList cons(N, IL) -> isNat# N)
(active# cons(X1, X2) -> active# X1, active# isNatIList cons(N, IL) -> isNatIList# IL)
(active# cons(X1, X2) -> active# X1, active# isNatIList cons(N, IL) -> and#(isNat N, isNatIList IL))
(active# cons(X1, X2) -> active# X1, active# isNatIList IL -> isNatList# IL)
(active# cons(X1, X2) -> active# X1, active# isNatList take(N, IL) -> isNat# N)
(active# cons(X1, X2) -> active# X1, active# isNatList take(N, IL) -> isNatIList# IL)
(active# cons(X1, X2) -> active# X1, active# isNatList take(N, IL) -> and#(isNat N, isNatIList IL))
(active# cons(X1, X2) -> active# X1, active# isNatList cons(N, L) -> isNat# N)
(active# cons(X1, X2) -> active# X1, active# isNatList cons(N, L) -> isNatList# L)
(active# cons(X1, X2) -> active# X1, active# isNatList cons(N, L) -> and#(isNat N, isNatList L))
(active# cons(X1, X2) -> active# X1, active# and(X1, X2) -> and#(active X1, X2))
(active# cons(X1, X2) -> active# X1, active# and(X1, X2) -> and#(X1, active X2))
(active# cons(X1, X2) -> active# X1, active# and(X1, X2) -> active# X2)
(active# cons(X1, X2) -> active# X1, active# and(X1, X2) -> active# X1)
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# uLength(tt(), L) -> length# L)
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# uLength(tt(), L) -> s# length L)
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# uLength(X1, X2) -> uLength#(active X1, X2))
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# uLength(X1, X2) -> active# X1)
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# uTake2(tt(), M, N, IL) -> take#(M, IL))
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# uTake2(tt(), M, N, IL) -> cons#(N, take(M, IL)))
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# uTake2(X1, X2, X3, X4) -> uTake2#(active X1, X2, X3, X4))
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# uTake2(X1, X2, X3, X4) -> active# X1)
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# uTake1 X -> uTake1# active X)
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# uTake1 X -> active# X)
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> uTake2#(and(isNat M, and(isNat N, isNatIList IL)), M, N, IL))
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# M)
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# N)
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIList# IL)
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat M, and(isNat N, isNatIList IL)))
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat N, isNatIList IL))
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# take(0(), IL) -> uTake1# isNatIList IL)
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# take(0(), IL) -> isNatIList# IL)
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# take(X1, X2) -> take#(active X1, X2))
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# take(X1, X2) -> take#(X1, active X2))
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# take(X1, X2) -> active# X2)
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# take(X1, X2) -> active# X1)
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2))
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# cons(X1, X2) -> active# X1)
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# zeros() -> cons#(0(), zeros()))
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# length cons(N, L) -> uLength#(and(isNat N, isNatList L), L))
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# length cons(N, L) -> isNat# N)
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# length cons(N, L) -> isNatList# L)
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# length cons(N, L) -> and#(isNat N, isNatList L))
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# length X -> length# active X)
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# length X -> active# X)
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# s X -> s# active X)
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# s X -> active# X)
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# isNat length L -> isNatList# L)
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# isNat s N -> isNat# N)
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# isNatIList cons(N, IL) -> isNat# N)
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# isNatIList cons(N, IL) -> isNatIList# IL)
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# isNatIList cons(N, IL) -> and#(isNat N, isNatIList IL))
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# isNatIList IL -> isNatList# IL)
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# isNatList take(N, IL) -> isNat# N)
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# isNatList take(N, IL) -> isNatIList# IL)
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# isNatList take(N, IL) -> and#(isNat N, isNatIList IL))
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# isNatList cons(N, L) -> isNat# N)
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# isNatList cons(N, L) -> isNatList# L)
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# isNatList cons(N, L) -> and#(isNat N, isNatList L))
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# and(X1, X2) -> and#(active X1, X2))
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# and(X1, X2) -> and#(X1, active X2))
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# and(X1, X2) -> active# X2)
(active# uTake2(X1, X2, X3, X4) -> active# X1, active# and(X1, X2) -> active# X1)
(proper# and(X1, X2) -> proper# X1, proper# uLength(X1, X2) -> proper# X2)
(proper# and(X1, X2) -> proper# X1, proper# uLength(X1, X2) -> proper# X1)
(proper# and(X1, X2) -> proper# X1, proper# uLength(X1, X2) -> uLength#(proper X1, proper X2))
(proper# and(X1, X2) -> proper# X1, proper# uTake2(X1, X2, X3, X4) -> proper# X4)
(proper# and(X1, X2) -> proper# X1, proper# uTake2(X1, X2, X3, X4) -> proper# X3)
(proper# and(X1, X2) -> proper# X1, proper# uTake2(X1, X2, X3, X4) -> proper# X2)
(proper# and(X1, X2) -> proper# X1, proper# uTake2(X1, X2, X3, X4) -> proper# X1)
(proper# and(X1, X2) -> proper# X1, proper# uTake2(X1, X2, X3, X4) -> uTake2#(proper X1, proper X2, proper X3, proper X4))
(proper# and(X1, X2) -> proper# X1, proper# uTake1 X -> proper# X)
(proper# and(X1, X2) -> proper# X1, proper# uTake1 X -> uTake1# proper X)
(proper# and(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X2)
(proper# and(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X1)
(proper# and(X1, X2) -> proper# X1, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# and(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2)
(proper# and(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1)
(proper# and(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# and(X1, X2) -> proper# X1, proper# length X -> proper# X)
(proper# and(X1, X2) -> proper# X1, proper# length X -> length# proper X)
(proper# and(X1, X2) -> proper# X1, proper# s X -> proper# X)
(proper# and(X1, X2) -> proper# X1, proper# s X -> s# proper X)
(proper# and(X1, X2) -> proper# X1, proper# isNat X -> proper# X)
(proper# and(X1, X2) -> proper# X1, proper# isNat X -> isNat# proper X)
(proper# and(X1, X2) -> proper# X1, proper# isNatIList X -> proper# X)
(proper# and(X1, X2) -> proper# X1, proper# isNatIList X -> isNatIList# proper X)
(proper# and(X1, X2) -> proper# X1, proper# isNatList X -> proper# X)
(proper# and(X1, X2) -> proper# X1, proper# isNatList X -> isNatList# proper X)
(proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2)
(proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X1)
(proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# take(X1, X2) -> proper# X1, proper# uLength(X1, X2) -> proper# X2)
(proper# take(X1, X2) -> proper# X1, proper# uLength(X1, X2) -> proper# X1)
(proper# take(X1, X2) -> proper# X1, proper# uLength(X1, X2) -> uLength#(proper X1, proper X2))
(proper# take(X1, X2) -> proper# X1, proper# uTake2(X1, X2, X3, X4) -> proper# X4)
(proper# take(X1, X2) -> proper# X1, proper# uTake2(X1, X2, X3, X4) -> proper# X3)
(proper# take(X1, X2) -> proper# X1, proper# uTake2(X1, X2, X3, X4) -> proper# X2)
(proper# take(X1, X2) -> proper# X1, proper# uTake2(X1, X2, X3, X4) -> proper# X1)
(proper# take(X1, X2) -> proper# X1, proper# uTake2(X1, X2, X3, X4) -> uTake2#(proper X1, proper X2, proper X3, proper X4))
(proper# take(X1, X2) -> proper# X1, proper# uTake1 X -> proper# X)
(proper# take(X1, X2) -> proper# X1, proper# uTake1 X -> uTake1# proper X)
(proper# take(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X2)
(proper# take(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X1)
(proper# take(X1, X2) -> proper# X1, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# take(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2)
(proper# take(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1)
(proper# take(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# take(X1, X2) -> proper# X1, proper# length X -> proper# X)
(proper# take(X1, X2) -> proper# X1, proper# length X -> length# proper X)
(proper# take(X1, X2) -> proper# X1, proper# s X -> proper# X)
(proper# take(X1, X2) -> proper# X1, proper# s X -> s# proper X)
(proper# take(X1, X2) -> proper# X1, proper# isNat X -> proper# X)
(proper# take(X1, X2) -> proper# X1, proper# isNat X -> isNat# proper X)
(proper# take(X1, X2) -> proper# X1, proper# isNatIList X -> proper# X)
(proper# take(X1, X2) -> proper# X1, proper# isNatIList X -> isNatIList# proper X)
(proper# take(X1, X2) -> proper# X1, proper# isNatList X -> proper# X)
(proper# take(X1, X2) -> proper# X1, proper# isNatList X -> isNatList# proper X)
(proper# take(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2)
(proper# take(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X1)
(proper# take(X1, X2) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# uLength(X1, X2) -> proper# X1, proper# uLength(X1, X2) -> proper# X2)
(proper# uLength(X1, X2) -> proper# X1, proper# uLength(X1, X2) -> proper# X1)
(proper# uLength(X1, X2) -> proper# X1, proper# uLength(X1, X2) -> uLength#(proper X1, proper X2))
(proper# uLength(X1, X2) -> proper# X1, proper# uTake2(X1, X2, X3, X4) -> proper# X4)
(proper# uLength(X1, X2) -> proper# X1, proper# uTake2(X1, X2, X3, X4) -> proper# X3)
(proper# uLength(X1, X2) -> proper# X1, proper# uTake2(X1, X2, X3, X4) -> proper# X2)
(proper# uLength(X1, X2) -> proper# X1, proper# uTake2(X1, X2, X3, X4) -> proper# X1)
(proper# uLength(X1, X2) -> proper# X1, proper# uTake2(X1, X2, X3, X4) -> uTake2#(proper X1, proper X2, proper X3, proper X4))
(proper# uLength(X1, X2) -> proper# X1, proper# uTake1 X -> proper# X)
(proper# uLength(X1, X2) -> proper# X1, proper# uTake1 X -> uTake1# proper X)
(proper# uLength(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X2)
(proper# uLength(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X1)
(proper# uLength(X1, X2) -> proper# X1, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# uLength(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2)
(proper# uLength(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1)
(proper# uLength(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# uLength(X1, X2) -> proper# X1, proper# length X -> proper# X)
(proper# uLength(X1, X2) -> proper# X1, proper# length X -> length# proper X)
(proper# uLength(X1, X2) -> proper# X1, proper# s X -> proper# X)
(proper# uLength(X1, X2) -> proper# X1, proper# s X -> s# proper X)
(proper# uLength(X1, X2) -> proper# X1, proper# isNat X -> proper# X)
(proper# uLength(X1, X2) -> proper# X1, proper# isNat X -> isNat# proper X)
(proper# uLength(X1, X2) -> proper# X1, proper# isNatIList X -> proper# X)
(proper# uLength(X1, X2) -> proper# X1, proper# isNatIList X -> isNatIList# proper X)
(proper# uLength(X1, X2) -> proper# X1, proper# isNatList X -> proper# X)
(proper# uLength(X1, X2) -> proper# X1, proper# isNatList X -> isNatList# proper X)
(proper# uLength(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2)
(proper# uLength(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X1)
(proper# uLength(X1, X2) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2))
(active# isNatList cons(N, L) -> and#(isNat N, isNatList L), and#(ok X1, ok X2) -> and#(X1, X2))
(active# isNatIList cons(N, IL) -> and#(isNat N, isNatIList IL), and#(ok X1, ok 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))
(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))
(proper# and(X1, X2) -> and#(proper X1, proper X2), and#(X1, mark X2) -> and#(X1, X2))
(proper# take(X1, X2) -> take#(proper X1, proper X2), take#(ok X1, ok 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#(X1, mark X2) -> take#(X1, X2))
(active# uTake2(tt(), M, N, IL) -> take#(M, IL), take#(ok X1, ok X2) -> take#(X1, X2))
(active# uTake2(tt(), M, N, IL) -> take#(M, IL), take#(mark X1, X2) -> take#(X1, X2))
(active# uTake2(tt(), M, N, IL) -> take#(M, IL), take#(X1, mark X2) -> take#(X1, X2))
(active# length X -> active# X, active# uLength(tt(), L) -> length# L)
(active# length X -> active# X, active# uLength(tt(), L) -> s# length L)
(active# length X -> active# X, active# uLength(X1, X2) -> uLength#(active X1, X2))
(active# length X -> active# X, active# uLength(X1, X2) -> active# X1)
(active# length X -> active# X, active# uTake2(tt(), M, N, IL) -> take#(M, IL))
(active# length X -> active# X, active# uTake2(tt(), M, N, IL) -> cons#(N, take(M, IL)))
(active# length X -> active# X, active# uTake2(X1, X2, X3, X4) -> uTake2#(active X1, X2, X3, X4))
(active# length X -> active# X, active# uTake2(X1, X2, X3, X4) -> active# X1)
(active# length X -> active# X, active# uTake1 X -> uTake1# active X)
(active# length X -> active# X, active# uTake1 X -> active# X)
(active# length X -> active# X, active# take(s M, cons(N, IL)) -> uTake2#(and(isNat M, and(isNat N, isNatIList IL)), M, N, IL))
(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)) -> isNat# N)
(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)) -> and#(isNat M, and(isNat N, isNatIList IL)))
(active# length X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNat N, isNatIList IL))
(active# length X -> active# X, active# take(0(), IL) -> uTake1# isNatIList IL)
(active# length X -> active# X, active# take(0(), IL) -> isNatIList# IL)
(active# length X -> active# X, active# take(X1, X2) -> take#(active X1, X2))
(active# length X -> active# X, active# take(X1, X2) -> take#(X1, active X2))
(active# length X -> active# X, active# take(X1, X2) -> active# X2)
(active# length X -> active# X, active# take(X1, X2) -> active# X1)
(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# length cons(N, L) -> uLength#(and(isNat N, isNatList L), L))
(active# length X -> active# X, active# length cons(N, L) -> isNat# N)
(active# length X -> active# X, active# length cons(N, L) -> isNatList# L)
(active# length X -> active# X, active# length cons(N, L) -> and#(isNat N, isNatList L))
(active# length X -> active# X, active# length X -> length# active X)
(active# length X -> active# X, active# length X -> active# X)
(active# length X -> active# X, active# s X -> s# active X)
(active# length X -> active# X, active# s X -> active# X)
(active# length X -> active# X, active# isNat length L -> isNatList# L)
(active# length X -> active# X, active# isNat s N -> isNat# N)
(active# length X -> active# X, active# isNatIList cons(N, IL) -> isNat# N)
(active# length X -> active# X, active# isNatIList cons(N, IL) -> isNatIList# IL)
(active# length X -> active# X, active# isNatIList cons(N, IL) -> and#(isNat N, isNatIList IL))
(active# length X -> active# X, active# isNatIList IL -> isNatList# IL)
(active# length X -> active# X, active# isNatList take(N, IL) -> isNat# N)
(active# length X -> active# X, active# isNatList take(N, IL) -> isNatIList# IL)
(active# length X -> active# X, active# isNatList take(N, IL) -> and#(isNat N, isNatIList IL))
(active# length X -> active# X, active# isNatList cons(N, L) -> isNat# N)
(active# length X -> active# X, active# isNatList cons(N, L) -> isNatList# L)
(active# length X -> active# X, active# isNatList cons(N, L) -> and#(isNat N, isNatList L))
(active# length X -> active# X, active# and(X1, X2) -> and#(active X1, X2))
(active# length X -> active# X, active# and(X1, X2) -> and#(X1, active X2))
(active# length X -> active# X, active# and(X1, X2) -> active# X2)
(active# length X -> active# X, active# and(X1, X2) -> active# X1)
(isNatList# ok X -> isNatList# X, isNatList# ok X -> isNatList# X)
(isNat# ok X -> isNat# X, isNat# ok X -> isNat# 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)
(uTake1# ok X -> uTake1# X, uTake1# ok X -> uTake1# X)
(uTake1# ok X -> uTake1# X, uTake1# mark X -> uTake1# X)
(proper# isNatIList X -> proper# X, proper# uLength(X1, X2) -> proper# X2)
(proper# isNatIList X -> proper# X, proper# uLength(X1, X2) -> proper# X1)
(proper# isNatIList X -> proper# X, proper# uLength(X1, X2) -> uLength#(proper X1, proper X2))
(proper# isNatIList X -> proper# X, proper# uTake2(X1, X2, X3, X4) -> proper# X4)
(proper# isNatIList X -> proper# X, proper# uTake2(X1, X2, X3, X4) -> proper# X3)
(proper# isNatIList X -> proper# X, proper# uTake2(X1, X2, X3, X4) -> proper# X2)
(proper# isNatIList X -> proper# X, proper# uTake2(X1, X2, X3, X4) -> proper# X1)
(proper# isNatIList X -> proper# X, proper# uTake2(X1, X2, X3, X4) -> uTake2#(proper X1, proper X2, proper X3, proper X4))
(proper# isNatIList X -> proper# X, proper# uTake1 X -> proper# X)
(proper# isNatIList X -> proper# X, proper# uTake1 X -> uTake1# proper X)
(proper# isNatIList X -> proper# X, proper# take(X1, X2) -> proper# X2)
(proper# isNatIList X -> proper# X, proper# take(X1, X2) -> proper# X1)
(proper# isNatIList X -> proper# X, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# isNatIList X -> proper# X, proper# cons(X1, X2) -> proper# X2)
(proper# isNatIList X -> proper# X, proper# cons(X1, X2) -> proper# X1)
(proper# isNatIList X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# isNatIList X -> proper# X, proper# length X -> proper# X)
(proper# isNatIList X -> proper# X, proper# length X -> length# proper X)
(proper# isNatIList X -> proper# X, proper# s X -> proper# X)
(proper# isNatIList X -> proper# X, proper# s X -> s# proper X)
(proper# isNatIList X -> proper# X, proper# isNat X -> proper# X)
(proper# isNatIList X -> proper# X, proper# isNat X -> isNat# proper X)
(proper# isNatIList X -> proper# X, proper# isNatIList X -> proper# X)
(proper# isNatIList X -> proper# X, proper# isNatIList X -> isNatIList# proper X)
(proper# isNatIList X -> proper# X, proper# isNatList X -> proper# X)
(proper# isNatIList X -> proper# X, proper# isNatList X -> isNatList# proper X)
(proper# isNatIList X -> proper# X, proper# and(X1, X2) -> proper# X2)
(proper# isNatIList X -> proper# X, proper# and(X1, X2) -> proper# X1)
(proper# isNatIList X -> proper# X, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# s X -> proper# X, proper# uLength(X1, X2) -> proper# X2)
(proper# s X -> proper# X, proper# uLength(X1, X2) -> proper# X1)
(proper# s X -> proper# X, proper# uLength(X1, X2) -> uLength#(proper X1, proper X2))
(proper# s X -> proper# X, proper# uTake2(X1, X2, X3, X4) -> proper# X4)
(proper# s X -> proper# X, proper# uTake2(X1, X2, X3, X4) -> proper# X3)
(proper# s X -> proper# X, proper# uTake2(X1, X2, X3, X4) -> proper# X2)
(proper# s X -> proper# X, proper# uTake2(X1, X2, X3, X4) -> proper# X1)
(proper# s X -> proper# X, proper# uTake2(X1, X2, X3, X4) -> uTake2#(proper X1, proper X2, proper X3, proper X4))
(proper# s X -> proper# X, proper# uTake1 X -> proper# X)
(proper# s X -> proper# X, proper# uTake1 X -> uTake1# proper X)
(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# 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# 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# isNat X -> proper# X)
(proper# s X -> proper# X, proper# isNat X -> isNat# proper X)
(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# isNatList X -> proper# X)
(proper# s X -> proper# X, proper# isNatList X -> isNatList# 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# uTake1 X -> proper# X, proper# uLength(X1, X2) -> proper# X2)
(proper# uTake1 X -> proper# X, proper# uLength(X1, X2) -> proper# X1)
(proper# uTake1 X -> proper# X, proper# uLength(X1, X2) -> uLength#(proper X1, proper X2))
(proper# uTake1 X -> proper# X, proper# uTake2(X1, X2, X3, X4) -> proper# X4)
(proper# uTake1 X -> proper# X, proper# uTake2(X1, X2, X3, X4) -> proper# X3)
(proper# uTake1 X -> proper# X, proper# uTake2(X1, X2, X3, X4) -> proper# X2)
(proper# uTake1 X -> proper# X, proper# uTake2(X1, X2, X3, X4) -> proper# X1)
(proper# uTake1 X -> proper# X, proper# uTake2(X1, X2, X3, X4) -> uTake2#(proper X1, proper X2, proper X3, proper X4))
(proper# uTake1 X -> proper# X, proper# uTake1 X -> proper# X)
(proper# uTake1 X -> proper# X, proper# uTake1 X -> uTake1# proper X)
(proper# uTake1 X -> proper# X, proper# take(X1, X2) -> proper# X2)
(proper# uTake1 X -> proper# X, proper# take(X1, X2) -> proper# X1)
(proper# uTake1 X -> proper# X, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# uTake1 X -> proper# X, proper# cons(X1, X2) -> proper# X2)
(proper# uTake1 X -> proper# X, proper# cons(X1, X2) -> proper# X1)
(proper# uTake1 X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# uTake1 X -> proper# X, proper# length X -> proper# X)
(proper# uTake1 X -> proper# X, proper# length X -> length# proper X)
(proper# uTake1 X -> proper# X, proper# s X -> proper# X)
(proper# uTake1 X -> proper# X, proper# s X -> s# proper X)
(proper# uTake1 X -> proper# X, proper# isNat X -> proper# X)
(proper# uTake1 X -> proper# X, proper# isNat X -> isNat# proper X)
(proper# uTake1 X -> proper# X, proper# isNatIList X -> proper# X)
(proper# uTake1 X -> proper# X, proper# isNatIList X -> isNatIList# proper X)
(proper# uTake1 X -> proper# X, proper# isNatList X -> proper# X)
(proper# uTake1 X -> proper# X, proper# isNatList X -> isNatList# proper X)
(proper# uTake1 X -> proper# X, proper# and(X1, X2) -> proper# X2)
(proper# uTake1 X -> proper# X, proper# and(X1, X2) -> proper# X1)
(proper# uTake1 X -> proper# X, proper# and(X1, X2) -> and#(proper X1, proper X2))
(top# ok X -> active# X, active# uLength(tt(), L) -> length# L)
(top# ok X -> active# X, active# uLength(tt(), L) -> s# length L)
(top# ok X -> active# X, active# uLength(X1, X2) -> uLength#(active X1, X2))
(top# ok X -> active# X, active# uLength(X1, X2) -> active# X1)
(top# ok X -> active# X, active# uTake2(tt(), M, N, IL) -> take#(M, IL))
(top# ok X -> active# X, active# uTake2(tt(), M, N, IL) -> cons#(N, take(M, IL)))
(top# ok X -> active# X, active# uTake2(X1, X2, X3, X4) -> uTake2#(active X1, X2, X3, X4))
(top# ok X -> active# X, active# uTake2(X1, X2, X3, X4) -> active# X1)
(top# ok X -> active# X, active# uTake1 X -> uTake1# active X)
(top# ok X -> active# X, active# uTake1 X -> active# X)
(top# ok X -> active# X, active# take(s M, cons(N, IL)) -> uTake2#(and(isNat M, and(isNat N, isNatIList IL)), M, N, 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(s M, cons(N, IL)) -> isNatIList# IL)
(top# ok X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNat M, and(isNat N, isNatIList IL)))
(top# ok X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNat N, isNatIList IL))
(top# ok X -> active# X, active# take(0(), IL) -> uTake1# isNatIList 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# cons(X1, X2) -> cons#(active X1, X2))
(top# ok X -> active# X, active# cons(X1, X2) -> active# X1)
(top# ok X -> active# X, active# zeros() -> cons#(0(), zeros()))
(top# ok X -> active# X, active# length cons(N, L) -> uLength#(and(isNat N, isNatList L), 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 cons(N, L) -> and#(isNat N, 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# isNat length L -> isNatList# L)
(top# ok X -> active# X, active# isNat s N -> isNat# N)
(top# ok X -> active# X, active# isNatIList cons(N, IL) -> isNat# N)
(top# ok X -> active# X, active# isNatIList cons(N, IL) -> isNatIList# IL)
(top# ok X -> active# X, active# isNatIList cons(N, IL) -> and#(isNat N, isNatIList IL))
(top# ok X -> active# X, active# isNatIList IL -> isNatList# IL)
(top# ok X -> active# X, active# isNatList take(N, IL) -> isNat# N)
(top# ok X -> active# X, active# isNatList take(N, IL) -> isNatIList# IL)
(top# ok X -> active# X, active# isNatList take(N, IL) -> and#(isNat N, isNatIList IL))
(top# ok X -> active# X, active# isNatList cons(N, L) -> isNat# N)
(top# ok X -> active# X, active# isNatList cons(N, L) -> isNatList# L)
(top# ok X -> active# X, active# isNatList cons(N, L) -> and#(isNat N, isNatList L))
(top# ok X -> active# X, active# and(X1, X2) -> and#(active X1, X2))
(top# ok X -> active# X, active# and(X1, X2) -> and#(X1, active X2))
(top# ok X -> active# X, active# and(X1, X2) -> active# X2)
(top# ok X -> active# X, active# and(X1, X2) -> active# X1)
(proper# uTake2(X1, X2, X3, X4) -> proper# X4, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# uTake2(X1, X2, X3, X4) -> proper# X4, proper# and(X1, X2) -> proper# X1)
(proper# uTake2(X1, X2, X3, X4) -> proper# X4, proper# and(X1, X2) -> proper# X2)
(proper# uTake2(X1, X2, X3, X4) -> proper# X4, proper# isNatList X -> isNatList# proper X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X4, proper# isNatList X -> proper# X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X4, proper# isNatIList X -> isNatIList# proper X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X4, proper# isNatIList X -> proper# X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X4, proper# isNat X -> isNat# proper X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X4, proper# isNat X -> proper# X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X4, proper# s X -> s# proper X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X4, proper# s X -> proper# X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X4, proper# length X -> length# proper X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X4, proper# length X -> proper# X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X4, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# uTake2(X1, X2, X3, X4) -> proper# X4, proper# cons(X1, X2) -> proper# X1)
(proper# uTake2(X1, X2, X3, X4) -> proper# X4, proper# cons(X1, X2) -> proper# X2)
(proper# uTake2(X1, X2, X3, X4) -> proper# X4, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# uTake2(X1, X2, X3, X4) -> proper# X4, proper# take(X1, X2) -> proper# X1)
(proper# uTake2(X1, X2, X3, X4) -> proper# X4, proper# take(X1, X2) -> proper# X2)
(proper# uTake2(X1, X2, X3, X4) -> proper# X4, proper# uTake1 X -> uTake1# proper X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X4, proper# uTake1 X -> proper# X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X4, proper# uTake2(X1, X2, X3, X4) -> uTake2#(proper X1, proper X2, proper X3, proper X4))
(proper# uTake2(X1, X2, X3, X4) -> proper# X4, proper# uTake2(X1, X2, X3, X4) -> proper# X1)
(proper# uTake2(X1, X2, X3, X4) -> proper# X4, proper# uTake2(X1, X2, X3, X4) -> proper# X2)
(proper# uTake2(X1, X2, X3, X4) -> proper# X4, proper# uTake2(X1, X2, X3, X4) -> proper# X3)
(proper# uTake2(X1, X2, X3, X4) -> proper# X4, proper# uTake2(X1, X2, X3, X4) -> proper# X4)
(proper# uTake2(X1, X2, X3, X4) -> proper# X4, proper# uLength(X1, X2) -> uLength#(proper X1, proper X2))
(proper# uTake2(X1, X2, X3, X4) -> proper# X4, proper# uLength(X1, X2) -> proper# X1)
(proper# uTake2(X1, X2, X3, X4) -> proper# X4, proper# uLength(X1, X2) -> proper# X2)
(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# isNatList X -> isNatList# proper X)
(top# mark X -> proper# X, proper# isNatList 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# isNat X -> isNat# proper X)
(top# mark X -> proper# X, proper# isNat 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# 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# 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# uTake1 X -> uTake1# proper X)
(top# mark X -> proper# X, proper# uTake1 X -> proper# X)
(top# mark X -> proper# X, proper# uTake2(X1, X2, X3, X4) -> uTake2#(proper X1, proper X2, proper X3, proper X4))
(top# mark X -> proper# X, proper# uTake2(X1, X2, X3, X4) -> proper# X1)
(top# mark X -> proper# X, proper# uTake2(X1, X2, X3, X4) -> proper# X2)
(top# mark X -> proper# X, proper# uTake2(X1, X2, X3, X4) -> proper# X3)
(top# mark X -> proper# X, proper# uTake2(X1, X2, X3, X4) -> proper# X4)
(top# mark X -> proper# X, proper# uLength(X1, X2) -> uLength#(proper X1, proper X2))
(top# mark X -> proper# X, proper# uLength(X1, X2) -> proper# X1)
(top# mark X -> proper# X, proper# uLength(X1, X2) -> proper# X2)
(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# isNatList X -> isNatList# proper X)
(proper# length X -> proper# X, proper# isNatList 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# isNat X -> isNat# proper X)
(proper# length X -> proper# X, proper# isNat 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# 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# 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# uTake1 X -> uTake1# proper X)
(proper# length X -> proper# X, proper# uTake1 X -> proper# X)
(proper# length X -> proper# X, proper# uTake2(X1, X2, X3, X4) -> uTake2#(proper X1, proper X2, proper X3, proper X4))
(proper# length X -> proper# X, proper# uTake2(X1, X2, X3, X4) -> proper# X1)
(proper# length X -> proper# X, proper# uTake2(X1, X2, X3, X4) -> proper# X2)
(proper# length X -> proper# X, proper# uTake2(X1, X2, X3, X4) -> proper# X3)
(proper# length X -> proper# X, proper# uTake2(X1, X2, X3, X4) -> proper# X4)
(proper# length X -> proper# X, proper# uLength(X1, X2) -> uLength#(proper X1, proper X2))
(proper# length X -> proper# X, proper# uLength(X1, X2) -> proper# X1)
(proper# length X -> proper# X, proper# uLength(X1, X2) -> proper# X2)
(proper# isNat X -> proper# X, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# isNat X -> proper# X, proper# and(X1, X2) -> proper# X1)
(proper# isNat X -> proper# X, proper# and(X1, X2) -> proper# X2)
(proper# isNat X -> proper# X, proper# isNatList X -> isNatList# proper X)
(proper# isNat X -> proper# X, proper# isNatList X -> proper# X)
(proper# isNat X -> proper# X, proper# isNatIList X -> isNatIList# proper X)
(proper# isNat X -> proper# X, proper# isNatIList X -> proper# X)
(proper# isNat X -> proper# X, proper# isNat X -> isNat# proper X)
(proper# isNat X -> proper# X, proper# isNat X -> proper# X)
(proper# isNat X -> proper# X, proper# s X -> s# proper X)
(proper# isNat X -> proper# X, proper# s X -> proper# X)
(proper# isNat X -> proper# X, proper# length X -> length# proper X)
(proper# isNat X -> proper# X, proper# length X -> proper# X)
(proper# isNat X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# isNat X -> proper# X, proper# cons(X1, X2) -> proper# X1)
(proper# isNat X -> proper# X, proper# cons(X1, X2) -> proper# X2)
(proper# isNat X -> proper# X, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# isNat X -> proper# X, proper# take(X1, X2) -> proper# X1)
(proper# isNat X -> proper# X, proper# take(X1, X2) -> proper# X2)
(proper# isNat X -> proper# X, proper# uTake1 X -> uTake1# proper X)
(proper# isNat X -> proper# X, proper# uTake1 X -> proper# X)
(proper# isNat X -> proper# X, proper# uTake2(X1, X2, X3, X4) -> uTake2#(proper X1, proper X2, proper X3, proper X4))
(proper# isNat X -> proper# X, proper# uTake2(X1, X2, X3, X4) -> proper# X1)
(proper# isNat X -> proper# X, proper# uTake2(X1, X2, X3, X4) -> proper# X2)
(proper# isNat X -> proper# X, proper# uTake2(X1, X2, X3, X4) -> proper# X3)
(proper# isNat X -> proper# X, proper# uTake2(X1, X2, X3, X4) -> proper# X4)
(proper# isNat X -> proper# X, proper# uLength(X1, X2) -> uLength#(proper X1, proper X2))
(proper# isNat X -> proper# X, proper# uLength(X1, X2) -> proper# X1)
(proper# isNat X -> proper# X, proper# uLength(X1, X2) -> proper# X2)
(proper# isNatList X -> proper# X, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# isNatList X -> proper# X, proper# and(X1, X2) -> proper# X1)
(proper# isNatList X -> proper# X, proper# and(X1, X2) -> proper# X2)
(proper# isNatList X -> proper# X, proper# isNatList X -> isNatList# proper X)
(proper# isNatList X -> proper# X, proper# isNatList X -> proper# X)
(proper# isNatList X -> proper# X, proper# isNatIList X -> isNatIList# proper X)
(proper# isNatList X -> proper# X, proper# isNatIList X -> proper# X)
(proper# isNatList X -> proper# X, proper# isNat X -> isNat# proper X)
(proper# isNatList X -> proper# X, proper# isNat X -> proper# X)
(proper# isNatList X -> proper# X, proper# s X -> s# proper X)
(proper# isNatList X -> proper# X, proper# s X -> proper# X)
(proper# isNatList X -> proper# X, proper# length X -> length# proper X)
(proper# isNatList X -> proper# X, proper# length X -> proper# X)
(proper# isNatList X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# isNatList X -> proper# X, proper# cons(X1, X2) -> proper# X1)
(proper# isNatList X -> proper# X, proper# cons(X1, X2) -> proper# X2)
(proper# isNatList X -> proper# X, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# isNatList X -> proper# X, proper# take(X1, X2) -> proper# X1)
(proper# isNatList X -> proper# X, proper# take(X1, X2) -> proper# X2)
(proper# isNatList X -> proper# X, proper# uTake1 X -> uTake1# proper X)
(proper# isNatList X -> proper# X, proper# uTake1 X -> proper# X)
(proper# isNatList X -> proper# X, proper# uTake2(X1, X2, X3, X4) -> uTake2#(proper X1, proper X2, proper X3, proper X4))
(proper# isNatList X -> proper# X, proper# uTake2(X1, X2, X3, X4) -> proper# X1)
(proper# isNatList X -> proper# X, proper# uTake2(X1, X2, X3, X4) -> proper# X2)
(proper# isNatList X -> proper# X, proper# uTake2(X1, X2, X3, X4) -> proper# X3)
(proper# isNatList X -> proper# X, proper# uTake2(X1, X2, X3, X4) -> proper# X4)
(proper# isNatList X -> proper# X, proper# uLength(X1, X2) -> uLength#(proper X1, proper X2))
(proper# isNatList X -> proper# X, proper# uLength(X1, X2) -> proper# X1)
(proper# isNatList X -> proper# X, proper# uLength(X1, X2) -> proper# X2)
(uTake1# mark X -> uTake1# X, uTake1# mark X -> uTake1# X)
(uTake1# mark X -> uTake1# X, uTake1# ok X -> uTake1# 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)
(isNatIList# ok X -> isNatIList# X, isNatIList# ok X -> isNatIList# X)
(active# uTake1 X -> active# X, active# and(X1, X2) -> active# X1)
(active# uTake1 X -> active# X, active# and(X1, X2) -> active# X2)
(active# uTake1 X -> active# X, active# and(X1, X2) -> and#(X1, active X2))
(active# uTake1 X -> active# X, active# and(X1, X2) -> and#(active X1, X2))
(active# uTake1 X -> active# X, active# isNatList cons(N, L) -> and#(isNat N, isNatList L))
(active# uTake1 X -> active# X, active# isNatList cons(N, L) -> isNatList# L)
(active# uTake1 X -> active# X, active# isNatList cons(N, L) -> isNat# N)
(active# uTake1 X -> active# X, active# isNatList take(N, IL) -> and#(isNat N, isNatIList IL))
(active# uTake1 X -> active# X, active# isNatList take(N, IL) -> isNatIList# IL)
(active# uTake1 X -> active# X, active# isNatList take(N, IL) -> isNat# N)
(active# uTake1 X -> active# X, active# isNatIList IL -> isNatList# IL)
(active# uTake1 X -> active# X, active# isNatIList cons(N, IL) -> and#(isNat N, isNatIList IL))
(active# uTake1 X -> active# X, active# isNatIList cons(N, IL) -> isNatIList# IL)
(active# uTake1 X -> active# X, active# isNatIList cons(N, IL) -> isNat# N)
(active# uTake1 X -> active# X, active# isNat s N -> isNat# N)
(active# uTake1 X -> active# X, active# isNat length L -> isNatList# L)
(active# uTake1 X -> active# X, active# s X -> active# X)
(active# uTake1 X -> active# X, active# s X -> s# active X)
(active# uTake1 X -> active# X, active# length X -> active# X)
(active# uTake1 X -> active# X, active# length X -> length# active X)
(active# uTake1 X -> active# X, active# length cons(N, L) -> and#(isNat N, isNatList L))
(active# uTake1 X -> active# X, active# length cons(N, L) -> isNatList# L)
(active# uTake1 X -> active# X, active# length cons(N, L) -> isNat# N)
(active# uTake1 X -> active# X, active# length cons(N, L) -> uLength#(and(isNat N, isNatList L), L))
(active# uTake1 X -> active# X, active# zeros() -> cons#(0(), zeros()))
(active# uTake1 X -> active# X, active# cons(X1, X2) -> active# X1)
(active# uTake1 X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2))
(active# uTake1 X -> active# X, active# take(X1, X2) -> active# X1)
(active# uTake1 X -> active# X, active# take(X1, X2) -> active# X2)
(active# uTake1 X -> active# X, active# take(X1, X2) -> take#(X1, active X2))
(active# uTake1 X -> active# X, active# take(X1, X2) -> take#(active X1, X2))
(active# uTake1 X -> active# X, active# take(0(), IL) -> isNatIList# IL)
(active# uTake1 X -> active# X, active# take(0(), IL) -> uTake1# isNatIList IL)
(active# uTake1 X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNat N, isNatIList IL))
(active# uTake1 X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNat M, and(isNat N, isNatIList IL)))
(active# uTake1 X -> active# X, active# take(s M, cons(N, IL)) -> isNatIList# IL)
(active# uTake1 X -> active# X, active# take(s M, cons(N, IL)) -> isNat# N)
(active# uTake1 X -> active# X, active# take(s M, cons(N, IL)) -> isNat# M)
(active# uTake1 X -> active# X, active# take(s M, cons(N, IL)) -> uTake2#(and(isNat M, and(isNat N, isNatIList IL)), M, N, IL))
(active# uTake1 X -> active# X, active# uTake1 X -> active# X)
(active# uTake1 X -> active# X, active# uTake1 X -> uTake1# active X)
(active# uTake1 X -> active# X, active# uTake2(X1, X2, X3, X4) -> active# X1)
(active# uTake1 X -> active# X, active# uTake2(X1, X2, X3, X4) -> uTake2#(active X1, X2, X3, X4))
(active# uTake1 X -> active# X, active# uTake2(tt(), M, N, IL) -> cons#(N, take(M, IL)))
(active# uTake1 X -> active# X, active# uTake2(tt(), M, N, IL) -> take#(M, IL))
(active# uTake1 X -> active# X, active# uLength(X1, X2) -> active# X1)
(active# uTake1 X -> active# X, active# uLength(X1, X2) -> uLength#(active X1, X2))
(active# uTake1 X -> active# X, active# uLength(tt(), L) -> s# length L)
(active# uTake1 X -> active# X, active# uLength(tt(), L) -> length# L)
(active# s X -> active# X, active# and(X1, X2) -> active# X1)
(active# s X -> active# X, active# and(X1, X2) -> active# X2)
(active# s X -> active# X, active# and(X1, X2) -> and#(X1, active X2))
(active# s X -> active# X, active# and(X1, X2) -> and#(active X1, X2))
(active# s X -> active# X, active# isNatList cons(N, L) -> and#(isNat N, isNatList L))
(active# s X -> active# X, active# isNatList cons(N, L) -> isNatList# L)
(active# s X -> active# X, active# isNatList cons(N, L) -> isNat# N)
(active# s X -> active# X, active# isNatList take(N, IL) -> and#(isNat N, isNatIList IL))
(active# s X -> active# X, active# isNatList take(N, IL) -> isNatIList# IL)
(active# s X -> active# X, active# isNatList take(N, IL) -> isNat# N)
(active# s X -> active# X, active# isNatIList IL -> isNatList# IL)
(active# s X -> active# X, active# isNatIList cons(N, IL) -> and#(isNat N, isNatIList IL))
(active# s X -> active# X, active# isNatIList cons(N, IL) -> isNatIList# IL)
(active# s X -> active# X, active# isNatIList cons(N, IL) -> isNat# N)
(active# s X -> active# X, active# isNat s N -> isNat# N)
(active# s X -> active# X, active# isNat length L -> isNatList# L)
(active# s X -> active# X, active# s X -> active# X)
(active# s X -> active# X, active# s X -> s# active X)
(active# s X -> active# X, active# length X -> active# X)
(active# s X -> active# X, active# length X -> length# active X)
(active# s X -> active# X, active# length cons(N, L) -> and#(isNat N, isNatList L))
(active# s X -> active# X, active# length cons(N, L) -> isNatList# L)
(active# s X -> active# X, active# length cons(N, L) -> isNat# N)
(active# s X -> active# X, active# length cons(N, L) -> uLength#(and(isNat N, isNatList L), L))
(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# s X -> active# X, active# take(X1, X2) -> active# X1)
(active# s X -> active# X, active# take(X1, X2) -> active# X2)
(active# s X -> active# X, active# take(X1, X2) -> take#(X1, active X2))
(active# s X -> active# X, active# take(X1, X2) -> take#(active X1, X2))
(active# s X -> active# X, active# take(0(), IL) -> isNatIList# IL)
(active# s X -> active# X, active# take(0(), IL) -> uTake1# isNatIList IL)
(active# s X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNat N, isNatIList IL))
(active# s X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNat M, and(isNat N, isNatIList IL)))
(active# s X -> active# X, active# take(s M, cons(N, IL)) -> isNatIList# IL)
(active# s X -> active# X, active# take(s M, cons(N, IL)) -> isNat# N)
(active# s X -> active# X, active# take(s M, cons(N, IL)) -> isNat# M)
(active# s X -> active# X, active# take(s M, cons(N, IL)) -> uTake2#(and(isNat M, and(isNat N, isNatIList IL)), M, N, IL))
(active# s X -> active# X, active# uTake1 X -> active# X)
(active# s X -> active# X, active# uTake1 X -> uTake1# active X)
(active# s X -> active# X, active# uTake2(X1, X2, X3, X4) -> active# X1)
(active# s X -> active# X, active# uTake2(X1, X2, X3, X4) -> uTake2#(active X1, X2, X3, X4))
(active# s X -> active# X, active# uTake2(tt(), M, N, IL) -> cons#(N, take(M, IL)))
(active# s X -> active# X, active# uTake2(tt(), M, N, IL) -> take#(M, IL))
(active# s X -> active# X, active# uLength(X1, X2) -> active# X1)
(active# s X -> active# X, active# uLength(X1, X2) -> uLength#(active X1, X2))
(active# s X -> active# X, active# uLength(tt(), L) -> s# length L)
(active# s X -> active# X, active# uLength(tt(), L) -> length# L)
(proper# uLength(X1, X2) -> uLength#(proper X1, proper X2), uLength#(mark X1, X2) -> uLength#(X1, X2))
(proper# uLength(X1, X2) -> uLength#(proper X1, proper X2), uLength#(ok X1, ok X2) -> uLength#(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# take(s M, cons(N, IL)) -> and#(isNat N, isNatIList IL), and#(ok X1, ok X2) -> and#(X1, X2))
(active# length cons(N, L) -> and#(isNat N, isNatList L), and#(ok X1, ok X2) -> and#(X1, X2))
(active# isNatList take(N, IL) -> and#(isNat N, isNatIList IL), and#(ok X1, ok X2) -> and#(X1, X2))
(active# and(X1, X2) -> and#(X1, active X2), and#(X1, mark X2) -> and#(X1, X2))
(active# and(X1, X2) -> and#(X1, active X2), and#(mark X1, X2) -> and#(X1, X2))
(active# and(X1, X2) -> and#(X1, active X2), and#(ok X1, ok X2) -> and#(X1, X2))
(proper# uTake2(X1, X2, X3, X4) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# uTake2(X1, X2, X3, X4) -> proper# X1, proper# and(X1, X2) -> proper# X1)
(proper# uTake2(X1, X2, X3, X4) -> proper# X1, proper# and(X1, X2) -> proper# X2)
(proper# uTake2(X1, X2, X3, X4) -> proper# X1, proper# isNatList X -> isNatList# proper X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X1, proper# isNatList X -> proper# X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X1, proper# isNatIList X -> isNatIList# proper X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X1, proper# isNatIList X -> proper# X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X1, proper# isNat X -> isNat# proper X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X1, proper# isNat X -> proper# X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X1, proper# s X -> s# proper X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X1, proper# s X -> proper# X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X1, proper# length X -> length# proper X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X1, proper# length X -> proper# X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# uTake2(X1, X2, X3, X4) -> proper# X1, proper# cons(X1, X2) -> proper# X1)
(proper# uTake2(X1, X2, X3, X4) -> proper# X1, proper# cons(X1, X2) -> proper# X2)
(proper# uTake2(X1, X2, X3, X4) -> proper# X1, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# uTake2(X1, X2, X3, X4) -> proper# X1, proper# take(X1, X2) -> proper# X1)
(proper# uTake2(X1, X2, X3, X4) -> proper# X1, proper# take(X1, X2) -> proper# X2)
(proper# uTake2(X1, X2, X3, X4) -> proper# X1, proper# uTake1 X -> uTake1# proper X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X1, proper# uTake1 X -> proper# X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X1, proper# uTake2(X1, X2, X3, X4) -> uTake2#(proper X1, proper X2, proper X3, proper X4))
(proper# uTake2(X1, X2, X3, X4) -> proper# X1, proper# uTake2(X1, X2, X3, X4) -> proper# X1)
(proper# uTake2(X1, X2, X3, X4) -> proper# X1, proper# uTake2(X1, X2, X3, X4) -> proper# X2)
(proper# uTake2(X1, X2, X3, X4) -> proper# X1, proper# uTake2(X1, X2, X3, X4) -> proper# X3)
(proper# uTake2(X1, X2, X3, X4) -> proper# X1, proper# uTake2(X1, X2, X3, X4) -> proper# X4)
(proper# uTake2(X1, X2, X3, X4) -> proper# X1, proper# uLength(X1, X2) -> uLength#(proper X1, proper X2))
(proper# uTake2(X1, X2, X3, X4) -> proper# X1, proper# uLength(X1, X2) -> proper# X1)
(proper# uTake2(X1, X2, X3, X4) -> proper# X1, proper# uLength(X1, X2) -> proper# X2)
(proper# cons(X1, X2) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# cons(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X1)
(proper# cons(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2)
(proper# cons(X1, X2) -> proper# X1, proper# isNatList X -> isNatList# proper X)
(proper# cons(X1, X2) -> proper# X1, proper# isNatList X -> proper# X)
(proper# cons(X1, X2) -> proper# X1, proper# isNatIList X -> isNatIList# proper X)
(proper# cons(X1, X2) -> proper# X1, proper# isNatIList X -> proper# X)
(proper# cons(X1, X2) -> proper# X1, proper# isNat X -> isNat# proper X)
(proper# cons(X1, X2) -> proper# X1, proper# isNat X -> proper# X)
(proper# cons(X1, X2) -> proper# X1, proper# s X -> s# proper X)
(proper# cons(X1, X2) -> proper# X1, proper# s X -> proper# X)
(proper# cons(X1, X2) -> proper# X1, proper# length X -> length# proper X)
(proper# cons(X1, X2) -> proper# X1, proper# length X -> proper# X)
(proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1)
(proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2)
(proper# cons(X1, X2) -> proper# X1, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# cons(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X1)
(proper# cons(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X2)
(proper# cons(X1, X2) -> proper# X1, proper# uTake1 X -> uTake1# proper X)
(proper# cons(X1, X2) -> proper# X1, proper# uTake1 X -> proper# X)
(proper# cons(X1, X2) -> proper# X1, proper# uTake2(X1, X2, X3, X4) -> uTake2#(proper X1, proper X2, proper X3, proper X4))
(proper# cons(X1, X2) -> proper# X1, proper# uTake2(X1, X2, X3, X4) -> proper# X1)
(proper# cons(X1, X2) -> proper# X1, proper# uTake2(X1, X2, X3, X4) -> proper# X2)
(proper# cons(X1, X2) -> proper# X1, proper# uTake2(X1, X2, X3, X4) -> proper# X3)
(proper# cons(X1, X2) -> proper# X1, proper# uTake2(X1, X2, X3, X4) -> proper# X4)
(proper# cons(X1, X2) -> proper# X1, proper# uLength(X1, X2) -> uLength#(proper X1, proper X2))
(proper# cons(X1, X2) -> proper# X1, proper# uLength(X1, X2) -> proper# X1)
(proper# cons(X1, X2) -> proper# X1, proper# uLength(X1, X2) -> proper# X2)
(active# uLength(X1, X2) -> active# X1, active# and(X1, X2) -> active# X1)
(active# uLength(X1, X2) -> active# X1, active# and(X1, X2) -> active# X2)
(active# uLength(X1, X2) -> active# X1, active# and(X1, X2) -> and#(X1, active X2))
(active# uLength(X1, X2) -> active# X1, active# and(X1, X2) -> and#(active X1, X2))
(active# uLength(X1, X2) -> active# X1, active# isNatList cons(N, L) -> and#(isNat N, isNatList L))
(active# uLength(X1, X2) -> active# X1, active# isNatList cons(N, L) -> isNatList# L)
(active# uLength(X1, X2) -> active# X1, active# isNatList cons(N, L) -> isNat# N)
(active# uLength(X1, X2) -> active# X1, active# isNatList take(N, IL) -> and#(isNat N, isNatIList IL))
(active# uLength(X1, X2) -> active# X1, active# isNatList take(N, IL) -> isNatIList# IL)
(active# uLength(X1, X2) -> active# X1, active# isNatList take(N, IL) -> isNat# N)
(active# uLength(X1, X2) -> active# X1, active# isNatIList IL -> isNatList# IL)
(active# uLength(X1, X2) -> active# X1, active# isNatIList cons(N, IL) -> and#(isNat N, isNatIList IL))
(active# uLength(X1, X2) -> active# X1, active# isNatIList cons(N, IL) -> isNatIList# IL)
(active# uLength(X1, X2) -> active# X1, active# isNatIList cons(N, IL) -> isNat# N)
(active# uLength(X1, X2) -> active# X1, active# isNat s N -> isNat# N)
(active# uLength(X1, X2) -> active# X1, active# isNat length L -> isNatList# L)
(active# uLength(X1, X2) -> active# X1, active# s X -> active# X)
(active# uLength(X1, X2) -> active# X1, active# s X -> s# active X)
(active# uLength(X1, X2) -> active# X1, active# length X -> active# X)
(active# uLength(X1, X2) -> active# X1, active# length X -> length# active X)
(active# uLength(X1, X2) -> active# X1, active# length cons(N, L) -> and#(isNat N, isNatList L))
(active# uLength(X1, X2) -> active# X1, active# length cons(N, L) -> isNatList# L)
(active# uLength(X1, X2) -> active# X1, active# length cons(N, L) -> isNat# N)
(active# uLength(X1, X2) -> active# X1, active# length cons(N, L) -> uLength#(and(isNat N, isNatList L), L))
(active# uLength(X1, X2) -> active# X1, active# zeros() -> cons#(0(), zeros()))
(active# uLength(X1, X2) -> active# X1, active# cons(X1, X2) -> active# X1)
(active# uLength(X1, X2) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2))
(active# uLength(X1, X2) -> active# X1, active# take(X1, X2) -> active# X1)
(active# uLength(X1, X2) -> active# X1, active# take(X1, X2) -> active# X2)
(active# uLength(X1, X2) -> active# X1, active# take(X1, X2) -> take#(X1, active X2))
(active# uLength(X1, X2) -> active# X1, active# take(X1, X2) -> take#(active X1, X2))
(active# uLength(X1, X2) -> active# X1, active# take(0(), IL) -> isNatIList# IL)
(active# uLength(X1, X2) -> active# X1, active# take(0(), IL) -> uTake1# isNatIList IL)
(active# uLength(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat N, isNatIList IL))
(active# uLength(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat M, and(isNat N, isNatIList IL)))
(active# uLength(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIList# IL)
(active# uLength(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# N)
(active# uLength(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# M)
(active# uLength(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> uTake2#(and(isNat M, and(isNat N, isNatIList IL)), M, N, IL))
(active# uLength(X1, X2) -> active# X1, active# uTake1 X -> active# X)
(active# uLength(X1, X2) -> active# X1, active# uTake1 X -> uTake1# active X)
(active# uLength(X1, X2) -> active# X1, active# uTake2(X1, X2, X3, X4) -> active# X1)
(active# uLength(X1, X2) -> active# X1, active# uTake2(X1, X2, X3, X4) -> uTake2#(active X1, X2, X3, X4))
(active# uLength(X1, X2) -> active# X1, active# uTake2(tt(), M, N, IL) -> cons#(N, take(M, IL)))
(active# uLength(X1, X2) -> active# X1, active# uTake2(tt(), M, N, IL) -> take#(M, IL))
(active# uLength(X1, X2) -> active# X1, active# uLength(X1, X2) -> active# X1)
(active# uLength(X1, X2) -> active# X1, active# uLength(X1, X2) -> uLength#(active X1, X2))
(active# uLength(X1, X2) -> active# X1, active# uLength(tt(), L) -> s# length L)
(active# uLength(X1, X2) -> active# X1, active# uLength(tt(), L) -> length# L)
(active# take(X1, X2) -> active# X1, active# and(X1, X2) -> active# X1)
(active# take(X1, X2) -> active# X1, active# and(X1, X2) -> active# X2)
(active# take(X1, X2) -> active# X1, active# and(X1, X2) -> and#(X1, active X2))
(active# take(X1, X2) -> active# X1, active# and(X1, X2) -> and#(active X1, X2))
(active# take(X1, X2) -> active# X1, active# isNatList cons(N, L) -> and#(isNat N, isNatList L))
(active# take(X1, X2) -> active# X1, active# isNatList cons(N, L) -> isNatList# L)
(active# take(X1, X2) -> active# X1, active# isNatList cons(N, L) -> isNat# N)
(active# take(X1, X2) -> active# X1, active# isNatList take(N, IL) -> and#(isNat N, isNatIList IL))
(active# take(X1, X2) -> active# X1, active# isNatList take(N, IL) -> isNatIList# IL)
(active# take(X1, X2) -> active# X1, active# isNatList take(N, IL) -> isNat# N)
(active# take(X1, X2) -> active# X1, active# isNatIList IL -> isNatList# IL)
(active# take(X1, X2) -> active# X1, active# isNatIList cons(N, IL) -> and#(isNat N, isNatIList IL))
(active# take(X1, X2) -> active# X1, active# isNatIList cons(N, IL) -> isNatIList# IL)
(active# take(X1, X2) -> active# X1, active# isNatIList cons(N, IL) -> isNat# N)
(active# take(X1, X2) -> active# X1, active# isNat s N -> isNat# N)
(active# take(X1, X2) -> active# X1, active# isNat length L -> isNatList# L)
(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) -> and#(isNat N, isNatList L))
(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) -> uLength#(and(isNat N, isNatList L), L))
(active# take(X1, X2) -> active# X1, active# zeros() -> cons#(0(), zeros()))
(active# take(X1, X2) -> active# X1, active# cons(X1, X2) -> active# X1)
(active# take(X1, X2) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2))
(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) -> uTake1# isNatIList IL)
(active# take(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat N, isNatIList IL))
(active# take(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat M, and(isNat N, isNatIList IL)))
(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)) -> 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)) -> uTake2#(and(isNat M, and(isNat N, isNatIList IL)), M, N, IL))
(active# take(X1, X2) -> active# X1, active# uTake1 X -> active# X)
(active# take(X1, X2) -> active# X1, active# uTake1 X -> uTake1# active X)
(active# take(X1, X2) -> active# X1, active# uTake2(X1, X2, X3, X4) -> active# X1)
(active# take(X1, X2) -> active# X1, active# uTake2(X1, X2, X3, X4) -> uTake2#(active X1, X2, X3, X4))
(active# take(X1, X2) -> active# X1, active# uTake2(tt(), M, N, IL) -> cons#(N, take(M, IL)))
(active# take(X1, X2) -> active# X1, active# uTake2(tt(), M, N, IL) -> take#(M, IL))
(active# take(X1, X2) -> active# X1, active# uLength(X1, X2) -> active# X1)
(active# take(X1, X2) -> active# X1, active# uLength(X1, X2) -> uLength#(active X1, X2))
(active# take(X1, X2) -> active# X1, active# uLength(tt(), L) -> s# length L)
(active# take(X1, X2) -> active# X1, active# uLength(tt(), L) -> length# L)
(active# and(X1, X2) -> active# X1, active# and(X1, X2) -> active# X1)
(active# and(X1, X2) -> active# X1, active# and(X1, X2) -> active# X2)
(active# and(X1, X2) -> active# X1, active# and(X1, X2) -> and#(X1, active X2))
(active# and(X1, X2) -> active# X1, active# and(X1, X2) -> and#(active X1, X2))
(active# and(X1, X2) -> active# X1, active# isNatList cons(N, L) -> and#(isNat N, isNatList L))
(active# and(X1, X2) -> active# X1, active# isNatList cons(N, L) -> isNatList# L)
(active# and(X1, X2) -> active# X1, active# isNatList cons(N, L) -> isNat# N)
(active# and(X1, X2) -> active# X1, active# isNatList take(N, IL) -> and#(isNat N, isNatIList IL))
(active# and(X1, X2) -> active# X1, active# isNatList take(N, IL) -> isNatIList# IL)
(active# and(X1, X2) -> active# X1, active# isNatList take(N, IL) -> isNat# N)
(active# and(X1, X2) -> active# X1, active# isNatIList IL -> isNatList# IL)
(active# and(X1, X2) -> active# X1, active# isNatIList cons(N, IL) -> and#(isNat N, isNatIList IL))
(active# and(X1, X2) -> active# X1, active# isNatIList cons(N, IL) -> isNatIList# IL)
(active# and(X1, X2) -> active# X1, active# isNatIList cons(N, IL) -> isNat# N)
(active# and(X1, X2) -> active# X1, active# isNat s N -> isNat# N)
(active# and(X1, X2) -> active# X1, active# isNat length L -> isNatList# L)
(active# and(X1, X2) -> active# X1, active# s X -> active# X)
(active# and(X1, X2) -> active# X1, active# s X -> s# active X)
(active# and(X1, X2) -> active# X1, active# length X -> active# X)
(active# and(X1, X2) -> active# X1, active# length X -> length# active X)
(active# and(X1, X2) -> active# X1, active# length cons(N, L) -> and#(isNat N, isNatList L))
(active# and(X1, X2) -> active# X1, active# length cons(N, L) -> isNatList# 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) -> uLength#(and(isNat N, isNatList L), L))
(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))
(active# and(X1, X2) -> active# X1, active# take(X1, X2) -> active# X1)
(active# and(X1, X2) -> active# X1, active# take(X1, X2) -> active# 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) -> take#(active X1, X2))
(active# and(X1, X2) -> active# X1, active# take(0(), IL) -> isNatIList# IL)
(active# and(X1, X2) -> active# X1, active# take(0(), IL) -> uTake1# isNatIList IL)
(active# and(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat N, isNatIList IL))
(active# and(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat M, and(isNat N, isNatIList IL)))
(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# N)
(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)) -> uTake2#(and(isNat M, and(isNat N, isNatIList IL)), M, N, IL))
(active# and(X1, X2) -> active# X1, active# uTake1 X -> active# X)
(active# and(X1, X2) -> active# X1, active# uTake1 X -> uTake1# active X)
(active# and(X1, X2) -> active# X1, active# uTake2(X1, X2, X3, X4) -> active# X1)
(active# and(X1, X2) -> active# X1, active# uTake2(X1, X2, X3, X4) -> uTake2#(active X1, X2, X3, X4))
(active# and(X1, X2) -> active# X1, active# uTake2(tt(), M, N, IL) -> cons#(N, take(M, IL)))
(active# and(X1, X2) -> active# X1, active# uTake2(tt(), M, N, IL) -> take#(M, IL))
(active# and(X1, X2) -> active# X1, active# uLength(X1, X2) -> active# X1)
(active# and(X1, X2) -> active# X1, active# uLength(X1, X2) -> uLength#(active X1, X2))
(active# and(X1, X2) -> active# X1, active# uLength(tt(), L) -> s# length L)
(active# and(X1, X2) -> active# X1, active# uLength(tt(), L) -> length# L)
(active# length cons(N, L) -> isNatList# L, isNatList# ok X -> isNatList# X)
(active# isNatList cons(N, L) -> isNatList# L, isNatList# ok X -> isNatList# X)
(active# take(0(), IL) -> isNatIList# IL, isNatIList# ok X -> isNatIList# X)
(active# isNatIList IL -> isNatList# IL, isNatList# ok X -> isNatList# X)
(active# uLength(tt(), L) -> s# length L, s# mark X -> s# X)
(active# uLength(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# length X -> length# proper X, length# mark X -> length# X)
(proper# length X -> length# proper X, length# ok X -> length# X)
(proper# isNat X -> isNat# proper X, isNat# ok X -> isNat# X)
(proper# isNatList X -> isNatList# proper X, isNatList# ok X -> isNatList# X)
(active# length X -> length# active X, length# mark X -> length# X)
(active# length X -> length# active X, length# ok X -> length# X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X3, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# uTake2(X1, X2, X3, X4) -> proper# X3, proper# and(X1, X2) -> proper# X1)
(proper# uTake2(X1, X2, X3, X4) -> proper# X3, proper# and(X1, X2) -> proper# X2)
(proper# uTake2(X1, X2, X3, X4) -> proper# X3, proper# isNatList X -> isNatList# proper X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X3, proper# isNatList X -> proper# X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X3, proper# isNatIList X -> isNatIList# proper X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X3, proper# isNatIList X -> proper# X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X3, proper# isNat X -> isNat# proper X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X3, proper# isNat X -> proper# X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X3, proper# s X -> s# proper X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X3, proper# s X -> proper# X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X3, proper# length X -> length# proper X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X3, proper# length X -> proper# X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X3, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# uTake2(X1, X2, X3, X4) -> proper# X3, proper# cons(X1, X2) -> proper# X1)
(proper# uTake2(X1, X2, X3, X4) -> proper# X3, proper# cons(X1, X2) -> proper# X2)
(proper# uTake2(X1, X2, X3, X4) -> proper# X3, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# uTake2(X1, X2, X3, X4) -> proper# X3, proper# take(X1, X2) -> proper# X1)
(proper# uTake2(X1, X2, X3, X4) -> proper# X3, proper# take(X1, X2) -> proper# X2)
(proper# uTake2(X1, X2, X3, X4) -> proper# X3, proper# uTake1 X -> uTake1# proper X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X3, proper# uTake1 X -> proper# X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X3, proper# uTake2(X1, X2, X3, X4) -> uTake2#(proper X1, proper X2, proper X3, proper X4))
(proper# uTake2(X1, X2, X3, X4) -> proper# X3, proper# uTake2(X1, X2, X3, X4) -> proper# X1)
(proper# uTake2(X1, X2, X3, X4) -> proper# X3, proper# uTake2(X1, X2, X3, X4) -> proper# X2)
(proper# uTake2(X1, X2, X3, X4) -> proper# X3, proper# uTake2(X1, X2, X3, X4) -> proper# X3)
(proper# uTake2(X1, X2, X3, X4) -> proper# X3, proper# uTake2(X1, X2, X3, X4) -> proper# X4)
(proper# uTake2(X1, X2, X3, X4) -> proper# X3, proper# uLength(X1, X2) -> uLength#(proper X1, proper X2))
(proper# uTake2(X1, X2, X3, X4) -> proper# X3, proper# uLength(X1, X2) -> proper# X1)
(proper# uTake2(X1, X2, X3, X4) -> proper# X3, proper# uLength(X1, X2) -> proper# X2)
(proper# uTake2(X1, X2, X3, X4) -> proper# X2, proper# and(X1, X2) -> and#(proper X1, proper X2))
(proper# uTake2(X1, X2, X3, X4) -> proper# X2, proper# and(X1, X2) -> proper# X1)
(proper# uTake2(X1, X2, X3, X4) -> proper# X2, proper# and(X1, X2) -> proper# X2)
(proper# uTake2(X1, X2, X3, X4) -> proper# X2, proper# isNatList X -> isNatList# proper X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X2, proper# isNatList X -> proper# X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X2, proper# isNatIList X -> isNatIList# proper X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X2, proper# isNatIList X -> proper# X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X2, proper# isNat X -> isNat# proper X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X2, proper# isNat X -> proper# X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X2, proper# s X -> s# proper X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X2, proper# s X -> proper# X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X2, proper# length X -> length# proper X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X2, proper# length X -> proper# X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2))
(proper# uTake2(X1, X2, X3, X4) -> proper# X2, proper# cons(X1, X2) -> proper# X1)
(proper# uTake2(X1, X2, X3, X4) -> proper# X2, proper# cons(X1, X2) -> proper# X2)
(proper# uTake2(X1, X2, X3, X4) -> proper# X2, proper# take(X1, X2) -> take#(proper X1, proper X2))
(proper# uTake2(X1, X2, X3, X4) -> proper# X2, proper# take(X1, X2) -> proper# X1)
(proper# uTake2(X1, X2, X3, X4) -> proper# X2, proper# take(X1, X2) -> proper# X2)
(proper# uTake2(X1, X2, X3, X4) -> proper# X2, proper# uTake1 X -> uTake1# proper X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X2, proper# uTake1 X -> proper# X)
(proper# uTake2(X1, X2, X3, X4) -> proper# X2, proper# uTake2(X1, X2, X3, X4) -> uTake2#(proper X1, proper X2, proper X3, proper X4))
(proper# uTake2(X1, X2, X3, X4) -> proper# X2, proper# uTake2(X1, X2, X3, X4) -> proper# X1)
(proper# uTake2(X1, X2, X3, X4) -> proper# X2, proper# uTake2(X1, X2, X3, X4) -> proper# X2)
(proper# uTake2(X1, X2, X3, X4) -> proper# X2, proper# uTake2(X1, X2, X3, X4) -> proper# X3)
(proper# uTake2(X1, X2, X3, X4) -> proper# X2, proper# uTake2(X1, X2, X3, X4) -> proper# X4)
(proper# uTake2(X1, X2, X3, X4) -> proper# X2, proper# uLength(X1, X2) -> uLength#(proper X1, proper X2))
(proper# uTake2(X1, X2, X3, X4) -> proper# X2, proper# uLength(X1, X2) -> proper# X1)
(proper# uTake2(X1, X2, X3, X4) -> proper# X2, proper# uLength(X1, X2) -> proper# X2)
(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# isNatList X -> isNatList# proper X)
(proper# cons(X1, X2) -> proper# X2, proper# isNatList 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# isNat X -> isNat# proper X)
(proper# cons(X1, X2) -> proper# X2, proper# isNat 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# 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# 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# uTake1 X -> uTake1# proper X)
(proper# cons(X1, X2) -> proper# X2, proper# uTake1 X -> proper# X)
(proper# cons(X1, X2) -> proper# X2, proper# uTake2(X1, X2, X3, X4) -> uTake2#(proper X1, proper X2, proper X3, proper X4))
(proper# cons(X1, X2) -> proper# X2, proper# uTake2(X1, X2, X3, X4) -> proper# X1)
(proper# cons(X1, X2) -> proper# X2, proper# uTake2(X1, X2, X3, X4) -> proper# X2)
(proper# cons(X1, X2) -> proper# X2, proper# uTake2(X1, X2, X3, X4) -> proper# X3)
(proper# cons(X1, X2) -> proper# X2, proper# uTake2(X1, X2, X3, X4) -> proper# X4)
(proper# cons(X1, X2) -> proper# X2, proper# uLength(X1, X2) -> uLength#(proper X1, proper X2))
(proper# cons(X1, X2) -> proper# X2, proper# uLength(X1, X2) -> proper# X1)
(proper# cons(X1, X2) -> proper# X2, proper# uLength(X1, X2) -> proper# X2)
(active# take(X1, X2) -> active# X2, active# and(X1, X2) -> active# X1)
(active# take(X1, X2) -> active# X2, active# and(X1, X2) -> active# X2)
(active# take(X1, X2) -> active# X2, active# and(X1, X2) -> and#(X1, active X2))
(active# take(X1, X2) -> active# X2, active# and(X1, X2) -> and#(active X1, X2))
(active# take(X1, X2) -> active# X2, active# isNatList cons(N, L) -> and#(isNat N, isNatList L))
(active# take(X1, X2) -> active# X2, active# isNatList cons(N, L) -> isNatList# L)
(active# take(X1, X2) -> active# X2, active# isNatList cons(N, L) -> isNat# N)
(active# take(X1, X2) -> active# X2, active# isNatList take(N, IL) -> and#(isNat N, isNatIList IL))
(active# take(X1, X2) -> active# X2, active# isNatList take(N, IL) -> isNatIList# IL)
(active# take(X1, X2) -> active# X2, active# isNatList take(N, IL) -> isNat# N)
(active# take(X1, X2) -> active# X2, active# isNatIList IL -> isNatList# IL)
(active# take(X1, X2) -> active# X2, active# isNatIList cons(N, IL) -> and#(isNat N, isNatIList IL))
(active# take(X1, X2) -> active# X2, active# isNatIList cons(N, IL) -> isNatIList# IL)
(active# take(X1, X2) -> active# X2, active# isNatIList cons(N, IL) -> isNat# N)
(active# take(X1, X2) -> active# X2, active# isNat s N -> isNat# N)
(active# take(X1, X2) -> active# X2, active# isNat length L -> isNatList# L)
(active# take(X1, X2) -> active# X2, active# s X -> active# X)
(active# take(X1, X2) -> active# X2, active# s X -> s# active X)
(active# take(X1, X2) -> active# X2, active# length X -> active# X)
(active# take(X1, X2) -> active# X2, active# length X -> length# active X)
(active# take(X1, X2) -> active# X2, active# length cons(N, L) -> and#(isNat N, isNatList L))
(active# take(X1, X2) -> active# X2, active# length cons(N, L) -> isNatList# 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) -> uLength#(and(isNat N, isNatList L), L))
(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))
(active# take(X1, X2) -> active# X2, active# take(X1, X2) -> active# X1)
(active# take(X1, X2) -> active# X2, active# take(X1, X2) -> active# 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) -> take#(active X1, X2))
(active# take(X1, X2) -> active# X2, active# take(0(), IL) -> isNatIList# IL)
(active# take(X1, X2) -> active# X2, active# take(0(), IL) -> uTake1# isNatIList IL)
(active# take(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> and#(isNat N, isNatIList IL))
(active# take(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> and#(isNat M, and(isNat N, isNatIList IL)))
(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# N)
(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)) -> uTake2#(and(isNat M, and(isNat N, isNatIList IL)), M, N, IL))
(active# take(X1, X2) -> active# X2, active# uTake1 X -> active# X)
(active# take(X1, X2) -> active# X2, active# uTake1 X -> uTake1# active X)
(active# take(X1, X2) -> active# X2, active# uTake2(X1, X2, X3, X4) -> active# X1)
(active# take(X1, X2) -> active# X2, active# uTake2(X1, X2, X3, X4) -> uTake2#(active X1, X2, X3, X4))
(active# take(X1, X2) -> active# X2, active# uTake2(tt(), M, N, IL) -> cons#(N, take(M, IL)))
(active# take(X1, X2) -> active# X2, active# uTake2(tt(), M, N, IL) -> take#(M, IL))
(active# take(X1, X2) -> active# X2, active# uLength(X1, X2) -> active# X1)
(active# take(X1, X2) -> active# X2, active# uLength(X1, X2) -> uLength#(active X1, X2))
(active# take(X1, X2) -> active# X2, active# uLength(tt(), L) -> s# length L)
(active# take(X1, X2) -> active# X2, active# uLength(tt(), L) -> length# L)
(active# take(s M, cons(N, IL)) -> uTake2#(and(isNat M, and(isNat N, isNatIList IL)), M, N, IL), uTake2#(ok X1, ok X2, ok X3, ok X4) -> uTake2#(X1, X2, X3, X4))
(uTake2#(mark X1, X2, X3, X4) -> uTake2#(X1, X2, X3, X4), uTake2#(mark X1, X2, X3, X4) -> uTake2#(X1, X2, X3, X4))
(uTake2#(mark X1, X2, X3, X4) -> uTake2#(X1, X2, X3, X4), uTake2#(ok X1, ok X2, ok X3, ok X4) -> uTake2#(X1, X2, X3, X4))
(active# take(s M, cons(N, IL)) -> isNat# M, isNat# ok X -> isNat# X)
(active# length cons(N, L) -> uLength#(and(isNat N, isNatList L), L), uLength#(ok X1, ok X2) -> uLength#(X1, X2))
(active# length cons(N, L) -> isNat# N, isNat# ok X -> isNat# X)
(active# isNatIList cons(N, IL) -> isNat# N, isNat# ok X -> isNat# X)
(active# isNatList cons(N, L) -> isNat# N, isNat# ok X -> isNat# X)
(proper# uTake2(X1, X2, X3, X4) -> uTake2#(proper X1, proper X2, proper X3, proper X4), uTake2#(mark X1, X2, X3, X4) -> uTake2#(X1, X2, X3, X4))
(proper# uTake2(X1, X2, X3, X4) -> uTake2#(proper X1, proper X2, proper X3, proper X4), uTake2#(ok X1, ok X2, ok X3, ok X4) -> uTake2#(X1, X2, X3, X4))
(uLength#(mark X1, X2) -> uLength#(X1, X2), uLength#(mark X1, X2) -> uLength#(X1, X2))
(uLength#(mark X1, X2) -> uLength#(X1, X2), uLength#(ok X1, ok X2) -> uLength#(X1, X2))
(take#(mark X1, X2) -> take#(X1, X2), take#(X1, mark 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#(ok X1, ok X2) -> take#(X1, X2))
(cons#(ok X1, ok X2) -> cons#(X1, X2), cons#(mark X1, X2) -> cons#(X1, X2))
(cons#(ok X1, ok X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2))
(and#(ok X1, ok X2) -> and#(X1, X2), and#(X1, mark X2) -> and#(X1, X2))
(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))
(and#(X1, mark X2) -> and#(X1, X2), and#(X1, mark X2) -> and#(X1, X2))
(and#(X1, mark X2) -> and#(X1, X2), and#(mark X1, X2) -> and#(X1, X2))
(and#(X1, mark X2) -> and#(X1, X2), and#(ok X1, ok X2) -> and#(X1, X2))
(active# take(X1, X2) -> take#(active X1, X2), take#(X1, mark 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#(ok X1, ok X2) -> take#(X1, X2))
(active# and(X1, X2) -> and#(active X1, X2), and#(X1, mark X2) -> and#(X1, X2))
(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))
}
STATUS:
arrows: 0.884909
SCCS (14):
Scc:
{top# mark X -> top# proper X,
top# ok X -> top# active X}
Scc:
{ proper# and(X1, X2) -> proper# X1,
proper# and(X1, X2) -> proper# X2,
proper# isNatList X -> proper# X,
proper# isNatIList X -> proper# X,
proper# isNat X -> proper# X,
proper# s X -> proper# X,
proper# length X -> proper# X,
proper# cons(X1, X2) -> proper# X1,
proper# cons(X1, X2) -> proper# X2,
proper# take(X1, X2) -> proper# X1,
proper# take(X1, X2) -> proper# X2,
proper# uTake1 X -> proper# X,
proper# uTake2(X1, X2, X3, X4) -> proper# X1,
proper# uTake2(X1, X2, X3, X4) -> proper# X2,
proper# uTake2(X1, X2, X3, X4) -> proper# X3,
proper# uTake2(X1, X2, X3, X4) -> proper# X4,
proper# uLength(X1, X2) -> proper# X1,
proper# uLength(X1, X2) -> proper# X2}
Scc:
{ active# and(X1, X2) -> active# X1,
active# and(X1, X2) -> active# X2,
active# s X -> active# X,
active# length X -> active# X,
active# cons(X1, X2) -> active# X1,
active# take(X1, X2) -> active# X1,
active# take(X1, X2) -> active# X2,
active# uTake1 X -> active# X,
active# uTake2(X1, X2, X3, X4) -> active# X1,
active# uLength(X1, X2) -> active# X1}
Scc:
{uTake1# mark X -> uTake1# X,
uTake1# ok X -> uTake1# X}
Scc:
{length# mark X -> length# X,
length# ok X -> length# X}
Scc:
{s# mark X -> s# X,
s# ok X -> s# X}
Scc:
{isNatIList# ok X -> isNatIList# X}
Scc:
{isNatList# ok X -> isNatList# X}
Scc:
{isNat# ok X -> isNat# X}
Scc:
{ uTake2#(mark X1, X2, X3, X4) -> uTake2#(X1, X2, X3, X4),
uTake2#(ok X1, ok X2, ok X3, ok X4) -> uTake2#(X1, X2, X3, X4)}
Scc:
{ uLength#(mark X1, X2) -> uLength#(X1, X2),
uLength#(ok X1, ok X2) -> uLength#(X1, X2)}
Scc:
{ take#(X1, mark X2) -> take#(X1, X2),
take#(mark X1, X2) -> take#(X1, X2),
take#(ok X1, ok X2) -> take#(X1, X2)}
Scc:
{ cons#(mark X1, X2) -> cons#(X1, X2),
cons#(ok X1, ok X2) -> cons#(X1, X2)}
Scc:
{ and#(X1, mark X2) -> and#(X1, X2),
and#(mark X1, X2) -> and#(X1, X2),
and#(ok X1, ok X2) -> and#(X1, X2)}
SCC (2):
Strict:
{top# mark X -> top# proper X,
top# ok X -> top# active X}
Weak:
{ active and(X1, X2) -> and(X1, active X2),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), T) -> mark T,
active isNatList cons(N, L) -> mark and(isNat N, isNatList L),
active isNatList nil() -> mark tt(),
active isNatList take(N, IL) -> mark and(isNat N, isNatIList IL),
active isNatIList IL -> mark isNatList IL,
active isNatIList zeros() -> mark tt(),
active isNatIList cons(N, IL) -> mark and(isNat N, isNatIList IL),
active isNat 0() -> mark tt(),
active isNat s N -> mark isNat N,
active isNat length L -> mark isNatList L,
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark uLength(and(isNat N, isNatList L), L),
active zeros() -> mark cons(0(), zeros()),
active cons(X1, X2) -> cons(active X1, X2),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark uTake1 isNatIList IL,
active take(s M, cons(N, IL)) -> mark uTake2(and(isNat M, and(isNat N, isNatIList IL)), M, N, IL),
active uTake1 X -> uTake1 active X,
active uTake1 tt() -> mark nil(),
active uTake2(X1, X2, X3, X4) -> uTake2(active X1, X2, X3, X4),
active uTake2(tt(), M, N, IL) -> mark cons(N, take(M, IL)),
active uLength(X1, X2) -> uLength(active X1, X2),
active uLength(tt(), L) -> mark s length L,
and(X1, mark X2) -> mark and(X1, X2),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatList ok X -> ok isNatList X,
isNatIList ok X -> ok isNatIList X,
isNat ok X -> ok isNat 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,
cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
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),
uTake1 mark X -> mark uTake1 X,
uTake1 ok X -> ok uTake1 X,
uTake2(mark X1, X2, X3, X4) -> mark uTake2(X1, X2, X3, X4),
uTake2(ok X1, ok X2, ok X3, ok X4) -> ok uTake2(X1, X2, X3, X4),
uLength(mark X1, X2) -> mark uLength(X1, X2),
uLength(ok X1, ok X2) -> ok uLength(X1, X2),
proper and(X1, X2) -> and(proper X1, proper X2),
proper tt() -> ok tt(),
proper isNatList X -> isNatList proper X,
proper isNatIList X -> isNatIList proper X,
proper isNat X -> isNat proper X,
proper 0() -> ok 0(),
proper s X -> s proper X,
proper length X -> length proper X,
proper zeros() -> ok zeros(),
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper nil() -> ok nil(),
proper take(X1, X2) -> take(proper X1, proper X2),
proper uTake1 X -> uTake1 proper X,
proper uTake2(X1, X2, X3, X4) -> uTake2(proper X1, proper X2, proper X3, proper X4),
proper uLength(X1, X2) -> uLength(proper X1, proper X2),
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (18):
Strict:
{ proper# and(X1, X2) -> proper# X1,
proper# and(X1, X2) -> proper# X2,
proper# isNatList X -> proper# X,
proper# isNatIList X -> proper# X,
proper# isNat X -> proper# X,
proper# s X -> proper# X,
proper# length X -> proper# X,
proper# cons(X1, X2) -> proper# X1,
proper# cons(X1, X2) -> proper# X2,
proper# take(X1, X2) -> proper# X1,
proper# take(X1, X2) -> proper# X2,
proper# uTake1 X -> proper# X,
proper# uTake2(X1, X2, X3, X4) -> proper# X1,
proper# uTake2(X1, X2, X3, X4) -> proper# X2,
proper# uTake2(X1, X2, X3, X4) -> proper# X3,
proper# uTake2(X1, X2, X3, X4) -> proper# X4,
proper# uLength(X1, X2) -> proper# X1,
proper# uLength(X1, X2) -> proper# X2}
Weak:
{ active and(X1, X2) -> and(X1, active X2),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), T) -> mark T,
active isNatList cons(N, L) -> mark and(isNat N, isNatList L),
active isNatList nil() -> mark tt(),
active isNatList take(N, IL) -> mark and(isNat N, isNatIList IL),
active isNatIList IL -> mark isNatList IL,
active isNatIList zeros() -> mark tt(),
active isNatIList cons(N, IL) -> mark and(isNat N, isNatIList IL),
active isNat 0() -> mark tt(),
active isNat s N -> mark isNat N,
active isNat length L -> mark isNatList L,
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark uLength(and(isNat N, isNatList L), L),
active zeros() -> mark cons(0(), zeros()),
active cons(X1, X2) -> cons(active X1, X2),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark uTake1 isNatIList IL,
active take(s M, cons(N, IL)) -> mark uTake2(and(isNat M, and(isNat N, isNatIList IL)), M, N, IL),
active uTake1 X -> uTake1 active X,
active uTake1 tt() -> mark nil(),
active uTake2(X1, X2, X3, X4) -> uTake2(active X1, X2, X3, X4),
active uTake2(tt(), M, N, IL) -> mark cons(N, take(M, IL)),
active uLength(X1, X2) -> uLength(active X1, X2),
active uLength(tt(), L) -> mark s length L,
and(X1, mark X2) -> mark and(X1, X2),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatList ok X -> ok isNatList X,
isNatIList ok X -> ok isNatIList X,
isNat ok X -> ok isNat 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,
cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
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),
uTake1 mark X -> mark uTake1 X,
uTake1 ok X -> ok uTake1 X,
uTake2(mark X1, X2, X3, X4) -> mark uTake2(X1, X2, X3, X4),
uTake2(ok X1, ok X2, ok X3, ok X4) -> ok uTake2(X1, X2, X3, X4),
uLength(mark X1, X2) -> mark uLength(X1, X2),
uLength(ok X1, ok X2) -> ok uLength(X1, X2),
proper and(X1, X2) -> and(proper X1, proper X2),
proper tt() -> ok tt(),
proper isNatList X -> isNatList proper X,
proper isNatIList X -> isNatIList proper X,
proper isNat X -> isNat proper X,
proper 0() -> ok 0(),
proper s X -> s proper X,
proper length X -> length proper X,
proper zeros() -> ok zeros(),
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper nil() -> ok nil(),
proper take(X1, X2) -> take(proper X1, proper X2),
proper uTake1 X -> uTake1 proper X,
proper uTake2(X1, X2, X3, X4) -> uTake2(proper X1, proper X2, proper X3, proper X4),
proper uLength(X1, X2) -> uLength(proper X1, proper X2),
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (10):
Strict:
{ active# and(X1, X2) -> active# X1,
active# and(X1, X2) -> active# X2,
active# s X -> active# X,
active# length X -> active# X,
active# cons(X1, X2) -> active# X1,
active# take(X1, X2) -> active# X1,
active# take(X1, X2) -> active# X2,
active# uTake1 X -> active# X,
active# uTake2(X1, X2, X3, X4) -> active# X1,
active# uLength(X1, X2) -> active# X1}
Weak:
{ active and(X1, X2) -> and(X1, active X2),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), T) -> mark T,
active isNatList cons(N, L) -> mark and(isNat N, isNatList L),
active isNatList nil() -> mark tt(),
active isNatList take(N, IL) -> mark and(isNat N, isNatIList IL),
active isNatIList IL -> mark isNatList IL,
active isNatIList zeros() -> mark tt(),
active isNatIList cons(N, IL) -> mark and(isNat N, isNatIList IL),
active isNat 0() -> mark tt(),
active isNat s N -> mark isNat N,
active isNat length L -> mark isNatList L,
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark uLength(and(isNat N, isNatList L), L),
active zeros() -> mark cons(0(), zeros()),
active cons(X1, X2) -> cons(active X1, X2),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark uTake1 isNatIList IL,
active take(s M, cons(N, IL)) -> mark uTake2(and(isNat M, and(isNat N, isNatIList IL)), M, N, IL),
active uTake1 X -> uTake1 active X,
active uTake1 tt() -> mark nil(),
active uTake2(X1, X2, X3, X4) -> uTake2(active X1, X2, X3, X4),
active uTake2(tt(), M, N, IL) -> mark cons(N, take(M, IL)),
active uLength(X1, X2) -> uLength(active X1, X2),
active uLength(tt(), L) -> mark s length L,
and(X1, mark X2) -> mark and(X1, X2),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatList ok X -> ok isNatList X,
isNatIList ok X -> ok isNatIList X,
isNat ok X -> ok isNat 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,
cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
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),
uTake1 mark X -> mark uTake1 X,
uTake1 ok X -> ok uTake1 X,
uTake2(mark X1, X2, X3, X4) -> mark uTake2(X1, X2, X3, X4),
uTake2(ok X1, ok X2, ok X3, ok X4) -> ok uTake2(X1, X2, X3, X4),
uLength(mark X1, X2) -> mark uLength(X1, X2),
uLength(ok X1, ok X2) -> ok uLength(X1, X2),
proper and(X1, X2) -> and(proper X1, proper X2),
proper tt() -> ok tt(),
proper isNatList X -> isNatList proper X,
proper isNatIList X -> isNatIList proper X,
proper isNat X -> isNat proper X,
proper 0() -> ok 0(),
proper s X -> s proper X,
proper length X -> length proper X,
proper zeros() -> ok zeros(),
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper nil() -> ok nil(),
proper take(X1, X2) -> take(proper X1, proper X2),
proper uTake1 X -> uTake1 proper X,
proper uTake2(X1, X2, X3, X4) -> uTake2(proper X1, proper X2, proper X3, proper X4),
proper uLength(X1, X2) -> uLength(proper X1, proper X2),
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (2):
Strict:
{uTake1# mark X -> uTake1# X,
uTake1# ok X -> uTake1# X}
Weak:
{ active and(X1, X2) -> and(X1, active X2),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), T) -> mark T,
active isNatList cons(N, L) -> mark and(isNat N, isNatList L),
active isNatList nil() -> mark tt(),
active isNatList take(N, IL) -> mark and(isNat N, isNatIList IL),
active isNatIList IL -> mark isNatList IL,
active isNatIList zeros() -> mark tt(),
active isNatIList cons(N, IL) -> mark and(isNat N, isNatIList IL),
active isNat 0() -> mark tt(),
active isNat s N -> mark isNat N,
active isNat length L -> mark isNatList L,
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark uLength(and(isNat N, isNatList L), L),
active zeros() -> mark cons(0(), zeros()),
active cons(X1, X2) -> cons(active X1, X2),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark uTake1 isNatIList IL,
active take(s M, cons(N, IL)) -> mark uTake2(and(isNat M, and(isNat N, isNatIList IL)), M, N, IL),
active uTake1 X -> uTake1 active X,
active uTake1 tt() -> mark nil(),
active uTake2(X1, X2, X3, X4) -> uTake2(active X1, X2, X3, X4),
active uTake2(tt(), M, N, IL) -> mark cons(N, take(M, IL)),
active uLength(X1, X2) -> uLength(active X1, X2),
active uLength(tt(), L) -> mark s length L,
and(X1, mark X2) -> mark and(X1, X2),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatList ok X -> ok isNatList X,
isNatIList ok X -> ok isNatIList X,
isNat ok X -> ok isNat 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,
cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
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),
uTake1 mark X -> mark uTake1 X,
uTake1 ok X -> ok uTake1 X,
uTake2(mark X1, X2, X3, X4) -> mark uTake2(X1, X2, X3, X4),
uTake2(ok X1, ok X2, ok X3, ok X4) -> ok uTake2(X1, X2, X3, X4),
uLength(mark X1, X2) -> mark uLength(X1, X2),
uLength(ok X1, ok X2) -> ok uLength(X1, X2),
proper and(X1, X2) -> and(proper X1, proper X2),
proper tt() -> ok tt(),
proper isNatList X -> isNatList proper X,
proper isNatIList X -> isNatIList proper X,
proper isNat X -> isNat proper X,
proper 0() -> ok 0(),
proper s X -> s proper X,
proper length X -> length proper X,
proper zeros() -> ok zeros(),
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper nil() -> ok nil(),
proper take(X1, X2) -> take(proper X1, proper X2),
proper uTake1 X -> uTake1 proper X,
proper uTake2(X1, X2, X3, X4) -> uTake2(proper X1, proper X2, proper X3, proper X4),
proper uLength(X1, X2) -> uLength(proper X1, proper X2),
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:
{ active and(X1, X2) -> and(X1, active X2),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), T) -> mark T,
active isNatList cons(N, L) -> mark and(isNat N, isNatList L),
active isNatList nil() -> mark tt(),
active isNatList take(N, IL) -> mark and(isNat N, isNatIList IL),
active isNatIList IL -> mark isNatList IL,
active isNatIList zeros() -> mark tt(),
active isNatIList cons(N, IL) -> mark and(isNat N, isNatIList IL),
active isNat 0() -> mark tt(),
active isNat s N -> mark isNat N,
active isNat length L -> mark isNatList L,
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark uLength(and(isNat N, isNatList L), L),
active zeros() -> mark cons(0(), zeros()),
active cons(X1, X2) -> cons(active X1, X2),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark uTake1 isNatIList IL,
active take(s M, cons(N, IL)) -> mark uTake2(and(isNat M, and(isNat N, isNatIList IL)), M, N, IL),
active uTake1 X -> uTake1 active X,
active uTake1 tt() -> mark nil(),
active uTake2(X1, X2, X3, X4) -> uTake2(active X1, X2, X3, X4),
active uTake2(tt(), M, N, IL) -> mark cons(N, take(M, IL)),
active uLength(X1, X2) -> uLength(active X1, X2),
active uLength(tt(), L) -> mark s length L,
and(X1, mark X2) -> mark and(X1, X2),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatList ok X -> ok isNatList X,
isNatIList ok X -> ok isNatIList X,
isNat ok X -> ok isNat 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,
cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
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),
uTake1 mark X -> mark uTake1 X,
uTake1 ok X -> ok uTake1 X,
uTake2(mark X1, X2, X3, X4) -> mark uTake2(X1, X2, X3, X4),
uTake2(ok X1, ok X2, ok X3, ok X4) -> ok uTake2(X1, X2, X3, X4),
uLength(mark X1, X2) -> mark uLength(X1, X2),
uLength(ok X1, ok X2) -> ok uLength(X1, X2),
proper and(X1, X2) -> and(proper X1, proper X2),
proper tt() -> ok tt(),
proper isNatList X -> isNatList proper X,
proper isNatIList X -> isNatIList proper X,
proper isNat X -> isNat proper X,
proper 0() -> ok 0(),
proper s X -> s proper X,
proper length X -> length proper X,
proper zeros() -> ok zeros(),
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper nil() -> ok nil(),
proper take(X1, X2) -> take(proper X1, proper X2),
proper uTake1 X -> uTake1 proper X,
proper uTake2(X1, X2, X3, X4) -> uTake2(proper X1, proper X2, proper X3, proper X4),
proper uLength(X1, X2) -> uLength(proper X1, proper X2),
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:
{ active and(X1, X2) -> and(X1, active X2),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), T) -> mark T,
active isNatList cons(N, L) -> mark and(isNat N, isNatList L),
active isNatList nil() -> mark tt(),
active isNatList take(N, IL) -> mark and(isNat N, isNatIList IL),
active isNatIList IL -> mark isNatList IL,
active isNatIList zeros() -> mark tt(),
active isNatIList cons(N, IL) -> mark and(isNat N, isNatIList IL),
active isNat 0() -> mark tt(),
active isNat s N -> mark isNat N,
active isNat length L -> mark isNatList L,
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark uLength(and(isNat N, isNatList L), L),
active zeros() -> mark cons(0(), zeros()),
active cons(X1, X2) -> cons(active X1, X2),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark uTake1 isNatIList IL,
active take(s M, cons(N, IL)) -> mark uTake2(and(isNat M, and(isNat N, isNatIList IL)), M, N, IL),
active uTake1 X -> uTake1 active X,
active uTake1 tt() -> mark nil(),
active uTake2(X1, X2, X3, X4) -> uTake2(active X1, X2, X3, X4),
active uTake2(tt(), M, N, IL) -> mark cons(N, take(M, IL)),
active uLength(X1, X2) -> uLength(active X1, X2),
active uLength(tt(), L) -> mark s length L,
and(X1, mark X2) -> mark and(X1, X2),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatList ok X -> ok isNatList X,
isNatIList ok X -> ok isNatIList X,
isNat ok X -> ok isNat 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,
cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
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),
uTake1 mark X -> mark uTake1 X,
uTake1 ok X -> ok uTake1 X,
uTake2(mark X1, X2, X3, X4) -> mark uTake2(X1, X2, X3, X4),
uTake2(ok X1, ok X2, ok X3, ok X4) -> ok uTake2(X1, X2, X3, X4),
uLength(mark X1, X2) -> mark uLength(X1, X2),
uLength(ok X1, ok X2) -> ok uLength(X1, X2),
proper and(X1, X2) -> and(proper X1, proper X2),
proper tt() -> ok tt(),
proper isNatList X -> isNatList proper X,
proper isNatIList X -> isNatIList proper X,
proper isNat X -> isNat proper X,
proper 0() -> ok 0(),
proper s X -> s proper X,
proper length X -> length proper X,
proper zeros() -> ok zeros(),
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper nil() -> ok nil(),
proper take(X1, X2) -> take(proper X1, proper X2),
proper uTake1 X -> uTake1 proper X,
proper uTake2(X1, X2, X3, X4) -> uTake2(proper X1, proper X2, proper X3, proper X4),
proper uLength(X1, X2) -> uLength(proper X1, proper X2),
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (1):
Strict:
{isNatIList# ok X -> isNatIList# X}
Weak:
{ active and(X1, X2) -> and(X1, active X2),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), T) -> mark T,
active isNatList cons(N, L) -> mark and(isNat N, isNatList L),
active isNatList nil() -> mark tt(),
active isNatList take(N, IL) -> mark and(isNat N, isNatIList IL),
active isNatIList IL -> mark isNatList IL,
active isNatIList zeros() -> mark tt(),
active isNatIList cons(N, IL) -> mark and(isNat N, isNatIList IL),
active isNat 0() -> mark tt(),
active isNat s N -> mark isNat N,
active isNat length L -> mark isNatList L,
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark uLength(and(isNat N, isNatList L), L),
active zeros() -> mark cons(0(), zeros()),
active cons(X1, X2) -> cons(active X1, X2),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark uTake1 isNatIList IL,
active take(s M, cons(N, IL)) -> mark uTake2(and(isNat M, and(isNat N, isNatIList IL)), M, N, IL),
active uTake1 X -> uTake1 active X,
active uTake1 tt() -> mark nil(),
active uTake2(X1, X2, X3, X4) -> uTake2(active X1, X2, X3, X4),
active uTake2(tt(), M, N, IL) -> mark cons(N, take(M, IL)),
active uLength(X1, X2) -> uLength(active X1, X2),
active uLength(tt(), L) -> mark s length L,
and(X1, mark X2) -> mark and(X1, X2),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatList ok X -> ok isNatList X,
isNatIList ok X -> ok isNatIList X,
isNat ok X -> ok isNat 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,
cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
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),
uTake1 mark X -> mark uTake1 X,
uTake1 ok X -> ok uTake1 X,
uTake2(mark X1, X2, X3, X4) -> mark uTake2(X1, X2, X3, X4),
uTake2(ok X1, ok X2, ok X3, ok X4) -> ok uTake2(X1, X2, X3, X4),
uLength(mark X1, X2) -> mark uLength(X1, X2),
uLength(ok X1, ok X2) -> ok uLength(X1, X2),
proper and(X1, X2) -> and(proper X1, proper X2),
proper tt() -> ok tt(),
proper isNatList X -> isNatList proper X,
proper isNatIList X -> isNatIList proper X,
proper isNat X -> isNat proper X,
proper 0() -> ok 0(),
proper s X -> s proper X,
proper length X -> length proper X,
proper zeros() -> ok zeros(),
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper nil() -> ok nil(),
proper take(X1, X2) -> take(proper X1, proper X2),
proper uTake1 X -> uTake1 proper X,
proper uTake2(X1, X2, X3, X4) -> uTake2(proper X1, proper X2, proper X3, proper X4),
proper uLength(X1, X2) -> uLength(proper X1, proper X2),
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (1):
Strict:
{isNatList# ok X -> isNatList# X}
Weak:
{ active and(X1, X2) -> and(X1, active X2),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), T) -> mark T,
active isNatList cons(N, L) -> mark and(isNat N, isNatList L),
active isNatList nil() -> mark tt(),
active isNatList take(N, IL) -> mark and(isNat N, isNatIList IL),
active isNatIList IL -> mark isNatList IL,
active isNatIList zeros() -> mark tt(),
active isNatIList cons(N, IL) -> mark and(isNat N, isNatIList IL),
active isNat 0() -> mark tt(),
active isNat s N -> mark isNat N,
active isNat length L -> mark isNatList L,
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark uLength(and(isNat N, isNatList L), L),
active zeros() -> mark cons(0(), zeros()),
active cons(X1, X2) -> cons(active X1, X2),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark uTake1 isNatIList IL,
active take(s M, cons(N, IL)) -> mark uTake2(and(isNat M, and(isNat N, isNatIList IL)), M, N, IL),
active uTake1 X -> uTake1 active X,
active uTake1 tt() -> mark nil(),
active uTake2(X1, X2, X3, X4) -> uTake2(active X1, X2, X3, X4),
active uTake2(tt(), M, N, IL) -> mark cons(N, take(M, IL)),
active uLength(X1, X2) -> uLength(active X1, X2),
active uLength(tt(), L) -> mark s length L,
and(X1, mark X2) -> mark and(X1, X2),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatList ok X -> ok isNatList X,
isNatIList ok X -> ok isNatIList X,
isNat ok X -> ok isNat 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,
cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
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),
uTake1 mark X -> mark uTake1 X,
uTake1 ok X -> ok uTake1 X,
uTake2(mark X1, X2, X3, X4) -> mark uTake2(X1, X2, X3, X4),
uTake2(ok X1, ok X2, ok X3, ok X4) -> ok uTake2(X1, X2, X3, X4),
uLength(mark X1, X2) -> mark uLength(X1, X2),
uLength(ok X1, ok X2) -> ok uLength(X1, X2),
proper and(X1, X2) -> and(proper X1, proper X2),
proper tt() -> ok tt(),
proper isNatList X -> isNatList proper X,
proper isNatIList X -> isNatIList proper X,
proper isNat X -> isNat proper X,
proper 0() -> ok 0(),
proper s X -> s proper X,
proper length X -> length proper X,
proper zeros() -> ok zeros(),
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper nil() -> ok nil(),
proper take(X1, X2) -> take(proper X1, proper X2),
proper uTake1 X -> uTake1 proper X,
proper uTake2(X1, X2, X3, X4) -> uTake2(proper X1, proper X2, proper X3, proper X4),
proper uLength(X1, X2) -> uLength(proper X1, proper X2),
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (1):
Strict:
{isNat# ok X -> isNat# X}
Weak:
{ active and(X1, X2) -> and(X1, active X2),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), T) -> mark T,
active isNatList cons(N, L) -> mark and(isNat N, isNatList L),
active isNatList nil() -> mark tt(),
active isNatList take(N, IL) -> mark and(isNat N, isNatIList IL),
active isNatIList IL -> mark isNatList IL,
active isNatIList zeros() -> mark tt(),
active isNatIList cons(N, IL) -> mark and(isNat N, isNatIList IL),
active isNat 0() -> mark tt(),
active isNat s N -> mark isNat N,
active isNat length L -> mark isNatList L,
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark uLength(and(isNat N, isNatList L), L),
active zeros() -> mark cons(0(), zeros()),
active cons(X1, X2) -> cons(active X1, X2),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark uTake1 isNatIList IL,
active take(s M, cons(N, IL)) -> mark uTake2(and(isNat M, and(isNat N, isNatIList IL)), M, N, IL),
active uTake1 X -> uTake1 active X,
active uTake1 tt() -> mark nil(),
active uTake2(X1, X2, X3, X4) -> uTake2(active X1, X2, X3, X4),
active uTake2(tt(), M, N, IL) -> mark cons(N, take(M, IL)),
active uLength(X1, X2) -> uLength(active X1, X2),
active uLength(tt(), L) -> mark s length L,
and(X1, mark X2) -> mark and(X1, X2),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatList ok X -> ok isNatList X,
isNatIList ok X -> ok isNatIList X,
isNat ok X -> ok isNat 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,
cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
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),
uTake1 mark X -> mark uTake1 X,
uTake1 ok X -> ok uTake1 X,
uTake2(mark X1, X2, X3, X4) -> mark uTake2(X1, X2, X3, X4),
uTake2(ok X1, ok X2, ok X3, ok X4) -> ok uTake2(X1, X2, X3, X4),
uLength(mark X1, X2) -> mark uLength(X1, X2),
uLength(ok X1, ok X2) -> ok uLength(X1, X2),
proper and(X1, X2) -> and(proper X1, proper X2),
proper tt() -> ok tt(),
proper isNatList X -> isNatList proper X,
proper isNatIList X -> isNatIList proper X,
proper isNat X -> isNat proper X,
proper 0() -> ok 0(),
proper s X -> s proper X,
proper length X -> length proper X,
proper zeros() -> ok zeros(),
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper nil() -> ok nil(),
proper take(X1, X2) -> take(proper X1, proper X2),
proper uTake1 X -> uTake1 proper X,
proper uTake2(X1, X2, X3, X4) -> uTake2(proper X1, proper X2, proper X3, proper X4),
proper uLength(X1, X2) -> uLength(proper X1, proper X2),
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (2):
Strict:
{ uTake2#(mark X1, X2, X3, X4) -> uTake2#(X1, X2, X3, X4),
uTake2#(ok X1, ok X2, ok X3, ok X4) -> uTake2#(X1, X2, X3, X4)}
Weak:
{ active and(X1, X2) -> and(X1, active X2),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), T) -> mark T,
active isNatList cons(N, L) -> mark and(isNat N, isNatList L),
active isNatList nil() -> mark tt(),
active isNatList take(N, IL) -> mark and(isNat N, isNatIList IL),
active isNatIList IL -> mark isNatList IL,
active isNatIList zeros() -> mark tt(),
active isNatIList cons(N, IL) -> mark and(isNat N, isNatIList IL),
active isNat 0() -> mark tt(),
active isNat s N -> mark isNat N,
active isNat length L -> mark isNatList L,
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark uLength(and(isNat N, isNatList L), L),
active zeros() -> mark cons(0(), zeros()),
active cons(X1, X2) -> cons(active X1, X2),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark uTake1 isNatIList IL,
active take(s M, cons(N, IL)) -> mark uTake2(and(isNat M, and(isNat N, isNatIList IL)), M, N, IL),
active uTake1 X -> uTake1 active X,
active uTake1 tt() -> mark nil(),
active uTake2(X1, X2, X3, X4) -> uTake2(active X1, X2, X3, X4),
active uTake2(tt(), M, N, IL) -> mark cons(N, take(M, IL)),
active uLength(X1, X2) -> uLength(active X1, X2),
active uLength(tt(), L) -> mark s length L,
and(X1, mark X2) -> mark and(X1, X2),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatList ok X -> ok isNatList X,
isNatIList ok X -> ok isNatIList X,
isNat ok X -> ok isNat 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,
cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
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),
uTake1 mark X -> mark uTake1 X,
uTake1 ok X -> ok uTake1 X,
uTake2(mark X1, X2, X3, X4) -> mark uTake2(X1, X2, X3, X4),
uTake2(ok X1, ok X2, ok X3, ok X4) -> ok uTake2(X1, X2, X3, X4),
uLength(mark X1, X2) -> mark uLength(X1, X2),
uLength(ok X1, ok X2) -> ok uLength(X1, X2),
proper and(X1, X2) -> and(proper X1, proper X2),
proper tt() -> ok tt(),
proper isNatList X -> isNatList proper X,
proper isNatIList X -> isNatIList proper X,
proper isNat X -> isNat proper X,
proper 0() -> ok 0(),
proper s X -> s proper X,
proper length X -> length proper X,
proper zeros() -> ok zeros(),
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper nil() -> ok nil(),
proper take(X1, X2) -> take(proper X1, proper X2),
proper uTake1 X -> uTake1 proper X,
proper uTake2(X1, X2, X3, X4) -> uTake2(proper X1, proper X2, proper X3, proper X4),
proper uLength(X1, X2) -> uLength(proper X1, proper X2),
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (2):
Strict:
{ uLength#(mark X1, X2) -> uLength#(X1, X2),
uLength#(ok X1, ok X2) -> uLength#(X1, X2)}
Weak:
{ active and(X1, X2) -> and(X1, active X2),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), T) -> mark T,
active isNatList cons(N, L) -> mark and(isNat N, isNatList L),
active isNatList nil() -> mark tt(),
active isNatList take(N, IL) -> mark and(isNat N, isNatIList IL),
active isNatIList IL -> mark isNatList IL,
active isNatIList zeros() -> mark tt(),
active isNatIList cons(N, IL) -> mark and(isNat N, isNatIList IL),
active isNat 0() -> mark tt(),
active isNat s N -> mark isNat N,
active isNat length L -> mark isNatList L,
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark uLength(and(isNat N, isNatList L), L),
active zeros() -> mark cons(0(), zeros()),
active cons(X1, X2) -> cons(active X1, X2),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark uTake1 isNatIList IL,
active take(s M, cons(N, IL)) -> mark uTake2(and(isNat M, and(isNat N, isNatIList IL)), M, N, IL),
active uTake1 X -> uTake1 active X,
active uTake1 tt() -> mark nil(),
active uTake2(X1, X2, X3, X4) -> uTake2(active X1, X2, X3, X4),
active uTake2(tt(), M, N, IL) -> mark cons(N, take(M, IL)),
active uLength(X1, X2) -> uLength(active X1, X2),
active uLength(tt(), L) -> mark s length L,
and(X1, mark X2) -> mark and(X1, X2),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatList ok X -> ok isNatList X,
isNatIList ok X -> ok isNatIList X,
isNat ok X -> ok isNat 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,
cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
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),
uTake1 mark X -> mark uTake1 X,
uTake1 ok X -> ok uTake1 X,
uTake2(mark X1, X2, X3, X4) -> mark uTake2(X1, X2, X3, X4),
uTake2(ok X1, ok X2, ok X3, ok X4) -> ok uTake2(X1, X2, X3, X4),
uLength(mark X1, X2) -> mark uLength(X1, X2),
uLength(ok X1, ok X2) -> ok uLength(X1, X2),
proper and(X1, X2) -> and(proper X1, proper X2),
proper tt() -> ok tt(),
proper isNatList X -> isNatList proper X,
proper isNatIList X -> isNatIList proper X,
proper isNat X -> isNat proper X,
proper 0() -> ok 0(),
proper s X -> s proper X,
proper length X -> length proper X,
proper zeros() -> ok zeros(),
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper nil() -> ok nil(),
proper take(X1, X2) -> take(proper X1, proper X2),
proper uTake1 X -> uTake1 proper X,
proper uTake2(X1, X2, X3, X4) -> uTake2(proper X1, proper X2, proper X3, proper X4),
proper uLength(X1, X2) -> uLength(proper X1, proper X2),
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:
{ active and(X1, X2) -> and(X1, active X2),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), T) -> mark T,
active isNatList cons(N, L) -> mark and(isNat N, isNatList L),
active isNatList nil() -> mark tt(),
active isNatList take(N, IL) -> mark and(isNat N, isNatIList IL),
active isNatIList IL -> mark isNatList IL,
active isNatIList zeros() -> mark tt(),
active isNatIList cons(N, IL) -> mark and(isNat N, isNatIList IL),
active isNat 0() -> mark tt(),
active isNat s N -> mark isNat N,
active isNat length L -> mark isNatList L,
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark uLength(and(isNat N, isNatList L), L),
active zeros() -> mark cons(0(), zeros()),
active cons(X1, X2) -> cons(active X1, X2),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark uTake1 isNatIList IL,
active take(s M, cons(N, IL)) -> mark uTake2(and(isNat M, and(isNat N, isNatIList IL)), M, N, IL),
active uTake1 X -> uTake1 active X,
active uTake1 tt() -> mark nil(),
active uTake2(X1, X2, X3, X4) -> uTake2(active X1, X2, X3, X4),
active uTake2(tt(), M, N, IL) -> mark cons(N, take(M, IL)),
active uLength(X1, X2) -> uLength(active X1, X2),
active uLength(tt(), L) -> mark s length L,
and(X1, mark X2) -> mark and(X1, X2),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatList ok X -> ok isNatList X,
isNatIList ok X -> ok isNatIList X,
isNat ok X -> ok isNat 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,
cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
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),
uTake1 mark X -> mark uTake1 X,
uTake1 ok X -> ok uTake1 X,
uTake2(mark X1, X2, X3, X4) -> mark uTake2(X1, X2, X3, X4),
uTake2(ok X1, ok X2, ok X3, ok X4) -> ok uTake2(X1, X2, X3, X4),
uLength(mark X1, X2) -> mark uLength(X1, X2),
uLength(ok X1, ok X2) -> ok uLength(X1, X2),
proper and(X1, X2) -> and(proper X1, proper X2),
proper tt() -> ok tt(),
proper isNatList X -> isNatList proper X,
proper isNatIList X -> isNatIList proper X,
proper isNat X -> isNat proper X,
proper 0() -> ok 0(),
proper s X -> s proper X,
proper length X -> length proper X,
proper zeros() -> ok zeros(),
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper nil() -> ok nil(),
proper take(X1, X2) -> take(proper X1, proper X2),
proper uTake1 X -> uTake1 proper X,
proper uTake2(X1, X2, X3, X4) -> uTake2(proper X1, proper X2, proper X3, proper X4),
proper uLength(X1, X2) -> uLength(proper X1, proper X2),
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:
{ active and(X1, X2) -> and(X1, active X2),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), T) -> mark T,
active isNatList cons(N, L) -> mark and(isNat N, isNatList L),
active isNatList nil() -> mark tt(),
active isNatList take(N, IL) -> mark and(isNat N, isNatIList IL),
active isNatIList IL -> mark isNatList IL,
active isNatIList zeros() -> mark tt(),
active isNatIList cons(N, IL) -> mark and(isNat N, isNatIList IL),
active isNat 0() -> mark tt(),
active isNat s N -> mark isNat N,
active isNat length L -> mark isNatList L,
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark uLength(and(isNat N, isNatList L), L),
active zeros() -> mark cons(0(), zeros()),
active cons(X1, X2) -> cons(active X1, X2),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark uTake1 isNatIList IL,
active take(s M, cons(N, IL)) -> mark uTake2(and(isNat M, and(isNat N, isNatIList IL)), M, N, IL),
active uTake1 X -> uTake1 active X,
active uTake1 tt() -> mark nil(),
active uTake2(X1, X2, X3, X4) -> uTake2(active X1, X2, X3, X4),
active uTake2(tt(), M, N, IL) -> mark cons(N, take(M, IL)),
active uLength(X1, X2) -> uLength(active X1, X2),
active uLength(tt(), L) -> mark s length L,
and(X1, mark X2) -> mark and(X1, X2),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatList ok X -> ok isNatList X,
isNatIList ok X -> ok isNatIList X,
isNat ok X -> ok isNat 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,
cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
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),
uTake1 mark X -> mark uTake1 X,
uTake1 ok X -> ok uTake1 X,
uTake2(mark X1, X2, X3, X4) -> mark uTake2(X1, X2, X3, X4),
uTake2(ok X1, ok X2, ok X3, ok X4) -> ok uTake2(X1, X2, X3, X4),
uLength(mark X1, X2) -> mark uLength(X1, X2),
uLength(ok X1, ok X2) -> ok uLength(X1, X2),
proper and(X1, X2) -> and(proper X1, proper X2),
proper tt() -> ok tt(),
proper isNatList X -> isNatList proper X,
proper isNatIList X -> isNatIList proper X,
proper isNat X -> isNat proper X,
proper 0() -> ok 0(),
proper s X -> s proper X,
proper length X -> length proper X,
proper zeros() -> ok zeros(),
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper nil() -> ok nil(),
proper take(X1, X2) -> take(proper X1, proper X2),
proper uTake1 X -> uTake1 proper X,
proper uTake2(X1, X2, X3, X4) -> uTake2(proper X1, proper X2, proper X3, proper X4),
proper uLength(X1, X2) -> uLength(proper X1, proper X2),
top mark X -> top proper X,
top ok X -> top active X}
Open
SCC (3):
Strict:
{ and#(X1, mark X2) -> and#(X1, X2),
and#(mark X1, X2) -> and#(X1, X2),
and#(ok X1, ok X2) -> and#(X1, X2)}
Weak:
{ active and(X1, X2) -> and(X1, active X2),
active and(X1, X2) -> and(active X1, X2),
active and(tt(), T) -> mark T,
active isNatList cons(N, L) -> mark and(isNat N, isNatList L),
active isNatList nil() -> mark tt(),
active isNatList take(N, IL) -> mark and(isNat N, isNatIList IL),
active isNatIList IL -> mark isNatList IL,
active isNatIList zeros() -> mark tt(),
active isNatIList cons(N, IL) -> mark and(isNat N, isNatIList IL),
active isNat 0() -> mark tt(),
active isNat s N -> mark isNat N,
active isNat length L -> mark isNatList L,
active s X -> s active X,
active length X -> length active X,
active length cons(N, L) -> mark uLength(and(isNat N, isNatList L), L),
active zeros() -> mark cons(0(), zeros()),
active cons(X1, X2) -> cons(active X1, X2),
active take(X1, X2) -> take(X1, active X2),
active take(X1, X2) -> take(active X1, X2),
active take(0(), IL) -> mark uTake1 isNatIList IL,
active take(s M, cons(N, IL)) -> mark uTake2(and(isNat M, and(isNat N, isNatIList IL)), M, N, IL),
active uTake1 X -> uTake1 active X,
active uTake1 tt() -> mark nil(),
active uTake2(X1, X2, X3, X4) -> uTake2(active X1, X2, X3, X4),
active uTake2(tt(), M, N, IL) -> mark cons(N, take(M, IL)),
active uLength(X1, X2) -> uLength(active X1, X2),
active uLength(tt(), L) -> mark s length L,
and(X1, mark X2) -> mark and(X1, X2),
and(mark X1, X2) -> mark and(X1, X2),
and(ok X1, ok X2) -> ok and(X1, X2),
isNatList ok X -> ok isNatList X,
isNatIList ok X -> ok isNatIList X,
isNat ok X -> ok isNat 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,
cons(mark X1, X2) -> mark cons(X1, X2),
cons(ok X1, ok X2) -> ok cons(X1, X2),
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),
uTake1 mark X -> mark uTake1 X,
uTake1 ok X -> ok uTake1 X,
uTake2(mark X1, X2, X3, X4) -> mark uTake2(X1, X2, X3, X4),
uTake2(ok X1, ok X2, ok X3, ok X4) -> ok uTake2(X1, X2, X3, X4),
uLength(mark X1, X2) -> mark uLength(X1, X2),
uLength(ok X1, ok X2) -> ok uLength(X1, X2),
proper and(X1, X2) -> and(proper X1, proper X2),
proper tt() -> ok tt(),
proper isNatList X -> isNatList proper X,
proper isNatIList X -> isNatIList proper X,
proper isNat X -> isNat proper X,
proper 0() -> ok 0(),
proper s X -> s proper X,
proper length X -> length proper X,
proper zeros() -> ok zeros(),
proper cons(X1, X2) -> cons(proper X1, proper X2),
proper nil() -> ok nil(),
proper take(X1, X2) -> take(proper X1, proper X2),
proper uTake1 X -> uTake1 proper X,
proper uTake2(X1, X2, X3, X4) -> uTake2(proper X1, proper X2, proper X3, proper X4),
proper uLength(X1, X2) -> uLength(proper X1, proper X2),
top mark X -> top proper X,
top ok X -> top active X}
Open