MAYBE Time: 0.444482 TRS: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U11(and(isNatList L, isNat N), L), active length nil() -> mark 0(), active U11(X1, X2) -> U11(active X1, X2), active U11(tt(), L) -> mark s length L, active U21 X -> U21 active X, active U21 tt() -> mark nil(), active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(0(), IL) -> mark U21 isNatIList IL, active take(s M, cons(N, IL)) -> mark U31(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N), active U31(X1, X2, X3, X4) -> U31(active X1, X2, X3, X4), active U31(tt(), IL, M, N) -> mark cons(N, take(M, IL)), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active isNat 0() -> mark tt(), active isNat s V1 -> mark isNat V1, active isNat length V1 -> mark isNatList V1, active isNatList cons(V1, V2) -> mark and(isNat V1, isNatList V2), active isNatList nil() -> mark tt(), active isNatList take(V1, V2) -> mark and(isNat V1, isNatIList V2), active isNatIList V -> mark isNatList V, active isNatIList cons(V1, V2) -> mark and(isNat V1, isNatIList V2), active isNatIList zeros() -> mark tt(), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, U11(mark X1, X2) -> mark U11(X1, X2), U11(ok X1, ok X2) -> ok U11(X1, X2), U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(X1, X2), U31(mark X1, X2, X3, X4) -> mark U31(X1, X2, X3, X4), U31(ok X1, ok X2, ok X3, ok X4) -> ok U31(X1, X2, X3, X4), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), isNat ok X -> ok isNat X, isNatList ok X -> ok isNatList X, isNatIList ok X -> ok isNatIList X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper s X -> s proper X, proper length X -> length proper X, proper U11(X1, X2) -> U11(proper X1, proper X2), proper tt() -> ok tt(), proper nil() -> ok nil(), proper U21 X -> U21 proper X, proper take(X1, X2) -> take(proper X1, proper X2), proper U31(X1, X2, X3, X4) -> U31(proper X1, proper X2, proper X3, proper X4), proper and(X1, X2) -> and(proper X1, proper X2), proper isNat X -> isNat proper X, proper isNatList X -> isNatList proper X, proper isNatIList X -> isNatIList proper X, top mark X -> top proper X, top ok X -> top active X} DP: DP: { cons#(mark X1, X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2), active# cons(X1, X2) -> cons#(active X1, X2), active# cons(X1, X2) -> active# X1, active# zeros() -> cons#(0(), zeros()), active# 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) -> U11#(and(isNatList L, isNat N), L), active# length cons(N, L) -> and#(isNatList L, isNat N), active# length cons(N, L) -> isNat# N, active# length cons(N, L) -> isNatList# L, active# U11(X1, X2) -> active# X1, active# U11(X1, X2) -> U11#(active X1, X2), active# U11(tt(), L) -> s# length L, active# U11(tt(), L) -> length# L, active# U21 X -> active# X, active# U21 X -> U21# active X, active# take(X1, X2) -> active# X1, active# take(X1, X2) -> active# X2, active# take(X1, X2) -> take#(X1, active X2), active# take(X1, X2) -> take#(active X1, X2), active# take(0(), IL) -> U21# isNatIList IL, active# take(0(), IL) -> isNatIList# IL, active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N), active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N), active# take(s M, cons(N, IL)) -> and#(isNatIList IL, and(isNat M, isNat N)), active# take(s M, cons(N, IL)) -> isNat# N, active# take(s M, cons(N, IL)) -> isNat# M, active# take(s M, cons(N, IL)) -> isNatIList# IL, active# U31(X1, X2, X3, X4) -> active# X1, active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4), active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL)), active# U31(tt(), IL, M, N) -> take#(M, IL), active# and(X1, X2) -> active# X1, active# and(X1, X2) -> and#(active X1, X2), active# isNat s V1 -> isNat# V1, active# isNat length V1 -> isNatList# V1, active# isNatList cons(V1, V2) -> and#(isNat V1, isNatList V2), active# isNatList cons(V1, V2) -> isNat# V1, active# isNatList cons(V1, V2) -> isNatList# V2, active# isNatList take(V1, V2) -> and#(isNat V1, isNatIList V2), active# isNatList take(V1, V2) -> isNat# V1, active# isNatList take(V1, V2) -> isNatIList# V2, active# isNatIList V -> isNatList# V, active# isNatIList cons(V1, V2) -> and#(isNat V1, isNatIList V2), active# isNatIList cons(V1, V2) -> isNat# V1, active# isNatIList cons(V1, V2) -> isNatIList# V2, s# mark X -> s# X, s# ok X -> s# X, length# mark X -> length# X, length# ok X -> length# X, U11#(mark X1, X2) -> U11#(X1, X2), U11#(ok X1, ok X2) -> U11#(X1, X2), U21# mark X -> U21# X, U21# ok X -> U21# X, take#(X1, mark X2) -> take#(X1, X2), take#(mark X1, X2) -> take#(X1, X2), take#(ok X1, ok X2) -> take#(X1, X2), U31#(mark X1, X2, X3, X4) -> U31#(X1, X2, X3, X4), U31#(ok X1, ok X2, ok X3, ok X4) -> U31#(X1, X2, X3, X4), and#(mark X1, X2) -> and#(X1, X2), and#(ok X1, ok X2) -> and#(X1, X2), isNat# ok X -> isNat# X, isNatList# ok X -> isNatList# X, isNatIList# ok X -> isNatIList# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2), proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# s X -> s# proper X, proper# s X -> proper# X, proper# length X -> length# proper X, proper# length X -> proper# X, proper# U11(X1, X2) -> U11#(proper X1, proper X2), proper# U11(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X2, proper# U21 X -> U21# proper X, proper# U21 X -> proper# X, proper# take(X1, X2) -> take#(proper X1, proper X2), proper# take(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4), proper# U31(X1, X2, X3, X4) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X3, proper# U31(X1, X2, X3, X4) -> proper# X4, proper# and(X1, X2) -> and#(proper X1, proper X2), proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2, proper# isNat X -> isNat# proper X, proper# isNat X -> proper# X, proper# isNatList X -> isNatList# proper X, proper# isNatList X -> proper# X, proper# isNatIList X -> isNatIList# proper X, proper# isNatIList X -> proper# X, top# mark X -> proper# X, top# mark X -> top# proper X, top# ok X -> active# X, top# ok X -> top# active X} TRS: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U11(and(isNatList L, isNat N), L), active length nil() -> mark 0(), active U11(X1, X2) -> U11(active X1, X2), active U11(tt(), L) -> mark s length L, active U21 X -> U21 active X, active U21 tt() -> mark nil(), active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(0(), IL) -> mark U21 isNatIList IL, active take(s M, cons(N, IL)) -> mark U31(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N), active U31(X1, X2, X3, X4) -> U31(active X1, X2, X3, X4), active U31(tt(), IL, M, N) -> mark cons(N, take(M, IL)), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active isNat 0() -> mark tt(), active isNat s V1 -> mark isNat V1, active isNat length V1 -> mark isNatList V1, active isNatList cons(V1, V2) -> mark and(isNat V1, isNatList V2), active isNatList nil() -> mark tt(), active isNatList take(V1, V2) -> mark and(isNat V1, isNatIList V2), active isNatIList V -> mark isNatList V, active isNatIList cons(V1, V2) -> mark and(isNat V1, isNatIList V2), active isNatIList zeros() -> mark tt(), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, U11(mark X1, X2) -> mark U11(X1, X2), U11(ok X1, ok X2) -> ok U11(X1, X2), U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(X1, X2), U31(mark X1, X2, X3, X4) -> mark U31(X1, X2, X3, X4), U31(ok X1, ok X2, ok X3, ok X4) -> ok U31(X1, X2, X3, X4), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), isNat ok X -> ok isNat X, isNatList ok X -> ok isNatList X, isNatIList ok X -> ok isNatIList X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper s X -> s proper X, proper length X -> length proper X, proper U11(X1, X2) -> U11(proper X1, proper X2), proper tt() -> ok tt(), proper nil() -> ok nil(), proper U21 X -> U21 proper X, proper take(X1, X2) -> take(proper X1, proper X2), proper U31(X1, X2, X3, X4) -> U31(proper X1, proper X2, proper X3, proper X4), proper and(X1, X2) -> and(proper X1, proper X2), proper isNat X -> isNat proper X, proper isNatList X -> isNatList proper X, proper isNatIList X -> isNatIList proper X, top mark X -> top proper X, top ok X -> top active X} UR: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U11(and(isNatList L, isNat N), L), active length nil() -> mark 0(), active U11(X1, X2) -> U11(active X1, X2), active U11(tt(), L) -> mark s length L, active U21 X -> U21 active X, active U21 tt() -> mark nil(), active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(0(), IL) -> mark U21 isNatIList IL, active take(s M, cons(N, IL)) -> mark U31(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N), active U31(X1, X2, X3, X4) -> U31(active X1, X2, X3, X4), active U31(tt(), IL, M, N) -> mark cons(N, take(M, IL)), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active isNat 0() -> mark tt(), active isNat s V1 -> mark isNat V1, active isNat length V1 -> mark isNatList V1, active isNatList cons(V1, V2) -> mark and(isNat V1, isNatList V2), active isNatList nil() -> mark tt(), active isNatList take(V1, V2) -> mark and(isNat V1, isNatIList V2), active isNatIList V -> mark isNatList V, active isNatIList cons(V1, V2) -> mark and(isNat V1, isNatIList V2), active isNatIList zeros() -> mark tt(), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, U11(mark X1, X2) -> mark U11(X1, X2), U11(ok X1, ok X2) -> ok U11(X1, X2), U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(X1, X2), U31(mark X1, X2, X3, X4) -> mark U31(X1, X2, X3, X4), U31(ok X1, ok X2, ok X3, ok X4) -> ok U31(X1, X2, X3, X4), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), isNat ok X -> ok isNat X, isNatList ok X -> ok isNatList X, isNatIList ok X -> ok isNatIList X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper s X -> s proper X, proper length X -> length proper X, proper U11(X1, X2) -> U11(proper X1, proper X2), proper tt() -> ok tt(), proper nil() -> ok nil(), proper U21 X -> U21 proper X, proper take(X1, X2) -> take(proper X1, proper X2), proper U31(X1, X2, X3, X4) -> U31(proper X1, proper X2, proper X3, proper X4), proper and(X1, X2) -> and(proper X1, proper X2), proper isNat X -> isNat proper X, proper isNatList X -> isNatList proper X, proper isNatIList X -> isNatIList proper X, a(x, y) -> x, a(x, y) -> y} EDG: { (active# take(s M, cons(N, IL)) -> isNat# N, isNat# ok X -> isNat# X) (proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4), U31#(ok X1, ok X2, ok X3, ok X4) -> U31#(X1, X2, X3, X4)) (proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4), U31#(mark X1, X2, X3, X4) -> U31#(X1, X2, X3, X4)) (active# s X -> s# active X, s# ok X -> s# X) (active# s X -> s# active X, s# mark X -> s# X) (active# U21 X -> U21# active X, U21# ok X -> U21# X) (active# U21 X -> U21# active X, U21# mark X -> U21# X) (proper# length X -> length# proper X, length# ok X -> length# X) (proper# length X -> length# proper X, length# mark X -> length# X) (proper# isNat X -> isNat# proper X, isNat# ok X -> isNat# X) (proper# isNatIList X -> isNatIList# proper X, isNatIList# ok X -> isNatIList# 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# U11(tt(), L) -> s# length L, s# ok X -> s# X) (active# U11(tt(), L) -> s# length L, s# mark X -> s# X) (active# U11(tt(), L) -> length# L, length# ok X -> length# X) (active# U11(tt(), L) -> length# L, length# mark X -> length# X) (active# isNat length V1 -> isNatList# V1, isNatList# ok X -> isNatList# X) (active# isNatList take(V1, V2) -> isNat# V1, isNat# ok X -> isNat# X) (active# U31(tt(), IL, M, N) -> take#(M, IL), take#(ok X1, ok X2) -> take#(X1, X2)) (active# U31(tt(), IL, M, N) -> take#(M, IL), take#(mark X1, X2) -> take#(X1, X2)) (active# U31(tt(), IL, M, N) -> take#(M, IL), take#(X1, mark X2) -> take#(X1, X2)) (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# take(X1, X2) -> take#(active X1, X2), take#(ok X1, ok X2) -> take#(X1, X2)) (active# take(X1, X2) -> take#(active X1, X2), take#(mark X1, X2) -> take#(X1, X2)) (active# take(X1, X2) -> take#(active X1, X2), take#(X1, mark X2) -> take#(X1, X2)) (active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4), U31#(ok X1, ok X2, ok X3, ok X4) -> U31#(X1, X2, X3, X4)) (active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4), U31#(mark X1, X2, X3, X4) -> U31#(X1, X2, X3, X4)) (U31#(ok X1, ok X2, ok X3, ok X4) -> U31#(X1, X2, X3, X4), U31#(ok X1, ok X2, ok X3, ok X4) -> U31#(X1, X2, X3, X4)) (U31#(ok X1, ok X2, ok X3, ok X4) -> U31#(X1, X2, X3, X4), U31#(mark X1, X2, X3, X4) -> U31#(X1, X2, X3, X4)) (cons#(ok X1, ok X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)) (cons#(ok X1, ok X2) -> cons#(X1, X2), cons#(mark X1, X2) -> cons#(X1, X2)) (U11#(ok X1, ok X2) -> U11#(X1, X2), U11#(ok X1, ok X2) -> U11#(X1, X2)) (U11#(ok X1, ok X2) -> U11#(X1, X2), U11#(mark X1, X2) -> U11#(X1, X2)) (take#(mark X1, X2) -> take#(X1, X2), take#(ok X1, ok X2) -> take#(X1, X2)) (take#(mark X1, X2) -> take#(X1, X2), take#(mark X1, X2) -> take#(X1, X2)) (take#(mark X1, X2) -> take#(X1, X2), take#(X1, mark X2) -> take#(X1, X2)) (and#(mark X1, X2) -> and#(X1, X2), and#(ok X1, ok X2) -> and#(X1, X2)) (and#(mark X1, X2) -> and#(X1, X2), and#(mark X1, X2) -> and#(X1, X2)) (active# s X -> active# X, active# isNatIList cons(V1, V2) -> isNatIList# V2) (active# s X -> active# X, active# isNatIList cons(V1, V2) -> isNat# V1) (active# s X -> active# X, active# isNatIList cons(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# s X -> active# X, active# isNatIList V -> isNatList# V) (active# s X -> active# X, active# isNatList take(V1, V2) -> isNatIList# V2) (active# s X -> active# X, active# isNatList take(V1, V2) -> isNat# V1) (active# s X -> active# X, active# isNatList take(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# s X -> active# X, active# isNatList cons(V1, V2) -> isNatList# V2) (active# s X -> active# X, active# isNatList cons(V1, V2) -> isNat# V1) (active# s X -> active# X, active# isNatList cons(V1, V2) -> and#(isNat V1, isNatList V2)) (active# s X -> active# X, active# isNat length V1 -> isNatList# V1) (active# s X -> active# X, active# isNat s V1 -> isNat# V1) (active# s X -> active# X, active# and(X1, X2) -> and#(active X1, X2)) (active# s X -> active# X, active# and(X1, X2) -> active# X1) (active# s X -> active# X, active# U31(tt(), IL, M, N) -> take#(M, IL)) (active# s X -> active# X, active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL))) (active# s X -> active# X, active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4)) (active# s X -> active# X, active# U31(X1, X2, X3, X4) -> active# X1) (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# M) (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)) -> and#(isNatIList IL, and(isNat M, isNat N))) (active# s X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N)) (active# s X -> active# X, active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N)) (active# s X -> active# X, active# take(0(), IL) -> isNatIList# IL) (active# s X -> active# X, active# take(0(), IL) -> U21# isNatIList IL) (active# s X -> active# X, active# take(X1, X2) -> take#(active X1, X2)) (active# s X -> active# X, active# take(X1, X2) -> take#(X1, active X2)) (active# s X -> active# X, active# take(X1, X2) -> active# X2) (active# s X -> active# X, active# take(X1, X2) -> active# X1) (active# s X -> active# X, active# U21 X -> U21# active X) (active# s X -> active# X, active# U21 X -> active# X) (active# s X -> active# X, active# U11(tt(), L) -> length# L) (active# s X -> active# X, active# U11(tt(), L) -> s# length L) (active# s X -> active# X, active# U11(X1, X2) -> U11#(active X1, X2)) (active# s X -> active# X, active# U11(X1, X2) -> active# X1) (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) -> and#(isNatList L, isNat N)) (active# s X -> active# X, active# length cons(N, L) -> U11#(and(isNatList L, isNat N), L)) (active# s X -> active# X, active# length X -> length# active X) (active# s X -> active# X, active# length X -> active# X) (active# s X -> active# X, active# s X -> s# active X) (active# s X -> active# X, active# s X -> active# X) (active# s X -> active# X, active# zeros() -> cons#(0(), zeros())) (active# s X -> active# X, active# cons(X1, X2) -> active# X1) (active# s X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (active# U21 X -> active# X, active# isNatIList cons(V1, V2) -> isNatIList# V2) (active# U21 X -> active# X, active# isNatIList cons(V1, V2) -> isNat# V1) (active# U21 X -> active# X, active# isNatIList cons(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# U21 X -> active# X, active# isNatIList V -> isNatList# V) (active# U21 X -> active# X, active# isNatList take(V1, V2) -> isNatIList# V2) (active# U21 X -> active# X, active# isNatList take(V1, V2) -> isNat# V1) (active# U21 X -> active# X, active# isNatList take(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# U21 X -> active# X, active# isNatList cons(V1, V2) -> isNatList# V2) (active# U21 X -> active# X, active# isNatList cons(V1, V2) -> isNat# V1) (active# U21 X -> active# X, active# isNatList cons(V1, V2) -> and#(isNat V1, isNatList V2)) (active# U21 X -> active# X, active# isNat length V1 -> isNatList# V1) (active# U21 X -> active# X, active# isNat s V1 -> isNat# V1) (active# U21 X -> active# X, active# and(X1, X2) -> and#(active X1, X2)) (active# U21 X -> active# X, active# and(X1, X2) -> active# X1) (active# U21 X -> active# X, active# U31(tt(), IL, M, N) -> take#(M, IL)) (active# U21 X -> active# X, active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL))) (active# U21 X -> active# X, active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4)) (active# U21 X -> active# X, active# U31(X1, X2, X3, X4) -> active# X1) (active# U21 X -> active# X, active# take(s M, cons(N, IL)) -> isNatIList# IL) (active# U21 X -> active# X, active# take(s M, cons(N, IL)) -> isNat# M) (active# U21 X -> active# X, active# take(s M, cons(N, IL)) -> isNat# N) (active# U21 X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, and(isNat M, isNat N))) (active# U21 X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N)) (active# U21 X -> active# X, active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N)) (active# U21 X -> active# X, active# take(0(), IL) -> isNatIList# IL) (active# U21 X -> active# X, active# take(0(), IL) -> U21# isNatIList IL) (active# U21 X -> active# X, active# take(X1, X2) -> take#(active X1, X2)) (active# U21 X -> active# X, active# take(X1, X2) -> take#(X1, active X2)) (active# U21 X -> active# X, active# take(X1, X2) -> active# X2) (active# U21 X -> active# X, active# take(X1, X2) -> active# X1) (active# U21 X -> active# X, active# U21 X -> U21# active X) (active# U21 X -> active# X, active# U21 X -> active# X) (active# U21 X -> active# X, active# U11(tt(), L) -> length# L) (active# U21 X -> active# X, active# U11(tt(), L) -> s# length L) (active# U21 X -> active# X, active# U11(X1, X2) -> U11#(active X1, X2)) (active# U21 X -> active# X, active# U11(X1, X2) -> active# X1) (active# U21 X -> active# X, active# length cons(N, L) -> isNatList# L) (active# U21 X -> active# X, active# length cons(N, L) -> isNat# N) (active# U21 X -> active# X, active# length cons(N, L) -> and#(isNatList L, isNat N)) (active# U21 X -> active# X, active# length cons(N, L) -> U11#(and(isNatList L, isNat N), L)) (active# U21 X -> active# X, active# length X -> length# active X) (active# U21 X -> active# X, active# length X -> active# X) (active# U21 X -> active# X, active# s X -> s# active X) (active# U21 X -> active# X, active# s X -> active# X) (active# U21 X -> active# X, active# zeros() -> cons#(0(), zeros())) 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active# isNatList take(V1, V2) -> isNat# V1) (active# take(X1, X2) -> active# X2, active# isNatList take(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# take(X1, X2) -> active# X2, active# isNatList cons(V1, V2) -> isNatList# V2) (active# take(X1, X2) -> active# X2, active# isNatList cons(V1, V2) -> isNat# V1) (active# take(X1, X2) -> active# X2, active# isNatList cons(V1, V2) -> and#(isNat V1, isNatList V2)) (active# take(X1, X2) -> active# X2, active# isNat length V1 -> isNatList# V1) (active# take(X1, X2) -> active# X2, active# isNat s V1 -> isNat# V1) (active# take(X1, X2) -> active# X2, active# and(X1, X2) -> and#(active X1, X2)) (active# take(X1, X2) -> active# X2, active# and(X1, X2) -> active# X1) (active# take(X1, X2) -> active# X2, active# U31(tt(), IL, M, N) -> take#(M, IL)) (active# take(X1, X2) -> active# X2, active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL))) (active# take(X1, X2) -> active# X2, active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4)) (active# take(X1, X2) -> active# X2, active# U31(X1, X2, X3, X4) -> active# X1) (active# take(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> isNatIList# IL) (active# take(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> isNat# M) (active# take(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> isNat# N) (active# take(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, and(isNat M, isNat N))) (active# take(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N)) (active# take(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N)) (active# take(X1, X2) -> active# X2, active# take(0(), IL) -> isNatIList# IL) (active# take(X1, X2) -> active# X2, active# take(0(), IL) -> U21# isNatIList IL) (active# take(X1, X2) -> active# X2, active# take(X1, X2) -> take#(active X1, X2)) (active# take(X1, X2) -> active# X2, active# take(X1, X2) -> take#(X1, active X2)) (active# 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(proper# U31(X1, X2, X3, X4) -> proper# X2, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# U21 X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# U21 X -> U21# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# U11(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# U11(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# length X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# length X -> length# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# s X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# s X -> s# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# cons(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# cons(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N), U31#(ok X1, ok X2, ok X3, ok X4) -> U31#(X1, X2, X3, X4)) (active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N), U31#(mark X1, X2, X3, X4) -> U31#(X1, X2, X3, X4)) (active# take(0(), IL) -> isNatIList# IL, isNatIList# ok X -> isNatIList# X) (active# cons(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNatIList# V2) (active# cons(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNat# V1) (active# cons(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# cons(X1, X2) -> active# X1, active# isNatIList V -> isNatList# V) (active# cons(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> isNatIList# V2) (active# cons(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> isNat# V1) (active# cons(X1, X2) -> active# X1, active# isNatList 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X1, active# take(s M, cons(N, IL)) -> isNatIList# 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)) -> and#(isNatIList IL, and(isNat M, isNat N))) (active# cons(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N)) (active# cons(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N)) (active# cons(X1, X2) -> active# X1, active# take(0(), IL) -> isNatIList# IL) (active# cons(X1, X2) -> active# X1, active# take(0(), IL) -> U21# 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# 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s X -> s# active X) (active# cons(X1, X2) -> active# X1, active# s X -> active# X) (active# cons(X1, X2) -> active# X1, active# zeros() -> cons#(0(), zeros())) (active# cons(X1, X2) -> active# X1, active# cons(X1, X2) -> active# X1) (active# cons(X1, X2) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2)) (active# take(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNatIList# V2) (active# take(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNat# V1) (active# take(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# take(X1, X2) -> active# X1, active# isNatIList V -> isNatList# V) (active# take(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> isNatIList# V2) (active# take(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> isNat# V1) (active# take(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# take(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> isNatList# V2) (active# take(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> isNat# V1) (active# take(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> and#(isNat V1, isNatList V2)) (active# take(X1, X2) -> active# X1, active# isNat length V1 -> isNatList# V1) (active# take(X1, X2) -> active# X1, active# isNat s V1 -> isNat# V1) (active# take(X1, X2) -> active# X1, active# and(X1, X2) -> and#(active X1, X2)) (active# take(X1, X2) -> active# X1, active# and(X1, X2) -> active# X1) (active# take(X1, X2) -> active# X1, active# U31(tt(), IL, M, N) -> take#(M, IL)) (active# take(X1, X2) -> active# X1, active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL))) (active# take(X1, X2) -> active# X1, active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4)) (active# take(X1, X2) -> active# X1, active# U31(X1, X2, X3, X4) -> active# X1) (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# M) (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)) -> and#(isNatIList IL, and(isNat M, isNat N))) (active# take(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N)) (active# take(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N)) (active# take(X1, X2) -> active# X1, active# take(0(), IL) -> isNatIList# IL) (active# take(X1, X2) -> active# X1, active# take(0(), IL) -> U21# isNatIList IL) (active# take(X1, X2) -> active# X1, active# take(X1, X2) -> take#(active X1, 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) -> active# X2) (active# take(X1, X2) -> active# X1, active# take(X1, X2) -> active# X1) (active# take(X1, X2) -> active# X1, active# U21 X -> U21# active X) (active# take(X1, X2) -> active# X1, active# U21 X -> active# X) (active# take(X1, X2) -> active# X1, active# U11(tt(), L) -> length# L) (active# take(X1, X2) -> active# X1, active# U11(tt(), L) -> s# length L) (active# take(X1, X2) -> active# X1, active# U11(X1, X2) -> U11#(active X1, X2)) (active# take(X1, X2) -> active# X1, active# U11(X1, X2) -> active# X1) (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) -> and#(isNatList L, isNat N)) (active# take(X1, X2) -> active# X1, active# length cons(N, L) -> U11#(and(isNatList L, isNat N), L)) (active# take(X1, X2) -> active# X1, active# length X -> length# active X) (active# take(X1, X2) -> active# X1, active# length X -> active# X) (active# take(X1, X2) -> active# X1, active# s X -> s# active X) (active# take(X1, X2) -> active# X1, active# s X -> active# X) (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# and(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNatIList# V2) (active# and(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNat# V1) (active# and(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# and(X1, X2) -> active# X1, active# isNatIList V -> isNatList# V) (active# and(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> isNatIList# V2) (active# and(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> isNat# V1) (active# and(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# and(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> isNatList# V2) (active# and(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> isNat# V1) (active# and(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> and#(isNat V1, isNatList V2)) (active# and(X1, X2) -> active# X1, active# isNat length V1 -> isNatList# V1) (active# and(X1, X2) -> active# X1, active# isNat s V1 -> isNat# V1) (active# and(X1, X2) -> active# X1, active# and(X1, X2) -> and#(active X1, X2)) (active# and(X1, X2) -> active# X1, active# and(X1, X2) -> active# X1) (active# and(X1, X2) -> active# X1, active# U31(tt(), IL, M, N) -> take#(M, IL)) (active# and(X1, X2) -> active# X1, active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL))) (active# and(X1, X2) -> active# X1, active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4)) (active# and(X1, X2) -> active# X1, active# U31(X1, X2, X3, X4) -> active# X1) (active# and(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIList# IL) (active# and(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# M) (active# and(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# N) (active# and(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, and(isNat M, isNat N))) (active# and(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N)) (active# and(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N)) (active# and(X1, X2) -> active# X1, active# take(0(), IL) -> isNatIList# IL) (active# and(X1, X2) -> active# X1, active# take(0(), IL) -> U21# isNatIList IL) (active# and(X1, X2) -> active# X1, active# take(X1, X2) -> take#(active X1, X2)) (active# and(X1, X2) -> active# X1, active# take(X1, X2) -> take#(X1, active X2)) (active# and(X1, X2) -> active# X1, active# take(X1, X2) -> active# X2) (active# and(X1, X2) -> active# X1, active# take(X1, X2) -> active# X1) (active# and(X1, X2) -> active# X1, active# U21 X -> U21# active X) (active# and(X1, X2) -> active# X1, active# U21 X -> active# X) (active# and(X1, X2) -> active# X1, active# U11(tt(), L) -> length# L) (active# and(X1, X2) -> active# X1, active# U11(tt(), L) -> s# length L) (active# and(X1, X2) -> active# X1, active# U11(X1, X2) -> U11#(active X1, X2)) (active# and(X1, X2) -> active# X1, active# U11(X1, X2) -> active# X1) (active# and(X1, X2) -> active# X1, active# 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) -> and#(isNatList L, isNat N)) (active# and(X1, X2) -> active# X1, active# length cons(N, L) -> U11#(and(isNatList L, isNat N), L)) (active# and(X1, X2) -> active# X1, active# length X -> length# active X) (active# and(X1, X2) -> active# X1, active# length X -> active# X) (active# and(X1, X2) -> active# X1, active# s X -> s# active X) (active# and(X1, X2) -> active# X1, active# s X -> active# X) (active# and(X1, X2) -> active# X1, active# zeros() -> cons#(0(), zeros())) (active# and(X1, X2) -> active# X1, active# cons(X1, X2) -> active# X1) (active# and(X1, X2) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2)) (proper# U11(X1, X2) -> proper# X1, proper# isNatIList X -> proper# X) (proper# U11(X1, X2) -> proper# X1, proper# isNatIList X -> isNatIList# proper X) (proper# U11(X1, X2) -> proper# X1, proper# isNatList X -> proper# X) (proper# U11(X1, X2) -> proper# X1, proper# isNatList X -> isNatList# proper X) (proper# U11(X1, X2) -> proper# X1, proper# isNat X -> proper# X) (proper# U11(X1, X2) -> proper# X1, proper# isNat X -> isNat# proper X) (proper# U11(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2) (proper# U11(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X1) (proper# U11(X1, X2) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# U11(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X4) (proper# U11(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# U11(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# U11(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# U11(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# U11(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X2) (proper# U11(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X1) (proper# U11(X1, X2) -> proper# X1, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# U11(X1, X2) -> proper# X1, proper# U21 X -> proper# X) (proper# U11(X1, X2) -> proper# X1, proper# U21 X -> U21# proper X) (proper# U11(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X2) (proper# U11(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X1) (proper# U11(X1, X2) -> proper# X1, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# U11(X1, X2) -> proper# X1, proper# length X -> proper# X) (proper# U11(X1, X2) -> proper# X1, proper# length X -> length# proper X) (proper# U11(X1, X2) -> proper# X1, proper# s X -> proper# X) (proper# U11(X1, X2) -> proper# X1, proper# s X -> s# proper X) (proper# U11(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2) (proper# U11(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1) (proper# U11(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# isNatIList X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# isNatIList X -> isNatIList# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# isNatList X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# isNatList X -> isNatList# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# isNat X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# isNat X -> isNat# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# and(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# and(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X4) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# take(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# take(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# U21 X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# U21 X -> U21# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# U11(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# U11(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# length X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# length X -> length# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# s X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# s X -> s# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# cons(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# cons(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (active# take(s M, cons(N, IL)) -> and#(isNatIList IL, and(isNat M, isNat N)), and#(ok X1, ok X2) -> and#(X1, X2)) (active# take(s M, cons(N, IL)) -> and#(isNatIList IL, and(isNat M, isNat N)), and#(mark X1, X2) -> and#(X1, X2)) (active# take(X1, X2) -> take#(X1, active X2), take#(ok X1, ok X2) -> take#(X1, X2)) (active# take(X1, X2) -> take#(X1, active X2), take#(mark X1, X2) -> take#(X1, X2)) (active# take(X1, X2) -> take#(X1, active X2), take#(X1, mark X2) -> take#(X1, X2)) (active# isNatList cons(V1, V2) -> and#(isNat V1, isNatList V2), and#(ok X1, ok X2) -> and#(X1, X2)) (active# isNatList cons(V1, V2) -> and#(isNat V1, isNatList V2), and#(mark X1, X2) -> and#(X1, X2)) (active# isNatIList cons(V1, V2) -> and#(isNat V1, isNatIList V2), and#(ok X1, ok X2) -> and#(X1, X2)) (active# isNatIList cons(V1, V2) -> and#(isNat V1, isNatIList V2), and#(mark X1, X2) -> and#(X1, X2)) (proper# U11(X1, X2) -> U11#(proper X1, proper X2), U11#(ok X1, ok X2) -> U11#(X1, X2)) (proper# U11(X1, X2) -> U11#(proper X1, proper X2), U11#(mark X1, X2) -> U11#(X1, X2)) (proper# and(X1, X2) -> and#(proper X1, proper X2), and#(ok X1, ok X2) -> and#(X1, X2)) (proper# and(X1, X2) -> and#(proper X1, proper X2), and#(mark X1, X2) -> and#(X1, X2)) (active# take(s M, cons(N, IL)) -> isNat# M, isNat# ok X -> isNat# X) (active# isNatList cons(V1, V2) -> isNatList# V2, isNatList# ok X -> isNatList# X) (active# isNatIList cons(V1, V2) -> isNatIList# V2, isNatIList# ok X -> isNatIList# X) (active# isNatList take(V1, V2) -> isNatIList# V2, isNatIList# ok X -> isNatIList# X) (active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL)), cons#(mark X1, X2) -> cons#(X1, X2)) (active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL)), cons#(ok X1, ok X2) -> cons#(X1, X2)) (active# zeros() -> cons#(0(), zeros()), cons#(mark X1, X2) -> cons#(X1, X2)) (active# zeros() -> cons#(0(), zeros()), cons#(ok X1, ok X2) -> cons#(X1, X2)) (proper# take(X1, X2) -> take#(proper X1, proper X2), take#(X1, mark X2) -> take#(X1, X2)) (proper# take(X1, X2) -> take#(proper X1, proper X2), take#(mark X1, X2) -> take#(X1, X2)) (proper# take(X1, X2) -> take#(proper X1, proper X2), take#(ok X1, ok X2) -> take#(X1, X2)) (proper# 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# isNatList take(V1, V2) -> and#(isNat V1, isNatIList V2), and#(mark X1, X2) -> and#(X1, X2)) (active# isNatList take(V1, V2) -> and#(isNat V1, isNatIList V2), and#(ok X1, ok X2) -> and#(X1, X2)) (active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N), and#(mark X1, X2) -> and#(X1, X2)) (active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N), and#(ok X1, ok X2) -> and#(X1, X2)) (active# length cons(N, L) -> and#(isNatList L, isNat N), and#(mark X1, X2) -> and#(X1, X2)) (active# length cons(N, L) -> and#(isNatList L, isNat N), and#(ok X1, ok X2) -> and#(X1, X2)) (proper# and(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# and(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X1, proper# s X -> s# proper X) (proper# and(X1, X2) -> proper# X1, proper# s X -> proper# X) (proper# and(X1, X2) -> proper# X1, proper# length X -> length# proper X) (proper# and(X1, X2) -> proper# X1, proper# length X -> proper# X) (proper# and(X1, X2) -> proper# X1, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# and(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X1, proper# U21 X -> U21# proper X) (proper# and(X1, X2) -> proper# X1, proper# U21 X -> proper# X) (proper# and(X1, X2) -> proper# X1, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# and(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# and(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# and(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# and(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# and(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X4) (proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X1, proper# isNat X -> isNat# proper X) (proper# and(X1, X2) -> proper# X1, proper# isNat X -> proper# X) (proper# and(X1, X2) -> proper# X1, proper# isNatList X -> isNatList# proper X) (proper# and(X1, X2) -> proper# X1, proper# isNatList X -> proper# X) (proper# and(X1, X2) -> proper# X1, proper# isNatIList X -> isNatIList# proper X) (proper# and(X1, X2) -> proper# X1, proper# isNatIList X -> proper# X) (proper# take(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# take(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1) (proper# take(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2) (proper# take(X1, X2) -> proper# X1, proper# s X -> s# proper X) (proper# take(X1, X2) -> proper# X1, proper# s X -> proper# X) (proper# take(X1, X2) -> proper# X1, proper# length X -> length# proper X) (proper# take(X1, X2) -> proper# X1, proper# length X -> proper# X) (proper# take(X1, X2) -> proper# X1, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# take(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X1) (proper# take(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X2) (proper# take(X1, X2) -> proper# X1, proper# U21 X -> U21# proper X) (proper# take(X1, X2) -> proper# X1, proper# U21 X -> proper# X) (proper# take(X1, X2) -> proper# X1, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# take(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X1) (proper# take(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X2) (proper# take(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# take(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# take(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# take(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# take(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X4) (proper# take(X1, X2) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# take(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X1) (proper# take(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2) (proper# take(X1, X2) -> proper# X1, proper# isNat X -> isNat# proper X) (proper# take(X1, X2) -> proper# X1, proper# isNat X -> proper# X) (proper# take(X1, X2) -> proper# X1, proper# isNatList X -> isNatList# proper X) (proper# take(X1, X2) -> proper# X1, proper# isNatList X -> proper# X) (proper# take(X1, X2) -> proper# X1, proper# isNatIList X -> isNatIList# proper X) (proper# take(X1, X2) -> proper# X1, proper# isNatIList 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# 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# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X1, proper# U21 X -> U21# proper X) (proper# cons(X1, X2) -> proper# X1, proper# U21 X -> proper# X) (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# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# cons(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# cons(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# cons(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# cons(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X4) (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# isNat X -> isNat# proper X) (proper# cons(X1, X2) -> proper# X1, proper# isNat X -> proper# X) (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) (active# U31(X1, X2, X3, X4) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2)) (active# U31(X1, X2, X3, X4) -> active# X1, active# cons(X1, X2) -> active# X1) (active# U31(X1, X2, X3, X4) -> active# X1, active# zeros() -> cons#(0(), zeros())) (active# U31(X1, X2, X3, X4) -> active# X1, active# s X -> active# X) (active# U31(X1, X2, X3, X4) -> active# X1, active# s X -> s# active X) (active# U31(X1, X2, X3, X4) -> active# X1, active# length X -> active# X) (active# U31(X1, X2, X3, X4) -> active# X1, active# length X -> length# active X) (active# U31(X1, X2, X3, X4) -> active# X1, active# length cons(N, L) -> U11#(and(isNatList L, isNat N), L)) (active# U31(X1, X2, X3, X4) -> active# X1, active# length cons(N, L) -> and#(isNatList L, isNat N)) (active# U31(X1, X2, X3, X4) -> active# X1, active# length cons(N, L) -> isNat# N) (active# U31(X1, X2, X3, X4) -> active# X1, active# length cons(N, L) -> isNatList# L) (active# U31(X1, X2, X3, X4) -> active# X1, active# U11(X1, X2) -> active# X1) (active# U31(X1, X2, X3, X4) -> active# X1, active# U11(X1, X2) -> U11#(active X1, X2)) (active# U31(X1, X2, X3, X4) -> active# X1, active# U11(tt(), L) -> s# length L) (active# U31(X1, X2, X3, X4) -> active# X1, active# U11(tt(), L) -> length# L) (active# U31(X1, X2, X3, X4) -> active# X1, active# U21 X -> active# X) (active# U31(X1, X2, X3, X4) -> active# X1, active# U21 X -> U21# active X) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(X1, X2) -> active# X1) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(X1, X2) -> active# X2) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(X1, X2) -> take#(X1, active X2)) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(X1, X2) -> take#(active X1, X2)) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(0(), IL) -> U21# isNatIList IL) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(0(), IL) -> isNatIList# IL) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N)) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N)) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, and(isNat M, isNat N))) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# N) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# M) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIList# IL) (active# U31(X1, X2, X3, X4) -> active# X1, active# U31(X1, X2, X3, X4) -> active# X1) (active# U31(X1, X2, X3, X4) -> active# X1, active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4)) (active# U31(X1, X2, X3, X4) -> active# X1, active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL))) (active# U31(X1, X2, X3, X4) -> active# X1, active# U31(tt(), IL, M, N) -> take#(M, IL)) (active# U31(X1, X2, X3, X4) -> active# X1, active# and(X1, X2) -> active# X1) (active# U31(X1, X2, X3, X4) -> active# X1, active# and(X1, X2) -> and#(active X1, X2)) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNat s V1 -> isNat# V1) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNat length V1 -> isNatList# V1) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatList cons(V1, V2) -> and#(isNat V1, isNatList V2)) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatList cons(V1, V2) -> isNat# V1) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatList cons(V1, V2) -> isNatList# V2) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatList take(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatList take(V1, V2) -> isNat# V1) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatList take(V1, V2) -> isNatIList# V2) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatIList V -> isNatList# V) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatIList cons(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatIList cons(V1, V2) -> isNat# V1) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatIList cons(V1, V2) -> isNatIList# V2) (active# U11(X1, X2) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2)) (active# U11(X1, X2) -> active# X1, active# cons(X1, X2) -> active# X1) (active# U11(X1, X2) -> active# X1, active# zeros() -> cons#(0(), zeros())) (active# U11(X1, X2) -> active# X1, active# s X -> active# X) (active# U11(X1, X2) -> active# X1, active# s X -> s# active X) (active# U11(X1, X2) -> active# X1, active# length X -> active# X) (active# U11(X1, X2) -> active# X1, active# length X -> length# active X) (active# U11(X1, X2) -> active# X1, active# length cons(N, L) -> U11#(and(isNatList L, isNat N), L)) (active# U11(X1, X2) -> active# X1, active# length cons(N, L) -> and#(isNatList L, isNat N)) (active# U11(X1, X2) -> active# X1, active# length cons(N, L) -> isNat# N) (active# U11(X1, X2) -> active# X1, active# length cons(N, L) -> isNatList# L) (active# U11(X1, X2) -> active# X1, active# U11(X1, X2) -> active# X1) (active# U11(X1, X2) -> active# X1, active# U11(X1, X2) -> U11#(active X1, X2)) (active# U11(X1, X2) -> active# X1, active# U11(tt(), L) -> s# length L) (active# U11(X1, X2) -> active# X1, active# U11(tt(), L) -> length# L) (active# U11(X1, X2) -> active# X1, active# U21 X -> active# X) (active# U11(X1, X2) -> active# X1, active# U21 X -> U21# active X) (active# U11(X1, X2) -> active# X1, active# take(X1, X2) -> active# X1) (active# U11(X1, X2) -> active# X1, active# take(X1, X2) -> active# X2) (active# U11(X1, X2) -> active# X1, active# take(X1, X2) -> take#(X1, active X2)) (active# U11(X1, X2) -> active# X1, active# take(X1, X2) -> take#(active X1, X2)) (active# U11(X1, X2) -> active# X1, active# take(0(), IL) -> U21# isNatIList IL) (active# U11(X1, X2) -> active# X1, active# take(0(), IL) -> isNatIList# IL) (active# U11(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N)) (active# U11(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N)) (active# U11(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, and(isNat M, isNat N))) (active# U11(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# N) (active# U11(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# M) (active# U11(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIList# IL) (active# U11(X1, X2) -> active# X1, active# U31(X1, X2, X3, X4) -> active# X1) (active# U11(X1, X2) -> active# X1, active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4)) (active# U11(X1, X2) -> active# X1, active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL))) (active# U11(X1, X2) -> active# X1, active# U31(tt(), IL, M, N) -> take#(M, IL)) (active# U11(X1, X2) -> active# X1, active# and(X1, X2) -> active# X1) (active# U11(X1, X2) -> active# X1, active# and(X1, X2) -> and#(active X1, X2)) (active# U11(X1, X2) -> active# X1, active# isNat s V1 -> isNat# V1) (active# U11(X1, X2) -> active# X1, active# isNat length V1 -> isNatList# V1) (active# U11(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> and#(isNat V1, isNatList V2)) (active# U11(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> isNat# V1) (active# U11(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> isNatList# V2) (active# U11(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# U11(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> isNat# V1) (active# U11(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> isNatIList# V2) (active# U11(X1, X2) -> active# X1, active# isNatIList V -> isNatList# V) (active# U11(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# U11(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNat# V1) (active# U11(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNatIList# V2) (active# take(s M, cons(N, IL)) -> isNatIList# IL, isNatIList# ok X -> isNatIList# X) (active# length cons(N, L) -> U11#(and(isNatList L, isNat N), L), U11#(mark X1, X2) -> U11#(X1, X2)) (active# length cons(N, L) -> U11#(and(isNatList L, isNat N), L), U11#(ok X1, ok X2) -> U11#(X1, X2)) (proper# and(X1, X2) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# and(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X2, proper# s X -> s# proper X) (proper# and(X1, X2) -> 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X2, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# and(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# and(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X4) (proper# and(X1, X2) -> proper# X2, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# and(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X2, proper# isNat X -> isNat# proper X) (proper# and(X1, X2) -> proper# X2, proper# isNat X -> proper# X) (proper# and(X1, X2) -> proper# X2, proper# isNatList X -> isNatList# proper X) (proper# and(X1, X2) -> proper# X2, proper# isNatList X -> proper# X) (proper# and(X1, X2) -> proper# X2, proper# isNatIList X -> isNatIList# proper X) (proper# and(X1, X2) -> proper# X2, proper# isNatIList X -> proper# X) (proper# take(X1, X2) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# take(X1, X2) -> proper# 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take(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# take(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# take(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# take(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# take(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X4) (proper# take(X1, X2) -> proper# X2, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# take(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X1) (proper# take(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X2) (proper# take(X1, X2) -> proper# X2, proper# isNat X -> isNat# proper X) (proper# take(X1, X2) -> proper# X2, proper# isNat X -> proper# X) (proper# take(X1, X2) -> proper# X2, proper# isNatList X -> isNatList# proper X) (proper# take(X1, X2) -> proper# X2, proper# isNatList X -> proper# X) (proper# take(X1, X2) -> proper# X2, proper# isNatIList X -> isNatIList# proper X) (proper# take(X1, X2) -> proper# X2, proper# isNatIList 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# 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# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X2, proper# U21 X -> U21# proper X) (proper# cons(X1, X2) -> proper# X2, proper# U21 X -> proper# X) (proper# cons(X1, X2) -> proper# X2, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X2, proper# take(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X2, proper# take(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# cons(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# cons(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# cons(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# cons(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X4) (proper# cons(X1, X2) -> proper# X2, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X2, proper# isNat X -> isNat# proper X) (proper# cons(X1, X2) -> proper# X2, proper# isNat X -> proper# X) (proper# cons(X1, X2) -> proper# X2, proper# isNatList X -> isNatList# proper X) (proper# cons(X1, X2) -> proper# X2, proper# isNatList X -> proper# X) (proper# cons(X1, X2) -> proper# X2, proper# isNatIList X -> isNatIList# proper X) (proper# cons(X1, X2) -> proper# X2, proper# isNatIList X -> proper# X) (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# s X -> active# X) (top# ok X -> active# X, active# s X -> s# active X) (top# ok X -> active# X, active# length X -> active# X) (top# ok X -> active# X, active# length X -> length# active X) (top# ok X -> active# X, active# length cons(N, L) -> U11#(and(isNatList L, isNat N), L)) (top# ok X -> active# X, active# length cons(N, L) -> and#(isNatList L, isNat N)) (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# U11(X1, X2) -> active# X1) (top# ok X -> active# X, active# U11(X1, X2) -> U11#(active X1, X2)) (top# ok X -> active# X, active# U11(tt(), L) -> s# length L) (top# ok X -> active# X, active# U11(tt(), L) -> length# L) (top# ok X -> active# X, active# U21 X -> active# X) (top# ok X -> active# X, active# U21 X -> U21# active X) (top# ok X -> active# X, active# take(X1, X2) -> active# X1) (top# ok X -> active# X, active# take(X1, X2) -> active# X2) (top# ok X -> active# X, active# take(X1, X2) -> take#(X1, active X2)) (top# ok X -> active# X, active# take(X1, X2) -> take#(active X1, X2)) (top# ok X -> active# X, active# take(0(), IL) -> U21# isNatIList IL) (top# ok X -> active# X, active# take(0(), IL) -> isNatIList# IL) (top# ok X -> active# X, active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N)) (top# ok X -> active# X, active# take(s M, cons(N, IL)) -> 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-> active# X, active# length cons(N, L) -> and#(isNatList L, isNat N)) (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# U11(X1, X2) -> active# X1) (active# length X -> active# X, active# U11(X1, X2) -> U11#(active X1, X2)) (active# length X -> active# X, active# U11(tt(), L) -> s# length L) (active# length X -> active# X, active# U11(tt(), L) -> length# L) (active# length X -> active# X, active# U21 X -> active# X) (active# length X -> active# X, active# U21 X -> U21# active X) (active# length X -> active# X, active# take(X1, X2) -> active# X1) (active# length X -> active# X, active# take(X1, X2) -> active# X2) (active# length X -> active# X, active# take(X1, X2) -> take#(X1, active X2)) (active# length X -> active# X, active# take(X1, X2) -> take#(active X1, X2)) (active# length X -> active# X, active# take(0(), IL) -> U21# isNatIList IL) (active# length X -> active# X, active# take(0(), IL) -> isNatIList# IL) (active# length X -> active# X, active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N)) (active# length X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N)) (active# length X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, and(isNat M, isNat N))) (active# length X -> active# X, active# take(s M, cons(N, IL)) -> isNat# N) (active# length X -> active# X, active# take(s M, cons(N, IL)) -> isNat# M) (active# length X -> active# X, active# take(s M, cons(N, IL)) -> isNatIList# IL) (active# length X -> active# X, active# U31(X1, X2, X3, X4) -> active# X1) (active# length X -> active# X, active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4)) (active# length X -> active# X, active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL))) (active# length X -> active# X, active# U31(tt(), IL, M, N) -> take#(M, IL)) (active# length X -> active# X, active# and(X1, 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isNat# X) (active# isNatList cons(V1, V2) -> isNat# V1, isNat# ok X -> isNat# X) (active# isNat s V1 -> isNat# V1, isNat# ok X -> isNat# X) (active# length cons(N, L) -> isNatList# L, isNatList# ok X -> isNatList# X) (active# take(0(), IL) -> U21# isNatIList IL, U21# mark X -> U21# X) (active# take(0(), IL) -> U21# isNatIList IL, U21# ok X -> U21# 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# isNatList X -> isNatList# proper X, isNatList# ok X -> isNatList# X) (proper# U21 X -> U21# proper X, U21# mark X -> U21# X) (proper# U21 X -> U21# proper X, U21# ok X -> U21# X) (proper# s X -> s# proper X, s# mark X -> s# X) (proper# s X -> s# proper X, s# ok X -> s# X) (active# length X -> length# active X, length# mark X -> length# X) (active# length X -> length# active X, length# ok X -> length# X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# cons(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# cons(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# s X -> s# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# s X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# length X -> length# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# length X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U11(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U11(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U21 X -> U21# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U21 X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# take(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# take(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U31(X1, X2, X3, X4) -> proper# X4) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# and(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# and(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# isNat X -> isNat# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# isNat X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# isNatList X -> isNatList# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# isNatList X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# isNatIList X -> isNatIList# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# isNatIList X -> proper# X) (active# isNatIList V -> isNatList# V, isNatList# ok X -> isNatList# X) (active# length cons(N, L) -> isNat# N, isNat# ok X -> isNat# X) } EDG: { (active# take(s M, cons(N, IL)) -> isNat# N, isNat# ok X -> isNat# X) (proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4), U31#(ok X1, ok X2, ok X3, ok X4) -> U31#(X1, X2, X3, X4)) (proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4), U31#(mark X1, X2, X3, X4) -> U31#(X1, X2, X3, X4)) (active# s X -> s# active X, s# ok X -> s# X) (active# s X -> s# active X, s# mark X -> s# X) (active# U21 X -> U21# active X, U21# ok X -> U21# X) (active# U21 X -> U21# active X, U21# mark X -> U21# X) (proper# length X -> length# proper X, length# ok X -> length# X) (proper# length X -> length# proper X, length# mark X -> length# X) (proper# isNat X -> isNat# proper X, isNat# ok X -> isNat# X) (proper# isNatIList X -> isNatIList# proper X, isNatIList# ok X -> isNatIList# 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# U11(tt(), L) -> s# length L, s# ok X -> s# X) (active# U11(tt(), L) -> s# length L, s# mark X -> s# X) (active# U11(tt(), L) -> length# L, length# ok X -> length# X) (active# U11(tt(), L) -> length# L, length# mark X -> length# X) (active# isNat length V1 -> isNatList# V1, isNatList# ok X -> isNatList# X) (active# isNatList take(V1, V2) -> isNat# V1, isNat# ok X -> isNat# X) (active# U31(tt(), IL, M, N) -> take#(M, IL), take#(ok X1, ok X2) -> take#(X1, X2)) (active# U31(tt(), IL, M, N) -> take#(M, IL), take#(mark X1, X2) -> take#(X1, X2)) (active# U31(tt(), IL, M, N) -> take#(M, IL), take#(X1, mark X2) -> take#(X1, X2)) (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# take(X1, X2) -> take#(active X1, X2), take#(ok X1, ok X2) -> take#(X1, X2)) (active# take(X1, X2) -> take#(active X1, X2), take#(mark X1, X2) -> take#(X1, X2)) (active# take(X1, X2) -> take#(active X1, X2), take#(X1, mark X2) -> take#(X1, X2)) (active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4), U31#(ok X1, ok X2, ok X3, ok X4) -> U31#(X1, X2, X3, X4)) (active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4), U31#(mark X1, X2, X3, X4) -> U31#(X1, X2, X3, X4)) (U31#(ok X1, ok X2, ok X3, ok X4) -> U31#(X1, X2, X3, X4), U31#(ok X1, ok X2, ok X3, ok X4) -> U31#(X1, X2, X3, X4)) (U31#(ok X1, ok X2, ok X3, ok X4) -> U31#(X1, X2, X3, X4), U31#(mark X1, X2, X3, X4) -> U31#(X1, X2, X3, X4)) (cons#(ok X1, ok X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)) (cons#(ok X1, ok X2) -> cons#(X1, X2), cons#(mark X1, X2) -> cons#(X1, X2)) (U11#(ok X1, ok X2) -> U11#(X1, X2), U11#(ok X1, ok X2) -> U11#(X1, X2)) (U11#(ok X1, ok X2) -> U11#(X1, X2), U11#(mark X1, X2) -> U11#(X1, X2)) (take#(mark X1, X2) -> take#(X1, X2), take#(ok X1, ok X2) -> take#(X1, X2)) (take#(mark X1, X2) -> take#(X1, X2), take#(mark X1, X2) -> take#(X1, X2)) (take#(mark X1, X2) -> take#(X1, X2), take#(X1, mark X2) -> take#(X1, X2)) (and#(mark X1, X2) -> and#(X1, X2), and#(ok X1, ok X2) -> and#(X1, X2)) (and#(mark X1, X2) -> and#(X1, X2), and#(mark X1, X2) -> and#(X1, X2)) (active# s X -> active# X, active# isNatIList cons(V1, V2) -> isNatIList# V2) (active# s X -> active# X, active# isNatIList cons(V1, V2) -> isNat# V1) (active# s X -> active# X, active# isNatIList cons(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# s X -> active# X, active# isNatIList V -> isNatList# V) (active# s X -> active# X, active# isNatList take(V1, V2) -> isNatIList# V2) (active# s X -> active# X, active# isNatList take(V1, V2) -> isNat# V1) (active# s X -> active# X, active# isNatList take(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# s X -> active# X, active# isNatList cons(V1, V2) -> isNatList# V2) (active# s X -> active# X, active# isNatList cons(V1, V2) -> isNat# V1) (active# s X -> active# X, active# isNatList cons(V1, V2) -> and#(isNat V1, isNatList V2)) (active# s X -> active# X, active# isNat length V1 -> isNatList# V1) (active# s X -> active# X, active# isNat s V1 -> isNat# V1) (active# s X -> active# X, active# and(X1, X2) -> and#(active X1, X2)) (active# s X -> active# X, active# and(X1, X2) -> active# X1) (active# s X -> active# X, active# U31(tt(), IL, M, N) -> take#(M, IL)) (active# s X -> active# X, active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL))) (active# s X -> active# X, active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4)) (active# s X -> active# X, active# U31(X1, X2, X3, X4) -> active# X1) (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# M) (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)) -> and#(isNatIList IL, and(isNat M, isNat N))) (active# s X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N)) (active# s X -> active# X, active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N)) (active# s X -> active# X, active# take(0(), IL) -> isNatIList# IL) (active# s X -> active# X, active# take(0(), IL) -> U21# isNatIList IL) (active# s X -> active# X, active# take(X1, X2) -> take#(active X1, X2)) (active# s X -> active# X, active# take(X1, X2) -> take#(X1, active X2)) (active# s X -> active# X, active# take(X1, X2) -> active# X2) (active# s X -> active# X, active# take(X1, X2) -> active# X1) (active# s X -> active# X, active# U21 X -> U21# active X) (active# s X -> active# X, active# U21 X -> active# X) (active# s X -> active# X, active# U11(tt(), L) -> length# L) (active# s X -> active# X, active# U11(tt(), L) -> s# length L) (active# s X -> active# X, active# U11(X1, X2) -> U11#(active X1, X2)) (active# s X -> active# X, active# U11(X1, X2) -> active# X1) (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) -> and#(isNatList L, isNat N)) (active# s X -> active# X, active# length cons(N, L) -> U11#(and(isNatList L, isNat N), L)) (active# s X -> active# X, active# length X -> length# active X) (active# s X -> active# X, active# length X -> active# X) (active# s X -> active# X, active# s X -> s# active X) (active# s X -> active# X, active# s X -> active# X) (active# s X -> active# X, active# zeros() -> cons#(0(), zeros())) (active# s X -> active# X, active# cons(X1, X2) -> active# X1) (active# s X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (active# U21 X -> active# X, active# isNatIList cons(V1, V2) -> isNatIList# V2) (active# U21 X -> active# X, active# isNatIList cons(V1, V2) -> isNat# V1) (active# U21 X -> active# X, active# isNatIList cons(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# U21 X -> active# X, active# isNatIList V -> isNatList# V) (active# U21 X -> active# X, active# isNatList take(V1, V2) -> isNatIList# V2) (active# U21 X -> active# X, active# isNatList take(V1, V2) -> isNat# V1) (active# U21 X -> active# X, active# isNatList take(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# U21 X -> active# X, active# isNatList cons(V1, V2) -> isNatList# V2) (active# U21 X -> active# X, active# isNatList cons(V1, V2) -> isNat# V1) (active# U21 X -> active# X, active# isNatList cons(V1, V2) -> and#(isNat V1, isNatList V2)) (active# U21 X -> active# X, active# isNat length V1 -> isNatList# V1) (active# U21 X -> active# X, active# isNat s V1 -> isNat# V1) (active# U21 X -> active# X, active# and(X1, X2) -> and#(active X1, X2)) (active# U21 X -> active# X, active# and(X1, X2) -> active# X1) (active# U21 X -> active# X, active# U31(tt(), IL, M, N) -> take#(M, IL)) (active# U21 X -> active# X, active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL))) (active# U21 X -> active# X, active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4)) (active# U21 X -> active# X, active# U31(X1, X2, X3, X4) -> active# X1) (active# U21 X -> active# X, active# take(s M, cons(N, IL)) -> isNatIList# IL) (active# U21 X -> active# X, active# take(s M, cons(N, IL)) -> isNat# M) (active# U21 X -> active# X, active# take(s M, cons(N, IL)) -> isNat# N) (active# U21 X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, and(isNat M, isNat N))) (active# U21 X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N)) (active# U21 X -> active# X, active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N)) (active# U21 X -> active# X, active# take(0(), IL) -> isNatIList# IL) (active# U21 X -> active# X, active# take(0(), IL) -> U21# isNatIList IL) (active# U21 X -> active# X, active# take(X1, X2) -> take#(active X1, X2)) (active# U21 X -> active# X, active# take(X1, X2) -> take#(X1, active X2)) (active# U21 X -> active# X, active# take(X1, X2) -> active# X2) (active# U21 X -> active# X, active# take(X1, X2) -> active# X1) (active# U21 X -> active# X, active# U21 X -> U21# active X) (active# U21 X -> active# X, active# U21 X -> active# X) (active# U21 X -> active# X, active# U11(tt(), L) -> length# L) (active# U21 X -> active# X, active# U11(tt(), L) -> s# length L) (active# U21 X -> active# X, active# U11(X1, X2) -> U11#(active X1, X2)) (active# U21 X -> active# X, active# U11(X1, X2) -> active# X1) (active# U21 X -> active# X, active# length cons(N, L) -> isNatList# L) (active# U21 X -> active# X, active# length cons(N, L) -> isNat# N) (active# U21 X -> active# X, active# length cons(N, L) -> and#(isNatList L, isNat N)) (active# U21 X -> active# X, active# length cons(N, L) -> U11#(and(isNatList L, isNat N), L)) (active# U21 X -> active# X, active# length X -> length# active X) (active# U21 X -> active# X, active# length X -> active# X) (active# U21 X -> active# X, active# s X -> s# active X) (active# U21 X -> active# X, active# s X -> active# X) (active# U21 X -> active# X, active# zeros() -> cons#(0(), zeros())) (active# U21 X -> active# X, active# cons(X1, X2) -> active# X1) (active# U21 X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (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) (U21# ok X -> U21# X, U21# ok X -> U21# X) (U21# ok X -> U21# X, U21# mark X -> U21# X) (isNatList# ok X -> isNatList# X, isNatList# ok X -> isNatList# 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# isNat X -> proper# X) (proper# s X -> proper# X, proper# isNat X -> isNat# proper X) (proper# s X -> proper# X, proper# and(X1, X2) -> proper# X2) (proper# s X -> proper# X, proper# and(X1, X2) -> proper# X1) (proper# s X -> proper# X, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# s X -> proper# X, proper# U31(X1, X2, X3, X4) -> proper# X4) (proper# s X -> proper# X, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# s X -> proper# X, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# s X -> proper# X, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# s X -> proper# X, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# s X -> proper# X, proper# take(X1, X2) -> proper# X2) (proper# s X -> proper# X, proper# take(X1, X2) -> proper# X1) (proper# s X -> proper# X, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# s X -> proper# X, proper# U21 X -> proper# X) (proper# s X -> proper# X, proper# U21 X -> U21# proper X) (proper# s X -> proper# X, proper# U11(X1, X2) -> proper# X2) (proper# s X -> proper# X, proper# U11(X1, X2) -> proper# X1) (proper# s X -> proper# X, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# s X -> proper# X, proper# 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# 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# U21 X -> proper# X, proper# isNatIList X -> proper# X) (proper# U21 X -> proper# X, proper# isNatIList X -> isNatIList# proper X) (proper# U21 X -> proper# X, proper# isNatList X -> proper# X) (proper# U21 X -> proper# X, proper# isNatList X -> isNatList# proper X) (proper# U21 X -> proper# X, proper# isNat X -> proper# X) (proper# U21 X -> proper# X, proper# isNat X -> isNat# proper X) (proper# U21 X -> proper# X, proper# and(X1, X2) -> proper# X2) (proper# U21 X -> proper# X, proper# and(X1, X2) -> proper# X1) (proper# U21 X -> proper# X, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# U21 X -> proper# X, proper# U31(X1, X2, X3, X4) -> proper# X4) (proper# U21 X -> proper# X, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# U21 X -> proper# X, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# U21 X -> proper# X, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# U21 X -> proper# X, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# U21 X -> proper# X, proper# take(X1, X2) -> proper# X2) (proper# U21 X -> proper# X, proper# take(X1, X2) -> proper# X1) (proper# U21 X -> proper# X, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# U21 X -> proper# X, proper# U21 X -> proper# X) (proper# U21 X -> proper# X, proper# U21 X -> U21# proper X) (proper# U21 X -> proper# X, proper# U11(X1, X2) -> proper# X2) (proper# U21 X -> proper# X, proper# U11(X1, X2) -> proper# X1) (proper# U21 X -> proper# X, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# U21 X -> proper# X, proper# length X -> proper# X) (proper# U21 X -> proper# X, proper# length X -> length# proper X) (proper# U21 X -> proper# X, proper# s X -> proper# X) (proper# U21 X -> proper# X, proper# s X -> s# proper X) (proper# U21 X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# U21 X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# U21 X -> proper# X, proper# 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X4) -> proper# X2) (top# mark X -> proper# X, proper# U31(X1, X2, X3, X4) -> proper# X1) (top# mark X -> proper# X, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (top# mark X -> proper# X, proper# take(X1, X2) -> proper# X2) (top# mark X -> proper# X, proper# take(X1, X2) -> proper# X1) (top# mark X -> proper# X, proper# take(X1, X2) -> take#(proper X1, proper X2)) (top# mark X -> proper# X, proper# U21 X -> proper# X) (top# mark X -> proper# X, proper# U21 X -> U21# proper X) (top# mark X -> proper# X, proper# U11(X1, X2) -> proper# X2) (top# mark X -> proper# X, proper# U11(X1, X2) -> proper# X1) (top# mark X -> proper# X, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (top# mark X -> proper# X, proper# length X -> proper# X) (top# mark X -> proper# X, proper# length X -> length# proper X) (top# mark X -> proper# X, proper# s X -> proper# X) (top# mark X -> proper# X, proper# s X -> s# proper X) (top# mark X -> proper# X, proper# cons(X1, X2) -> 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cons(V1, V2) -> and#(isNat V1, isNatList V2)) (active# take(X1, X2) -> active# X2, active# isNat length V1 -> isNatList# V1) (active# take(X1, X2) -> active# X2, active# isNat s V1 -> isNat# V1) (active# take(X1, X2) -> active# X2, active# and(X1, X2) -> and#(active X1, X2)) (active# take(X1, X2) -> active# X2, active# and(X1, X2) -> active# X1) (active# take(X1, X2) -> active# X2, active# U31(tt(), IL, M, N) -> take#(M, IL)) (active# take(X1, X2) -> active# X2, active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL))) (active# take(X1, X2) -> active# X2, active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4)) (active# take(X1, X2) -> active# X2, active# U31(X1, X2, X3, X4) -> active# X1) (active# take(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> isNatIList# IL) (active# take(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> isNat# M) (active# take(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> isNat# N) (active# take(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, and(isNat M, isNat N))) (active# take(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N)) (active# take(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N)) (active# take(X1, X2) -> active# X2, active# take(0(), IL) -> isNatIList# IL) (active# take(X1, X2) -> active# X2, active# take(0(), IL) -> U21# isNatIList IL) (active# take(X1, X2) -> active# X2, active# take(X1, X2) -> take#(active X1, X2)) (active# take(X1, X2) -> active# X2, active# take(X1, X2) -> take#(X1, active X2)) (active# take(X1, X2) -> active# X2, active# take(X1, X2) -> active# X2) (active# take(X1, X2) -> active# X2, active# take(X1, X2) -> active# X1) (active# take(X1, X2) -> active# X2, active# U21 X -> U21# active X) (active# take(X1, X2) -> active# X2, active# U21 X -> active# X) (active# take(X1, X2) -> active# X2, active# U11(tt(), L) -> length# L) (active# take(X1, X2) -> active# X2, active# U11(tt(), L) -> s# length L) (active# take(X1, X2) -> active# X2, active# U11(X1, X2) -> U11#(active X1, X2)) (active# take(X1, X2) -> active# X2, active# U11(X1, X2) -> active# X1) (active# take(X1, X2) -> active# X2, active# 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) -> and#(isNatList L, isNat N)) (active# take(X1, X2) -> active# X2, active# length cons(N, L) -> U11#(and(isNatList L, isNat N), L)) (active# take(X1, X2) -> active# X2, active# length X -> length# active X) (active# take(X1, X2) -> active# X2, active# length X -> active# X) (active# take(X1, X2) -> active# X2, active# s X -> s# active X) (active# take(X1, X2) -> active# X2, active# s X -> active# X) (active# take(X1, X2) -> active# X2, active# zeros() -> cons#(0(), zeros())) (active# take(X1, X2) -> active# X2, active# cons(X1, X2) -> active# X1) (active# take(X1, X2) -> active# X2, active# cons(X1, X2) -> cons#(active X1, X2)) (proper# U11(X1, X2) -> proper# X2, proper# isNatIList X -> proper# X) (proper# U11(X1, X2) -> proper# X2, proper# isNatIList X -> isNatIList# proper X) (proper# U11(X1, X2) -> proper# X2, proper# isNatList X -> proper# X) (proper# U11(X1, X2) -> proper# X2, proper# isNatList X -> isNatList# proper X) (proper# U11(X1, X2) -> proper# X2, proper# isNat X -> proper# X) (proper# U11(X1, X2) -> proper# X2, proper# isNat X -> isNat# proper X) (proper# U11(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X2) (proper# U11(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X1) (proper# U11(X1, X2) -> proper# X2, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# U11(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X4) (proper# U11(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# U11(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# U11(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# U11(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# U11(X1, X2) -> proper# X2, proper# take(X1, X2) -> proper# X2) (proper# U11(X1, X2) -> proper# X2, proper# take(X1, X2) -> proper# X1) (proper# U11(X1, X2) -> proper# X2, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# U11(X1, X2) -> proper# X2, proper# U21 X -> proper# X) (proper# U11(X1, X2) -> proper# X2, proper# U21 X -> U21# proper X) (proper# U11(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X2) (proper# U11(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X1) (proper# U11(X1, X2) -> proper# X2, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# U11(X1, X2) -> proper# X2, proper# length X -> proper# X) (proper# U11(X1, X2) -> proper# X2, proper# length X -> length# proper X) (proper# U11(X1, X2) -> proper# X2, proper# s X -> proper# X) (proper# U11(X1, X2) -> proper# X2, proper# s X -> 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U31(X1, X2, X3, X4) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X4) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# take(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# take(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# U21 X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# U21 X -> U21# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# U11(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# U11(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# length X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# length X -> length# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# s X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# s X -> s# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# cons(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# cons(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N), U31#(ok X1, ok X2, ok X3, ok X4) -> U31#(X1, X2, X3, X4)) (active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N), U31#(mark X1, X2, X3, X4) -> U31#(X1, X2, X3, X4)) (active# take(0(), IL) -> isNatIList# IL, isNatIList# ok X -> isNatIList# X) (active# cons(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNatIList# V2) (active# cons(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNat# V1) (active# cons(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# cons(X1, X2) -> active# X1, active# isNatIList V -> isNatList# V) (active# cons(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> isNatIList# V2) (active# cons(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> isNat# V1) (active# cons(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# cons(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> isNatList# V2) (active# cons(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> isNat# V1) (active# cons(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> and#(isNat V1, isNatList V2)) (active# cons(X1, X2) -> active# X1, active# isNat length V1 -> isNatList# V1) (active# cons(X1, X2) -> active# X1, active# isNat s V1 -> isNat# V1) (active# cons(X1, X2) -> active# X1, active# and(X1, X2) -> and#(active X1, X2)) (active# cons(X1, X2) -> active# X1, active# and(X1, X2) -> active# X1) (active# cons(X1, X2) -> active# X1, active# U31(tt(), IL, M, N) -> take#(M, IL)) (active# cons(X1, X2) -> active# X1, active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL))) (active# cons(X1, X2) -> active# X1, active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4)) (active# cons(X1, X2) -> active# X1, active# U31(X1, X2, X3, X4) -> active# X1) (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)) -> 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)) -> and#(isNatIList IL, and(isNat M, isNat N))) (active# cons(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N)) (active# cons(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N)) (active# cons(X1, X2) -> active# X1, active# take(0(), IL) -> isNatIList# IL) (active# cons(X1, X2) -> active# X1, active# take(0(), IL) -> U21# 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# U21 X -> U21# active X) (active# cons(X1, X2) -> active# X1, active# U21 X -> active# X) (active# cons(X1, X2) -> active# X1, active# U11(tt(), L) -> length# L) (active# cons(X1, X2) -> active# X1, active# U11(tt(), L) -> s# length L) (active# cons(X1, X2) -> active# X1, active# U11(X1, X2) -> 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U31(X1, X2, X3, X4) -> proper# X1, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# take(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# take(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# U21 X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# U21 X -> U21# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# U11(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# U11(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# length X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# length X -> length# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# s X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# s X -> s# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# cons(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# cons(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (active# take(s M, cons(N, IL)) -> and#(isNatIList IL, and(isNat M, isNat N)), and#(ok X1, ok X2) -> and#(X1, X2)) (active# take(s M, cons(N, IL)) -> and#(isNatIList IL, and(isNat M, isNat N)), and#(mark X1, X2) -> and#(X1, X2)) (active# take(X1, X2) -> take#(X1, active X2), take#(ok X1, ok X2) -> take#(X1, X2)) (active# take(X1, X2) -> take#(X1, active X2), take#(mark X1, X2) -> take#(X1, X2)) (active# take(X1, X2) -> take#(X1, active X2), take#(X1, mark X2) -> take#(X1, X2)) (active# isNatList cons(V1, V2) -> and#(isNat V1, isNatList V2), and#(ok X1, ok X2) -> and#(X1, X2)) (active# isNatList cons(V1, V2) -> and#(isNat V1, isNatList V2), and#(mark X1, X2) -> and#(X1, X2)) (active# isNatIList cons(V1, V2) -> and#(isNat V1, isNatIList V2), and#(ok X1, ok X2) -> and#(X1, X2)) (active# isNatIList cons(V1, V2) -> and#(isNat V1, isNatIList V2), and#(mark X1, X2) -> and#(X1, X2)) (proper# U11(X1, X2) -> U11#(proper X1, proper X2), U11#(ok X1, ok X2) -> U11#(X1, X2)) (proper# U11(X1, X2) -> U11#(proper X1, proper X2), U11#(mark X1, X2) -> U11#(X1, X2)) (proper# and(X1, X2) -> and#(proper X1, proper X2), and#(ok X1, ok X2) -> and#(X1, X2)) (proper# and(X1, X2) -> and#(proper X1, proper X2), and#(mark X1, X2) -> and#(X1, X2)) (active# take(s M, cons(N, IL)) -> isNat# M, isNat# ok X -> isNat# X) (active# isNatList cons(V1, V2) -> isNatList# V2, isNatList# ok X -> isNatList# X) (active# isNatIList cons(V1, V2) -> isNatIList# V2, isNatIList# ok X -> isNatIList# X) (active# isNatList take(V1, V2) -> isNatIList# V2, isNatIList# ok X -> isNatIList# X) (active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL)), cons#(mark X1, X2) -> cons#(X1, X2)) (active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL)), cons#(ok X1, ok X2) -> cons#(X1, X2)) (proper# take(X1, X2) -> take#(proper X1, proper X2), take#(X1, mark X2) -> take#(X1, X2)) (proper# take(X1, X2) -> take#(proper X1, proper X2), take#(mark X1, X2) -> take#(X1, X2)) (proper# take(X1, X2) -> take#(proper X1, proper X2), take#(ok X1, ok X2) -> take#(X1, X2)) (proper# 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# isNatList take(V1, V2) -> and#(isNat V1, isNatIList V2), and#(mark X1, X2) -> and#(X1, X2)) (active# isNatList take(V1, V2) -> and#(isNat V1, isNatIList V2), and#(ok X1, ok X2) -> and#(X1, X2)) (active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N), and#(mark X1, X2) -> and#(X1, X2)) (active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N), and#(ok X1, ok X2) -> and#(X1, X2)) (active# length cons(N, L) -> and#(isNatList L, isNat N), and#(mark X1, X2) -> and#(X1, X2)) (active# length cons(N, L) -> and#(isNatList L, isNat N), and#(ok X1, ok X2) -> and#(X1, X2)) (proper# and(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# and(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X1, proper# s X -> s# proper X) (proper# and(X1, X2) -> proper# X1, proper# s X -> proper# X) (proper# and(X1, X2) -> proper# X1, proper# length X -> length# proper X) (proper# and(X1, X2) -> proper# X1, proper# length X -> proper# X) (proper# and(X1, X2) -> proper# X1, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# and(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X1, proper# U21 X -> U21# proper X) (proper# and(X1, X2) -> proper# X1, proper# U21 X -> proper# X) (proper# and(X1, X2) -> proper# X1, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# and(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# and(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# and(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# and(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# and(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X4) (proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X1, proper# isNat X -> isNat# proper X) (proper# and(X1, X2) -> proper# X1, proper# isNat X -> proper# X) (proper# and(X1, X2) -> proper# X1, proper# isNatList X -> isNatList# proper X) (proper# and(X1, X2) -> proper# X1, proper# isNatList X -> proper# X) (proper# and(X1, X2) -> proper# X1, proper# isNatIList X -> isNatIList# proper X) (proper# and(X1, X2) -> proper# X1, proper# isNatIList X -> proper# X) (proper# take(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# take(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1) (proper# take(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2) (proper# take(X1, X2) -> proper# X1, proper# s X -> s# proper X) (proper# take(X1, X2) -> proper# X1, proper# s X -> proper# X) (proper# take(X1, X2) -> proper# X1, proper# length X -> length# proper X) (proper# take(X1, X2) -> proper# X1, proper# length X -> proper# X) (proper# take(X1, X2) -> proper# X1, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# take(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X1) (proper# take(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X2) (proper# take(X1, X2) -> proper# X1, proper# U21 X -> U21# proper X) (proper# take(X1, X2) -> proper# X1, proper# U21 X -> proper# X) (proper# take(X1, X2) -> proper# X1, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# take(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X1) (proper# take(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X2) (proper# take(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# take(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# take(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# take(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# take(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X4) (proper# take(X1, X2) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# take(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X1) (proper# take(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2) (proper# take(X1, X2) -> proper# X1, proper# isNat X -> isNat# proper X) (proper# take(X1, X2) -> proper# X1, proper# isNat X -> proper# X) (proper# take(X1, X2) -> proper# X1, proper# isNatList X -> isNatList# proper X) (proper# take(X1, X2) -> proper# X1, proper# isNatList X -> proper# X) (proper# take(X1, X2) -> proper# X1, proper# isNatIList X -> isNatIList# proper X) (proper# take(X1, X2) -> proper# X1, proper# isNatIList 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# 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# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X1, proper# U21 X -> U21# proper X) (proper# cons(X1, X2) -> proper# X1, proper# U21 X -> proper# X) (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# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# cons(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# cons(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# cons(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# cons(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X4) (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# isNat X -> isNat# proper X) (proper# cons(X1, X2) -> proper# X1, proper# isNat X -> proper# X) (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) (active# U31(X1, X2, X3, X4) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2)) (active# U31(X1, X2, X3, X4) -> active# X1, active# cons(X1, X2) -> active# X1) (active# U31(X1, X2, X3, X4) -> active# X1, active# zeros() -> cons#(0(), zeros())) (active# U31(X1, X2, X3, X4) -> active# X1, active# s X -> active# X) (active# U31(X1, X2, X3, X4) -> active# X1, active# s X -> s# active X) (active# U31(X1, X2, X3, X4) -> active# X1, active# length X -> active# X) (active# U31(X1, X2, X3, X4) -> active# X1, active# length X -> length# active X) (active# U31(X1, X2, X3, X4) -> active# X1, active# length cons(N, L) -> U11#(and(isNatList L, isNat N), L)) (active# U31(X1, X2, X3, X4) -> active# X1, active# length cons(N, L) -> and#(isNatList L, isNat N)) (active# U31(X1, X2, X3, X4) -> active# X1, active# length cons(N, L) -> isNat# N) (active# U31(X1, X2, X3, X4) -> active# X1, active# length cons(N, L) -> isNatList# L) (active# U31(X1, X2, X3, X4) -> active# X1, active# U11(X1, X2) -> active# X1) (active# U31(X1, X2, X3, X4) -> active# X1, active# U11(X1, X2) -> U11#(active X1, X2)) (active# U31(X1, X2, X3, X4) -> active# X1, active# U11(tt(), L) -> s# length L) (active# U31(X1, X2, X3, X4) -> active# X1, active# U11(tt(), L) -> length# L) (active# U31(X1, X2, X3, X4) -> active# X1, active# U21 X -> active# X) (active# U31(X1, X2, X3, X4) -> active# X1, active# U21 X -> U21# active X) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(X1, X2) -> active# X1) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(X1, X2) -> active# X2) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(X1, X2) -> take#(X1, active X2)) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(X1, X2) -> take#(active X1, X2)) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(0(), IL) -> U21# isNatIList IL) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(0(), IL) -> isNatIList# IL) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N)) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N)) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, and(isNat M, isNat N))) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# N) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# M) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIList# IL) (active# U31(X1, X2, X3, X4) -> active# X1, active# U31(X1, X2, X3, X4) -> active# X1) (active# U31(X1, X2, X3, X4) -> active# X1, active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4)) (active# U31(X1, X2, X3, X4) -> active# X1, active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL))) (active# U31(X1, X2, X3, X4) -> active# X1, active# U31(tt(), IL, M, N) -> take#(M, IL)) (active# U31(X1, X2, X3, X4) -> active# X1, active# and(X1, X2) -> active# X1) (active# U31(X1, X2, X3, X4) -> active# X1, active# and(X1, X2) -> and#(active X1, X2)) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNat s V1 -> isNat# V1) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNat length V1 -> isNatList# V1) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatList cons(V1, V2) -> and#(isNat V1, isNatList V2)) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatList cons(V1, V2) -> isNat# V1) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatList cons(V1, V2) -> isNatList# V2) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatList take(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatList take(V1, V2) -> isNat# V1) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatList take(V1, V2) -> isNatIList# V2) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatIList V -> isNatList# V) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatIList cons(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatIList cons(V1, V2) -> isNat# V1) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatIList cons(V1, V2) -> isNatIList# V2) (active# U11(X1, X2) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2)) (active# U11(X1, X2) -> active# X1, active# cons(X1, X2) -> active# X1) (active# U11(X1, X2) -> active# X1, active# zeros() -> cons#(0(), zeros())) (active# U11(X1, X2) -> active# X1, active# s X -> active# X) (active# U11(X1, X2) -> active# X1, active# s X -> s# active X) (active# U11(X1, X2) -> active# X1, active# length X -> active# X) (active# U11(X1, X2) -> active# X1, active# length X -> length# active X) (active# U11(X1, X2) -> active# X1, active# length cons(N, L) -> U11#(and(isNatList L, isNat N), L)) (active# U11(X1, X2) -> active# X1, active# length cons(N, L) -> and#(isNatList L, isNat N)) (active# U11(X1, X2) -> active# X1, active# length cons(N, L) -> isNat# N) (active# U11(X1, X2) -> active# X1, active# length cons(N, L) -> isNatList# L) (active# U11(X1, X2) -> active# X1, active# U11(X1, X2) -> active# X1) (active# U11(X1, X2) -> active# X1, active# U11(X1, X2) -> U11#(active X1, X2)) (active# U11(X1, X2) -> active# X1, active# U11(tt(), L) -> s# length L) (active# U11(X1, X2) -> active# X1, active# U11(tt(), L) -> length# L) (active# U11(X1, X2) -> active# X1, active# U21 X -> active# X) (active# U11(X1, X2) -> active# X1, active# U21 X -> U21# active X) (active# U11(X1, X2) -> active# X1, active# take(X1, X2) -> active# X1) (active# U11(X1, X2) -> active# X1, active# take(X1, X2) -> active# X2) (active# U11(X1, X2) -> active# X1, active# take(X1, X2) -> take#(X1, active X2)) (active# U11(X1, X2) -> active# X1, active# take(X1, X2) -> take#(active X1, X2)) (active# U11(X1, X2) -> active# X1, active# take(0(), IL) -> U21# isNatIList IL) (active# U11(X1, X2) -> active# X1, active# take(0(), IL) -> isNatIList# IL) (active# U11(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N)) (active# U11(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N)) (active# U11(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, and(isNat M, isNat N))) (active# U11(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# N) (active# U11(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# M) (active# U11(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIList# IL) (active# U11(X1, X2) -> active# X1, active# U31(X1, X2, X3, X4) -> active# X1) (active# U11(X1, X2) -> active# X1, active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4)) (active# U11(X1, X2) -> active# X1, active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL))) (active# U11(X1, X2) -> active# X1, active# U31(tt(), IL, M, N) -> take#(M, IL)) (active# U11(X1, X2) -> active# X1, active# and(X1, X2) -> active# X1) (active# U11(X1, X2) -> active# X1, active# and(X1, X2) -> and#(active X1, X2)) (active# U11(X1, X2) -> active# X1, active# isNat s V1 -> isNat# V1) (active# U11(X1, X2) -> active# X1, active# isNat length V1 -> isNatList# V1) (active# U11(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> and#(isNat V1, isNatList V2)) (active# U11(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> isNat# V1) (active# U11(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> isNatList# V2) (active# U11(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# U11(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> isNat# V1) (active# U11(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> isNatIList# V2) (active# U11(X1, X2) -> active# X1, active# isNatIList V -> isNatList# V) (active# U11(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# U11(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNat# V1) (active# U11(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNatIList# V2) (active# take(s M, cons(N, IL)) -> isNatIList# IL, isNatIList# ok X -> isNatIList# X) (active# length cons(N, L) -> U11#(and(isNatList L, isNat N), L), 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proper X) (proper# cons(X1, X2) -> proper# X2, proper# length X -> proper# X) (proper# cons(X1, X2) -> proper# X2, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X2, proper# U21 X -> U21# proper X) (proper# cons(X1, X2) -> proper# X2, proper# U21 X -> proper# X) (proper# cons(X1, X2) -> proper# X2, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X2, proper# take(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X2, proper# take(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# cons(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# cons(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# cons(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# cons(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X4) (proper# cons(X1, X2) -> proper# X2, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X2, proper# isNat X -> isNat# proper X) (proper# cons(X1, X2) -> proper# X2, proper# isNat X -> proper# X) (proper# cons(X1, X2) -> proper# X2, proper# isNatList X -> isNatList# proper X) (proper# cons(X1, X2) -> proper# X2, proper# isNatList X -> proper# X) (proper# cons(X1, X2) -> proper# X2, proper# isNatIList X -> isNatIList# proper X) (proper# cons(X1, X2) -> proper# X2, proper# isNatIList X -> proper# X) (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# s X -> active# X) (top# ok X -> active# X, active# s X -> s# active X) (top# ok X -> active# X, active# length X -> active# X) (top# ok X -> active# X, active# length X -> length# active X) (top# ok X -> active# X, active# length cons(N, L) -> U11#(and(isNatList L, isNat N), L)) (top# ok X -> active# X, active# length cons(N, L) -> and#(isNatList L, isNat N)) (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# U11(X1, X2) -> active# X1) (top# ok X -> active# X, active# U11(X1, X2) -> U11#(active X1, X2)) (top# ok X -> active# X, active# U11(tt(), L) -> s# length L) (top# ok X -> active# X, active# U11(tt(), L) -> length# L) (top# ok X -> active# X, active# U21 X -> active# X) (top# ok X -> active# X, active# U21 X -> U21# active X) (top# ok X -> active# X, active# take(X1, X2) -> active# X1) (top# ok X -> active# X, active# take(X1, X2) -> active# X2) (top# ok X -> active# X, active# take(X1, X2) -> take#(X1, active X2)) (top# ok X -> active# X, active# take(X1, X2) -> take#(active X1, X2)) (top# ok X -> active# X, active# take(0(), IL) -> U21# isNatIList IL) (top# ok X -> active# X, active# take(0(), IL) -> isNatIList# IL) (top# ok X -> active# X, active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N)) (top# ok X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N)) (top# ok X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, and(isNat M, isNat N))) (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)) -> isNat# M) (top# ok X -> active# X, active# take(s M, cons(N, IL)) -> isNatIList# IL) (top# ok X -> active# X, active# U31(X1, X2, X3, X4) -> active# X1) (top# ok X -> active# X, active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4)) (top# ok X -> active# X, active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL))) (top# ok X -> active# X, active# U31(tt(), IL, M, N) -> take#(M, IL)) (top# ok X -> active# X, active# and(X1, X2) -> active# X1) (top# ok X -> active# X, active# and(X1, X2) -> and#(active X1, X2)) (top# ok X -> active# X, active# isNat s V1 -> isNat# V1) (top# ok X -> active# X, active# isNat length V1 -> isNatList# V1) (top# ok X -> active# X, active# isNatList cons(V1, V2) -> and#(isNat V1, isNatList V2)) (top# ok X -> active# X, active# isNatList cons(V1, V2) -> isNat# V1) (top# ok X -> active# X, active# isNatList cons(V1, V2) -> isNatList# V2) (top# ok X -> active# X, active# isNatList take(V1, V2) -> and#(isNat V1, isNatIList V2)) (top# ok X -> active# X, active# isNatList take(V1, V2) -> isNat# V1) (top# ok X -> active# X, active# isNatList take(V1, V2) -> isNatIList# V2) (top# ok X -> active# X, active# isNatIList V -> isNatList# V) (top# ok X -> active# X, active# isNatIList cons(V1, V2) -> and#(isNat V1, isNatIList V2)) (top# ok X -> active# X, active# isNatIList cons(V1, V2) -> isNat# V1) (top# ok X -> active# X, active# isNatIList cons(V1, V2) -> isNatIList# V2) (proper# isNatIList X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# isNatIList X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# isNatIList X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# isNatIList X -> proper# X, proper# s X -> s# proper X) (proper# isNatIList X -> proper# X, proper# s X -> proper# X) (proper# isNatIList X -> proper# X, proper# length X -> length# proper X) (proper# isNatIList X -> proper# X, proper# length X -> proper# X) (proper# isNatIList X -> proper# X, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# isNatIList X -> proper# X, proper# U11(X1, X2) -> proper# X1) (proper# isNatIList X -> proper# X, proper# U11(X1, X2) -> proper# X2) (proper# isNatIList X -> proper# X, proper# U21 X -> U21# proper X) (proper# isNatIList X -> proper# X, proper# U21 X -> proper# X) 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-> proper# X2) (proper# isNat X -> proper# X, proper# U21 X -> U21# proper X) (proper# isNat X -> proper# X, proper# U21 X -> proper# X) (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# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# isNat X -> proper# X, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# isNat X -> proper# X, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# isNat X -> proper# X, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# isNat X -> proper# X, proper# U31(X1, X2, X3, X4) -> proper# X4) (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# isNat X -> isNat# proper X) (proper# isNat X -> proper# X, proper# isNat X -> proper# X) (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# 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# 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# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# length X -> proper# X, proper# U11(X1, X2) -> proper# X1) (proper# length X -> proper# X, proper# U11(X1, X2) -> proper# X2) (proper# length X -> proper# X, proper# U21 X -> U21# proper X) (proper# length X -> proper# X, proper# U21 X -> proper# X) (proper# length X -> proper# X, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# length X -> proper# X, proper# take(X1, X2) -> proper# X1) (proper# length X -> proper# X, proper# take(X1, X2) -> proper# X2) (proper# length X -> proper# X, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# length X -> proper# X, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# length X -> proper# X, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# length X -> proper# X, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# length X -> proper# X, proper# U31(X1, X2, X3, X4) -> proper# X4) (proper# length X -> proper# X, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# length X -> proper# X, proper# and(X1, X2) -> proper# X1) (proper# length X -> proper# X, proper# and(X1, X2) -> proper# X2) (proper# length X -> proper# X, proper# isNat X -> isNat# proper X) (proper# length X -> proper# X, proper# isNat X -> proper# X) (proper# length X -> proper# X, proper# isNatList X -> isNatList# proper X) (proper# length X -> proper# X, proper# isNatList X -> proper# X) (proper# length X -> proper# X, proper# isNatIList X -> isNatIList# proper X) (proper# length X -> proper# X, proper# isNatIList X -> proper# X) (isNatIList# ok X -> isNatIList# X, isNatIList# ok X -> isNatIList# X) (isNat# ok X -> isNat# X, isNat# ok X -> isNat# X) (U21# mark X -> U21# X, U21# mark X -> U21# X) (U21# mark X -> U21# X, U21# ok X -> U21# 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) (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# s X -> active# X) (active# length X -> active# X, active# s X -> s# active X) (active# length X -> active# X, active# length X -> active# X) (active# length X -> active# X, active# length X -> length# active X) (active# length X -> active# X, active# length cons(N, L) -> U11#(and(isNatList L, isNat N), L)) (active# length X -> active# X, active# length cons(N, L) -> and#(isNatList L, isNat N)) (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# U11(X1, X2) -> active# X1) (active# length X -> active# X, active# U11(X1, X2) -> U11#(active X1, X2)) (active# length X -> active# X, active# U11(tt(), L) -> s# length L) (active# length X -> active# X, active# U11(tt(), L) -> length# L) (active# length X -> active# X, active# U21 X -> active# X) (active# length X -> active# X, active# U21 X -> U21# active X) (active# length X -> active# X, active# take(X1, X2) -> active# X1) (active# length X -> active# X, active# take(X1, X2) -> active# X2) (active# length X -> active# X, active# take(X1, X2) -> take#(X1, active X2)) (active# length X -> active# X, active# take(X1, X2) -> take#(active X1, X2)) (active# length X -> active# X, active# take(0(), IL) -> U21# isNatIList IL) (active# length X -> active# X, active# take(0(), IL) -> isNatIList# IL) (active# length X -> active# X, active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N)) (active# length X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N)) (active# length X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, and(isNat M, isNat N))) (active# length X -> active# X, active# take(s M, cons(N, IL)) -> isNat# N) (active# length X -> active# X, active# take(s M, cons(N, IL)) -> isNat# M) (active# length X -> active# X, active# take(s M, cons(N, IL)) -> isNatIList# IL) (active# length X -> active# X, active# U31(X1, X2, X3, X4) -> active# X1) (active# length X -> active# X, active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4)) (active# length X -> active# X, active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL))) (active# length X -> active# X, active# U31(tt(), IL, M, N) -> take#(M, IL)) (active# length X -> active# X, active# and(X1, X2) -> active# X1) (active# length X -> active# X, active# and(X1, X2) -> and#(active X1, X2)) (active# length X -> active# X, active# isNat s V1 -> isNat# V1) (active# length X -> active# X, active# isNat length V1 -> isNatList# V1) (active# length X -> active# X, active# isNatList cons(V1, V2) -> and#(isNat V1, isNatList V2)) (active# length X -> active# X, active# isNatList cons(V1, V2) -> isNat# V1) (active# length X -> active# X, active# isNatList cons(V1, V2) -> isNatList# V2) (active# length X -> active# X, active# isNatList take(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# length X -> active# X, active# isNatList take(V1, V2) -> isNat# V1) (active# length X -> active# X, active# isNatList take(V1, V2) -> isNatIList# V2) (active# length X -> active# X, active# isNatIList V -> isNatList# V) (active# length X -> active# X, active# isNatIList cons(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# length X -> active# X, active# isNatIList cons(V1, V2) -> isNat# V1) (active# length X -> active# X, active# isNatIList cons(V1, V2) -> isNatIList# V2) (and#(ok X1, ok X2) -> and#(X1, X2), and#(mark X1, X2) -> and#(X1, X2)) (and#(ok X1, ok X2) -> and#(X1, X2), and#(ok X1, ok X2) -> and#(X1, X2)) (take#(ok X1, ok X2) -> take#(X1, X2), take#(X1, mark X2) -> take#(X1, X2)) (take#(ok X1, ok X2) -> take#(X1, X2), take#(mark X1, X2) -> take#(X1, X2)) (take#(ok X1, ok X2) -> take#(X1, X2), take#(ok X1, ok X2) -> take#(X1, X2)) (take#(X1, mark X2) -> take#(X1, X2), take#(X1, mark X2) -> take#(X1, X2)) (take#(X1, mark X2) -> take#(X1, X2), take#(mark X1, X2) -> take#(X1, X2)) (take#(X1, mark X2) -> take#(X1, X2), take#(ok X1, ok X2) -> take#(X1, X2)) (U11#(mark X1, X2) -> U11#(X1, X2), U11#(mark X1, X2) -> U11#(X1, X2)) (U11#(mark X1, X2) -> U11#(X1, X2), U11#(ok X1, ok X2) -> U11#(X1, X2)) (cons#(mark X1, X2) -> cons#(X1, X2), cons#(mark X1, X2) -> cons#(X1, X2)) (cons#(mark X1, X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)) (U31#(mark X1, X2, X3, X4) -> U31#(X1, X2, X3, X4), U31#(mark X1, X2, X3, X4) -> U31#(X1, X2, X3, X4)) (U31#(mark X1, X2, X3, X4) -> U31#(X1, X2, X3, X4), U31#(ok X1, ok X2, ok X3, ok X4) -> U31#(X1, X2, X3, X4)) (active# and(X1, X2) -> and#(active X1, X2), and#(mark X1, X2) -> and#(X1, X2)) (active# and(X1, X2) -> and#(active X1, X2), and#(ok X1, ok X2) -> and#(X1, X2)) (active# U11(X1, X2) -> U11#(active X1, X2), U11#(mark X1, X2) -> U11#(X1, X2)) (active# U11(X1, X2) -> U11#(active X1, X2), U11#(ok X1, ok X2) -> U11#(X1, X2)) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# cons(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# cons(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# s X -> s# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# s X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# length X -> length# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# length X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# U11(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# U11(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# U21 X -> U21# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# U21 X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# take(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# take(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# U31(X1, X2, X3, X4) -> proper# X4) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# and(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# and(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# isNat X -> isNat# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# isNat X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# isNatList X -> isNatList# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# isNatList X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# isNatIList X -> isNatIList# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# isNatIList X -> proper# X) (active# isNatIList cons(V1, V2) -> isNat# V1, isNat# ok X -> isNat# X) (active# isNatList cons(V1, V2) -> isNat# V1, isNat# ok X -> isNat# X) (active# isNat s V1 -> isNat# V1, isNat# ok X -> isNat# X) (active# length cons(N, L) -> isNatList# L, isNatList# ok X -> isNatList# X) (active# take(0(), IL) -> U21# isNatIList IL, U21# mark X -> U21# X) (active# take(0(), IL) -> U21# isNatIList IL, U21# ok X -> U21# 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# isNatList X -> isNatList# proper X, isNatList# ok X -> isNatList# X) (proper# U21 X -> U21# proper X, U21# mark X -> U21# X) (proper# U21 X -> U21# proper X, U21# ok X -> U21# X) (proper# s X -> s# proper X, s# mark X -> s# X) (proper# s X -> s# proper X, s# ok X -> s# X) (active# length X -> length# active X, length# mark X -> length# X) (active# length X -> length# active X, length# ok X -> length# X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# cons(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# cons(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# s X -> s# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# s X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# length X -> length# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# length X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U11(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U11(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U21 X -> U21# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U21 X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# take(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# take(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U31(X1, X2, X3, X4) -> proper# X4) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# and(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# and(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# isNat X -> isNat# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# isNat X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# isNatList X -> isNatList# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# isNatList X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# isNatIList X -> isNatIList# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# isNatIList X -> proper# X) (active# isNatIList V -> isNatList# V, isNatList# ok X -> isNatList# X) (active# length cons(N, L) -> isNat# N, isNat# ok X -> isNat# X) } EDG: { (active# take(s M, cons(N, IL)) -> isNat# N, isNat# ok X -> isNat# X) (proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4), U31#(ok X1, ok X2, ok X3, ok X4) -> U31#(X1, X2, X3, X4)) (proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4), U31#(mark X1, X2, X3, X4) -> U31#(X1, X2, X3, X4)) (active# s X -> s# active X, s# ok X -> s# X) (active# s X -> s# active X, s# mark X -> s# X) (active# U21 X -> U21# active X, U21# ok X -> U21# X) (active# U21 X -> U21# active X, U21# mark X -> U21# X) (proper# length X -> length# proper X, length# ok X -> length# X) (proper# length X -> length# proper X, length# mark X -> length# X) (proper# isNat X -> isNat# proper X, isNat# ok X -> isNat# X) (proper# isNatIList X -> isNatIList# proper X, isNatIList# ok X -> isNatIList# 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# U11(tt(), L) -> s# length L, s# ok X -> s# X) (active# U11(tt(), L) -> s# length L, s# mark X -> s# X) (active# U11(tt(), L) -> length# L, length# ok X -> length# X) (active# U11(tt(), L) -> length# L, length# mark X -> length# X) (active# isNat length V1 -> isNatList# V1, isNatList# ok X -> isNatList# X) (active# isNatList take(V1, V2) -> isNat# V1, isNat# ok X -> isNat# X) (active# U31(tt(), IL, M, N) -> take#(M, IL), take#(ok X1, ok X2) -> take#(X1, X2)) (active# U31(tt(), IL, M, N) -> take#(M, IL), take#(mark X1, X2) -> take#(X1, X2)) (active# U31(tt(), IL, M, N) -> take#(M, IL), take#(X1, mark X2) -> take#(X1, X2)) (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# take(X1, X2) -> take#(active X1, X2), take#(ok X1, ok X2) -> take#(X1, X2)) (active# take(X1, X2) -> take#(active X1, X2), take#(mark X1, X2) -> take#(X1, X2)) (active# take(X1, X2) -> take#(active X1, X2), take#(X1, mark X2) -> take#(X1, X2)) (active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4), U31#(ok X1, ok X2, ok X3, ok X4) -> U31#(X1, X2, X3, X4)) (active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4), U31#(mark X1, X2, X3, X4) -> U31#(X1, X2, X3, X4)) (U31#(ok X1, ok X2, ok X3, ok X4) -> U31#(X1, X2, X3, X4), U31#(ok X1, ok X2, ok X3, ok X4) -> U31#(X1, X2, X3, X4)) (U31#(ok X1, ok X2, ok X3, ok X4) -> U31#(X1, X2, X3, X4), U31#(mark X1, X2, X3, X4) -> U31#(X1, X2, X3, X4)) (cons#(ok X1, ok X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)) (cons#(ok X1, ok X2) -> cons#(X1, X2), cons#(mark X1, X2) -> cons#(X1, X2)) (U11#(ok X1, ok X2) -> U11#(X1, X2), U11#(ok X1, ok X2) -> U11#(X1, X2)) (U11#(ok X1, ok X2) -> U11#(X1, X2), U11#(mark X1, X2) -> U11#(X1, X2)) (take#(mark X1, X2) -> take#(X1, X2), take#(ok X1, ok X2) -> take#(X1, X2)) (take#(mark X1, X2) -> take#(X1, X2), take#(mark X1, X2) -> take#(X1, X2)) (take#(mark X1, X2) -> take#(X1, X2), take#(X1, mark X2) -> take#(X1, X2)) (and#(mark X1, X2) -> and#(X1, X2), and#(ok X1, ok X2) -> and#(X1, X2)) (and#(mark X1, X2) -> and#(X1, X2), and#(mark X1, X2) -> and#(X1, X2)) (active# s X -> active# X, active# isNatIList cons(V1, V2) -> isNatIList# V2) (active# s X -> active# X, active# isNatIList cons(V1, V2) -> isNat# V1) (active# s X -> active# X, active# isNatIList cons(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# s X -> active# X, active# isNatIList V -> isNatList# V) (active# s X -> active# X, active# isNatList take(V1, V2) -> isNatIList# V2) (active# s X -> active# X, active# isNatList take(V1, V2) -> isNat# V1) (active# s X -> active# X, active# isNatList take(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# s X -> active# X, active# isNatList cons(V1, V2) -> isNatList# V2) (active# s X -> active# X, active# isNatList cons(V1, V2) -> isNat# V1) (active# 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and(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> and#(isNat V1, isNatList V2)) (active# and(X1, X2) -> active# X1, active# isNat length V1 -> isNatList# V1) (active# and(X1, X2) -> active# X1, active# isNat s V1 -> isNat# V1) (active# and(X1, X2) -> active# X1, active# and(X1, X2) -> and#(active X1, X2)) (active# and(X1, X2) -> active# X1, active# and(X1, X2) -> active# X1) (active# and(X1, X2) -> active# X1, active# U31(tt(), IL, M, N) -> take#(M, IL)) (active# and(X1, X2) -> active# X1, active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL))) (active# and(X1, X2) -> active# X1, active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4)) (active# and(X1, X2) -> active# X1, active# U31(X1, X2, X3, X4) -> active# X1) (active# and(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIList# IL) (active# and(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# M) (active# and(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# N) (active# and(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, and(isNat M, isNat N))) (active# and(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N)) (active# and(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N)) (active# and(X1, X2) -> active# X1, active# take(0(), IL) -> isNatIList# IL) (active# and(X1, X2) -> active# X1, active# take(0(), IL) -> U21# isNatIList IL) (active# and(X1, X2) -> active# X1, active# take(X1, X2) -> take#(active X1, X2)) (active# and(X1, X2) -> active# X1, active# take(X1, X2) -> take#(X1, active X2)) (active# and(X1, X2) -> active# X1, active# take(X1, X2) -> active# X2) (active# and(X1, X2) -> active# X1, active# take(X1, X2) -> active# X1) (active# and(X1, X2) -> active# X1, active# U21 X -> U21# active X) (active# and(X1, X2) -> active# X1, active# U21 X -> active# X) (active# and(X1, X2) -> active# X1, active# U11(tt(), L) -> length# L) (active# and(X1, X2) -> active# X1, active# U11(tt(), L) -> s# length L) (active# and(X1, X2) -> active# X1, active# U11(X1, X2) -> U11#(active X1, X2)) (active# and(X1, X2) -> active# X1, active# U11(X1, X2) -> active# X1) (active# and(X1, X2) -> active# X1, active# 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) -> and#(isNatList L, isNat N)) (active# and(X1, X2) -> active# X1, active# length cons(N, L) -> U11#(and(isNatList L, isNat N), L)) (active# and(X1, X2) -> active# X1, active# length X -> length# active X) (active# and(X1, X2) -> active# X1, active# length X -> active# X) (active# and(X1, X2) -> active# X1, active# s X -> s# active X) (active# and(X1, X2) -> active# X1, active# s X -> active# X) (active# and(X1, X2) -> active# X1, active# zeros() -> cons#(0(), zeros())) (active# and(X1, X2) -> active# X1, active# cons(X1, X2) -> active# X1) (active# and(X1, X2) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2)) (proper# U11(X1, X2) -> proper# X1, proper# isNatIList X -> proper# X) (proper# U11(X1, X2) -> proper# X1, proper# isNatIList X -> isNatIList# proper X) (proper# U11(X1, X2) -> proper# X1, proper# isNatList X -> proper# X) (proper# U11(X1, X2) -> proper# X1, proper# isNatList X -> isNatList# proper X) (proper# U11(X1, X2) -> proper# X1, proper# isNat X -> proper# X) (proper# U11(X1, X2) -> proper# X1, proper# isNat X -> isNat# proper X) (proper# U11(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2) (proper# U11(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X1) (proper# U11(X1, X2) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# U11(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X4) (proper# U11(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# U11(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# U11(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# U11(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# U11(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X2) (proper# U11(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X1) (proper# U11(X1, X2) -> proper# X1, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# U11(X1, X2) -> proper# X1, proper# U21 X -> proper# X) (proper# U11(X1, X2) -> proper# X1, proper# U21 X -> U21# proper X) (proper# U11(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X2) (proper# U11(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X1) (proper# U11(X1, X2) -> proper# X1, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# U11(X1, X2) -> proper# X1, proper# length X -> proper# X) (proper# U11(X1, X2) -> proper# X1, proper# length X -> length# proper X) (proper# U11(X1, X2) -> proper# X1, proper# s X -> proper# X) (proper# U11(X1, X2) -> proper# X1, proper# s X -> s# proper X) (proper# U11(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2) (proper# U11(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1) (proper# U11(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# isNatIList X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# isNatIList X -> isNatIList# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# isNatList X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# isNatList X -> isNatList# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# isNat X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# isNat X -> isNat# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# and(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# and(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X4) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# take(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# take(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# U21 X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# U21 X -> U21# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# U11(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# U11(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# length X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# length X -> length# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# s X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# s X -> s# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# cons(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# cons(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (active# take(s M, cons(N, IL)) -> and#(isNatIList IL, and(isNat M, isNat N)), 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)) (active# isNatList cons(V1, V2) -> and#(isNat V1, isNatList V2), and#(ok X1, ok X2) -> and#(X1, X2)) (active# isNatIList cons(V1, V2) -> and#(isNat V1, isNatIList V2), and#(ok X1, ok X2) -> and#(X1, X2)) (proper# U11(X1, X2) -> U11#(proper X1, proper X2), U11#(ok X1, ok X2) -> U11#(X1, X2)) (proper# U11(X1, X2) -> U11#(proper X1, proper X2), U11#(mark X1, X2) -> U11#(X1, X2)) (proper# and(X1, X2) -> and#(proper X1, proper X2), and#(ok X1, ok X2) -> and#(X1, X2)) (proper# and(X1, X2) -> and#(proper X1, proper X2), and#(mark X1, X2) -> and#(X1, X2)) (active# take(s M, cons(N, IL)) -> isNat# M, isNat# ok X -> isNat# X) (active# isNatList cons(V1, V2) -> isNatList# V2, isNatList# ok X -> isNatList# X) (active# isNatIList cons(V1, V2) -> isNatIList# V2, isNatIList# ok X -> isNatIList# X) (active# isNatList take(V1, V2) -> isNatIList# V2, isNatIList# ok X -> isNatIList# X) (active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL)), cons#(mark X1, X2) -> cons#(X1, X2)) (active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL)), cons#(ok X1, ok X2) -> cons#(X1, X2)) (proper# take(X1, X2) -> take#(proper X1, proper X2), take#(X1, mark X2) -> take#(X1, X2)) (proper# take(X1, X2) -> take#(proper X1, proper X2), take#(mark X1, X2) -> take#(X1, X2)) (proper# take(X1, X2) -> take#(proper X1, proper X2), take#(ok X1, ok X2) -> take#(X1, X2)) (proper# 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# isNatList take(V1, V2) -> and#(isNat V1, isNatIList V2), and#(ok X1, ok X2) -> and#(X1, X2)) (active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N), and#(ok X1, ok X2) -> and#(X1, X2)) (active# length cons(N, L) -> and#(isNatList L, isNat N), and#(ok X1, ok X2) -> and#(X1, X2)) (proper# and(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# and(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X1, proper# s X -> s# proper X) (proper# and(X1, X2) -> proper# X1, proper# s X -> proper# X) (proper# and(X1, X2) -> proper# X1, proper# length X -> length# proper X) (proper# and(X1, X2) -> proper# X1, proper# length X -> proper# X) (proper# and(X1, X2) -> proper# X1, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# and(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X1, proper# U21 X -> U21# proper X) (proper# and(X1, X2) -> proper# X1, proper# U21 X -> proper# X) (proper# and(X1, X2) -> proper# X1, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# and(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# and(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# and(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# and(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# and(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X4) (proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X1, proper# isNat X -> isNat# proper X) (proper# and(X1, X2) -> proper# X1, proper# isNat X -> proper# X) (proper# and(X1, X2) -> proper# X1, proper# isNatList X -> isNatList# proper X) (proper# and(X1, X2) -> proper# X1, proper# isNatList X -> proper# X) (proper# and(X1, X2) -> proper# X1, proper# isNatIList X -> isNatIList# proper X) (proper# and(X1, X2) -> proper# X1, proper# isNatIList X -> proper# X) (proper# take(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# take(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1) (proper# take(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2) (proper# take(X1, X2) -> proper# X1, proper# s X -> s# proper X) (proper# take(X1, X2) -> proper# X1, proper# s X -> proper# X) (proper# take(X1, X2) -> proper# X1, proper# length X -> length# proper X) (proper# take(X1, X2) -> proper# X1, proper# length X -> proper# X) (proper# take(X1, X2) -> proper# X1, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# take(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X1) (proper# take(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X2) (proper# take(X1, X2) -> proper# X1, proper# U21 X -> U21# proper X) (proper# take(X1, X2) -> proper# X1, proper# U21 X -> proper# X) (proper# take(X1, X2) -> proper# X1, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# take(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X1) (proper# take(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X2) (proper# take(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# take(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# take(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# take(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# take(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X4) (proper# take(X1, X2) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# take(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X1) (proper# take(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2) (proper# take(X1, X2) -> proper# X1, proper# isNat X -> isNat# proper X) (proper# take(X1, X2) -> proper# X1, proper# isNat X -> proper# X) (proper# take(X1, X2) -> proper# X1, proper# isNatList X -> isNatList# proper X) (proper# take(X1, X2) -> proper# X1, proper# isNatList X -> proper# X) (proper# take(X1, X2) -> proper# X1, proper# isNatIList X -> isNatIList# proper X) (proper# take(X1, X2) -> proper# X1, proper# isNatIList 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# 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# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X1, proper# U21 X -> U21# proper X) (proper# cons(X1, X2) -> proper# X1, proper# U21 X -> proper# X) (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# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# cons(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# cons(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# cons(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# cons(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X4) (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# isNat X -> isNat# proper X) (proper# cons(X1, X2) -> proper# X1, proper# isNat X -> proper# X) (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) (active# U31(X1, X2, X3, X4) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2)) (active# U31(X1, X2, X3, X4) -> active# X1, active# cons(X1, X2) -> active# X1) (active# U31(X1, X2, X3, X4) -> active# X1, active# zeros() -> cons#(0(), zeros())) (active# U31(X1, X2, X3, X4) -> active# X1, active# s X -> active# X) (active# U31(X1, X2, X3, X4) -> active# X1, active# s X -> s# active X) (active# U31(X1, X2, X3, X4) -> active# X1, active# length X -> active# X) (active# U31(X1, X2, X3, X4) -> active# X1, active# length X -> length# active X) (active# U31(X1, X2, X3, X4) -> active# X1, active# length cons(N, L) -> U11#(and(isNatList L, isNat N), L)) (active# U31(X1, X2, X3, X4) -> active# X1, active# length cons(N, L) -> and#(isNatList L, isNat N)) (active# U31(X1, X2, X3, X4) -> active# X1, active# length cons(N, L) -> isNat# N) (active# U31(X1, X2, X3, X4) -> active# X1, active# length cons(N, L) -> isNatList# L) (active# U31(X1, X2, X3, X4) -> active# X1, active# U11(X1, X2) -> active# X1) (active# U31(X1, X2, X3, X4) -> active# X1, active# U11(X1, X2) -> U11#(active X1, X2)) (active# U31(X1, X2, X3, X4) -> active# X1, active# U11(tt(), L) -> s# length L) (active# U31(X1, X2, X3, X4) -> active# X1, active# U11(tt(), L) -> length# L) (active# U31(X1, X2, X3, X4) -> active# X1, active# U21 X -> active# X) (active# U31(X1, X2, X3, X4) -> active# X1, active# U21 X -> U21# active X) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(X1, X2) -> active# X1) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(X1, X2) -> active# X2) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(X1, X2) -> take#(X1, active X2)) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(X1, X2) -> take#(active X1, X2)) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(0(), IL) -> U21# isNatIList IL) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(0(), IL) -> isNatIList# IL) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N)) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N)) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, and(isNat M, isNat N))) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# N) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# M) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIList# IL) (active# U31(X1, X2, X3, X4) -> active# X1, active# U31(X1, X2, X3, X4) -> active# X1) (active# U31(X1, X2, X3, X4) -> active# X1, active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4)) (active# U31(X1, X2, X3, X4) -> active# X1, active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL))) (active# U31(X1, X2, X3, X4) -> active# X1, active# U31(tt(), IL, M, N) -> take#(M, IL)) (active# U31(X1, X2, X3, X4) -> active# X1, active# and(X1, X2) -> active# X1) (active# U31(X1, X2, X3, X4) -> active# X1, active# and(X1, X2) -> and#(active X1, X2)) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNat s V1 -> isNat# V1) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNat length V1 -> isNatList# V1) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatList cons(V1, V2) -> and#(isNat V1, isNatList V2)) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatList cons(V1, V2) -> isNat# V1) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatList cons(V1, V2) -> isNatList# V2) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatList take(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatList take(V1, V2) -> isNat# V1) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatList take(V1, V2) -> isNatIList# V2) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatIList V -> isNatList# V) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatIList cons(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatIList cons(V1, V2) -> isNat# V1) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatIList cons(V1, V2) -> isNatIList# V2) (active# U11(X1, X2) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2)) (active# U11(X1, X2) -> active# X1, active# cons(X1, X2) -> active# X1) (active# U11(X1, X2) -> active# X1, active# zeros() -> cons#(0(), zeros())) (active# U11(X1, X2) -> active# X1, active# s X -> active# X) (active# U11(X1, X2) -> active# X1, active# s X -> s# active X) (active# U11(X1, X2) -> active# X1, active# length X -> active# X) (active# U11(X1, X2) -> active# X1, active# length X -> length# active X) (active# U11(X1, X2) -> active# X1, active# length cons(N, L) -> U11#(and(isNatList L, isNat N), L)) (active# U11(X1, X2) -> active# X1, active# length cons(N, L) -> and#(isNatList L, isNat N)) (active# U11(X1, X2) -> active# X1, active# length cons(N, L) -> isNat# N) (active# U11(X1, X2) -> active# X1, active# length cons(N, L) -> isNatList# L) (active# U11(X1, X2) -> active# X1, active# U11(X1, X2) -> active# X1) (active# U11(X1, X2) -> active# X1, active# U11(X1, X2) -> U11#(active X1, X2)) (active# U11(X1, X2) -> active# X1, active# U11(tt(), L) -> s# length L) (active# U11(X1, X2) -> active# X1, active# U11(tt(), L) -> length# L) (active# U11(X1, X2) -> active# X1, active# U21 X -> active# X) (active# U11(X1, X2) -> active# X1, active# U21 X -> U21# active X) (active# U11(X1, X2) -> active# X1, active# take(X1, X2) -> active# X1) (active# U11(X1, X2) -> active# X1, active# take(X1, X2) -> active# X2) (active# U11(X1, X2) -> active# X1, active# take(X1, X2) -> take#(X1, active X2)) (active# U11(X1, X2) -> active# X1, active# take(X1, X2) -> take#(active X1, X2)) (active# U11(X1, X2) -> active# X1, active# take(0(), IL) -> U21# isNatIList IL) (active# U11(X1, X2) -> active# X1, active# take(0(), IL) -> isNatIList# IL) (active# U11(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N)) (active# U11(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N)) (active# U11(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, and(isNat M, isNat N))) (active# U11(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# N) (active# U11(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# M) (active# U11(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIList# IL) (active# U11(X1, X2) -> active# X1, active# U31(X1, X2, X3, X4) -> active# X1) (active# U11(X1, X2) -> active# X1, active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4)) (active# U11(X1, X2) -> active# X1, active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL))) (active# U11(X1, X2) -> active# X1, active# U31(tt(), IL, M, N) -> take#(M, IL)) (active# U11(X1, X2) -> active# X1, active# and(X1, X2) -> active# X1) (active# U11(X1, X2) -> active# X1, active# and(X1, X2) -> and#(active X1, X2)) (active# U11(X1, X2) -> active# X1, active# isNat s V1 -> isNat# V1) (active# U11(X1, X2) -> active# X1, active# isNat length V1 -> isNatList# V1) (active# U11(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> and#(isNat V1, isNatList V2)) (active# U11(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> isNat# V1) (active# U11(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> isNatList# V2) (active# U11(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# U11(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> isNat# V1) (active# U11(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> isNatIList# V2) (active# U11(X1, X2) -> active# X1, active# isNatIList V -> isNatList# V) (active# U11(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# U11(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNat# V1) (active# U11(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNatIList# V2) (active# take(s M, cons(N, IL)) -> isNatIList# IL, isNatIList# ok X -> isNatIList# X) (active# length cons(N, L) -> U11#(and(isNatList L, isNat N), L), U11#(ok X1, ok X2) -> U11#(X1, X2)) (proper# and(X1, X2) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# and(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X2, proper# s X -> s# proper X) (proper# and(X1, X2) -> proper# X2, proper# s X -> proper# X) (proper# and(X1, X2) -> proper# X2, proper# length X -> length# proper X) (proper# and(X1, X2) -> proper# X2, proper# length X -> proper# X) (proper# and(X1, X2) -> proper# X2, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# and(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X2, proper# U21 X -> U21# proper X) (proper# and(X1, X2) -> proper# X2, proper# U21 X -> proper# X) (proper# and(X1, X2) -> proper# X2, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# and(X1, X2) -> proper# X2, proper# take(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X2, proper# take(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# and(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# and(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# and(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# and(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X4) (proper# and(X1, X2) -> proper# X2, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# and(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X2, proper# isNat X -> isNat# proper X) (proper# and(X1, X2) -> proper# X2, proper# isNat X -> proper# X) (proper# and(X1, X2) -> proper# X2, proper# isNatList X -> isNatList# proper X) (proper# and(X1, X2) -> proper# X2, proper# isNatList X -> proper# X) (proper# and(X1, X2) -> proper# X2, proper# isNatIList X -> isNatIList# proper X) (proper# and(X1, X2) -> proper# X2, proper# isNatIList X -> proper# X) (proper# take(X1, X2) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# take(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X1) (proper# take(X1, X2) -> proper# X2, proper# cons(X1, X2) -> proper# X2) (proper# take(X1, X2) -> proper# X2, proper# s X -> s# proper X) (proper# take(X1, X2) -> proper# X2, proper# s X -> proper# X) (proper# take(X1, X2) -> proper# X2, proper# length X -> length# proper X) (proper# take(X1, X2) -> proper# X2, proper# length X -> proper# X) (proper# take(X1, X2) -> proper# X2, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# take(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X1) (proper# take(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X2) (proper# take(X1, X2) -> proper# X2, proper# U21 X -> U21# proper X) (proper# take(X1, X2) -> proper# X2, proper# U21 X -> proper# X) (proper# take(X1, X2) -> proper# X2, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# take(X1, X2) -> proper# X2, proper# take(X1, X2) -> proper# X1) (proper# take(X1, X2) -> proper# X2, proper# take(X1, X2) -> proper# X2) (proper# take(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# take(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# take(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# take(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# take(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X4) (proper# take(X1, X2) -> proper# X2, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# take(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X1) (proper# take(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X2) (proper# take(X1, X2) -> proper# X2, proper# isNat X -> isNat# proper X) (proper# take(X1, X2) -> proper# X2, proper# isNat X -> proper# X) (proper# take(X1, X2) -> proper# X2, proper# isNatList X -> isNatList# proper X) (proper# take(X1, X2) -> proper# X2, proper# isNatList X -> proper# X) (proper# take(X1, X2) -> proper# X2, proper# isNatIList X -> isNatIList# proper X) (proper# take(X1, X2) -> proper# X2, proper# isNatIList 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# 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# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X2, proper# U21 X -> U21# proper X) (proper# cons(X1, X2) -> proper# X2, proper# U21 X -> proper# X) (proper# cons(X1, X2) -> proper# X2, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X2, proper# take(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X2, proper# take(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# cons(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# cons(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# cons(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# cons(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X4) (proper# cons(X1, X2) -> proper# X2, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X2, proper# and(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X2, proper# isNat X -> isNat# proper X) (proper# cons(X1, X2) -> proper# X2, proper# isNat X -> proper# X) (proper# cons(X1, X2) -> proper# X2, proper# isNatList X -> isNatList# proper X) (proper# cons(X1, X2) -> proper# X2, proper# isNatList X -> proper# X) (proper# cons(X1, X2) -> proper# X2, proper# isNatIList X -> isNatIList# proper X) (proper# cons(X1, X2) -> proper# X2, proper# isNatIList X -> proper# X) (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# s X -> active# X) (top# ok X -> active# X, active# s X -> s# active X) (top# ok X -> active# X, active# length X -> active# X) (top# ok X -> active# X, active# length X -> length# active X) (top# ok X -> active# X, active# length cons(N, L) -> U11#(and(isNatList L, isNat N), L)) (top# ok X -> active# X, 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IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N)) (top# ok X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N)) (top# ok X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, and(isNat M, isNat N))) (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)) -> isNat# M) (top# ok X -> active# X, active# take(s M, cons(N, IL)) -> isNatIList# IL) (top# ok X -> active# X, active# U31(X1, X2, X3, X4) -> active# X1) (top# ok X -> active# X, active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4)) (top# ok X -> active# X, active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL))) (top# ok X -> active# X, active# U31(tt(), IL, M, N) -> take#(M, IL)) (top# ok X -> active# X, active# and(X1, X2) -> active# X1) (top# ok X -> active# X, active# and(X1, X2) -> and#(active X1, X2)) (top# ok X -> active# X, active# isNat s V1 -> isNat# V1) (top# ok X -> active# X, active# isNat length 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-> proper# X, proper# isNatIList X -> isNatIList# proper X) (proper# length X -> proper# X, proper# isNatIList X -> proper# X) (isNatIList# ok X -> isNatIList# X, isNatIList# ok X -> isNatIList# X) (isNat# ok X -> isNat# X, isNat# ok X -> isNat# X) (U21# mark X -> U21# X, U21# mark X -> U21# X) (U21# mark X -> U21# X, U21# ok X -> U21# 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) (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# s X -> active# X) (active# length X -> active# X, active# s X -> s# active X) (active# length X -> active# X, active# length X -> active# X) (active# length X -> active# X, active# length X -> length# active X) (active# length X -> active# X, active# length cons(N, L) -> U11#(and(isNatList L, isNat N), L)) (active# length X -> active# X, active# length cons(N, L) -> and#(isNatList L, isNat N)) (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# U11(X1, X2) -> active# X1) (active# length X -> active# X, active# U11(X1, X2) -> U11#(active X1, X2)) (active# length X -> active# X, active# U11(tt(), L) -> s# length L) (active# length X -> active# X, active# U11(tt(), L) -> length# L) (active# length X -> active# X, active# U21 X -> active# X) (active# length X -> active# X, active# U21 X -> U21# active X) (active# length X -> active# X, active# take(X1, X2) -> active# X1) (active# length X -> active# X, active# take(X1, X2) -> active# X2) (active# length X -> active# X, active# take(X1, X2) -> take#(X1, active X2)) (active# length X -> active# X, active# take(X1, X2) -> take#(active X1, X2)) (active# length X -> active# X, active# take(0(), IL) -> U21# isNatIList IL) (active# length X -> active# X, active# take(0(), IL) -> isNatIList# IL) (active# length X -> active# X, active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N)) (active# length X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N)) (active# length X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, and(isNat M, isNat N))) (active# length X -> active# X, active# take(s M, cons(N, IL)) -> isNat# N) (active# length X -> active# X, active# take(s M, cons(N, IL)) -> isNat# M) (active# length X -> active# X, active# take(s M, cons(N, IL)) -> isNatIList# IL) (active# length X -> active# X, active# U31(X1, X2, X3, X4) -> active# X1) (active# length X -> active# X, active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4)) (active# length X -> active# X, active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL))) (active# length X -> active# X, active# U31(tt(), IL, M, N) -> take#(M, IL)) (active# length X -> active# X, active# and(X1, X2) -> active# X1) (active# length X -> active# X, active# and(X1, X2) -> and#(active X1, X2)) (active# length X -> active# X, active# isNat s V1 -> isNat# V1) (active# length X -> active# X, active# isNat length V1 -> isNatList# V1) (active# length X -> active# X, active# isNatList cons(V1, V2) -> and#(isNat V1, isNatList V2)) (active# length X -> active# X, active# isNatList cons(V1, V2) -> isNat# V1) (active# length X -> active# X, active# isNatList cons(V1, V2) -> isNatList# V2) (active# length X -> active# X, active# isNatList take(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# length X -> active# X, active# isNatList take(V1, V2) -> isNat# V1) (active# length X -> active# X, active# isNatList take(V1, V2) -> isNatIList# V2) (active# length X -> active# X, active# isNatIList V -> isNatList# V) (active# length X -> active# X, active# isNatIList cons(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# length X -> active# X, active# isNatIList cons(V1, V2) -> isNat# V1) (active# length X -> active# X, active# isNatIList cons(V1, V2) -> isNatIList# V2) (and#(ok X1, ok X2) -> and#(X1, X2), and#(mark X1, X2) -> and#(X1, X2)) (and#(ok X1, ok X2) -> and#(X1, X2), and#(ok X1, ok X2) -> and#(X1, X2)) (take#(ok X1, ok X2) -> take#(X1, X2), take#(X1, mark X2) -> take#(X1, X2)) (take#(ok X1, ok X2) -> take#(X1, X2), take#(mark X1, X2) -> take#(X1, X2)) (take#(ok X1, ok X2) -> take#(X1, X2), take#(ok X1, ok X2) -> take#(X1, X2)) (take#(X1, mark X2) -> take#(X1, X2), take#(X1, mark X2) -> take#(X1, X2)) (take#(X1, mark X2) -> take#(X1, X2), take#(mark X1, X2) -> take#(X1, X2)) (take#(X1, mark X2) -> take#(X1, X2), take#(ok X1, ok X2) -> take#(X1, X2)) (U11#(mark X1, X2) -> U11#(X1, X2), U11#(mark X1, X2) -> U11#(X1, X2)) (U11#(mark X1, X2) -> U11#(X1, X2), U11#(ok X1, ok X2) -> U11#(X1, X2)) (cons#(mark X1, X2) -> cons#(X1, X2), cons#(mark X1, X2) -> cons#(X1, X2)) (cons#(mark X1, X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)) (U31#(mark X1, X2, X3, X4) -> U31#(X1, X2, X3, X4), U31#(mark X1, X2, X3, X4) -> U31#(X1, X2, X3, X4)) (U31#(mark X1, X2, X3, X4) -> U31#(X1, X2, X3, X4), U31#(ok X1, ok X2, ok X3, ok X4) -> U31#(X1, X2, X3, X4)) (active# and(X1, X2) -> and#(active X1, X2), and#(mark X1, X2) -> and#(X1, X2)) (active# and(X1, X2) -> and#(active X1, X2), and#(ok X1, ok X2) -> and#(X1, X2)) (active# U11(X1, X2) -> U11#(active X1, X2), U11#(mark X1, X2) -> U11#(X1, X2)) (active# U11(X1, X2) -> U11#(active X1, X2), U11#(ok X1, ok X2) -> U11#(X1, X2)) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# cons(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# cons(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# s X -> s# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# s X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# length X -> length# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# length X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# U11(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# U11(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# U21 X -> U21# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# U21 X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# take(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# take(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# U31(X1, X2, X3, X4) -> proper# X4) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# and(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# and(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# isNat X -> isNat# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# isNat X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# isNatList X -> isNatList# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# isNatList X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# isNatIList X -> isNatIList# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# isNatIList X -> proper# X) (active# isNatIList cons(V1, V2) -> isNat# V1, isNat# ok X -> isNat# X) (active# isNatList cons(V1, V2) -> isNat# V1, isNat# ok X -> isNat# X) (active# isNat s V1 -> isNat# V1, isNat# ok X -> isNat# X) (active# length cons(N, L) -> isNatList# L, isNatList# ok X -> isNatList# X) (active# take(0(), IL) -> U21# isNatIList IL, U21# ok X -> U21# 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# isNatList X -> isNatList# proper X, isNatList# ok X -> isNatList# X) (proper# U21 X -> U21# proper X, U21# mark X -> U21# X) (proper# U21 X -> U21# proper X, U21# ok X -> U21# X) (proper# s X -> s# proper X, s# mark X -> s# X) (proper# s X -> s# proper X, s# ok X -> s# X) (active# length X -> length# active X, length# mark X -> length# X) (active# length X -> length# active X, length# ok X -> length# X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# cons(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# cons(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# s X -> s# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# s X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# length X -> length# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# length X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U11(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U11(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U21 X -> U21# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U21 X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# take(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# take(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U31(X1, X2, X3, X4) -> proper# X4) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# and(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# and(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# isNat X -> isNat# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# isNat X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# isNatList X -> isNatList# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# isNatList X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# isNatIList X -> isNatIList# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# isNatIList X -> proper# X) (active# isNatIList V -> isNatList# V, isNatList# ok X -> isNatList# X) (active# length cons(N, L) -> isNat# N, isNat# ok X -> isNat# X) } EDG: { (active# take(s M, cons(N, IL)) -> isNat# N, isNat# ok X -> isNat# X) (proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4), U31#(ok X1, ok X2, ok X3, ok X4) -> U31#(X1, X2, X3, X4)) (proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4), U31#(mark X1, X2, X3, X4) -> U31#(X1, X2, X3, X4)) (active# s X -> s# active X, s# ok X -> s# X) (active# s X -> s# active X, s# mark X -> s# X) (active# U21 X -> U21# active X, U21# ok X -> U21# X) (active# U21 X -> U21# active X, U21# mark X -> U21# X) (proper# length X -> length# proper X, length# ok X -> length# X) (proper# length X -> length# proper X, length# mark X -> length# X) (proper# isNat X -> isNat# proper X, isNat# ok X -> isNat# X) (proper# isNatIList X -> isNatIList# proper X, isNatIList# ok X -> isNatIList# 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# U11(tt(), L) -> s# length L, s# ok X -> s# X) (active# U11(tt(), L) -> s# length L, s# mark X -> s# X) (active# U11(tt(), L) -> length# L, length# ok X -> length# X) (active# U11(tt(), L) -> length# L, length# mark X -> length# X) (active# isNat length V1 -> isNatList# V1, isNatList# ok X -> isNatList# X) (active# isNatList take(V1, V2) -> isNat# V1, isNat# ok X -> isNat# X) (active# U31(tt(), IL, M, N) -> take#(M, IL), take#(ok X1, ok X2) -> take#(X1, X2)) (active# U31(tt(), IL, M, N) -> take#(M, IL), take#(mark X1, X2) -> take#(X1, X2)) (active# U31(tt(), IL, M, N) -> take#(M, IL), take#(X1, mark X2) -> take#(X1, X2)) (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# take(X1, X2) -> take#(active X1, X2), take#(ok X1, ok X2) -> take#(X1, X2)) (active# take(X1, X2) -> take#(active X1, X2), take#(mark X1, X2) -> take#(X1, X2)) (active# take(X1, X2) -> take#(active X1, X2), take#(X1, mark X2) -> take#(X1, X2)) (active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4), U31#(ok X1, ok X2, ok X3, ok X4) -> U31#(X1, X2, X3, X4)) (active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4), U31#(mark X1, X2, X3, X4) -> U31#(X1, X2, X3, X4)) (U31#(ok X1, ok X2, ok X3, ok X4) -> U31#(X1, X2, X3, X4), U31#(ok X1, ok X2, ok X3, ok X4) -> U31#(X1, X2, X3, X4)) (U31#(ok X1, ok X2, ok X3, ok X4) -> U31#(X1, X2, X3, X4), U31#(mark X1, X2, X3, X4) -> U31#(X1, X2, X3, X4)) (cons#(ok X1, ok X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)) (cons#(ok X1, ok X2) -> cons#(X1, X2), cons#(mark X1, X2) -> cons#(X1, X2)) (U11#(ok X1, ok X2) -> U11#(X1, X2), U11#(ok X1, ok X2) -> U11#(X1, X2)) (U11#(ok X1, ok X2) -> U11#(X1, X2), U11#(mark X1, X2) -> U11#(X1, X2)) (take#(mark X1, X2) -> take#(X1, X2), take#(ok X1, ok X2) -> take#(X1, X2)) (take#(mark X1, X2) -> take#(X1, X2), take#(mark X1, X2) -> take#(X1, X2)) (take#(mark X1, X2) -> take#(X1, X2), take#(X1, mark X2) -> take#(X1, X2)) (and#(mark X1, X2) -> and#(X1, X2), and#(ok X1, ok X2) -> and#(X1, X2)) (and#(mark X1, X2) -> and#(X1, X2), and#(mark X1, X2) -> and#(X1, X2)) (active# s X -> active# X, active# isNatIList cons(V1, V2) -> isNatIList# V2) (active# s X -> active# X, active# isNatIList cons(V1, V2) -> isNat# V1) (active# s X -> active# X, active# isNatIList cons(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# s X -> active# X, active# isNatIList V -> isNatList# V) (active# s X -> active# X, active# isNatList take(V1, V2) -> isNatIList# V2) (active# s X -> active# X, active# isNatList take(V1, V2) -> isNat# V1) (active# s X -> active# X, active# isNatList take(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# s X -> active# X, active# isNatList cons(V1, V2) -> isNatList# V2) (active# s X -> active# X, active# isNatList cons(V1, V2) -> isNat# V1) (active# s X -> active# X, active# isNatList cons(V1, V2) -> and#(isNat V1, isNatList V2)) (active# s X -> active# X, active# isNat length V1 -> isNatList# V1) (active# s X -> active# X, active# isNat s V1 -> isNat# V1) (active# s X -> active# X, active# and(X1, X2) -> and#(active X1, X2)) (active# s X -> active# X, active# and(X1, X2) -> active# X1) (active# s X -> active# X, active# U31(tt(), IL, M, N) -> take#(M, IL)) (active# s X -> active# X, active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL))) (active# s X -> active# X, active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4)) (active# s X -> active# X, active# U31(X1, X2, X3, X4) -> active# X1) (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# M) (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)) -> and#(isNatIList IL, and(isNat M, isNat N))) (active# s X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N)) (active# s X -> active# X, active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N)) (active# s X -> active# X, active# take(0(), IL) -> isNatIList# IL) (active# s X -> active# X, active# take(0(), IL) -> U21# isNatIList IL) (active# s X -> active# X, active# take(X1, X2) -> take#(active X1, X2)) (active# s X -> active# X, active# take(X1, X2) -> take#(X1, active X2)) (active# s X -> active# X, active# take(X1, X2) -> active# X2) (active# s X -> active# X, active# take(X1, X2) -> active# X1) (active# s X -> active# X, active# U21 X -> U21# active X) (active# s X -> active# X, active# U21 X -> active# X) (active# s X -> active# X, active# U11(tt(), L) -> length# L) (active# s X -> active# X, active# U11(tt(), L) -> s# length L) (active# s X -> active# X, active# U11(X1, X2) -> U11#(active X1, X2)) (active# s X -> active# X, active# U11(X1, X2) -> active# X1) (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) -> and#(isNatList L, isNat N)) (active# s X -> active# X, active# length cons(N, L) -> U11#(and(isNatList L, isNat N), L)) (active# s X -> active# X, active# length X -> length# active X) (active# s X -> active# X, active# length X -> active# X) (active# s X -> active# X, active# s X -> s# active X) (active# s X -> active# X, active# s X -> active# X) (active# s X -> active# X, active# zeros() -> cons#(0(), zeros())) (active# s X -> active# X, active# cons(X1, X2) -> active# X1) (active# s X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (active# U21 X -> active# X, active# isNatIList cons(V1, V2) -> isNatIList# V2) (active# U21 X -> active# X, active# isNatIList cons(V1, V2) -> isNat# V1) (active# U21 X -> active# X, active# isNatIList cons(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# U21 X -> active# X, active# isNatIList V -> isNatList# V) (active# U21 X -> active# X, active# isNatList take(V1, V2) -> isNatIList# V2) (active# U21 X -> active# X, active# isNatList take(V1, V2) -> isNat# V1) (active# U21 X -> active# X, active# isNatList take(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# U21 X -> active# X, active# isNatList cons(V1, V2) -> isNatList# V2) (active# U21 X -> active# X, active# isNatList cons(V1, V2) -> isNat# V1) (active# U21 X -> active# X, active# isNatList cons(V1, V2) -> and#(isNat V1, isNatList V2)) (active# U21 X -> active# X, active# isNat length V1 -> isNatList# V1) (active# U21 X -> active# X, active# isNat s V1 -> isNat# V1) (active# U21 X -> active# X, active# and(X1, X2) -> and#(active X1, X2)) (active# U21 X -> active# X, active# and(X1, X2) -> active# X1) (active# U21 X -> active# X, active# U31(tt(), IL, M, N) -> take#(M, IL)) (active# U21 X -> active# X, active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL))) (active# U21 X -> active# X, active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4)) (active# U21 X -> active# X, active# U31(X1, X2, X3, X4) -> active# X1) (active# U21 X -> active# X, active# take(s M, cons(N, IL)) -> isNatIList# IL) (active# U21 X -> active# X, active# take(s M, cons(N, IL)) -> isNat# M) (active# U21 X -> active# X, active# take(s M, cons(N, IL)) -> isNat# N) (active# U21 X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, and(isNat M, isNat N))) (active# U21 X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N)) (active# U21 X -> active# X, active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N)) (active# U21 X -> active# X, active# take(0(), IL) -> isNatIList# IL) (active# U21 X -> active# X, active# take(0(), IL) -> U21# isNatIList IL) (active# U21 X -> active# X, active# take(X1, X2) -> take#(active X1, X2)) (active# U21 X -> active# X, active# take(X1, X2) -> take#(X1, active X2)) (active# U21 X -> active# X, active# take(X1, X2) -> active# X2) (active# U21 X -> active# X, active# take(X1, X2) -> active# X1) (active# U21 X -> active# X, active# U21 X -> U21# active X) (active# U21 X -> active# X, active# U21 X -> active# X) (active# U21 X -> active# X, active# U11(tt(), L) -> length# L) (active# U21 X -> active# X, active# U11(tt(), L) -> s# length L) (active# U21 X -> active# X, active# U11(X1, X2) -> U11#(active X1, X2)) (active# U21 X -> active# X, active# U11(X1, X2) -> active# X1) (active# U21 X -> active# X, active# length cons(N, L) -> isNatList# L) (active# U21 X -> active# X, active# length cons(N, L) -> isNat# N) (active# U21 X -> active# X, active# length cons(N, L) -> and#(isNatList L, isNat N)) (active# U21 X -> active# X, active# length cons(N, L) -> U11#(and(isNatList L, isNat N), L)) (active# U21 X -> active# X, active# length X -> length# active X) (active# U21 X -> active# X, active# length X -> active# X) (active# U21 X -> active# X, active# s X -> s# active X) (active# U21 X -> active# X, active# s X -> active# X) (active# U21 X -> active# X, active# zeros() -> cons#(0(), zeros())) (active# U21 X -> active# X, active# cons(X1, X2) -> active# X1) (active# U21 X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (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) (U21# ok X -> U21# X, U21# ok X -> U21# X) (U21# ok X -> U21# X, U21# mark X -> U21# X) (isNatList# ok X -> isNatList# X, isNatList# ok X -> isNatList# 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# isNat X -> proper# X) (proper# s X -> proper# X, proper# isNat X -> isNat# proper X) (proper# s X -> proper# X, proper# and(X1, X2) -> proper# X2) (proper# s X -> proper# X, proper# and(X1, X2) -> proper# X1) (proper# s X -> proper# X, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# s X -> proper# X, proper# U31(X1, X2, X3, X4) -> proper# X4) (proper# s X -> proper# X, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# s X -> proper# X, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# s X -> proper# X, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# s X -> proper# X, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# s X -> proper# X, proper# take(X1, X2) -> proper# X2) (proper# s X -> proper# X, proper# take(X1, X2) -> proper# X1) (proper# s X -> proper# X, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# s X -> proper# X, proper# U21 X -> proper# X) (proper# s X -> proper# X, proper# U21 X -> U21# proper X) (proper# s X -> proper# X, proper# U11(X1, X2) -> proper# X2) (proper# s X -> proper# X, proper# U11(X1, X2) -> proper# X1) (proper# s X -> proper# X, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# s X -> proper# X, proper# 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# cons(X1, X2) -> proper# X2) (proper# s X -> proper# X, 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isNat# V1) (active# take(X1, X2) -> active# X2, active# isNatList cons(V1, V2) -> and#(isNat V1, isNatList V2)) (active# take(X1, X2) -> active# X2, active# isNat length V1 -> isNatList# V1) (active# take(X1, X2) -> active# X2, active# isNat s V1 -> isNat# V1) (active# take(X1, X2) -> active# X2, active# and(X1, X2) -> and#(active X1, X2)) (active# take(X1, X2) -> active# X2, active# and(X1, X2) -> active# X1) (active# take(X1, X2) -> active# X2, active# U31(tt(), IL, M, N) -> take#(M, IL)) (active# take(X1, X2) -> active# X2, active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL))) (active# take(X1, X2) -> active# X2, active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4)) (active# take(X1, X2) -> active# X2, active# U31(X1, X2, X3, X4) -> active# X1) (active# take(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> isNatIList# IL) (active# take(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> isNat# M) (active# take(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> isNat# N) (active# take(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, and(isNat M, isNat N))) (active# take(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N)) (active# take(X1, X2) -> active# X2, active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N)) (active# take(X1, X2) -> active# X2, active# take(0(), IL) -> isNatIList# IL) (active# take(X1, X2) -> active# X2, active# take(0(), IL) -> U21# isNatIList IL) (active# take(X1, X2) -> active# X2, active# take(X1, X2) -> take#(active X1, X2)) (active# take(X1, X2) -> active# X2, active# take(X1, X2) -> take#(X1, active X2)) (active# take(X1, X2) -> active# X2, active# take(X1, X2) -> active# X2) (active# take(X1, X2) -> active# X2, active# take(X1, X2) -> active# X1) (active# take(X1, X2) -> active# X2, active# U21 X -> U21# active X) (active# take(X1, X2) -> active# X2, active# U21 X -> active# X) (active# take(X1, X2) -> active# X2, 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X2, X3, X4) -> proper# X2) (proper# U11(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# U11(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# U11(X1, X2) -> proper# X2, proper# take(X1, X2) -> proper# X2) (proper# U11(X1, X2) -> proper# X2, proper# take(X1, X2) -> proper# X1) (proper# U11(X1, X2) -> proper# X2, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# U11(X1, X2) -> proper# X2, proper# U21 X -> proper# X) (proper# U11(X1, X2) -> proper# X2, proper# U21 X -> U21# proper X) (proper# U11(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X2) (proper# U11(X1, X2) -> proper# X2, proper# U11(X1, X2) -> proper# X1) (proper# U11(X1, X2) -> proper# X2, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# U11(X1, X2) -> proper# X2, proper# length X -> proper# X) (proper# U11(X1, X2) -> proper# X2, proper# length X -> length# proper X) (proper# U11(X1, X2) -> proper# X2, 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-> proper# X2, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X4) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# take(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# take(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# U21 X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# U21 X -> U21# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# U11(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# U11(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# length X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# length X -> length# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# s X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# s X -> s# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# cons(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# cons(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X2, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N), U31#(ok X1, ok X2, ok X3, ok X4) -> U31#(X1, X2, X3, X4)) (active# take(0(), IL) -> isNatIList# IL, isNatIList# ok X -> isNatIList# X) (active# cons(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNatIList# V2) (active# cons(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNat# V1) (active# cons(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# cons(X1, X2) -> active# X1, active# isNatIList V -> isNatList# V) (active# cons(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> isNatIList# V2) (active# cons(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> isNat# V1) (active# cons(X1, X2) -> active# X1, active# isNatList take(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# cons(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> isNatList# V2) (active# cons(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> isNat# V1) (active# cons(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> and#(isNat V1, isNatList V2)) (active# cons(X1, X2) -> active# X1, active# isNat length V1 -> isNatList# V1) (active# cons(X1, X2) -> active# X1, 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(active# cons(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N)) (active# cons(X1, X2) -> active# X1, active# take(0(), IL) -> isNatIList# IL) (active# cons(X1, X2) -> active# X1, active# take(0(), IL) -> U21# 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# U21 X -> U21# active X) (active# cons(X1, X2) -> active# X1, active# U21 X -> active# X) (active# cons(X1, X2) -> active# X1, active# U11(tt(), L) -> length# L) (active# cons(X1, X2) -> active# X1, active# U11(tt(), L) -> s# length L) (active# cons(X1, X2) -> active# X1, active# U11(X1, X2) -> U11#(active X1, X2)) (active# cons(X1, X2) -> active# X1, 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X1, X2)) (active# take(X1, X2) -> active# X1, active# and(X1, X2) -> active# X1) (active# take(X1, X2) -> active# X1, active# U31(tt(), IL, M, N) -> take#(M, IL)) (active# take(X1, X2) -> active# X1, active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL))) (active# take(X1, X2) -> active# X1, active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4)) (active# take(X1, X2) -> active# X1, active# U31(X1, X2, X3, X4) -> active# X1) (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# M) (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)) -> and#(isNatIList IL, and(isNat M, isNat N))) (active# take(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N)) (active# take(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, 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active# X1, active# U31(tt(), IL, M, N) -> take#(M, IL)) (active# and(X1, X2) -> active# X1, active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL))) (active# and(X1, X2) -> active# X1, active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4)) (active# and(X1, X2) -> active# X1, active# U31(X1, X2, X3, X4) -> active# X1) (active# and(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIList# IL) (active# and(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# M) (active# and(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# N) (active# and(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, and(isNat M, isNat N))) (active# and(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N)) (active# and(X1, X2) -> active# X1, active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N)) (active# and(X1, X2) -> active# X1, active# take(0(), IL) -> isNatIList# IL) (active# and(X1, 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U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# take(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# take(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# U21 X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# U21 X -> U21# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# U11(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# U11(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# length X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# length X -> length# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# s X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# s X -> s# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# cons(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# cons(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (active# take(s M, cons(N, IL)) -> and#(isNatIList IL, and(isNat M, isNat N)), 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)) (active# isNatList cons(V1, V2) -> and#(isNat V1, isNatList V2), and#(ok X1, ok X2) -> and#(X1, X2)) (active# isNatIList cons(V1, V2) -> and#(isNat V1, isNatIList V2), and#(ok X1, ok X2) -> and#(X1, X2)) (proper# U11(X1, X2) -> U11#(proper X1, proper X2), U11#(ok X1, ok X2) -> U11#(X1, X2)) (proper# U11(X1, X2) -> U11#(proper X1, proper X2), U11#(mark X1, X2) -> U11#(X1, X2)) (proper# and(X1, X2) -> and#(proper X1, proper X2), and#(ok X1, ok X2) -> and#(X1, X2)) (proper# and(X1, X2) -> and#(proper X1, proper X2), and#(mark X1, X2) -> and#(X1, X2)) (active# take(s M, cons(N, IL)) -> isNat# M, isNat# ok X -> isNat# X) (active# isNatList cons(V1, V2) -> isNatList# V2, isNatList# ok X -> isNatList# X) (active# isNatIList cons(V1, V2) -> isNatIList# V2, isNatIList# ok X -> isNatIList# X) (active# isNatList take(V1, V2) -> isNatIList# V2, isNatIList# ok X -> isNatIList# X) (active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL)), cons#(mark X1, X2) -> cons#(X1, X2)) (active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL)), cons#(ok X1, ok X2) -> cons#(X1, X2)) (proper# take(X1, X2) -> take#(proper X1, proper X2), take#(X1, mark X2) -> take#(X1, X2)) (proper# take(X1, X2) -> take#(proper X1, proper X2), take#(mark X1, X2) -> take#(X1, X2)) (proper# take(X1, X2) -> take#(proper X1, proper X2), take#(ok X1, ok X2) -> take#(X1, X2)) (proper# 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# isNatList take(V1, V2) -> and#(isNat V1, isNatIList V2), and#(ok X1, ok X2) -> and#(X1, X2)) (active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N), and#(ok X1, ok X2) -> and#(X1, X2)) (active# length cons(N, L) -> and#(isNatList L, isNat N), and#(ok X1, ok X2) -> and#(X1, X2)) (proper# and(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# and(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X1, proper# s X -> s# proper X) (proper# and(X1, X2) -> proper# X1, proper# s X -> proper# X) (proper# and(X1, X2) -> proper# X1, proper# length X -> length# proper X) (proper# and(X1, X2) -> proper# X1, proper# length X -> proper# X) (proper# and(X1, X2) -> proper# X1, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# and(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X1, proper# U21 X -> U21# proper X) (proper# and(X1, X2) -> proper# X1, proper# U21 X -> proper# X) (proper# and(X1, X2) -> proper# X1, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# and(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# and(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# and(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# and(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# and(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X4) (proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X1) (proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2) (proper# and(X1, X2) -> proper# X1, proper# isNat X -> isNat# proper X) (proper# and(X1, X2) -> proper# X1, proper# isNat X -> proper# X) (proper# and(X1, X2) -> proper# X1, proper# isNatList X -> isNatList# proper X) (proper# and(X1, X2) -> proper# X1, proper# isNatList X -> proper# X) (proper# and(X1, X2) -> proper# X1, proper# isNatIList X -> isNatIList# proper X) (proper# and(X1, X2) -> proper# X1, proper# isNatIList X -> proper# X) (proper# take(X1, X2) -> proper# X1, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# take(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X1) (proper# take(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2) (proper# take(X1, X2) -> proper# X1, proper# s X -> s# proper X) (proper# take(X1, X2) -> proper# X1, proper# s X -> proper# X) (proper# take(X1, X2) -> proper# X1, proper# length X -> length# proper X) (proper# take(X1, X2) -> proper# X1, proper# length X -> proper# X) (proper# take(X1, X2) -> proper# X1, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# take(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X1) (proper# take(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X2) (proper# take(X1, X2) -> proper# X1, proper# U21 X -> U21# proper X) (proper# take(X1, X2) -> proper# X1, proper# U21 X -> proper# X) (proper# take(X1, X2) -> proper# X1, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# take(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X1) (proper# take(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X2) (proper# take(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# take(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# take(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# take(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# take(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X4) (proper# take(X1, X2) -> proper# X1, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# take(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X1) (proper# take(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2) (proper# take(X1, X2) -> proper# X1, proper# isNat X -> isNat# proper X) (proper# take(X1, X2) -> proper# X1, proper# isNat X -> proper# X) (proper# take(X1, X2) -> proper# X1, proper# isNatList X -> isNatList# proper X) (proper# take(X1, X2) -> proper# X1, proper# isNatList X -> proper# X) (proper# take(X1, X2) -> proper# X1, proper# isNatIList X -> isNatIList# proper X) (proper# take(X1, X2) -> proper# X1, proper# isNatIList 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# 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# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# cons(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X1) (proper# cons(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X2) (proper# cons(X1, X2) -> proper# X1, proper# U21 X -> U21# proper X) (proper# cons(X1, X2) -> proper# X1, proper# U21 X -> proper# X) (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# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# cons(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# cons(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# cons(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# cons(X1, X2) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X4) (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# isNat X -> isNat# proper X) (proper# cons(X1, X2) -> proper# X1, proper# isNat X -> proper# X) (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) (active# U31(X1, X2, X3, X4) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2)) (active# U31(X1, X2, X3, X4) -> active# X1, active# cons(X1, X2) -> active# X1) (active# U31(X1, X2, X3, X4) -> active# X1, active# zeros() -> cons#(0(), zeros())) (active# U31(X1, X2, X3, X4) -> active# X1, active# s X -> active# X) (active# U31(X1, X2, X3, X4) -> active# X1, active# s X -> s# active X) (active# U31(X1, X2, X3, X4) -> active# X1, active# length X -> active# X) (active# U31(X1, X2, X3, X4) -> active# X1, active# length X -> length# active X) (active# U31(X1, X2, X3, X4) -> active# X1, active# length cons(N, L) -> U11#(and(isNatList L, isNat N), L)) (active# U31(X1, X2, X3, X4) -> active# X1, active# length cons(N, L) -> and#(isNatList L, isNat N)) (active# U31(X1, X2, X3, X4) -> active# X1, active# length cons(N, L) -> isNat# N) (active# U31(X1, X2, X3, X4) -> active# X1, active# length cons(N, L) -> isNatList# L) (active# U31(X1, X2, X3, X4) -> active# X1, active# U11(X1, X2) -> active# X1) (active# U31(X1, X2, X3, X4) -> active# X1, active# U11(X1, X2) -> U11#(active X1, X2)) (active# U31(X1, X2, X3, X4) -> active# X1, active# U11(tt(), L) -> s# length L) (active# U31(X1, X2, X3, X4) -> active# X1, active# U11(tt(), L) -> length# L) (active# U31(X1, X2, X3, X4) -> active# X1, active# U21 X -> active# X) (active# U31(X1, X2, X3, X4) -> active# X1, active# U21 X -> U21# active X) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(X1, X2) -> active# X1) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(X1, X2) -> active# X2) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(X1, X2) -> take#(X1, active X2)) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(X1, X2) -> take#(active X1, X2)) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(0(), IL) -> U21# isNatIList IL) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(0(), IL) -> isNatIList# IL) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N)) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N)) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, and(isNat M, isNat N))) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# N) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> isNat# M) (active# U31(X1, X2, X3, X4) -> active# X1, active# take(s M, cons(N, IL)) -> isNatIList# IL) (active# U31(X1, X2, X3, X4) -> active# X1, active# U31(X1, X2, X3, X4) -> active# X1) (active# U31(X1, X2, X3, X4) -> active# X1, active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4)) (active# U31(X1, X2, X3, X4) -> active# X1, active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL))) (active# U31(X1, X2, X3, X4) -> active# X1, active# U31(tt(), IL, M, N) -> take#(M, IL)) (active# U31(X1, X2, X3, X4) -> active# X1, active# and(X1, X2) -> active# X1) (active# U31(X1, X2, X3, X4) -> active# X1, active# and(X1, X2) -> and#(active X1, X2)) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNat s V1 -> isNat# V1) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNat length V1 -> isNatList# V1) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatList cons(V1, V2) -> and#(isNat V1, isNatList V2)) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatList cons(V1, V2) -> isNat# V1) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatList cons(V1, V2) -> isNatList# V2) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatList take(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatList take(V1, V2) -> isNat# V1) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatList take(V1, V2) -> isNatIList# V2) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatIList V -> isNatList# V) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatIList cons(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatIList cons(V1, V2) -> isNat# V1) (active# U31(X1, X2, X3, X4) -> active# X1, active# isNatIList cons(V1, V2) -> isNatIList# V2) (active# U11(X1, X2) -> active# X1, active# cons(X1, X2) -> cons#(active X1, X2)) (active# U11(X1, X2) -> active# X1, active# cons(X1, X2) -> active# X1) (active# U11(X1, X2) -> active# X1, active# zeros() -> cons#(0(), zeros())) (active# U11(X1, X2) -> active# X1, active# s X -> active# X) (active# U11(X1, X2) -> active# X1, active# s X -> s# active X) (active# U11(X1, X2) -> active# X1, active# length X -> active# X) (active# U11(X1, X2) -> active# X1, active# length X -> length# active X) (active# U11(X1, X2) -> active# X1, active# length cons(N, L) -> U11#(and(isNatList L, isNat N), L)) (active# U11(X1, X2) -> active# X1, active# length 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-> proper# X2, proper# isNatIList X -> proper# X) (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# s X -> active# X) (top# ok X -> active# X, active# s X -> s# active X) (top# ok X -> active# X, active# length X -> active# X) (top# ok X -> active# X, active# length X -> length# active X) (top# ok X -> active# X, active# length cons(N, L) -> U11#(and(isNatList L, isNat N), L)) (top# ok X -> active# X, active# length cons(N, L) -> and#(isNatList L, isNat N)) (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# U11(X1, X2) -> active# X1) (top# ok X -> active# X, active# U11(X1, X2) -> U11#(active X1, X2)) (top# ok X -> active# X, active# U11(tt(), L) -> s# length L) (top# ok X -> active# X, active# U11(tt(), L) -> length# L) (top# ok X -> active# X, active# U21 X -> active# X) (top# ok X -> active# X, active# U21 X -> U21# active X) (top# ok X -> active# X, active# take(X1, X2) -> active# X1) (top# ok X -> active# X, active# take(X1, X2) -> active# X2) (top# ok X -> active# X, active# take(X1, X2) -> take#(X1, active X2)) (top# ok X -> active# X, active# take(X1, X2) -> take#(active X1, X2)) (top# ok X -> active# X, active# take(0(), IL) -> U21# isNatIList IL) (top# ok X -> active# X, active# take(0(), IL) -> isNatIList# IL) (top# ok X -> active# X, active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N)) (top# ok X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N)) (top# ok X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, and(isNat M, isNat N))) (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)) -> isNat# M) (top# ok X -> active# 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X -> proper# X, proper# length X -> proper# X) (proper# isNat X -> proper# X, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# isNat X -> proper# X, proper# U11(X1, X2) -> proper# X1) (proper# isNat X -> proper# X, proper# U11(X1, X2) -> proper# X2) (proper# isNat X -> proper# X, proper# U21 X -> U21# proper X) (proper# isNat X -> proper# X, proper# U21 X -> proper# X) (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# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# isNat X -> proper# X, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# isNat X -> proper# X, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# isNat X -> proper# X, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# isNat X -> proper# X, proper# U31(X1, X2, X3, X4) -> proper# X4) (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# isNat X -> isNat# proper X) (proper# isNat X -> proper# X, proper# isNat X -> proper# X) (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# 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# 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# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# length X -> proper# X, proper# U11(X1, X2) -> proper# X1) (proper# length X -> proper# X, proper# U11(X1, X2) -> proper# X2) (proper# length X -> proper# X, proper# U21 X -> U21# proper X) (proper# length X -> proper# X, proper# U21 X -> proper# X) (proper# length X -> proper# X, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# length X -> proper# X, proper# take(X1, X2) -> proper# X1) (proper# length X -> proper# X, proper# take(X1, X2) -> proper# X2) (proper# length X -> proper# X, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# length X -> proper# X, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# length X -> proper# X, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# length X -> proper# X, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# length X -> proper# X, proper# U31(X1, X2, X3, X4) -> proper# X4) (proper# length X -> proper# X, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# length X -> proper# X, proper# and(X1, X2) -> proper# X1) (proper# length X -> proper# X, proper# and(X1, X2) -> proper# X2) (proper# length X -> proper# X, proper# isNat X -> isNat# proper X) (proper# length X -> proper# X, proper# isNat X -> proper# X) (proper# length X -> proper# X, proper# isNatList X -> isNatList# proper X) (proper# length X -> proper# X, proper# isNatList X -> proper# X) (proper# length X -> proper# X, proper# isNatIList X -> isNatIList# proper X) (proper# length X -> proper# X, proper# isNatIList X -> proper# X) (isNatIList# ok X -> isNatIList# X, isNatIList# ok X -> isNatIList# X) (isNat# ok X -> isNat# X, isNat# ok X -> isNat# X) (U21# mark X -> U21# X, U21# mark X -> U21# X) (U21# mark X -> U21# X, U21# ok X -> U21# 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) (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# s X -> active# X) (active# length X -> active# X, active# s X -> s# active X) (active# length X -> active# X, active# length X -> active# X) (active# length X -> active# X, active# length X -> length# active X) (active# length X -> active# X, active# length cons(N, L) -> U11#(and(isNatList L, isNat N), L)) (active# length X -> active# X, active# length cons(N, L) -> and#(isNatList L, isNat N)) (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# U11(X1, X2) -> active# X1) (active# length X -> active# X, active# U11(X1, X2) -> U11#(active X1, X2)) (active# length X -> active# X, active# U11(tt(), L) -> s# length L) (active# length X -> active# X, active# U11(tt(), L) -> length# L) (active# length X -> active# X, active# U21 X -> active# X) (active# length X -> active# X, active# U21 X -> U21# active X) (active# length X -> active# X, active# take(X1, X2) -> active# X1) (active# length X -> active# X, active# take(X1, X2) -> active# X2) (active# length X -> active# X, active# take(X1, X2) -> take#(X1, active X2)) (active# length X -> active# X, active# take(X1, X2) -> take#(active X1, X2)) (active# length X -> active# X, active# take(0(), IL) -> U21# isNatIList IL) (active# length X -> active# X, active# take(0(), IL) -> isNatIList# IL) (active# length X -> active# X, active# take(s M, cons(N, IL)) -> U31#(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N)) (active# length X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNat M, isNat N)) (active# length X -> active# X, active# take(s M, cons(N, IL)) -> and#(isNatIList IL, and(isNat M, isNat N))) (active# length X -> active# X, active# take(s M, cons(N, IL)) -> isNat# N) (active# length X -> active# X, active# take(s M, cons(N, IL)) -> isNat# M) (active# length X -> active# X, active# take(s M, cons(N, IL)) -> isNatIList# IL) (active# length X -> active# X, active# U31(X1, X2, X3, X4) -> active# X1) (active# length X -> active# X, active# U31(X1, X2, X3, X4) -> U31#(active X1, X2, X3, X4)) (active# length X -> active# X, active# U31(tt(), IL, M, N) -> cons#(N, take(M, IL))) (active# length X -> active# X, active# U31(tt(), IL, M, N) -> take#(M, IL)) (active# length X -> active# X, active# and(X1, X2) -> active# X1) (active# length X -> active# X, active# and(X1, X2) -> and#(active X1, X2)) (active# length X -> active# X, active# isNat s V1 -> isNat# V1) (active# length X -> active# X, active# isNat length V1 -> isNatList# V1) (active# length X -> active# X, active# isNatList cons(V1, V2) -> and#(isNat V1, isNatList V2)) (active# length X -> active# X, active# isNatList cons(V1, V2) -> isNat# V1) (active# length X -> active# X, active# isNatList cons(V1, V2) -> isNatList# V2) (active# length X -> active# X, active# isNatList take(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# length X -> active# X, active# isNatList take(V1, V2) -> isNat# V1) (active# length X -> active# X, active# isNatList take(V1, V2) -> isNatIList# V2) (active# length X -> active# X, active# isNatIList V -> isNatList# V) (active# length X -> active# X, active# isNatIList cons(V1, V2) -> and#(isNat V1, isNatIList V2)) (active# length X -> active# X, active# isNatIList cons(V1, V2) -> isNat# V1) (active# length X -> active# X, active# isNatIList cons(V1, V2) -> isNatIList# V2) (and#(ok X1, ok X2) -> and#(X1, X2), and#(mark X1, X2) -> and#(X1, X2)) (and#(ok X1, ok X2) -> and#(X1, X2), and#(ok X1, ok X2) -> and#(X1, X2)) (take#(ok X1, ok X2) -> take#(X1, X2), take#(X1, mark X2) -> take#(X1, X2)) (take#(ok X1, ok X2) -> take#(X1, X2), take#(mark X1, X2) -> take#(X1, X2)) (take#(ok X1, ok X2) -> take#(X1, X2), take#(ok X1, ok X2) -> take#(X1, X2)) (take#(X1, mark X2) -> take#(X1, X2), take#(X1, mark X2) -> take#(X1, X2)) (take#(X1, mark X2) -> take#(X1, X2), take#(mark X1, X2) -> take#(X1, X2)) (take#(X1, mark X2) -> take#(X1, X2), take#(ok X1, ok X2) -> take#(X1, X2)) (U11#(mark X1, X2) -> U11#(X1, X2), U11#(mark X1, X2) -> U11#(X1, X2)) (U11#(mark X1, X2) -> U11#(X1, X2), U11#(ok X1, ok X2) -> U11#(X1, X2)) (cons#(mark X1, X2) -> cons#(X1, X2), cons#(mark X1, X2) -> cons#(X1, X2)) (cons#(mark X1, X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)) (U31#(mark X1, X2, X3, X4) -> U31#(X1, X2, X3, X4), U31#(mark X1, X2, X3, X4) -> U31#(X1, X2, X3, X4)) (U31#(mark X1, X2, X3, X4) -> U31#(X1, X2, X3, X4), U31#(ok X1, ok X2, ok X3, ok X4) -> U31#(X1, X2, X3, X4)) (active# and(X1, X2) -> and#(active X1, X2), and#(mark X1, X2) -> and#(X1, X2)) (active# and(X1, X2) -> and#(active X1, X2), and#(ok X1, ok X2) -> and#(X1, X2)) (active# U11(X1, X2) -> U11#(active X1, X2), U11#(mark X1, X2) -> U11#(X1, X2)) (active# U11(X1, X2) -> U11#(active X1, X2), U11#(ok X1, ok X2) -> U11#(X1, X2)) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# cons(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# cons(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# s X -> s# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# s X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# length X -> length# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# length X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# U11(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# U11(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# U21 X -> U21# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# U21 X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# take(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# take(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# U31(X1, X2, X3, X4) -> proper# X4) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# and(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# and(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# isNat X -> isNat# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# isNat X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# isNatList X -> isNatList# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# isNatList X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# isNatIList X -> isNatIList# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X3, proper# isNatIList X -> proper# X) (active# isNatIList cons(V1, V2) -> isNat# V1, isNat# ok X -> isNat# X) (active# isNatList cons(V1, V2) -> isNat# V1, isNat# ok X -> isNat# X) (active# isNat s V1 -> isNat# V1, isNat# ok X -> isNat# X) (active# length cons(N, L) -> isNatList# L, isNatList# ok X -> isNatList# X) (active# take(0(), IL) -> U21# isNatIList IL, U21# ok X -> U21# 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# isNatList X -> isNatList# proper X, isNatList# ok X -> isNatList# X) (proper# U21 X -> U21# proper X, U21# mark X -> U21# X) (proper# U21 X -> U21# proper X, U21# ok X -> U21# X) (proper# s X -> s# proper X, s# mark X -> s# X) (proper# s X -> s# proper X, s# ok X -> s# X) (active# length X -> length# active X, length# mark X -> length# X) (active# length X -> length# active X, length# ok X -> length# X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# cons(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# cons(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# s X -> s# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# s X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# length X -> length# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# length X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U11(X1, X2) -> U11#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U11(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U11(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U21 X -> U21# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U21 X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# take(X1, X2) -> take#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# take(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# take(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U31(X1, X2, X3, X4) -> U31#(proper X1, proper X2, proper X3, proper X4)) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U31(X1, X2, X3, X4) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U31(X1, X2, X3, X4) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U31(X1, X2, X3, X4) -> proper# X3) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# U31(X1, X2, X3, X4) -> proper# X4) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# and(X1, X2) -> and#(proper X1, proper X2)) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# and(X1, X2) -> proper# X1) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# and(X1, X2) -> proper# X2) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# isNat X -> isNat# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# isNat X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# isNatList X -> isNatList# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# isNatList X -> proper# X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# isNatIList X -> isNatIList# proper X) (proper# U31(X1, X2, X3, X4) -> proper# X4, proper# isNatIList X -> proper# X) (active# isNatIList V -> isNatList# V, isNatList# ok X -> isNatList# X) (active# length cons(N, L) -> isNat# N, isNat# ok X -> isNat# X) } STATUS: arrows: 0.885800 SCCS (14): Scc: {top# mark X -> top# proper X, top# ok X -> top# active X} Scc: { active# cons(X1, X2) -> active# X1, active# s X -> active# X, active# length X -> active# X, active# U11(X1, X2) -> active# X1, active# U21 X -> active# X, active# take(X1, X2) -> active# X1, active# take(X1, X2) -> active# X2, active# U31(X1, X2, X3, X4) -> active# X1, active# and(X1, X2) -> active# X1} Scc: { proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# s X -> proper# X, proper# length X -> proper# X, proper# U11(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X2, proper# U21 X -> proper# X, proper# take(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X3, proper# U31(X1, X2, X3, X4) -> proper# X4, proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2, proper# isNat X -> proper# X, proper# isNatList X -> proper# X, proper# isNatIList X -> proper# X} Scc: {isNatIList# ok X -> isNatIList# X} Scc: { and#(mark X1, X2) -> and#(X1, X2), and#(ok X1, ok X2) -> and#(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: {U21# mark X -> U21# X, U21# ok X -> U21# X} Scc: { U11#(mark X1, X2) -> U11#(X1, X2), U11#(ok X1, ok X2) -> U11#(X1, X2)} Scc: {length# mark X -> length# X, length# ok X -> length# X} Scc: {s# mark X -> s# X, s# ok X -> s# X} Scc: { cons#(mark X1, X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)} Scc: { U31#(mark X1, X2, X3, X4) -> U31#(X1, X2, X3, X4), U31#(ok X1, ok X2, ok X3, ok X4) -> U31#(X1, X2, X3, X4)} Scc: {isNatList# ok X -> isNatList# X} Scc: {isNat# ok X -> isNat# X} SCC (2): Strict: {top# mark X -> top# proper X, top# ok X -> top# active X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U11(and(isNatList L, isNat N), L), active length nil() -> mark 0(), active U11(X1, X2) -> U11(active X1, X2), active U11(tt(), L) -> mark s length L, active U21 X -> U21 active X, active U21 tt() -> mark nil(), active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(0(), IL) -> mark U21 isNatIList IL, active take(s M, cons(N, IL)) -> mark U31(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N), active U31(X1, X2, X3, X4) -> U31(active X1, X2, X3, X4), active U31(tt(), IL, M, N) -> mark cons(N, take(M, IL)), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active isNat 0() -> mark tt(), active isNat s V1 -> mark isNat V1, active isNat length V1 -> mark isNatList V1, active isNatList cons(V1, V2) -> mark and(isNat V1, isNatList V2), active isNatList nil() -> mark tt(), active isNatList take(V1, V2) -> mark and(isNat V1, isNatIList V2), active isNatIList V -> mark isNatList V, active isNatIList cons(V1, V2) -> mark and(isNat V1, isNatIList V2), active isNatIList zeros() -> mark tt(), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, U11(mark X1, X2) -> mark U11(X1, X2), U11(ok X1, ok X2) -> ok U11(X1, X2), U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(X1, X2), U31(mark X1, X2, X3, X4) -> mark U31(X1, X2, X3, X4), U31(ok X1, ok X2, ok X3, ok X4) -> ok U31(X1, X2, X3, X4), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), isNat ok X -> ok isNat X, isNatList ok X -> ok isNatList X, isNatIList ok X -> ok isNatIList X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper s X -> s proper X, proper length X -> length proper X, proper U11(X1, X2) -> U11(proper X1, proper X2), proper tt() -> ok tt(), proper nil() -> ok nil(), proper U21 X -> U21 proper X, proper take(X1, X2) -> take(proper X1, proper X2), proper U31(X1, X2, X3, X4) -> U31(proper X1, proper X2, proper X3, proper X4), proper and(X1, X2) -> and(proper X1, proper X2), proper isNat X -> isNat proper X, proper isNatList X -> isNatList proper X, proper isNatIList X -> isNatIList proper X, top mark X -> top proper X, top ok X -> top active X} Open SCC (9): Strict: { active# cons(X1, X2) -> active# X1, active# s X -> active# X, active# length X -> active# X, active# U11(X1, X2) -> active# X1, active# U21 X -> active# X, active# take(X1, X2) -> active# X1, active# take(X1, X2) -> active# X2, active# U31(X1, X2, X3, X4) -> active# X1, active# and(X1, X2) -> active# X1} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U11(and(isNatList L, isNat N), L), active length nil() -> mark 0(), active U11(X1, X2) -> U11(active X1, X2), active U11(tt(), L) -> mark s length L, active U21 X -> U21 active X, active U21 tt() -> mark nil(), active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(0(), IL) -> mark U21 isNatIList IL, active take(s M, cons(N, IL)) -> mark U31(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N), active U31(X1, X2, X3, X4) -> U31(active X1, X2, X3, X4), active U31(tt(), IL, M, N) -> mark cons(N, take(M, IL)), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active isNat 0() -> mark tt(), active isNat s V1 -> mark isNat V1, active isNat length V1 -> mark isNatList V1, active isNatList cons(V1, V2) -> mark and(isNat V1, isNatList V2), active isNatList nil() -> mark tt(), active isNatList take(V1, V2) -> mark and(isNat V1, isNatIList V2), active isNatIList V -> mark isNatList V, active isNatIList cons(V1, V2) -> mark and(isNat V1, isNatIList V2), active isNatIList zeros() -> mark tt(), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, U11(mark X1, X2) -> mark U11(X1, X2), U11(ok X1, ok X2) -> ok U11(X1, X2), U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(X1, X2), U31(mark X1, X2, X3, X4) -> mark U31(X1, X2, X3, X4), U31(ok X1, ok X2, ok X3, ok X4) -> ok U31(X1, X2, X3, X4), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), isNat ok X -> ok isNat X, isNatList ok X -> ok isNatList X, isNatIList ok X -> ok isNatIList X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper s X -> s proper X, proper length X -> length proper X, proper U11(X1, X2) -> U11(proper X1, proper X2), proper tt() -> ok tt(), proper nil() -> ok nil(), proper U21 X -> U21 proper X, proper take(X1, X2) -> take(proper X1, proper X2), proper U31(X1, X2, X3, X4) -> U31(proper X1, proper X2, proper X3, proper X4), proper and(X1, X2) -> and(proper X1, proper X2), proper isNat X -> isNat proper X, proper isNatList X -> isNatList proper X, proper isNatIList X -> isNatIList proper X, top mark X -> top proper X, top ok X -> top active X} Open SCC (18): Strict: { proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# s X -> proper# X, proper# length X -> proper# X, proper# U11(X1, X2) -> proper# X1, proper# U11(X1, X2) -> proper# X2, proper# U21 X -> proper# X, proper# take(X1, X2) -> proper# X1, proper# take(X1, X2) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X1, proper# U31(X1, X2, X3, X4) -> proper# X2, proper# U31(X1, X2, X3, X4) -> proper# X3, proper# U31(X1, X2, X3, X4) -> proper# X4, proper# and(X1, X2) -> proper# X1, proper# and(X1, X2) -> proper# X2, proper# isNat X -> proper# X, proper# isNatList X -> proper# X, proper# isNatIList X -> proper# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U11(and(isNatList L, isNat N), L), active length nil() -> mark 0(), active U11(X1, X2) -> U11(active X1, X2), active U11(tt(), L) -> mark s length L, active U21 X -> U21 active X, active U21 tt() -> mark nil(), active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(0(), IL) -> mark U21 isNatIList IL, active take(s M, cons(N, IL)) -> mark U31(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N), active U31(X1, X2, X3, X4) -> U31(active X1, X2, X3, X4), active U31(tt(), IL, M, N) -> mark cons(N, take(M, IL)), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active isNat 0() -> mark tt(), active isNat s V1 -> mark isNat V1, active isNat length V1 -> mark isNatList V1, active isNatList cons(V1, V2) -> mark and(isNat V1, isNatList V2), active isNatList nil() -> mark tt(), active isNatList take(V1, V2) -> mark and(isNat V1, isNatIList V2), active isNatIList V -> mark isNatList V, active isNatIList cons(V1, V2) -> mark and(isNat V1, isNatIList V2), active isNatIList zeros() -> mark tt(), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, U11(mark X1, X2) -> mark U11(X1, X2), U11(ok X1, ok X2) -> ok U11(X1, X2), U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(X1, X2), U31(mark X1, X2, X3, X4) -> mark U31(X1, X2, X3, X4), U31(ok X1, ok X2, ok X3, ok X4) -> ok U31(X1, X2, X3, X4), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), isNat ok X -> ok isNat X, isNatList ok X -> ok isNatList X, isNatIList ok X -> ok isNatIList X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper s X -> s proper X, proper length X -> length proper X, proper U11(X1, X2) -> U11(proper X1, proper X2), proper tt() -> ok tt(), proper nil() -> ok nil(), proper U21 X -> U21 proper X, proper take(X1, X2) -> take(proper X1, proper X2), proper U31(X1, X2, X3, X4) -> U31(proper X1, proper X2, proper X3, proper X4), proper and(X1, X2) -> and(proper X1, proper X2), proper isNat X -> isNat proper X, proper isNatList X -> isNatList proper X, proper isNatIList X -> isNatIList proper X, top mark X -> top proper X, top ok X -> top active X} Open SCC (1): Strict: {isNatIList# ok X -> isNatIList# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U11(and(isNatList L, isNat N), L), active length nil() -> mark 0(), active U11(X1, X2) -> U11(active X1, X2), active U11(tt(), L) -> mark s length L, active U21 X -> U21 active X, active U21 tt() -> mark nil(), active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(0(), IL) -> mark U21 isNatIList IL, active take(s M, cons(N, IL)) -> mark U31(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N), active U31(X1, X2, X3, X4) -> U31(active X1, X2, X3, X4), active U31(tt(), IL, M, N) -> mark cons(N, take(M, IL)), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active isNat 0() -> mark tt(), active isNat s V1 -> mark isNat V1, active isNat length V1 -> mark isNatList V1, active isNatList cons(V1, V2) -> mark and(isNat V1, isNatList V2), active isNatList nil() -> mark tt(), active isNatList take(V1, V2) -> mark and(isNat V1, isNatIList V2), active isNatIList V -> mark isNatList V, active isNatIList cons(V1, V2) -> mark and(isNat V1, isNatIList V2), active isNatIList zeros() -> mark tt(), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, U11(mark X1, X2) -> mark U11(X1, X2), U11(ok X1, ok X2) -> ok U11(X1, X2), U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(X1, X2), U31(mark X1, X2, X3, X4) -> mark U31(X1, X2, X3, X4), U31(ok X1, ok X2, ok X3, ok X4) -> ok U31(X1, X2, X3, X4), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), isNat ok X -> ok isNat X, isNatList ok X -> ok isNatList X, isNatIList ok X -> ok isNatIList X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper s X -> s proper X, proper length X -> length proper X, proper U11(X1, X2) -> U11(proper X1, proper X2), proper tt() -> ok tt(), proper nil() -> ok nil(), proper U21 X -> U21 proper X, proper take(X1, X2) -> take(proper X1, proper X2), proper U31(X1, X2, X3, X4) -> U31(proper X1, proper X2, proper X3, proper X4), proper and(X1, X2) -> and(proper X1, proper X2), proper isNat X -> isNat proper X, proper isNatList X -> isNatList proper X, proper isNatIList X -> isNatIList proper X, top mark X -> top proper X, top ok X -> top active X} Open SCC (2): Strict: { and#(mark X1, X2) -> and#(X1, X2), and#(ok X1, ok X2) -> and#(X1, X2)} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U11(and(isNatList L, isNat N), L), active length nil() -> mark 0(), active U11(X1, X2) -> U11(active X1, X2), active U11(tt(), L) -> mark s length L, active U21 X -> U21 active X, active U21 tt() -> mark nil(), active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(0(), IL) -> mark U21 isNatIList IL, active take(s M, cons(N, IL)) -> mark U31(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N), active U31(X1, X2, X3, X4) -> U31(active X1, X2, X3, X4), active U31(tt(), IL, M, N) -> mark cons(N, take(M, IL)), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active isNat 0() -> mark tt(), active isNat s V1 -> mark isNat V1, active isNat length V1 -> mark isNatList V1, active isNatList cons(V1, V2) -> mark and(isNat V1, isNatList V2), active isNatList nil() -> mark tt(), active isNatList take(V1, V2) -> mark and(isNat V1, isNatIList V2), active isNatIList V -> mark isNatList V, active isNatIList cons(V1, V2) -> mark and(isNat V1, isNatIList V2), active isNatIList zeros() -> mark tt(), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, U11(mark X1, X2) -> mark U11(X1, X2), U11(ok X1, ok X2) -> ok U11(X1, X2), U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(X1, X2), U31(mark X1, X2, X3, X4) -> mark U31(X1, X2, X3, X4), U31(ok X1, ok X2, ok X3, ok X4) -> ok U31(X1, X2, X3, X4), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), isNat ok X -> ok isNat X, isNatList ok X -> ok isNatList X, isNatIList ok X -> ok isNatIList X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper s X -> s proper X, proper length X -> length proper X, proper U11(X1, X2) -> U11(proper X1, proper X2), proper tt() -> ok tt(), proper nil() -> ok nil(), proper U21 X -> U21 proper X, proper take(X1, X2) -> take(proper X1, proper X2), proper U31(X1, X2, X3, X4) -> U31(proper X1, proper X2, proper X3, proper X4), proper and(X1, X2) -> and(proper X1, proper X2), proper isNat X -> isNat proper X, proper isNatList X -> isNatList proper X, proper isNatIList X -> isNatIList proper X, top mark X -> top proper X, top ok X -> top active X} Open SCC (3): Strict: { take#(X1, mark X2) -> take#(X1, X2), take#(mark X1, X2) -> take#(X1, X2), take#(ok X1, ok X2) -> take#(X1, X2)} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U11(and(isNatList L, isNat N), L), active length nil() -> mark 0(), active U11(X1, X2) -> U11(active X1, X2), active U11(tt(), L) -> mark s length L, active U21 X -> U21 active X, active U21 tt() -> mark nil(), active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(0(), IL) -> mark U21 isNatIList IL, active take(s M, cons(N, IL)) -> mark U31(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N), active U31(X1, X2, X3, X4) -> U31(active X1, X2, X3, X4), active U31(tt(), IL, M, N) -> mark cons(N, take(M, IL)), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active isNat 0() -> mark tt(), active isNat s V1 -> mark isNat V1, active isNat length V1 -> mark isNatList V1, active isNatList cons(V1, V2) -> mark and(isNat V1, isNatList V2), active isNatList nil() -> mark tt(), active isNatList take(V1, V2) -> mark and(isNat V1, isNatIList V2), active isNatIList V -> mark isNatList V, active isNatIList cons(V1, V2) -> mark and(isNat V1, isNatIList V2), active isNatIList zeros() -> mark tt(), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, U11(mark X1, X2) -> mark U11(X1, X2), U11(ok X1, ok X2) -> ok U11(X1, X2), U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(X1, X2), U31(mark X1, X2, X3, X4) -> mark U31(X1, X2, X3, X4), U31(ok X1, ok X2, ok X3, ok X4) -> ok U31(X1, X2, X3, X4), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), isNat ok X -> ok isNat X, isNatList ok X -> ok isNatList X, isNatIList ok X -> ok isNatIList X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper s X -> s proper X, proper length X -> length proper X, proper U11(X1, X2) -> U11(proper X1, proper X2), proper tt() -> ok tt(), proper nil() -> ok nil(), proper U21 X -> U21 proper X, proper take(X1, X2) -> take(proper X1, proper X2), proper U31(X1, X2, X3, X4) -> U31(proper X1, proper X2, proper X3, proper X4), proper and(X1, X2) -> and(proper X1, proper X2), proper isNat X -> isNat proper X, proper isNatList X -> isNatList proper X, proper isNatIList X -> isNatIList proper X, top mark X -> top proper X, top ok X -> top active X} Open SCC (2): Strict: {U21# mark X -> U21# X, U21# ok X -> U21# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U11(and(isNatList L, isNat N), L), active length nil() -> mark 0(), active U11(X1, X2) -> U11(active X1, X2), active U11(tt(), L) -> mark s length L, active U21 X -> U21 active X, active U21 tt() -> mark nil(), active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(0(), IL) -> mark U21 isNatIList IL, active take(s M, cons(N, IL)) -> mark U31(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N), active U31(X1, X2, X3, X4) -> U31(active X1, X2, X3, X4), active U31(tt(), IL, M, N) -> mark cons(N, take(M, IL)), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active isNat 0() -> mark tt(), active isNat s V1 -> mark isNat V1, active isNat length V1 -> mark isNatList V1, active isNatList cons(V1, V2) -> mark and(isNat V1, isNatList V2), active isNatList nil() -> mark tt(), active isNatList take(V1, V2) -> mark and(isNat V1, isNatIList V2), active isNatIList V -> mark isNatList V, active isNatIList cons(V1, V2) -> mark and(isNat V1, isNatIList V2), active isNatIList zeros() -> mark tt(), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, U11(mark X1, X2) -> mark U11(X1, X2), U11(ok X1, ok X2) -> ok U11(X1, X2), U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(X1, X2), U31(mark X1, X2, X3, X4) -> mark U31(X1, X2, X3, X4), U31(ok X1, ok X2, ok X3, ok X4) -> ok U31(X1, X2, X3, X4), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), isNat ok X -> ok isNat X, isNatList ok X -> ok isNatList X, isNatIList ok X -> ok isNatIList X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper s X -> s proper X, proper length X -> length proper X, proper U11(X1, X2) -> U11(proper X1, proper X2), proper tt() -> ok tt(), proper nil() -> ok nil(), proper U21 X -> U21 proper X, proper take(X1, X2) -> take(proper X1, proper X2), proper U31(X1, X2, X3, X4) -> U31(proper X1, proper X2, proper X3, proper X4), proper and(X1, X2) -> and(proper X1, proper X2), proper isNat X -> isNat proper X, proper isNatList X -> isNatList proper X, proper isNatIList X -> isNatIList proper X, top mark X -> top proper X, top ok X -> top active X} Open SCC (2): Strict: { U11#(mark X1, X2) -> U11#(X1, X2), U11#(ok X1, ok X2) -> U11#(X1, X2)} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U11(and(isNatList L, isNat N), L), active length nil() -> mark 0(), active U11(X1, X2) -> U11(active X1, X2), active U11(tt(), L) -> mark s length L, active U21 X -> U21 active X, active U21 tt() -> mark nil(), active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(0(), IL) -> mark U21 isNatIList IL, active take(s M, cons(N, IL)) -> mark U31(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N), active U31(X1, X2, X3, X4) -> U31(active X1, X2, X3, X4), active U31(tt(), IL, M, N) -> mark cons(N, take(M, IL)), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active isNat 0() -> mark tt(), active isNat s V1 -> mark isNat V1, active isNat length V1 -> mark isNatList V1, active isNatList cons(V1, V2) -> mark and(isNat V1, isNatList V2), active isNatList nil() -> mark tt(), active isNatList take(V1, V2) -> mark and(isNat V1, isNatIList V2), active isNatIList V -> mark isNatList V, active isNatIList cons(V1, V2) -> mark and(isNat V1, isNatIList V2), active isNatIList zeros() -> mark tt(), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, U11(mark X1, X2) -> mark U11(X1, X2), U11(ok X1, ok X2) -> ok U11(X1, X2), U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(X1, X2), U31(mark X1, X2, X3, X4) -> mark U31(X1, X2, X3, X4), U31(ok X1, ok X2, ok X3, ok X4) -> ok U31(X1, X2, X3, X4), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), isNat ok X -> ok isNat X, isNatList ok X -> ok isNatList X, isNatIList ok X -> ok isNatIList X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper s X -> s proper X, proper length X -> length proper X, proper U11(X1, X2) -> U11(proper X1, proper X2), proper tt() -> ok tt(), proper nil() -> ok nil(), proper U21 X -> U21 proper X, proper take(X1, X2) -> take(proper X1, proper X2), proper U31(X1, X2, X3, X4) -> U31(proper X1, proper X2, proper X3, proper X4), proper and(X1, X2) -> and(proper X1, proper X2), proper isNat X -> isNat proper X, proper isNatList X -> isNatList proper X, proper isNatIList X -> isNatIList proper X, top mark X -> top proper X, top ok X -> top active X} Open SCC (2): Strict: {length# mark X -> length# X, length# ok X -> length# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U11(and(isNatList L, isNat N), L), active length nil() -> mark 0(), active U11(X1, X2) -> U11(active X1, X2), active U11(tt(), L) -> mark s length L, active U21 X -> U21 active X, active U21 tt() -> mark nil(), active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(0(), IL) -> mark U21 isNatIList IL, active take(s M, cons(N, IL)) -> mark U31(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N), active U31(X1, X2, X3, X4) -> U31(active X1, X2, X3, X4), active U31(tt(), IL, M, N) -> mark cons(N, take(M, IL)), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active isNat 0() -> mark tt(), active isNat s V1 -> mark isNat V1, active isNat length V1 -> mark isNatList V1, active isNatList cons(V1, V2) -> mark and(isNat V1, isNatList V2), active isNatList nil() -> mark tt(), active isNatList take(V1, V2) -> mark and(isNat V1, isNatIList V2), active isNatIList V -> mark isNatList V, active isNatIList cons(V1, V2) -> mark and(isNat V1, isNatIList V2), active isNatIList zeros() -> mark tt(), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, U11(mark X1, X2) -> mark U11(X1, X2), U11(ok X1, ok X2) -> ok U11(X1, X2), U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(X1, X2), U31(mark X1, X2, X3, X4) -> mark U31(X1, X2, X3, X4), U31(ok X1, ok X2, ok X3, ok X4) -> ok U31(X1, X2, X3, X4), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), isNat ok X -> ok isNat X, isNatList ok X -> ok isNatList X, isNatIList ok X -> ok isNatIList X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper s X -> s proper X, proper length X -> length proper X, proper U11(X1, X2) -> U11(proper X1, proper X2), proper tt() -> ok tt(), proper nil() -> ok nil(), proper U21 X -> U21 proper X, proper take(X1, X2) -> take(proper X1, proper X2), proper U31(X1, X2, X3, X4) -> U31(proper X1, proper X2, proper X3, proper X4), proper and(X1, X2) -> and(proper X1, proper X2), proper isNat X -> isNat proper X, proper isNatList X -> isNatList proper X, proper isNatIList X -> isNatIList proper X, top mark X -> top proper X, top ok X -> top active X} Open SCC (2): Strict: {s# mark X -> s# X, s# ok X -> s# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U11(and(isNatList L, isNat N), L), active length nil() -> mark 0(), active U11(X1, X2) -> U11(active X1, X2), active U11(tt(), L) -> mark s length L, active U21 X -> U21 active X, active U21 tt() -> mark nil(), active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(0(), IL) -> mark U21 isNatIList IL, active take(s M, cons(N, IL)) -> mark U31(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N), active U31(X1, X2, X3, X4) -> U31(active X1, X2, X3, X4), active U31(tt(), IL, M, N) -> mark cons(N, take(M, IL)), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active isNat 0() -> mark tt(), active isNat s V1 -> mark isNat V1, active isNat length V1 -> mark isNatList V1, active isNatList cons(V1, V2) -> mark and(isNat V1, isNatList V2), active isNatList nil() -> mark tt(), active isNatList take(V1, V2) -> mark and(isNat V1, isNatIList V2), active isNatIList V -> mark isNatList V, active isNatIList cons(V1, V2) -> mark and(isNat V1, isNatIList V2), active isNatIList zeros() -> mark tt(), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, U11(mark X1, X2) -> mark U11(X1, X2), U11(ok X1, ok X2) -> ok U11(X1, X2), U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(X1, X2), U31(mark X1, X2, X3, X4) -> mark U31(X1, X2, X3, X4), U31(ok X1, ok X2, ok X3, ok X4) -> ok U31(X1, X2, X3, X4), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), isNat ok X -> ok isNat X, isNatList ok X -> ok isNatList X, isNatIList ok X -> ok isNatIList X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper s X -> s proper X, proper length X -> length proper X, proper U11(X1, X2) -> U11(proper X1, proper X2), proper tt() -> ok tt(), proper nil() -> ok nil(), proper U21 X -> U21 proper X, proper take(X1, X2) -> take(proper X1, proper X2), proper U31(X1, X2, X3, X4) -> U31(proper X1, proper X2, proper X3, proper X4), proper and(X1, X2) -> and(proper X1, proper X2), proper isNat X -> isNat proper X, proper isNatList X -> isNatList proper X, proper isNatIList X -> isNatIList proper X, top mark X -> top proper X, top ok X -> top active X} Open SCC (2): Strict: { cons#(mark X1, X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U11(and(isNatList L, isNat N), L), active length nil() -> mark 0(), active U11(X1, X2) -> U11(active X1, X2), active U11(tt(), L) -> mark s length L, active U21 X -> U21 active X, active U21 tt() -> mark nil(), active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(0(), IL) -> mark U21 isNatIList IL, active take(s M, cons(N, IL)) -> mark U31(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N), active U31(X1, X2, X3, X4) -> U31(active X1, X2, X3, X4), active U31(tt(), IL, M, N) -> mark cons(N, take(M, IL)), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active isNat 0() -> mark tt(), active isNat s V1 -> mark isNat V1, active isNat length V1 -> mark isNatList V1, active isNatList cons(V1, V2) -> mark and(isNat V1, isNatList V2), active isNatList nil() -> mark tt(), active isNatList take(V1, V2) -> mark and(isNat V1, isNatIList V2), active isNatIList V -> mark isNatList V, active isNatIList cons(V1, V2) -> mark and(isNat V1, isNatIList V2), active isNatIList zeros() -> mark tt(), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, U11(mark X1, X2) -> mark U11(X1, X2), U11(ok X1, ok X2) -> ok U11(X1, X2), U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(X1, X2), U31(mark X1, X2, X3, X4) -> mark U31(X1, X2, X3, X4), U31(ok X1, ok X2, ok X3, ok X4) -> ok U31(X1, X2, X3, X4), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), isNat ok X -> ok isNat X, isNatList ok X -> ok isNatList X, isNatIList ok X -> ok isNatIList X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper s X -> s proper X, proper length X -> length proper X, proper U11(X1, X2) -> U11(proper X1, proper X2), proper tt() -> ok tt(), proper nil() -> ok nil(), proper U21 X -> U21 proper X, proper take(X1, X2) -> take(proper X1, proper X2), proper U31(X1, X2, X3, X4) -> U31(proper X1, proper X2, proper X3, proper X4), proper and(X1, X2) -> and(proper X1, proper X2), proper isNat X -> isNat proper X, proper isNatList X -> isNatList proper X, proper isNatIList X -> isNatIList proper X, top mark X -> top proper X, top ok X -> top active X} Open SCC (2): Strict: { U31#(mark X1, X2, X3, X4) -> U31#(X1, X2, X3, X4), U31#(ok X1, ok X2, ok X3, ok X4) -> U31#(X1, X2, X3, X4)} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U11(and(isNatList L, isNat N), L), active length nil() -> mark 0(), active U11(X1, X2) -> U11(active X1, X2), active U11(tt(), L) -> mark s length L, active U21 X -> U21 active X, active U21 tt() -> mark nil(), active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(0(), IL) -> mark U21 isNatIList IL, active take(s M, cons(N, IL)) -> mark U31(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N), active U31(X1, X2, X3, X4) -> U31(active X1, X2, X3, X4), active U31(tt(), IL, M, N) -> mark cons(N, take(M, IL)), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active isNat 0() -> mark tt(), active isNat s V1 -> mark isNat V1, active isNat length V1 -> mark isNatList V1, active isNatList cons(V1, V2) -> mark and(isNat V1, isNatList V2), active isNatList nil() -> mark tt(), active isNatList take(V1, V2) -> mark and(isNat V1, isNatIList V2), active isNatIList V -> mark isNatList V, active isNatIList cons(V1, V2) -> mark and(isNat V1, isNatIList V2), active isNatIList zeros() -> mark tt(), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, U11(mark X1, X2) -> mark U11(X1, X2), U11(ok X1, ok X2) -> ok U11(X1, X2), U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(X1, X2), U31(mark X1, X2, X3, X4) -> mark U31(X1, X2, X3, X4), U31(ok X1, ok X2, ok X3, ok X4) -> ok U31(X1, X2, X3, X4), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), isNat ok X -> ok isNat X, isNatList ok X -> ok isNatList X, isNatIList ok X -> ok isNatIList X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper s X -> s proper X, proper length X -> length proper X, proper U11(X1, X2) -> U11(proper X1, proper X2), proper tt() -> ok tt(), proper nil() -> ok nil(), proper U21 X -> U21 proper X, proper take(X1, X2) -> take(proper X1, proper X2), proper U31(X1, X2, X3, X4) -> U31(proper X1, proper X2, proper X3, proper X4), proper and(X1, X2) -> and(proper X1, proper X2), proper isNat X -> isNat proper X, proper isNatList X -> isNatList proper X, proper isNatIList X -> isNatIList proper X, top mark X -> top proper X, top ok X -> top active X} Open SCC (1): Strict: {isNatList# ok X -> isNatList# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U11(and(isNatList L, isNat N), L), active length nil() -> mark 0(), active U11(X1, X2) -> U11(active X1, X2), active U11(tt(), L) -> mark s length L, active U21 X -> U21 active X, active U21 tt() -> mark nil(), active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(0(), IL) -> mark U21 isNatIList IL, active take(s M, cons(N, IL)) -> mark U31(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N), active U31(X1, X2, X3, X4) -> U31(active X1, X2, X3, X4), active U31(tt(), IL, M, N) -> mark cons(N, take(M, IL)), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active isNat 0() -> mark tt(), active isNat s V1 -> mark isNat V1, active isNat length V1 -> mark isNatList V1, active isNatList cons(V1, V2) -> mark and(isNat V1, isNatList V2), active isNatList nil() -> mark tt(), active isNatList take(V1, V2) -> mark and(isNat V1, isNatIList V2), active isNatIList V -> mark isNatList V, active isNatIList cons(V1, V2) -> mark and(isNat V1, isNatIList V2), active isNatIList zeros() -> mark tt(), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, U11(mark X1, X2) -> mark U11(X1, X2), U11(ok X1, ok X2) -> ok U11(X1, X2), U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(X1, X2), U31(mark X1, X2, X3, X4) -> mark U31(X1, X2, X3, X4), U31(ok X1, ok X2, ok X3, ok X4) -> ok U31(X1, X2, X3, X4), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), isNat ok X -> ok isNat X, isNatList ok X -> ok isNatList X, isNatIList ok X -> ok isNatIList X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper s X -> s proper X, proper length X -> length proper X, proper U11(X1, X2) -> U11(proper X1, proper X2), proper tt() -> ok tt(), proper nil() -> ok nil(), proper U21 X -> U21 proper X, proper take(X1, X2) -> take(proper X1, proper X2), proper U31(X1, X2, X3, X4) -> U31(proper X1, proper X2, proper X3, proper X4), proper and(X1, X2) -> and(proper X1, proper X2), proper isNat X -> isNat proper X, proper isNatList X -> isNatList proper X, proper isNatIList X -> isNatIList proper X, top mark X -> top proper X, top ok X -> top active X} Open SCC (1): Strict: {isNat# ok X -> isNat# X} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U11(and(isNatList L, isNat N), L), active length nil() -> mark 0(), active U11(X1, X2) -> U11(active X1, X2), active U11(tt(), L) -> mark s length L, active U21 X -> U21 active X, active U21 tt() -> mark nil(), active take(X1, X2) -> take(X1, active X2), active take(X1, X2) -> take(active X1, X2), active take(0(), IL) -> mark U21 isNatIList IL, active take(s M, cons(N, IL)) -> mark U31(and(isNatIList IL, and(isNat M, isNat N)), IL, M, N), active U31(X1, X2, X3, X4) -> U31(active X1, X2, X3, X4), active U31(tt(), IL, M, N) -> mark cons(N, take(M, IL)), active and(X1, X2) -> and(active X1, X2), active and(tt(), X) -> mark X, active isNat 0() -> mark tt(), active isNat s V1 -> mark isNat V1, active isNat length V1 -> mark isNatList V1, active isNatList cons(V1, V2) -> mark and(isNat V1, isNatList V2), active isNatList nil() -> mark tt(), active isNatList take(V1, V2) -> mark and(isNat V1, isNatIList V2), active isNatIList V -> mark isNatList V, active isNatIList cons(V1, V2) -> mark and(isNat V1, isNatIList V2), active isNatIList zeros() -> mark tt(), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, U11(mark X1, X2) -> mark U11(X1, X2), U11(ok X1, ok X2) -> ok U11(X1, X2), U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, take(X1, mark X2) -> mark take(X1, X2), take(mark X1, X2) -> mark take(X1, X2), take(ok X1, ok X2) -> ok take(X1, X2), U31(mark X1, X2, X3, X4) -> mark U31(X1, X2, X3, X4), U31(ok X1, ok X2, ok X3, ok X4) -> ok U31(X1, X2, X3, X4), and(mark X1, X2) -> mark and(X1, X2), and(ok X1, ok X2) -> ok and(X1, X2), isNat ok X -> ok isNat X, isNatList ok X -> ok isNatList X, isNatIList ok X -> ok isNatIList X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper s X -> s proper X, proper length X -> length proper X, proper U11(X1, X2) -> U11(proper X1, proper X2), proper tt() -> ok tt(), proper nil() -> ok nil(), proper U21 X -> U21 proper X, proper take(X1, X2) -> take(proper X1, proper X2), proper U31(X1, X2, X3, X4) -> U31(proper X1, proper X2, proper X3, proper X4), proper and(X1, X2) -> and(proper X1, proper X2), proper isNat X -> isNat proper X, proper isNatList X -> isNatList proper X, proper isNatIList X -> isNatIList proper X, top mark X -> top proper X, top ok X -> top active X} Open