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