MAYBE Time: 0.205979 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 U11 X -> U11 active X, active U11 tt() -> mark tt(), active U21 X -> U21 active X, active U21 tt() -> mark tt(), active U31 X -> U31 active X, active U31 tt() -> mark tt(), active U42 X -> U42 active X, active U42 tt() -> mark tt(), active isNatIList V -> mark U31 isNatList V, active isNatIList cons(V1, V2) -> mark U41(isNat V1, V2), active isNatIList zeros() -> mark tt(), active U41(X1, X2) -> U41(active X1, X2), active U41(tt(), V2) -> mark U42 isNatIList V2, active U52 X -> U52 active X, active U52 tt() -> mark tt(), active isNatList cons(V1, V2) -> mark U51(isNat V1, V2), active isNatList nil() -> mark tt(), active U51(X1, X2) -> U51(active X1, X2), active U51(tt(), V2) -> mark U52 isNatList V2, active U62(X1, X2) -> U62(active X1, X2), active U62(tt(), L) -> mark s length L, active isNat 0() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat length V1 -> mark U11 isNatList V1, active U61(X1, X2, X3) -> U61(active X1, X2, X3), active U61(tt(), L, N) -> mark U62(isNat N, L), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U61(isNatList L, L, N), active length nil() -> mark 0(), U11 mark X -> mark U11 X, U11 ok X -> ok U11 X, U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, U31 mark X -> mark U31 X, U31 ok X -> ok U31 X, U42 mark X -> mark U42 X, U42 ok X -> ok U42 X, isNatIList ok X -> ok isNatIList X, U41(mark X1, X2) -> mark U41(X1, X2), U41(ok X1, ok X2) -> ok U41(X1, X2), U52 mark X -> mark U52 X, U52 ok X -> ok U52 X, isNatList ok X -> ok isNatList X, U51(mark X1, X2) -> mark U51(X1, X2), U51(ok X1, ok X2) -> ok U51(X1, X2), U62(mark X1, X2) -> mark U62(X1, X2), U62(ok X1, ok X2) -> ok U62(X1, X2), isNat ok X -> ok isNat X, U61(mark X1, X2, X3) -> mark U61(X1, X2, X3), U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper tt() -> ok tt(), proper U11 X -> U11 proper X, proper U21 X -> U21 proper X, proper U31 X -> U31 proper X, proper U42 X -> U42 proper X, proper isNatIList X -> isNatIList proper X, proper U41(X1, X2) -> U41(proper X1, proper X2), proper U52 X -> U52 proper X, proper isNatList X -> isNatList proper X, proper U51(X1, X2) -> U51(proper X1, proper X2), proper U62(X1, X2) -> U62(proper X1, proper X2), proper isNat X -> isNat proper X, proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3), proper s X -> s proper X, proper length X -> length proper X, proper nil() -> ok nil(), 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# U11 X -> active# X, active# U11 X -> U11# active X, active# U21 X -> active# X, active# U21 X -> U21# active X, active# U31 X -> active# X, active# U31 X -> U31# active X, active# U42 X -> active# X, active# U42 X -> U42# active X, active# isNatIList V -> U31# isNatList V, active# isNatIList V -> isNatList# V, active# isNatIList cons(V1, V2) -> U41#(isNat V1, V2), active# isNatIList cons(V1, V2) -> isNat# V1, active# U41(X1, X2) -> active# X1, active# U41(X1, X2) -> U41#(active X1, X2), active# U41(tt(), V2) -> U42# isNatIList V2, active# U41(tt(), V2) -> isNatIList# V2, active# U52 X -> active# X, active# U52 X -> U52# active X, active# isNatList cons(V1, V2) -> U51#(isNat V1, V2), active# isNatList cons(V1, V2) -> isNat# V1, active# U51(X1, X2) -> active# X1, active# U51(X1, X2) -> U51#(active X1, X2), active# U51(tt(), V2) -> U52# isNatList V2, active# U51(tt(), V2) -> isNatList# V2, active# U62(X1, X2) -> active# X1, active# U62(X1, X2) -> U62#(active X1, X2), active# U62(tt(), L) -> s# length L, active# U62(tt(), L) -> length# L, active# isNat s V1 -> U21# isNat V1, active# isNat s V1 -> isNat# V1, active# isNat length V1 -> U11# isNatList V1, active# isNat length V1 -> isNatList# V1, active# U61(X1, X2, X3) -> active# X1, active# U61(X1, X2, X3) -> U61#(active X1, X2, X3), active# U61(tt(), L, N) -> U62#(isNat N, L), active# U61(tt(), L, N) -> isNat# N, active# s X -> active# X, active# s X -> s# active X, active# length X -> active# X, active# length X -> length# active X, active# length cons(N, L) -> isNatList# L, active# length cons(N, L) -> U61#(isNatList L, L, N), U11# mark X -> U11# X, U11# ok X -> U11# X, U21# mark X -> U21# X, U21# ok X -> U21# X, U31# mark X -> U31# X, U31# ok X -> U31# X, U42# mark X -> U42# X, U42# ok X -> U42# X, isNatIList# ok X -> isNatIList# X, U41#(mark X1, X2) -> U41#(X1, X2), U41#(ok X1, ok X2) -> U41#(X1, X2), U52# mark X -> U52# X, U52# ok X -> U52# X, isNatList# ok X -> isNatList# X, U51#(mark X1, X2) -> U51#(X1, X2), U51#(ok X1, ok X2) -> U51#(X1, X2), U62#(mark X1, X2) -> U62#(X1, X2), U62#(ok X1, ok X2) -> U62#(X1, X2), isNat# ok X -> isNat# X, U61#(mark X1, X2, X3) -> U61#(X1, X2, X3), U61#(ok X1, ok X2, ok X3) -> U61#(X1, X2, X3), s# mark X -> s# X, s# ok X -> s# X, length# mark X -> length# X, length# ok X -> length# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2), proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# U11 X -> U11# proper X, proper# U11 X -> proper# X, proper# U21 X -> U21# proper X, proper# U21 X -> proper# X, proper# U31 X -> U31# proper X, proper# U31 X -> proper# X, proper# U42 X -> U42# proper X, proper# U42 X -> proper# X, proper# isNatIList X -> isNatIList# proper X, proper# isNatIList X -> proper# X, proper# U41(X1, X2) -> U41#(proper X1, proper X2), proper# U41(X1, X2) -> proper# X1, proper# U41(X1, X2) -> proper# X2, proper# U52 X -> U52# proper X, proper# U52 X -> proper# X, proper# isNatList X -> isNatList# proper X, proper# isNatList X -> proper# X, proper# U51(X1, X2) -> U51#(proper X1, proper X2), proper# U51(X1, X2) -> proper# X1, proper# U51(X1, X2) -> proper# X2, proper# U62(X1, X2) -> U62#(proper X1, proper X2), proper# U62(X1, X2) -> proper# X1, proper# U62(X1, X2) -> proper# X2, proper# isNat X -> isNat# proper X, proper# isNat X -> proper# X, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3), proper# U61(X1, X2, X3) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X3, proper# s X -> s# proper X, proper# s X -> proper# X, proper# length X -> length# proper X, proper# length 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 U11 X -> U11 active X, active U11 tt() -> mark tt(), active U21 X -> U21 active X, active U21 tt() -> mark tt(), active U31 X -> U31 active X, active U31 tt() -> mark tt(), active U42 X -> U42 active X, active U42 tt() -> mark tt(), active isNatIList V -> mark U31 isNatList V, active isNatIList cons(V1, V2) -> mark U41(isNat V1, V2), active isNatIList zeros() -> mark tt(), active U41(X1, X2) -> U41(active X1, X2), active U41(tt(), V2) -> mark U42 isNatIList V2, active U52 X -> U52 active X, active U52 tt() -> mark tt(), active isNatList cons(V1, V2) -> mark U51(isNat V1, V2), active isNatList nil() -> mark tt(), active U51(X1, X2) -> U51(active X1, X2), active U51(tt(), V2) -> mark U52 isNatList V2, active U62(X1, X2) -> U62(active X1, X2), active U62(tt(), L) -> mark s length L, active isNat 0() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat length V1 -> mark U11 isNatList V1, active U61(X1, X2, X3) -> U61(active X1, X2, X3), active U61(tt(), L, N) -> mark U62(isNat N, L), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U61(isNatList L, L, N), active length nil() -> mark 0(), U11 mark X -> mark U11 X, U11 ok X -> ok U11 X, U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, U31 mark X -> mark U31 X, U31 ok X -> ok U31 X, U42 mark X -> mark U42 X, U42 ok X -> ok U42 X, isNatIList ok X -> ok isNatIList X, U41(mark X1, X2) -> mark U41(X1, X2), U41(ok X1, ok X2) -> ok U41(X1, X2), U52 mark X -> mark U52 X, U52 ok X -> ok U52 X, isNatList ok X -> ok isNatList X, U51(mark X1, X2) -> mark U51(X1, X2), U51(ok X1, ok X2) -> ok U51(X1, X2), U62(mark X1, X2) -> mark U62(X1, X2), U62(ok X1, ok X2) -> ok U62(X1, X2), isNat ok X -> ok isNat X, U61(mark X1, X2, X3) -> mark U61(X1, X2, X3), U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper tt() -> ok tt(), proper U11 X -> U11 proper X, proper U21 X -> U21 proper X, proper U31 X -> U31 proper X, proper U42 X -> U42 proper X, proper isNatIList X -> isNatIList proper X, proper U41(X1, X2) -> U41(proper X1, proper X2), proper U52 X -> U52 proper X, proper isNatList X -> isNatList proper X, proper U51(X1, X2) -> U51(proper X1, proper X2), proper U62(X1, X2) -> U62(proper X1, proper X2), proper isNat X -> isNat proper X, proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3), proper s X -> s proper X, proper length X -> length proper X, proper nil() -> ok nil(), 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 U11 X -> U11 active X, active U11 tt() -> mark tt(), active U21 X -> U21 active X, active U21 tt() -> mark tt(), active U31 X -> U31 active X, active U31 tt() -> mark tt(), active U42 X -> U42 active X, active U42 tt() -> mark tt(), active isNatIList V -> mark U31 isNatList V, active isNatIList cons(V1, V2) -> mark U41(isNat V1, V2), active isNatIList zeros() -> mark tt(), active U41(X1, X2) -> U41(active X1, X2), active U41(tt(), V2) -> mark U42 isNatIList V2, active U52 X -> U52 active X, active U52 tt() -> mark tt(), active isNatList cons(V1, V2) -> mark U51(isNat V1, V2), active isNatList nil() -> mark tt(), active U51(X1, X2) -> U51(active X1, X2), active U51(tt(), V2) -> mark U52 isNatList V2, active U62(X1, X2) -> U62(active X1, X2), active U62(tt(), L) -> mark s length L, active isNat 0() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat length V1 -> mark U11 isNatList V1, active U61(X1, X2, X3) -> U61(active X1, X2, X3), active U61(tt(), L, N) -> mark U62(isNat N, L), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U61(isNatList L, L, N), active length nil() -> mark 0(), U11 mark X -> mark U11 X, U11 ok X -> ok U11 X, U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, U31 mark X -> mark U31 X, U31 ok X -> ok U31 X, U42 mark X -> mark U42 X, U42 ok X -> ok U42 X, isNatIList ok X -> ok isNatIList X, U41(mark X1, X2) -> mark U41(X1, X2), U41(ok X1, ok X2) -> ok U41(X1, X2), U52 mark X -> mark U52 X, U52 ok X -> ok U52 X, isNatList ok X -> ok isNatList X, U51(mark X1, X2) -> mark U51(X1, X2), U51(ok X1, ok X2) -> ok U51(X1, X2), U62(mark X1, X2) -> mark U62(X1, X2), U62(ok X1, ok X2) -> ok U62(X1, X2), isNat ok X -> ok isNat X, U61(mark X1, X2, X3) -> mark U61(X1, X2, X3), U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper tt() -> ok tt(), proper U11 X -> U11 proper X, proper U21 X -> U21 proper X, proper U31 X -> U31 proper X, proper U42 X -> U42 proper X, proper isNatIList X -> isNatIList proper X, proper U41(X1, X2) -> U41(proper X1, proper X2), proper U52 X -> U52 proper X, proper isNatList X -> isNatList proper X, proper U51(X1, X2) -> U51(proper X1, proper X2), proper U62(X1, X2) -> U62(proper X1, proper X2), proper isNat X -> isNat proper X, proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3), proper s X -> s proper X, proper length X -> length proper X, proper nil() -> ok nil()} EDG: { (active# length cons(N, L) -> U61#(isNatList L, L, N), U61#(ok X1, ok X2, ok X3) -> U61#(X1, X2, X3)) (active# length cons(N, L) -> U61#(isNatList L, L, N), U61#(mark X1, X2, X3) -> U61#(X1, X2, X3)) (active# isNatList cons(V1, V2) -> isNat# V1, isNat# ok X -> isNat# X) (active# isNat length V1 -> isNatList# V1, isNatList# ok X -> isNatList# X) (active# U21 X -> U21# active X, U21# ok X -> U21# X) (active# U21 X -> U21# active X, U21# mark X -> U21# X) (active# U42 X -> U42# active X, U42# ok X -> U42# X) (active# U42 X -> U42# active X, U42# mark X -> U42# X) (active# s X -> s# active X, s# ok X -> s# X) (active# s X -> s# active X, s# mark X -> s# X) (proper# U11 X -> U11# proper X, U11# ok X -> U11# X) (proper# U11 X -> U11# proper X, U11# mark X -> U11# X) (proper# U31 X -> U31# proper X, U31# ok X -> U31# X) (proper# U31 X -> U31# proper X, U31# mark X -> U31# X) (proper# isNatIList X -> isNatIList# proper X, isNatIList# ok X -> isNatIList# X) (proper# isNatList X -> isNatList# proper X, isNatList# ok X -> isNatList# X) (proper# s X -> s# proper X, s# ok X -> s# X) (proper# s X -> s# proper X, s# mark X -> s# X) (top# mark X -> top# proper X, top# ok X -> top# active X) (top# mark X -> top# proper X, top# ok X -> active# X) (top# mark X -> top# proper X, top# mark X -> top# proper X) (top# mark X -> top# proper X, top# mark X -> proper# X) (active# isNatIList V -> U31# isNatList V, U31# ok X -> U31# X) (active# isNatIList V -> U31# isNatList V, U31# mark X -> U31# X) (active# isNat length V1 -> U11# isNatList V1, U11# ok X -> U11# X) (active# isNat length V1 -> U11# isNatList V1, U11# mark X -> U11# X) (active# U41(tt(), V2) -> U42# isNatIList V2, U42# ok X -> U42# X) (active# U41(tt(), V2) -> U42# isNatIList V2, U42# mark X -> U42# X) (proper# cons(X1, X2) -> cons#(proper X1, proper X2), cons#(ok X1, ok X2) -> cons#(X1, X2)) (proper# cons(X1, X2) -> cons#(proper X1, proper X2), cons#(mark X1, X2) -> cons#(X1, X2)) (proper# U51(X1, X2) -> U51#(proper X1, proper X2), U51#(ok X1, ok X2) -> U51#(X1, X2)) (proper# U51(X1, X2) -> U51#(proper X1, proper X2), U51#(mark X1, X2) -> U51#(X1, X2)) (active# zeros() -> cons#(0(), zeros()), cons#(ok X1, ok X2) -> cons#(X1, X2)) (active# zeros() -> cons#(0(), zeros()), cons#(mark X1, X2) -> cons#(X1, X2)) (active# U61(tt(), L, N) -> U62#(isNat N, L), U62#(ok X1, ok X2) -> U62#(X1, X2)) (active# U61(tt(), L, N) -> U62#(isNat N, L), U62#(mark X1, X2) -> U62#(X1, X2)) (U61#(mark X1, X2, X3) -> U61#(X1, X2, X3), U61#(ok X1, ok X2, ok X3) -> U61#(X1, X2, X3)) (U61#(mark X1, X2, X3) -> U61#(X1, X2, X3), U61#(mark X1, X2, X3) -> U61#(X1, X2, X3)) (active# cons(X1, X2) -> active# X1, active# length cons(N, L) -> U61#(isNatList L, L, N)) (active# cons(X1, X2) -> active# X1, active# length cons(N, L) -> 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# U61(tt(), L, N) -> isNat# N) (active# cons(X1, X2) -> active# X1, active# U61(tt(), L, N) -> U62#(isNat N, L)) (active# cons(X1, X2) -> active# X1, active# U61(X1, X2, X3) -> U61#(active X1, X2, X3)) (active# cons(X1, X2) -> active# X1, active# U61(X1, X2, X3) -> active# X1) (active# cons(X1, X2) -> active# X1, active# isNat length V1 -> isNatList# V1) (active# cons(X1, X2) -> active# X1, active# isNat length V1 -> U11# isNatList V1) (active# cons(X1, X2) -> active# X1, active# isNat s V1 -> isNat# V1) (active# cons(X1, X2) -> active# X1, active# isNat s V1 -> U21# isNat V1) (active# cons(X1, X2) -> active# X1, active# U62(tt(), L) -> length# L) (active# cons(X1, X2) -> active# X1, active# U62(tt(), L) -> s# length L) (active# cons(X1, X2) -> active# X1, active# U62(X1, X2) -> U62#(active X1, X2)) (active# cons(X1, X2) -> active# X1, active# U62(X1, X2) -> active# X1) (active# cons(X1, X2) -> active# X1, active# U51(tt(), V2) -> isNatList# V2) (active# cons(X1, X2) -> active# X1, active# U51(tt(), V2) -> U52# isNatList V2) (active# cons(X1, X2) -> active# X1, active# U51(X1, X2) -> U51#(active X1, X2)) (active# cons(X1, X2) -> active# X1, active# U51(X1, X2) -> active# X1) (active# cons(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> isNat# V1) (active# cons(X1, X2) -> active# X1, active# isNatList cons(V1, V2) -> U51#(isNat V1, V2)) (active# cons(X1, X2) -> active# X1, active# U52 X -> U52# active X) (active# cons(X1, X2) -> active# X1, active# U52 X -> active# X) (active# cons(X1, X2) -> active# X1, active# U41(tt(), V2) -> isNatIList# V2) (active# cons(X1, X2) -> active# X1, active# U41(tt(), V2) -> U42# isNatIList V2) (active# cons(X1, X2) -> active# X1, active# U41(X1, X2) -> U41#(active X1, X2)) (active# cons(X1, X2) -> active# X1, active# U41(X1, X2) -> active# X1) (active# cons(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> isNat# V1) (active# cons(X1, X2) -> active# X1, active# isNatIList cons(V1, V2) -> U41#(isNat V1, V2)) (active# cons(X1, X2) -> active# X1, active# isNatIList V -> isNatList# V) (active# cons(X1, X2) -> active# X1, active# isNatIList V -> U31# isNatList V) (active# cons(X1, X2) -> active# X1, active# U42 X -> U42# active X) (active# cons(X1, X2) -> active# X1, active# U42 X -> active# X) (active# cons(X1, X2) -> active# X1, active# U31 X -> U31# active X) (active# cons(X1, X2) -> active# X1, active# U31 X -> active# X) (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 X -> U11# active X) (active# cons(X1, X2) -> active# X1, active# U11 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# U51(X1, X2) -> active# X1, active# length cons(N, L) -> U61#(isNatList L, L, N)) (active# U51(X1, X2) -> active# X1, active# length cons(N, L) -> isNatList# L) (active# U51(X1, X2) -> active# X1, active# length X -> length# active X) (active# U51(X1, X2) -> active# X1, active# length X -> active# X) (active# U51(X1, X2) -> active# X1, active# s X -> s# active X) (active# U51(X1, X2) -> active# X1, active# s X -> active# X) (active# U51(X1, X2) -> active# X1, active# 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-> U21# proper X) (proper# U21 X -> proper# X, proper# U11 X -> proper# X) (proper# U21 X -> proper# X, proper# U11 X -> U11# 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# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# U42 X -> proper# X, proper# length X -> proper# X) (proper# U42 X -> proper# X, proper# length X -> length# proper X) (proper# U42 X -> proper# X, proper# s X -> proper# X) (proper# U42 X -> proper# X, proper# s X -> s# proper X) (proper# U42 X -> proper# X, proper# U61(X1, X2, X3) -> proper# X3) (proper# U42 X -> proper# X, proper# U61(X1, X2, X3) -> proper# X2) (proper# U42 X -> proper# X, proper# U61(X1, X2, X3) -> proper# X1) (proper# U42 X -> proper# X, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3)) (proper# U42 X -> proper# X, proper# isNat X -> proper# X) (proper# U42 X -> proper# X, proper# isNat X -> isNat# proper X) (proper# U42 X -> proper# X, proper# U62(X1, X2) -> proper# X2) (proper# U42 X -> proper# X, proper# U62(X1, X2) -> proper# X1) (proper# U42 X -> proper# X, proper# U62(X1, X2) -> U62#(proper X1, proper X2)) (proper# U42 X -> proper# X, proper# U51(X1, X2) -> proper# X2) (proper# U42 X -> proper# X, proper# U51(X1, X2) -> proper# X1) (proper# U42 X -> proper# X, proper# U51(X1, X2) -> U51#(proper X1, proper X2)) (proper# U42 X -> proper# X, proper# isNatList X -> proper# X) (proper# U42 X -> proper# X, proper# isNatList X -> isNatList# proper X) (proper# U42 X -> proper# X, proper# U52 X -> proper# X) (proper# U42 X -> proper# X, proper# U52 X -> U52# proper X) (proper# U42 X -> proper# X, proper# U41(X1, X2) -> proper# X2) (proper# U42 X -> proper# X, proper# U41(X1, X2) -> proper# X1) (proper# U42 X -> proper# X, proper# U41(X1, X2) -> U41#(proper X1, proper X2)) (proper# U42 X -> proper# X, proper# isNatIList X -> proper# X) (proper# U42 X -> proper# X, proper# isNatIList 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X3) -> proper# X3) (proper# U52 X -> proper# X, proper# U61(X1, X2, X3) -> proper# X2) (proper# U52 X -> proper# X, proper# U61(X1, X2, X3) -> proper# X1) (proper# U52 X -> proper# X, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3)) (proper# U52 X -> proper# X, proper# isNat X -> proper# X) (proper# U52 X -> proper# X, proper# isNat X -> isNat# proper X) (proper# U52 X -> proper# X, proper# U62(X1, X2) -> proper# X2) (proper# U52 X -> proper# X, proper# U62(X1, X2) -> proper# X1) (proper# U52 X -> proper# X, proper# U62(X1, X2) -> U62#(proper X1, proper X2)) (proper# U52 X -> proper# X, proper# U51(X1, X2) -> proper# X2) (proper# U52 X -> proper# X, proper# U51(X1, X2) -> proper# X1) (proper# U52 X -> proper# X, proper# U51(X1, X2) -> U51#(proper X1, proper X2)) (proper# U52 X -> proper# X, proper# isNatList X -> proper# X) (proper# U52 X -> proper# X, proper# isNatList X -> isNatList# proper X) (proper# U52 X -> proper# X, proper# U52 X -> proper# X) (proper# U52 X -> proper# X, proper# U52 X -> U52# proper X) (proper# U52 X -> proper# X, proper# U41(X1, X2) -> proper# X2) (proper# U52 X -> proper# X, proper# U41(X1, X2) -> proper# X1) (proper# U52 X -> proper# X, proper# U41(X1, X2) -> U41#(proper X1, proper X2)) (proper# U52 X -> proper# X, proper# isNatIList X -> proper# X) (proper# U52 X -> proper# X, proper# isNatIList X -> isNatIList# proper X) (proper# U52 X -> proper# X, proper# U42 X -> proper# X) (proper# U52 X -> proper# X, proper# U42 X -> U42# proper X) (proper# U52 X -> proper# X, proper# U31 X -> proper# X) (proper# U52 X -> proper# X, proper# U31 X -> U31# proper X) (proper# U52 X -> proper# X, proper# U21 X -> proper# X) (proper# U52 X -> proper# X, proper# U21 X -> U21# proper X) (proper# U52 X -> proper# X, proper# U11 X -> proper# X) (proper# U52 X -> proper# X, proper# U11 X -> U11# proper X) (proper# U52 X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# U52 X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# U52 X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# isNat X -> proper# X, proper# length X -> proper# X) (proper# isNat X -> proper# X, proper# length X -> length# proper X) (proper# isNat X -> proper# X, proper# s X -> proper# X) (proper# isNat X -> proper# X, proper# s X -> s# proper X) (proper# isNat X -> proper# X, proper# U61(X1, X2, X3) -> proper# X3) (proper# isNat X -> proper# X, proper# U61(X1, X2, X3) -> proper# X2) (proper# isNat X -> proper# X, proper# U61(X1, X2, X3) -> proper# X1) (proper# isNat X -> proper# X, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3)) (proper# isNat X -> proper# X, proper# isNat X -> proper# X) (proper# isNat X -> proper# X, proper# isNat X -> isNat# proper X) (proper# isNat X -> proper# X, proper# U62(X1, X2) -> proper# X2) (proper# isNat X -> proper# X, proper# U62(X1, X2) -> proper# X1) (proper# isNat X -> proper# X, proper# U62(X1, X2) -> U62#(proper X1, proper X2)) (proper# isNat X -> proper# X, proper# U51(X1, X2) -> proper# X2) (proper# isNat X -> proper# X, proper# U51(X1, X2) -> proper# X1) (proper# isNat X -> proper# X, proper# U51(X1, X2) -> U51#(proper X1, proper X2)) (proper# isNat X -> proper# X, proper# isNatList X -> proper# X) (proper# isNat X -> proper# X, proper# isNatList X -> isNatList# proper X) (proper# isNat X -> proper# X, proper# U52 X -> proper# X) (proper# isNat X -> proper# X, proper# U52 X -> U52# proper X) (proper# isNat X -> proper# X, proper# U41(X1, X2) -> proper# X2) (proper# isNat X -> proper# X, proper# U41(X1, X2) -> proper# X1) (proper# isNat X -> proper# X, proper# U41(X1, X2) -> U41#(proper X1, proper X2)) (proper# isNat X -> proper# X, proper# isNatIList X -> proper# X) (proper# isNat X -> proper# X, proper# isNatIList X -> isNatIList# proper X) (proper# isNat X -> proper# X, proper# U42 X -> proper# X) (proper# isNat X -> proper# X, proper# U42 X -> U42# proper X) (proper# isNat X -> proper# X, proper# U31 X -> proper# X) (proper# isNat X -> proper# X, proper# U31 X -> U31# proper X) (proper# isNat X -> proper# X, proper# U21 X -> proper# X) (proper# isNat X -> proper# X, proper# U21 X -> U21# proper X) (proper# isNat X -> proper# X, proper# U11 X -> proper# X) (proper# isNat X -> proper# X, proper# U11 X -> U11# proper X) (proper# isNat X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# isNat X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# isNat X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# length X -> proper# X, proper# length X -> proper# X) (proper# length X -> proper# X, proper# length X -> length# proper X) (proper# length X -> proper# X, proper# s X -> proper# X) (proper# length X -> proper# X, proper# s X -> s# proper X) (proper# length X -> proper# X, proper# U61(X1, X2, X3) -> proper# X3) (proper# length X -> proper# X, proper# U61(X1, X2, X3) -> proper# X2) (proper# length X -> proper# X, proper# U61(X1, X2, X3) -> proper# X1) (proper# length X -> proper# X, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3)) (proper# length X -> proper# X, proper# isNat X -> proper# X) (proper# length X -> proper# X, proper# isNat X -> isNat# proper X) (proper# length X -> proper# X, proper# U62(X1, X2) -> proper# X2) (proper# length X -> proper# X, proper# U62(X1, X2) -> proper# X1) (proper# length X -> proper# X, proper# U62(X1, X2) -> U62#(proper X1, proper X2)) (proper# length X -> proper# X, proper# U51(X1, X2) -> proper# X2) (proper# length X -> proper# X, proper# U51(X1, X2) -> proper# X1) (proper# length X -> proper# X, proper# U51(X1, X2) -> U51#(proper X1, proper X2)) (proper# length X -> proper# X, proper# isNatList X -> proper# X) (proper# length X -> proper# X, proper# isNatList X -> isNatList# proper X) (proper# length X -> proper# X, proper# U52 X -> proper# X) (proper# length X -> proper# X, proper# U52 X -> U52# proper X) (proper# length X -> proper# X, proper# U41(X1, X2) -> proper# X2) (proper# length X -> proper# X, proper# U41(X1, X2) -> proper# X1) (proper# length X -> proper# X, proper# U41(X1, X2) -> U41#(proper X1, proper X2)) (proper# length X -> proper# X, proper# isNatIList X -> proper# X) (proper# length X -> proper# X, proper# isNatIList X -> isNatIList# proper X) (proper# length X -> proper# X, proper# U42 X -> proper# X) (proper# length X -> proper# X, proper# U42 X -> U42# proper X) (proper# length X -> proper# X, proper# U31 X -> proper# X) (proper# length X -> proper# X, proper# U31 X -> U31# proper X) (proper# length X -> proper# X, proper# U21 X -> proper# X) (proper# length X -> proper# X, proper# U21 X -> U21# proper X) (proper# length X -> proper# X, proper# U11 X -> proper# X) (proper# length X -> proper# X, proper# U11 X -> U11# proper X) (proper# length X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# length X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# length X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (top# ok X -> active# X, active# length cons(N, L) -> U61#(isNatList L, L, N)) (top# ok X -> active# X, active# length cons(N, L) -> isNatList# L) (top# ok X -> active# X, active# length X -> length# active X) (top# ok X -> active# X, active# length X -> active# X) (top# ok X -> active# X, active# s X -> s# active X) (top# ok X -> active# X, active# s X -> active# X) (top# ok X -> active# X, active# U61(tt(), L, N) -> isNat# N) (top# ok X -> active# X, active# U61(tt(), L, N) -> U62#(isNat N, L)) (top# ok X -> active# X, active# U61(X1, X2, X3) -> U61#(active X1, X2, X3)) (top# ok X -> active# X, active# U61(X1, X2, X3) -> active# X1) (top# ok X -> active# X, active# isNat length V1 -> isNatList# V1) (top# ok X -> active# X, active# isNat length V1 -> U11# isNatList V1) (top# ok X -> active# X, active# isNat s V1 -> isNat# V1) (top# ok X -> active# X, active# isNat s V1 -> U21# isNat V1) (top# ok X -> active# X, active# U62(tt(), L) -> length# L) (top# ok X -> active# X, active# U62(tt(), L) -> s# length L) (top# ok X -> active# X, active# U62(X1, X2) -> U62#(active X1, X2)) (top# ok X -> active# X, active# U62(X1, X2) -> active# X1) (top# ok X -> active# X, active# U51(tt(), V2) -> isNatList# V2) (top# ok X -> active# X, active# U51(tt(), V2) -> U52# isNatList V2) (top# ok X -> active# X, active# U51(X1, X2) -> U51#(active X1, X2)) (top# ok X -> active# X, active# U51(X1, X2) -> active# X1) (top# ok X -> active# X, active# isNatList cons(V1, V2) -> isNat# V1) (top# ok X -> active# X, active# isNatList cons(V1, V2) -> U51#(isNat V1, V2)) (top# ok X -> active# X, active# U52 X -> U52# active X) (top# ok X -> active# X, active# U52 X -> active# X) (top# ok X -> active# X, active# U41(tt(), V2) -> isNatIList# V2) (top# ok X -> active# X, active# U41(tt(), V2) -> U42# isNatIList V2) (top# ok X -> active# X, active# U41(X1, X2) -> U41#(active X1, X2)) (top# ok X -> active# X, active# U41(X1, X2) -> active# X1) (top# ok X -> active# X, active# isNatIList cons(V1, V2) -> isNat# V1) (top# ok X -> active# X, active# isNatIList cons(V1, V2) -> U41#(isNat V1, V2)) (top# ok X -> active# X, active# isNatIList V -> isNatList# V) (top# ok X -> active# X, active# isNatIList V -> U31# isNatList V) (top# ok X -> active# X, active# U42 X -> U42# active X) (top# ok X -> active# X, active# U42 X -> active# X) (top# ok X -> active# X, active# U31 X -> U31# active X) (top# ok X -> active# X, active# U31 X -> active# X) (top# ok X -> active# X, active# U21 X -> U21# active X) (top# ok X -> active# X, active# U21 X -> active# X) (top# ok X -> active# X, active# U11 X -> U11# active X) (top# ok X -> active# X, active# U11 X -> active# X) (top# ok X -> active# X, active# zeros() -> cons#(0(), zeros())) (top# ok X -> active# X, active# cons(X1, X2) -> active# X1) (top# ok X -> active# X, active# cons(X1, X2) -> cons#(active X1, X2)) (active# U41(X1, X2) -> U41#(active X1, X2), U41#(ok X1, ok X2) -> U41#(X1, X2)) (active# U41(X1, X2) -> U41#(active X1, X2), U41#(mark X1, X2) -> U41#(X1, X2)) (active# U62(X1, X2) -> U62#(active X1, X2), U62#(ok X1, ok X2) -> U62#(X1, X2)) (active# U62(X1, X2) -> U62#(active X1, X2), U62#(mark X1, X2) -> U62#(X1, X2)) (active# length cons(N, L) -> isNatList# L, isNatList# ok X -> isNatList# X) (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)) (U41#(ok X1, ok X2) -> U41#(X1, X2), U41#(ok X1, ok X2) -> U41#(X1, X2)) (U41#(ok X1, ok X2) -> U41#(X1, X2), U41#(mark X1, X2) -> U41#(X1, X2)) (U51#(ok X1, ok X2) -> U51#(X1, X2), U51#(ok X1, ok X2) -> U51#(X1, X2)) (U51#(ok X1, ok X2) -> U51#(X1, X2), U51#(mark X1, X2) -> U51#(X1, X2)) (U62#(ok X1, ok X2) -> U62#(X1, X2), U62#(ok X1, ok X2) -> U62#(X1, X2)) (U62#(ok X1, ok X2) -> U62#(X1, X2), U62#(mark X1, X2) -> U62#(X1, X2)) (U62#(mark X1, X2) -> U62#(X1, X2), U62#(mark X1, X2) -> U62#(X1, X2)) (U62#(mark X1, X2) -> U62#(X1, X2), U62#(ok X1, ok X2) -> U62#(X1, X2)) (U51#(mark X1, X2) -> U51#(X1, X2), U51#(mark X1, X2) -> U51#(X1, X2)) (U51#(mark X1, X2) -> U51#(X1, X2), U51#(ok X1, ok X2) -> U51#(X1, X2)) (U41#(mark X1, X2) -> U41#(X1, X2), U41#(mark X1, X2) -> U41#(X1, X2)) (U41#(mark X1, X2) -> U41#(X1, X2), U41#(ok X1, ok X2) -> U41#(X1, X2)) (cons#(mark X1, X2) -> cons#(X1, X2), cons#(mark X1, X2) -> cons#(X1, X2)) (cons#(mark X1, X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)) (active# U62(tt(), L) -> length# L, length# mark X -> length# X) (active# U62(tt(), L) -> length# L, length# ok X -> length# X) (active# U51(X1, X2) -> U51#(active X1, X2), U51#(mark X1, X2) -> U51#(X1, X2)) (active# U51(X1, X2) -> U51#(active X1, X2), U51#(ok X1, ok X2) -> U51#(X1, X2)) (active# cons(X1, X2) -> cons#(active X1, X2), cons#(mark X1, X2) -> cons#(X1, X2)) (active# cons(X1, X2) -> cons#(active X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)) (top# mark X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (top# mark X -> proper# X, proper# cons(X1, X2) -> proper# X1) (top# mark X -> proper# X, proper# cons(X1, X2) -> proper# X2) (top# mark X -> proper# X, proper# U11 X -> U11# proper X) (top# mark X -> proper# X, proper# U11 X -> proper# X) (top# mark X -> proper# X, proper# U21 X -> U21# proper X) (top# mark X -> proper# X, proper# U21 X -> proper# X) (top# mark X -> proper# X, proper# U31 X -> U31# proper X) (top# mark X -> proper# X, proper# U31 X -> proper# X) (top# mark X -> proper# X, proper# U42 X -> U42# proper X) (top# mark X -> proper# X, proper# U42 X -> proper# X) (top# mark X -> proper# X, proper# isNatIList X -> isNatIList# proper X) (top# mark X -> proper# X, proper# isNatIList X -> proper# X) (top# mark X -> proper# X, proper# U41(X1, X2) -> U41#(proper X1, proper X2)) (top# mark X -> proper# X, proper# U41(X1, X2) -> proper# X1) (top# mark X -> proper# X, proper# U41(X1, X2) -> proper# X2) (top# mark X -> proper# X, proper# U52 X -> U52# proper X) (top# mark X -> proper# X, proper# U52 X -> proper# X) (top# mark X -> proper# X, proper# isNatList X -> isNatList# proper X) (top# mark X -> proper# X, proper# isNatList X -> proper# X) (top# mark X -> proper# X, proper# U51(X1, X2) -> U51#(proper X1, proper X2)) (top# mark X -> proper# X, proper# U51(X1, X2) -> proper# X1) (top# mark X -> proper# X, proper# U51(X1, X2) -> proper# X2) (top# mark X -> proper# X, proper# U62(X1, X2) -> U62#(proper X1, proper X2)) (top# mark X -> proper# X, proper# U62(X1, X2) -> proper# X1) (top# mark X -> proper# X, proper# U62(X1, X2) -> proper# X2) (top# mark X -> proper# X, proper# isNat X -> isNat# proper X) (top# mark X -> proper# X, proper# isNat X -> proper# X) (top# mark X -> proper# X, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3)) (top# mark X -> proper# X, proper# U61(X1, X2, X3) -> proper# X1) (top# mark X -> proper# X, proper# U61(X1, X2, X3) -> proper# X2) (top# mark X -> proper# X, proper# U61(X1, X2, X3) -> proper# X3) (top# mark X -> proper# X, proper# s X -> s# proper X) (top# mark X -> proper# X, proper# s X -> proper# X) (top# mark X -> proper# X, proper# length X -> length# proper X) (top# mark X -> proper# X, proper# length X -> proper# X) (proper# s X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# s X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# s X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# s X -> proper# X, proper# U11 X -> U11# proper X) (proper# s X -> proper# X, proper# U11 X -> proper# X) (proper# s X -> proper# X, proper# U21 X -> U21# proper X) (proper# s X -> proper# X, proper# U21 X -> proper# X) (proper# s X -> proper# X, proper# U31 X -> U31# proper X) (proper# s X -> proper# X, proper# U31 X -> proper# X) (proper# s X -> proper# X, proper# U42 X -> U42# proper X) (proper# s X -> proper# X, proper# U42 X -> proper# X) (proper# s X -> proper# X, proper# isNatIList X -> isNatIList# proper X) (proper# s X -> proper# X, proper# isNatIList X -> proper# X) (proper# s X -> proper# X, proper# U41(X1, X2) -> U41#(proper X1, proper X2)) (proper# s X -> proper# X, proper# U41(X1, X2) -> proper# X1) (proper# s X -> proper# X, proper# U41(X1, X2) -> proper# X2) (proper# s X -> proper# X, proper# U52 X -> U52# proper X) (proper# s X -> proper# X, proper# U52 X -> proper# X) (proper# s X -> proper# X, proper# isNatList X -> isNatList# proper X) (proper# s X -> proper# X, proper# isNatList X -> proper# X) (proper# s X -> proper# X, proper# U51(X1, X2) -> U51#(proper X1, proper X2)) (proper# s X -> proper# X, proper# U51(X1, X2) -> proper# X1) (proper# s X -> proper# X, proper# U51(X1, X2) -> proper# X2) (proper# s X -> proper# X, proper# U62(X1, X2) -> U62#(proper X1, proper X2)) (proper# s X -> proper# X, proper# U62(X1, X2) -> proper# X1) (proper# s X -> proper# X, proper# U62(X1, X2) -> proper# X2) (proper# s X -> proper# X, proper# isNat X -> isNat# proper X) (proper# s X -> proper# X, proper# isNat X -> proper# X) (proper# s X -> proper# X, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3)) (proper# s X -> proper# X, proper# U61(X1, X2, X3) -> proper# X1) (proper# s X -> proper# X, proper# U61(X1, X2, X3) -> proper# X2) (proper# s X -> proper# X, proper# U61(X1, X2, X3) -> proper# X3) (proper# s X -> proper# X, proper# s X -> s# proper X) (proper# s X -> proper# X, proper# s X -> proper# X) (proper# s X -> proper# X, proper# length X -> length# proper X) (proper# s X -> proper# X, proper# length X -> proper# X) (proper# isNatList X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# isNatList X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# isNatList X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# isNatList X -> proper# X, proper# U11 X -> U11# proper X) (proper# isNatList X -> proper# X, proper# U11 X -> proper# X) (proper# isNatList X -> proper# X, proper# U21 X -> U21# proper X) (proper# isNatList X -> proper# X, proper# U21 X -> proper# X) (proper# isNatList X -> proper# X, proper# U31 X -> U31# proper X) (proper# isNatList X -> proper# X, proper# U31 X -> proper# X) (proper# isNatList X -> proper# X, proper# U42 X -> U42# proper X) (proper# isNatList X -> proper# X, proper# U42 X -> proper# X) (proper# isNatList X -> proper# X, proper# isNatIList X -> isNatIList# proper X) (proper# isNatList X -> proper# X, proper# isNatIList X -> proper# X) (proper# isNatList X -> proper# X, proper# U41(X1, X2) -> U41#(proper X1, proper X2)) (proper# isNatList X -> proper# X, proper# U41(X1, X2) -> proper# X1) (proper# isNatList X -> proper# X, proper# U41(X1, X2) -> proper# X2) (proper# isNatList X -> proper# X, proper# U52 X -> U52# proper X) (proper# isNatList X -> proper# X, proper# U52 X -> proper# X) (proper# isNatList X -> proper# X, proper# isNatList X -> isNatList# proper X) (proper# isNatList X -> proper# X, proper# isNatList X -> proper# X) (proper# isNatList X -> proper# X, proper# U51(X1, X2) -> U51#(proper X1, proper X2)) (proper# isNatList X -> proper# X, proper# U51(X1, X2) -> proper# X1) (proper# isNatList X -> proper# X, proper# U51(X1, X2) -> proper# X2) (proper# isNatList X -> proper# X, proper# U62(X1, X2) -> U62#(proper X1, proper X2)) (proper# isNatList X -> proper# X, proper# U62(X1, X2) -> proper# X1) (proper# isNatList X -> proper# X, proper# U62(X1, X2) -> proper# X2) (proper# isNatList X -> proper# X, proper# isNat X -> isNat# proper X) (proper# isNatList X -> proper# X, proper# isNat X -> proper# X) (proper# isNatList X -> proper# X, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3)) (proper# isNatList X -> proper# X, proper# U61(X1, X2, X3) -> proper# X1) (proper# isNatList X -> proper# X, proper# U61(X1, X2, X3) -> proper# X2) (proper# isNatList X -> proper# X, proper# U61(X1, X2, X3) -> proper# X3) (proper# isNatList X -> proper# X, proper# s X -> s# proper X) (proper# isNatList X -> proper# X, proper# s X -> proper# X) (proper# isNatList X -> proper# X, proper# length X -> length# proper X) (proper# isNatList X -> proper# X, proper# length X -> proper# X) (proper# 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# U11 X -> U11# proper X) (proper# isNatIList X -> proper# X, proper# U11 X -> proper# X) (proper# isNatIList X -> proper# X, proper# U21 X -> U21# proper X) (proper# isNatIList X -> proper# X, proper# U21 X -> proper# X) (proper# isNatIList X -> proper# X, proper# U31 X -> U31# proper X) (proper# isNatIList X -> proper# X, proper# U31 X -> proper# X) (proper# isNatIList X -> proper# X, proper# U42 X -> U42# proper X) (proper# isNatIList X -> proper# X, proper# U42 X -> proper# X) (proper# isNatIList X -> proper# X, proper# isNatIList X -> isNatIList# proper X) (proper# isNatIList X -> proper# X, proper# isNatIList X -> proper# X) (proper# isNatIList X -> proper# X, proper# U41(X1, X2) -> U41#(proper X1, proper X2)) (proper# isNatIList X -> proper# X, proper# U41(X1, X2) -> proper# X1) (proper# isNatIList X -> proper# X, proper# U41(X1, X2) -> proper# X2) (proper# isNatIList X -> proper# X, proper# U52 X -> U52# proper X) (proper# isNatIList X -> proper# X, proper# U52 X -> proper# X) (proper# isNatIList X -> proper# X, proper# isNatList X -> isNatList# proper X) (proper# isNatIList X -> proper# X, proper# isNatList X -> proper# X) (proper# isNatIList X -> proper# X, proper# U51(X1, X2) -> U51#(proper X1, proper X2)) (proper# isNatIList X -> proper# X, proper# U51(X1, X2) -> proper# X1) (proper# isNatIList X -> proper# X, proper# U51(X1, X2) -> proper# X2) (proper# isNatIList X -> proper# X, proper# U62(X1, X2) -> U62#(proper X1, proper X2)) (proper# isNatIList X -> proper# X, proper# U62(X1, X2) -> proper# X1) (proper# isNatIList X -> proper# X, proper# U62(X1, X2) -> proper# X2) (proper# isNatIList X -> proper# X, proper# isNat X -> isNat# proper X) (proper# isNatIList X -> proper# X, proper# isNat X -> proper# X) (proper# isNatIList X -> proper# X, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3)) (proper# isNatIList X -> proper# X, proper# U61(X1, X2, X3) -> proper# X1) (proper# isNatIList X -> proper# X, proper# U61(X1, X2, X3) -> proper# X2) (proper# isNatIList X -> proper# X, proper# U61(X1, X2, X3) -> proper# X3) (proper# isNatIList X -> proper# X, proper# 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# U31 X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# U31 X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# U31 X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# U31 X -> proper# X, proper# U11 X -> U11# proper X) (proper# U31 X -> proper# X, proper# U11 X -> proper# X) (proper# U31 X -> proper# X, proper# U21 X -> U21# proper X) (proper# U31 X -> proper# X, proper# U21 X -> proper# X) (proper# U31 X -> proper# X, proper# U31 X -> U31# proper X) (proper# U31 X -> proper# X, proper# U31 X -> proper# X) (proper# U31 X -> proper# X, proper# U42 X -> U42# proper X) (proper# U31 X -> proper# X, proper# U42 X -> proper# X) (proper# U31 X -> proper# X, proper# isNatIList X -> isNatIList# proper X) (proper# U31 X -> proper# X, proper# isNatIList X -> proper# X) (proper# U31 X -> proper# X, proper# U41(X1, X2) -> U41#(proper X1, proper X2)) (proper# U31 X -> proper# X, proper# U41(X1, X2) -> proper# X1) (proper# U31 X -> proper# X, proper# U41(X1, X2) -> proper# X2) (proper# U31 X -> proper# X, proper# U52 X -> U52# proper X) (proper# U31 X -> proper# X, proper# U52 X -> proper# X) (proper# U31 X -> proper# X, proper# isNatList X -> isNatList# proper X) (proper# U31 X -> proper# X, proper# isNatList X -> proper# X) (proper# U31 X -> proper# X, proper# U51(X1, X2) -> U51#(proper X1, proper X2)) (proper# U31 X -> proper# X, proper# U51(X1, X2) -> proper# X1) (proper# U31 X -> proper# X, proper# U51(X1, X2) -> proper# X2) (proper# U31 X -> proper# X, proper# U62(X1, X2) -> U62#(proper X1, proper X2)) (proper# U31 X -> proper# X, proper# U62(X1, X2) -> proper# X1) (proper# U31 X -> proper# X, proper# U62(X1, X2) -> proper# X2) (proper# U31 X -> proper# X, proper# isNat X -> isNat# proper X) (proper# U31 X -> proper# X, proper# isNat X -> proper# X) (proper# U31 X -> proper# X, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3)) (proper# U31 X -> proper# X, proper# U61(X1, X2, X3) -> proper# X1) (proper# U31 X -> proper# X, proper# U61(X1, X2, X3) -> proper# X2) (proper# U31 X -> proper# X, proper# U61(X1, X2, X3) -> proper# X3) (proper# U31 X -> proper# X, proper# s X -> s# proper X) (proper# U31 X -> proper# X, proper# s X -> proper# X) (proper# U31 X -> proper# X, proper# length X -> length# proper X) (proper# U31 X -> proper# X, proper# length X -> proper# X) (proper# U11 X -> proper# X, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# U11 X -> proper# X, proper# cons(X1, X2) -> proper# X1) (proper# U11 X -> proper# X, proper# cons(X1, X2) -> proper# X2) (proper# U11 X -> proper# X, proper# U11 X -> U11# proper X) (proper# U11 X -> proper# X, proper# U11 X -> proper# X) (proper# U11 X -> proper# X, proper# U21 X -> U21# proper X) (proper# U11 X -> proper# X, proper# U21 X -> proper# X) (proper# U11 X -> proper# X, proper# U31 X -> U31# proper X) (proper# U11 X -> proper# X, proper# U31 X -> proper# X) (proper# U11 X -> proper# X, proper# U42 X -> U42# proper X) (proper# U11 X -> proper# X, proper# U42 X -> proper# X) (proper# U11 X -> proper# X, proper# isNatIList X -> isNatIList# proper X) (proper# U11 X -> proper# X, proper# isNatIList X -> proper# X) (proper# U11 X -> proper# X, proper# U41(X1, X2) -> U41#(proper X1, proper X2)) (proper# U11 X -> proper# X, proper# U41(X1, X2) -> proper# X1) (proper# U11 X -> proper# X, proper# U41(X1, X2) -> proper# X2) (proper# U11 X -> proper# X, proper# U52 X -> U52# proper X) (proper# U11 X -> proper# X, proper# U52 X -> proper# X) (proper# U11 X -> proper# X, proper# isNatList X -> isNatList# proper X) (proper# U11 X -> proper# X, proper# isNatList X -> proper# X) (proper# U11 X -> proper# X, proper# U51(X1, X2) -> U51#(proper X1, proper X2)) (proper# U11 X -> proper# X, proper# U51(X1, X2) -> proper# X1) (proper# U11 X -> proper# X, proper# U51(X1, X2) -> proper# X2) (proper# U11 X -> proper# X, proper# U62(X1, X2) -> U62#(proper X1, proper X2)) (proper# U11 X -> proper# X, proper# U62(X1, X2) -> proper# X1) (proper# U11 X -> proper# X, proper# U62(X1, X2) -> proper# X2) (proper# U11 X -> proper# X, proper# isNat X -> isNat# proper X) (proper# U11 X -> proper# X, proper# isNat X -> proper# X) (proper# U11 X -> proper# X, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3)) (proper# U11 X -> proper# X, proper# U61(X1, X2, X3) -> proper# X1) (proper# U11 X -> proper# X, proper# U61(X1, X2, X3) -> proper# X2) (proper# U11 X -> proper# X, proper# U61(X1, X2, X3) -> proper# X3) (proper# U11 X -> proper# X, proper# s X -> s# proper X) (proper# U11 X -> proper# X, proper# s X -> proper# X) (proper# U11 X -> proper# X, proper# length X -> length# proper X) (proper# U11 X -> proper# X, proper# length X -> proper# 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) (isNatList# ok X -> isNatList# X, isNatList# ok X -> isNatList# X) (U52# mark X -> U52# X, U52# mark X -> U52# X) (U52# mark X -> U52# X, U52# ok X -> U52# X) (U42# ok X -> U42# X, U42# mark X -> U42# X) (U42# ok X -> U42# X, U42# ok X -> U42# X) (U31# ok X -> U31# X, U31# mark X -> U31# X) (U31# ok X -> U31# X, U31# ok X -> U31# X) (U21# ok X -> U21# X, U21# mark X -> U21# X) (U21# ok X -> U21# X, U21# ok X -> U21# X) (U11# ok X -> U11# X, U11# mark X -> U11# X) (U11# ok X -> U11# X, U11# ok X -> U11# 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# U11 X -> active# X) (active# length X -> active# X, active# U11 X -> U11# active X) (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# U31 X -> active# X) (active# length X -> active# X, active# U31 X -> U31# active X) (active# length X -> active# X, active# U42 X -> active# X) (active# length X -> active# X, active# U42 X -> U42# active X) (active# length X -> active# X, active# isNatIList V -> U31# isNatList V) (active# length X -> active# X, active# isNatIList V -> isNatList# V) (active# length X -> 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isNatList# V2) (active# length X -> active# X, active# U62(X1, X2) -> active# X1) (active# length X -> active# X, active# U62(X1, X2) -> U62#(active X1, X2)) (active# length X -> active# X, active# U62(tt(), L) -> s# length L) (active# length X -> active# X, active# U62(tt(), L) -> length# L) (active# length X -> active# X, active# isNat s V1 -> U21# isNat V1) (active# length X -> active# X, active# isNat s V1 -> isNat# V1) (active# length X -> active# X, active# isNat length V1 -> U11# isNatList V1) (active# length X -> active# X, active# isNat length V1 -> isNatList# V1) (active# length X -> active# X, active# U61(X1, X2, X3) -> active# X1) (active# length X -> active# X, active# U61(X1, X2, X3) -> U61#(active X1, X2, X3)) (active# length X -> active# X, active# U61(tt(), L, N) -> U62#(isNat N, L)) (active# length X -> active# X, active# U61(tt(), L, N) -> isNat# N) (active# length X -> active# X, active# s X -> active# X) (active# length X -> active# X, active# s X -> s# active X) 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-> active# X1) (active# U41(X1, X2) -> active# X1, active# U61(X1, X2, X3) -> U61#(active X1, X2, X3)) (active# U41(X1, X2) -> active# X1, active# U61(tt(), L, N) -> U62#(isNat N, L)) (active# U41(X1, X2) -> active# X1, active# U61(tt(), L, N) -> isNat# N) (active# U41(X1, X2) -> active# X1, active# s X -> active# X) (active# U41(X1, X2) -> active# X1, active# s X -> s# active X) (active# U41(X1, X2) -> active# X1, active# length X -> active# X) (active# U41(X1, X2) -> active# X1, active# length X -> length# active X) (active# U41(X1, X2) -> active# X1, active# length cons(N, L) -> isNatList# L) (active# U41(X1, X2) -> active# X1, active# length cons(N, L) -> U61#(isNatList L, L, N)) (U61#(ok X1, ok X2, ok X3) -> U61#(X1, X2, X3), U61#(mark X1, X2, X3) -> U61#(X1, X2, X3)) (U61#(ok X1, ok X2, ok X3) -> U61#(X1, X2, X3), U61#(ok X1, ok X2, ok X3) -> U61#(X1, X2, X3)) (active# U61(X1, X2, X3) -> U61#(active X1, X2, X3), U61#(mark X1, X2, X3) -> U61#(X1, X2, X3)) (active# U61(X1, X2, X3) -> U61#(active X1, X2, X3), U61#(ok X1, ok X2, ok X3) -> U61#(X1, X2, X3)) (active# isNatIList V -> isNatList# V, isNatList# ok X -> isNatList# X) (proper# U62(X1, X2) -> U62#(proper X1, proper X2), U62#(mark X1, X2) -> U62#(X1, X2)) (proper# U62(X1, X2) -> U62#(proper X1, proper X2), U62#(ok X1, ok X2) -> U62#(X1, X2)) (proper# U41(X1, X2) -> U41#(proper X1, proper X2), U41#(mark X1, X2) -> U41#(X1, X2)) (proper# U41(X1, X2) -> U41#(proper X1, proper X2), U41#(ok X1, ok X2) -> U41#(X1, X2)) (active# U51(tt(), V2) -> U52# isNatList V2, U52# mark X -> U52# X) (active# U51(tt(), V2) -> U52# isNatList V2, U52# ok X -> U52# X) (active# U62(tt(), L) -> s# length L, s# mark X -> s# X) (active# U62(tt(), L) -> s# length L, s# ok X -> s# X) (active# isNat s V1 -> U21# isNat V1, U21# mark X -> U21# X) (active# isNat s V1 -> U21# isNat V1, U21# ok X -> U21# X) (top# ok X -> top# active X, top# mark X -> proper# X) (top# ok X -> top# active X, top# mark X -> top# proper X) (top# ok X -> top# active X, top# ok X -> active# X) (top# ok X -> top# active X, top# ok X -> top# active X) (proper# length X -> length# proper X, length# mark X -> length# X) (proper# length X -> length# proper X, length# ok X -> length# X) (proper# isNat X -> isNat# proper X, isNat# ok X -> isNat# X) (proper# U52 X -> U52# proper X, U52# mark X -> U52# X) (proper# U52 X -> U52# proper X, U52# ok X -> U52# X) (proper# U42 X -> U42# proper X, U42# mark X -> U42# X) (proper# U42 X -> U42# proper X, U42# ok X -> U42# X) (proper# U21 X -> U21# proper X, U21# mark X -> U21# X) (proper# U21 X -> U21# proper X, U21# ok X -> U21# X) (active# length X -> length# active X, length# mark X -> length# X) (active# length X -> length# active X, length# ok X -> length# X) (active# U52 X -> U52# active X, U52# mark X -> U52# X) (active# U52 X -> U52# active X, U52# ok X -> U52# X) (active# U31 X -> U31# active X, U31# mark X -> U31# X) (active# U31 X -> U31# active X, U31# ok X -> U31# X) (active# U11 X -> U11# active X, U11# mark X -> U11# X) (active# U11 X -> U11# active X, U11# ok X -> U11# X) (active# isNat s V1 -> isNat# V1, isNat# ok X -> isNat# X) (active# isNatIList cons(V1, V2) -> isNat# V1, isNat# ok X -> isNat# X) (proper# U61(X1, X2, X3) -> proper# X3, proper# cons(X1, X2) -> cons#(proper X1, proper X2)) (proper# U61(X1, X2, X3) -> proper# X3, proper# cons(X1, X2) -> proper# X1) (proper# U61(X1, X2, X3) -> proper# X3, proper# cons(X1, X2) -> proper# X2) (proper# U61(X1, X2, X3) -> proper# X3, proper# U11 X -> U11# proper X) (proper# U61(X1, X2, X3) -> proper# X3, proper# U11 X -> proper# X) (proper# U61(X1, X2, X3) -> proper# X3, proper# U21 X -> U21# proper X) (proper# U61(X1, X2, X3) -> proper# X3, proper# U21 X -> proper# X) (proper# U61(X1, X2, X3) -> proper# X3, proper# U31 X -> U31# proper X) (proper# U61(X1, X2, X3) -> proper# X3, proper# U31 X -> proper# X) (proper# U61(X1, X2, X3) -> proper# X3, proper# U42 X -> U42# proper X) (proper# U61(X1, X2, X3) -> proper# X3, proper# U42 X -> proper# X) (proper# U61(X1, X2, X3) -> proper# X3, proper# isNatIList X -> isNatIList# proper X) (proper# U61(X1, X2, X3) -> proper# X3, proper# isNatIList X -> proper# X) (proper# U61(X1, X2, X3) -> proper# X3, proper# U41(X1, X2) -> U41#(proper X1, proper X2)) (proper# U61(X1, X2, X3) -> proper# X3, proper# U41(X1, X2) -> proper# X1) (proper# U61(X1, X2, X3) -> proper# X3, proper# U41(X1, X2) -> proper# X2) (proper# U61(X1, X2, X3) -> proper# X3, proper# U52 X -> U52# proper X) (proper# U61(X1, X2, X3) -> proper# X3, proper# U52 X -> proper# X) (proper# U61(X1, X2, X3) -> proper# X3, proper# isNatList X -> isNatList# proper X) (proper# U61(X1, X2, X3) -> proper# X3, proper# isNatList X -> proper# X) (proper# U61(X1, X2, X3) -> proper# X3, proper# U51(X1, X2) -> U51#(proper X1, proper X2)) (proper# U61(X1, X2, X3) -> proper# X3, proper# U51(X1, X2) -> proper# X1) (proper# U61(X1, X2, X3) -> proper# X3, proper# U51(X1, X2) -> proper# X2) (proper# U61(X1, X2, X3) -> proper# X3, proper# U62(X1, X2) -> U62#(proper X1, proper X2)) (proper# U61(X1, X2, X3) -> proper# X3, proper# U62(X1, X2) -> proper# X1) (proper# U61(X1, X2, X3) -> proper# X3, proper# U62(X1, X2) -> proper# X2) (proper# U61(X1, X2, X3) -> proper# X3, proper# isNat X -> isNat# proper X) (proper# U61(X1, X2, X3) -> proper# X3, proper# isNat X -> proper# X) (proper# U61(X1, X2, X3) -> proper# X3, proper# U61(X1, X2, X3) -> U61#(proper X1, proper X2, proper X3)) (proper# U61(X1, X2, X3) -> proper# X3, proper# U61(X1, X2, X3) -> proper# X1) (proper# U61(X1, X2, X3) -> proper# X3, proper# U61(X1, X2, X3) -> proper# X2) (proper# U61(X1, X2, X3) -> proper# X3, proper# U61(X1, X2, X3) -> proper# X3) (proper# U61(X1, X2, X3) -> proper# X3, proper# s X -> s# proper X) (proper# U61(X1, X2, X3) -> proper# X3, proper# s X -> proper# X) (proper# U61(X1, X2, X3) -> proper# X3, proper# length X -> length# proper X) (proper# U61(X1, X2, X3) -> proper# X3, proper# length X -> proper# X) } STATUS: arrows: 0.878827 SCCS (18): Scc: {top# mark X -> top# proper X, top# ok X -> top# active X} Scc: { active# cons(X1, X2) -> active# X1, active# U11 X -> active# X, active# U21 X -> active# X, active# U31 X -> active# X, active# U42 X -> active# X, active# U41(X1, X2) -> active# X1, active# U52 X -> active# X, active# U51(X1, X2) -> active# X1, active# U62(X1, X2) -> active# X1, active# U61(X1, X2, X3) -> active# X1, active# s X -> active# X, active# length X -> active# X} Scc: { proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# U11 X -> proper# X, proper# U21 X -> proper# X, proper# U31 X -> proper# X, proper# U42 X -> proper# X, proper# isNatIList X -> proper# X, proper# U41(X1, X2) -> proper# X1, proper# U41(X1, X2) -> proper# X2, proper# U52 X -> proper# X, proper# isNatList X -> proper# X, proper# U51(X1, X2) -> proper# X1, proper# U51(X1, X2) -> proper# X2, proper# U62(X1, X2) -> proper# X1, proper# U62(X1, X2) -> proper# X2, proper# isNat X -> proper# X, proper# U61(X1, X2, X3) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X3, proper# s X -> proper# X, proper# length X -> proper# X} Scc: {length# mark X -> length# X, length# ok X -> length# X} Scc: {s# mark X -> s# X, s# ok X -> s# X} Scc: { U61#(mark X1, X2, X3) -> U61#(X1, X2, X3), U61#(ok X1, ok X2, ok X3) -> U61#(X1, X2, X3)} Scc: {isNat# ok X -> isNat# X} Scc: { U62#(mark X1, X2) -> U62#(X1, X2), U62#(ok X1, ok X2) -> U62#(X1, X2)} Scc: { U51#(mark X1, X2) -> U51#(X1, X2), U51#(ok X1, ok X2) -> U51#(X1, X2)} Scc: {isNatList# ok X -> isNatList# X} Scc: {U52# mark X -> U52# X, U52# ok X -> U52# X} Scc: { U41#(mark X1, X2) -> U41#(X1, X2), U41#(ok X1, ok X2) -> U41#(X1, X2)} Scc: {isNatIList# ok X -> isNatIList# X} Scc: {U42# mark X -> U42# X, U42# ok X -> U42# X} Scc: {U31# mark X -> U31# X, U31# ok X -> U31# X} Scc: {U21# mark X -> U21# X, U21# ok X -> U21# X} Scc: {U11# mark X -> U11# X, U11# ok X -> U11# X} Scc: { cons#(mark X1, X2) -> cons#(X1, X2), cons#(ok X1, ok X2) -> cons#(X1, X2)} 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 U11 X -> U11 active X, active U11 tt() -> mark tt(), active U21 X -> U21 active X, active U21 tt() -> mark tt(), active U31 X -> U31 active X, active U31 tt() -> mark tt(), active U42 X -> U42 active X, active U42 tt() -> mark tt(), active isNatIList V -> mark U31 isNatList V, active isNatIList cons(V1, V2) -> mark U41(isNat V1, V2), active isNatIList zeros() -> mark tt(), active U41(X1, X2) -> U41(active X1, X2), active U41(tt(), V2) -> mark U42 isNatIList V2, active U52 X -> U52 active X, active U52 tt() -> mark tt(), active isNatList cons(V1, V2) -> mark U51(isNat V1, V2), active isNatList nil() -> mark tt(), active U51(X1, X2) -> U51(active X1, X2), active U51(tt(), V2) -> mark U52 isNatList V2, active U62(X1, X2) -> U62(active X1, X2), active U62(tt(), L) -> mark s length L, active isNat 0() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat length V1 -> mark U11 isNatList V1, active U61(X1, X2, X3) -> U61(active X1, X2, X3), active U61(tt(), L, N) -> mark U62(isNat N, L), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U61(isNatList L, L, N), active length nil() -> mark 0(), U11 mark X -> mark U11 X, U11 ok X -> ok U11 X, U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, U31 mark X -> mark U31 X, U31 ok X -> ok U31 X, U42 mark X -> mark U42 X, U42 ok X -> ok U42 X, isNatIList ok X -> ok isNatIList X, U41(mark X1, X2) -> mark U41(X1, X2), U41(ok X1, ok X2) -> ok U41(X1, X2), U52 mark X -> mark U52 X, U52 ok X -> ok U52 X, isNatList ok X -> ok isNatList X, U51(mark X1, X2) -> mark U51(X1, X2), U51(ok X1, ok X2) -> ok U51(X1, X2), U62(mark X1, X2) -> mark U62(X1, X2), U62(ok X1, ok X2) -> ok U62(X1, X2), isNat ok X -> ok isNat X, U61(mark X1, X2, X3) -> mark U61(X1, X2, X3), U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper tt() -> ok tt(), proper U11 X -> U11 proper X, proper U21 X -> U21 proper X, proper U31 X -> U31 proper X, proper U42 X -> U42 proper X, proper isNatIList X -> isNatIList proper X, proper U41(X1, X2) -> U41(proper X1, proper X2), proper U52 X -> U52 proper X, proper isNatList X -> isNatList proper X, proper U51(X1, X2) -> U51(proper X1, proper X2), proper U62(X1, X2) -> U62(proper X1, proper X2), proper isNat X -> isNat proper X, proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3), proper s X -> s proper X, proper length X -> length proper X, proper nil() -> ok nil(), top mark X -> top proper X, top ok X -> top active X} Open SCC (12): Strict: { active# cons(X1, X2) -> active# X1, active# U11 X -> active# X, active# U21 X -> active# X, active# U31 X -> active# X, active# U42 X -> active# X, active# U41(X1, X2) -> active# X1, active# U52 X -> active# X, active# U51(X1, X2) -> active# X1, active# U62(X1, X2) -> active# X1, active# U61(X1, X2, X3) -> active# X1, active# s X -> active# X, active# length X -> 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 U11 X -> U11 active X, active U11 tt() -> mark tt(), active U21 X -> U21 active X, active U21 tt() -> mark tt(), active U31 X -> U31 active X, active U31 tt() -> mark tt(), active U42 X -> U42 active X, active U42 tt() -> mark tt(), active isNatIList V -> mark U31 isNatList V, active isNatIList cons(V1, V2) -> mark U41(isNat V1, V2), active isNatIList zeros() -> mark tt(), active U41(X1, X2) -> U41(active X1, X2), active U41(tt(), V2) -> mark U42 isNatIList V2, active U52 X -> U52 active X, active U52 tt() -> mark tt(), active isNatList cons(V1, V2) -> mark U51(isNat V1, V2), active isNatList nil() -> mark tt(), active U51(X1, X2) -> U51(active X1, X2), active U51(tt(), V2) -> mark U52 isNatList V2, active U62(X1, X2) -> U62(active X1, X2), active U62(tt(), L) -> mark s length L, active isNat 0() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat length V1 -> mark U11 isNatList V1, active U61(X1, X2, X3) -> U61(active X1, X2, X3), active U61(tt(), L, N) -> mark U62(isNat N, L), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U61(isNatList L, L, N), active length nil() -> mark 0(), U11 mark X -> mark U11 X, U11 ok X -> ok U11 X, U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, U31 mark X -> mark U31 X, U31 ok X -> ok U31 X, U42 mark X -> mark U42 X, U42 ok X -> ok U42 X, isNatIList ok X -> ok isNatIList X, U41(mark X1, X2) -> mark U41(X1, X2), U41(ok X1, ok X2) -> ok U41(X1, X2), U52 mark X -> mark U52 X, U52 ok X -> ok U52 X, isNatList ok X -> ok isNatList X, U51(mark X1, X2) -> mark U51(X1, X2), U51(ok X1, ok X2) -> ok U51(X1, X2), U62(mark X1, X2) -> mark U62(X1, X2), U62(ok X1, ok X2) -> ok U62(X1, X2), isNat ok X -> ok isNat X, U61(mark X1, X2, X3) -> mark U61(X1, X2, X3), U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper tt() -> ok tt(), proper U11 X -> U11 proper X, proper U21 X -> U21 proper X, proper U31 X -> U31 proper X, proper U42 X -> U42 proper X, proper isNatIList X -> isNatIList proper X, proper U41(X1, X2) -> U41(proper X1, proper X2), proper U52 X -> U52 proper X, proper isNatList X -> isNatList proper X, proper U51(X1, X2) -> U51(proper X1, proper X2), proper U62(X1, X2) -> U62(proper X1, proper X2), proper isNat X -> isNat proper X, proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3), proper s X -> s proper X, proper length X -> length proper X, proper nil() -> ok nil(), top mark X -> top proper X, top ok X -> top active X} Open SCC (21): Strict: { proper# cons(X1, X2) -> proper# X1, proper# cons(X1, X2) -> proper# X2, proper# U11 X -> proper# X, proper# U21 X -> proper# X, proper# U31 X -> proper# X, proper# U42 X -> proper# X, proper# isNatIList X -> proper# X, proper# U41(X1, X2) -> proper# X1, proper# U41(X1, X2) -> proper# X2, proper# U52 X -> proper# X, proper# isNatList X -> proper# X, proper# U51(X1, X2) -> proper# X1, proper# U51(X1, X2) -> proper# X2, proper# U62(X1, X2) -> proper# X1, proper# U62(X1, X2) -> proper# X2, proper# isNat X -> proper# X, proper# U61(X1, X2, X3) -> proper# X1, proper# U61(X1, X2, X3) -> proper# X2, proper# U61(X1, X2, X3) -> proper# X3, proper# s X -> proper# X, proper# length 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 U11 X -> U11 active X, active U11 tt() -> mark tt(), active U21 X -> U21 active X, active U21 tt() -> mark tt(), active U31 X -> U31 active X, active U31 tt() -> mark tt(), active U42 X -> U42 active X, active U42 tt() -> mark tt(), active isNatIList V -> mark U31 isNatList V, active isNatIList cons(V1, V2) -> mark U41(isNat V1, V2), active isNatIList zeros() -> mark tt(), active U41(X1, X2) -> U41(active X1, X2), active U41(tt(), V2) -> mark U42 isNatIList V2, active U52 X -> U52 active X, active U52 tt() -> mark tt(), active isNatList cons(V1, V2) -> mark U51(isNat V1, V2), active isNatList nil() -> mark tt(), active U51(X1, X2) -> U51(active X1, X2), active U51(tt(), V2) -> mark U52 isNatList V2, active U62(X1, X2) -> U62(active X1, X2), active U62(tt(), L) -> mark s length L, active isNat 0() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat length V1 -> mark U11 isNatList V1, active U61(X1, X2, X3) -> U61(active X1, X2, X3), active U61(tt(), L, N) -> mark U62(isNat N, L), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U61(isNatList L, L, N), active length nil() -> mark 0(), U11 mark X -> mark U11 X, U11 ok X -> ok U11 X, U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, U31 mark X -> mark U31 X, U31 ok X -> ok U31 X, U42 mark X -> mark U42 X, U42 ok X -> ok U42 X, isNatIList ok X -> ok isNatIList X, U41(mark X1, X2) -> mark U41(X1, X2), U41(ok X1, ok X2) -> ok U41(X1, X2), U52 mark X -> mark U52 X, U52 ok X -> ok U52 X, isNatList ok X -> ok isNatList X, U51(mark X1, X2) -> mark U51(X1, X2), U51(ok X1, ok X2) -> ok U51(X1, X2), U62(mark X1, X2) -> mark U62(X1, X2), U62(ok X1, ok X2) -> ok U62(X1, X2), isNat ok X -> ok isNat X, U61(mark X1, X2, X3) -> mark U61(X1, X2, X3), U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper tt() -> ok tt(), proper U11 X -> U11 proper X, proper U21 X -> U21 proper X, proper U31 X -> U31 proper X, proper U42 X -> U42 proper X, proper isNatIList X -> isNatIList proper X, proper U41(X1, X2) -> U41(proper X1, proper X2), proper U52 X -> U52 proper X, proper isNatList X -> isNatList proper X, proper U51(X1, X2) -> U51(proper X1, proper X2), proper U62(X1, X2) -> U62(proper X1, proper X2), proper isNat X -> isNat proper X, proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3), proper s X -> s proper X, proper length X -> length proper X, proper nil() -> ok nil(), 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 U11 X -> U11 active X, active U11 tt() -> mark tt(), active U21 X -> U21 active X, active U21 tt() -> mark tt(), active U31 X -> U31 active X, active U31 tt() -> mark tt(), active U42 X -> U42 active X, active U42 tt() -> mark tt(), active isNatIList V -> mark U31 isNatList V, active isNatIList cons(V1, V2) -> mark U41(isNat V1, V2), active isNatIList zeros() -> mark tt(), active U41(X1, X2) -> U41(active X1, X2), active U41(tt(), V2) -> mark U42 isNatIList V2, active U52 X -> U52 active X, active U52 tt() -> mark tt(), active isNatList cons(V1, V2) -> mark U51(isNat V1, V2), active isNatList nil() -> mark tt(), active U51(X1, X2) -> U51(active X1, X2), active U51(tt(), V2) -> mark U52 isNatList V2, active U62(X1, X2) -> U62(active X1, X2), active U62(tt(), L) -> mark s length L, active isNat 0() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat length V1 -> mark U11 isNatList V1, active U61(X1, X2, X3) -> U61(active X1, X2, X3), active U61(tt(), L, N) -> mark U62(isNat N, L), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U61(isNatList L, L, N), active length nil() -> mark 0(), U11 mark X -> mark U11 X, U11 ok X -> ok U11 X, U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, U31 mark X -> mark U31 X, U31 ok X -> ok U31 X, U42 mark X -> mark U42 X, U42 ok X -> ok U42 X, isNatIList ok X -> ok isNatIList X, U41(mark X1, X2) -> mark U41(X1, X2), U41(ok X1, ok X2) -> ok U41(X1, X2), U52 mark X -> mark U52 X, U52 ok X -> ok U52 X, isNatList ok X -> ok isNatList X, U51(mark X1, X2) -> mark U51(X1, X2), U51(ok X1, ok X2) -> ok U51(X1, X2), U62(mark X1, X2) -> mark U62(X1, X2), U62(ok X1, ok X2) -> ok U62(X1, X2), isNat ok X -> ok isNat X, U61(mark X1, X2, X3) -> mark U61(X1, X2, X3), U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper tt() -> ok tt(), proper U11 X -> U11 proper X, proper U21 X -> U21 proper X, proper U31 X -> U31 proper X, proper U42 X -> U42 proper X, proper isNatIList X -> isNatIList proper X, proper U41(X1, X2) -> U41(proper X1, proper X2), proper U52 X -> U52 proper X, proper isNatList X -> isNatList proper X, proper U51(X1, X2) -> U51(proper X1, proper X2), proper U62(X1, X2) -> U62(proper X1, proper X2), proper isNat X -> isNat proper X, proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3), proper s X -> s proper X, proper length X -> length proper X, proper nil() -> ok nil(), 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 U11 X -> U11 active X, active U11 tt() -> mark tt(), active U21 X -> U21 active X, active U21 tt() -> mark tt(), active U31 X -> U31 active X, active U31 tt() -> mark tt(), active U42 X -> U42 active X, active U42 tt() -> mark tt(), active isNatIList V -> mark U31 isNatList V, active isNatIList cons(V1, V2) -> mark U41(isNat V1, V2), active isNatIList zeros() -> mark tt(), active U41(X1, X2) -> U41(active X1, X2), active U41(tt(), V2) -> mark U42 isNatIList V2, active U52 X -> U52 active X, active U52 tt() -> mark tt(), active isNatList cons(V1, V2) -> mark U51(isNat V1, V2), active isNatList nil() -> mark tt(), active U51(X1, X2) -> U51(active X1, X2), active U51(tt(), V2) -> mark U52 isNatList V2, active U62(X1, X2) -> U62(active X1, X2), active U62(tt(), L) -> mark s length L, active isNat 0() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat length V1 -> mark U11 isNatList V1, active U61(X1, X2, X3) -> U61(active X1, X2, X3), active U61(tt(), L, N) -> mark U62(isNat N, L), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U61(isNatList L, L, N), active length nil() -> mark 0(), U11 mark X -> mark U11 X, U11 ok X -> ok U11 X, U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, U31 mark X -> mark U31 X, U31 ok X -> ok U31 X, U42 mark X -> mark U42 X, U42 ok X -> ok U42 X, isNatIList ok X -> ok isNatIList X, U41(mark X1, X2) -> mark U41(X1, X2), U41(ok X1, ok X2) -> ok U41(X1, X2), U52 mark X -> mark U52 X, U52 ok X -> ok U52 X, isNatList ok X -> ok isNatList X, U51(mark X1, X2) -> mark U51(X1, X2), U51(ok X1, ok X2) -> ok U51(X1, X2), U62(mark X1, X2) -> mark U62(X1, X2), U62(ok X1, ok X2) -> ok U62(X1, X2), isNat ok X -> ok isNat X, U61(mark X1, X2, X3) -> mark U61(X1, X2, X3), U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper tt() -> ok tt(), proper U11 X -> U11 proper X, proper U21 X -> U21 proper X, proper U31 X -> U31 proper X, proper U42 X -> U42 proper X, proper isNatIList X -> isNatIList proper X, proper U41(X1, X2) -> U41(proper X1, proper X2), proper U52 X -> U52 proper X, proper isNatList X -> isNatList proper X, proper U51(X1, X2) -> U51(proper X1, proper X2), proper U62(X1, X2) -> U62(proper X1, proper X2), proper isNat X -> isNat proper X, proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3), proper s X -> s proper X, proper length X -> length proper X, proper nil() -> ok nil(), top mark X -> top proper X, top ok X -> top active X} Open SCC (2): Strict: { U61#(mark X1, X2, X3) -> U61#(X1, X2, X3), U61#(ok X1, ok X2, ok X3) -> U61#(X1, X2, X3)} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active U11 X -> U11 active X, active U11 tt() -> mark tt(), active U21 X -> U21 active X, active U21 tt() -> mark tt(), active U31 X -> U31 active X, active U31 tt() -> mark tt(), active U42 X -> U42 active X, active U42 tt() -> mark tt(), active isNatIList V -> mark U31 isNatList V, active isNatIList cons(V1, V2) -> mark U41(isNat V1, V2), active isNatIList zeros() -> mark tt(), active U41(X1, X2) -> U41(active X1, X2), active U41(tt(), V2) -> mark U42 isNatIList V2, active U52 X -> U52 active X, active U52 tt() -> mark tt(), active isNatList cons(V1, V2) -> mark U51(isNat V1, V2), active isNatList nil() -> mark tt(), active U51(X1, X2) -> U51(active X1, X2), active U51(tt(), V2) -> mark U52 isNatList V2, active U62(X1, X2) -> U62(active X1, X2), active U62(tt(), L) -> mark s length L, active isNat 0() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat length V1 -> mark U11 isNatList V1, active U61(X1, X2, X3) -> U61(active X1, X2, X3), active U61(tt(), L, N) -> mark U62(isNat N, L), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U61(isNatList L, L, N), active length nil() -> mark 0(), U11 mark X -> mark U11 X, U11 ok X -> ok U11 X, U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, U31 mark X -> mark U31 X, U31 ok X -> ok U31 X, U42 mark X -> mark U42 X, U42 ok X -> ok U42 X, isNatIList ok X -> ok isNatIList X, U41(mark X1, X2) -> mark U41(X1, X2), U41(ok X1, ok X2) -> ok U41(X1, X2), U52 mark X -> mark U52 X, U52 ok X -> ok U52 X, isNatList ok X -> ok isNatList X, U51(mark X1, X2) -> mark U51(X1, X2), U51(ok X1, ok X2) -> ok U51(X1, X2), U62(mark X1, X2) -> mark U62(X1, X2), U62(ok X1, ok X2) -> ok U62(X1, X2), isNat ok X -> ok isNat X, U61(mark X1, X2, X3) -> mark U61(X1, X2, X3), U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper tt() -> ok tt(), proper U11 X -> U11 proper X, proper U21 X -> U21 proper X, proper U31 X -> U31 proper X, proper U42 X -> U42 proper X, proper isNatIList X -> isNatIList proper X, proper U41(X1, X2) -> U41(proper X1, proper X2), proper U52 X -> U52 proper X, proper isNatList X -> isNatList proper X, proper U51(X1, X2) -> U51(proper X1, proper X2), proper U62(X1, X2) -> U62(proper X1, proper X2), proper isNat X -> isNat proper X, proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3), proper s X -> s proper X, proper length X -> length proper X, proper nil() -> ok nil(), 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 U11 X -> U11 active X, active U11 tt() -> mark tt(), active U21 X -> U21 active X, active U21 tt() -> mark tt(), active U31 X -> U31 active X, active U31 tt() -> mark tt(), active U42 X -> U42 active X, active U42 tt() -> mark tt(), active isNatIList V -> mark U31 isNatList V, active isNatIList cons(V1, V2) -> mark U41(isNat V1, V2), active isNatIList zeros() -> mark tt(), active U41(X1, X2) -> U41(active X1, X2), active U41(tt(), V2) -> mark U42 isNatIList V2, active U52 X -> U52 active X, active U52 tt() -> mark tt(), active isNatList cons(V1, V2) -> mark U51(isNat V1, V2), active isNatList nil() -> mark tt(), active U51(X1, X2) -> U51(active X1, X2), active U51(tt(), V2) -> mark U52 isNatList V2, active U62(X1, X2) -> U62(active X1, X2), active U62(tt(), L) -> mark s length L, active isNat 0() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat length V1 -> mark U11 isNatList V1, active U61(X1, X2, X3) -> U61(active X1, X2, X3), active U61(tt(), L, N) -> mark U62(isNat N, L), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U61(isNatList L, L, N), active length nil() -> mark 0(), U11 mark X -> mark U11 X, U11 ok X -> ok U11 X, U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, U31 mark X -> mark U31 X, U31 ok X -> ok U31 X, U42 mark X -> mark U42 X, U42 ok X -> ok U42 X, isNatIList ok X -> ok isNatIList X, U41(mark X1, X2) -> mark U41(X1, X2), U41(ok X1, ok X2) -> ok U41(X1, X2), U52 mark X -> mark U52 X, U52 ok X -> ok U52 X, isNatList ok X -> ok isNatList X, U51(mark X1, X2) -> mark U51(X1, X2), U51(ok X1, ok X2) -> ok U51(X1, X2), U62(mark X1, X2) -> mark U62(X1, X2), U62(ok X1, ok X2) -> ok U62(X1, X2), isNat ok X -> ok isNat X, U61(mark X1, X2, X3) -> mark U61(X1, X2, X3), U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper tt() -> ok tt(), proper U11 X -> U11 proper X, proper U21 X -> U21 proper X, proper U31 X -> U31 proper X, proper U42 X -> U42 proper X, proper isNatIList X -> isNatIList proper X, proper U41(X1, X2) -> U41(proper X1, proper X2), proper U52 X -> U52 proper X, proper isNatList X -> isNatList proper X, proper U51(X1, X2) -> U51(proper X1, proper X2), proper U62(X1, X2) -> U62(proper X1, proper X2), proper isNat X -> isNat proper X, proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3), proper s X -> s proper X, proper length X -> length proper X, proper nil() -> ok nil(), top mark X -> top proper X, top ok X -> top active X} Open SCC (2): Strict: { U62#(mark X1, X2) -> U62#(X1, X2), U62#(ok X1, ok X2) -> U62#(X1, X2)} Weak: { cons(mark X1, X2) -> mark cons(X1, X2), cons(ok X1, ok X2) -> ok cons(X1, X2), active cons(X1, X2) -> cons(active X1, X2), active zeros() -> mark cons(0(), zeros()), active U11 X -> U11 active X, active U11 tt() -> mark tt(), active U21 X -> U21 active X, active U21 tt() -> mark tt(), active U31 X -> U31 active X, active U31 tt() -> mark tt(), active U42 X -> U42 active X, active U42 tt() -> mark tt(), active isNatIList V -> mark U31 isNatList V, active isNatIList cons(V1, V2) -> mark U41(isNat V1, V2), active isNatIList zeros() -> mark tt(), active U41(X1, X2) -> U41(active X1, X2), active U41(tt(), V2) -> mark U42 isNatIList V2, active U52 X -> U52 active X, active U52 tt() -> mark tt(), active isNatList cons(V1, V2) -> mark U51(isNat V1, V2), active isNatList nil() -> mark tt(), active U51(X1, X2) -> U51(active X1, X2), active U51(tt(), V2) -> mark U52 isNatList V2, active U62(X1, X2) -> U62(active X1, X2), active U62(tt(), L) -> mark s length L, active isNat 0() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat length V1 -> mark U11 isNatList V1, active U61(X1, X2, X3) -> U61(active X1, X2, X3), active U61(tt(), L, N) -> mark U62(isNat N, L), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U61(isNatList L, L, N), active length nil() -> mark 0(), U11 mark X -> mark U11 X, U11 ok X -> ok U11 X, U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, U31 mark X -> mark U31 X, U31 ok X -> ok U31 X, U42 mark X -> mark U42 X, U42 ok X -> ok U42 X, isNatIList ok X -> ok isNatIList X, U41(mark X1, X2) -> mark U41(X1, X2), U41(ok X1, ok X2) -> ok U41(X1, X2), U52 mark X -> mark U52 X, U52 ok X -> ok U52 X, isNatList ok X -> ok isNatList X, U51(mark X1, X2) -> mark U51(X1, X2), U51(ok X1, ok X2) -> ok U51(X1, X2), U62(mark X1, X2) -> mark U62(X1, X2), U62(ok X1, ok X2) -> ok U62(X1, X2), isNat ok X -> ok isNat X, U61(mark X1, X2, X3) -> mark U61(X1, X2, X3), U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper tt() -> ok tt(), proper U11 X -> U11 proper X, proper U21 X -> U21 proper X, proper U31 X -> U31 proper X, proper U42 X -> U42 proper X, proper isNatIList X -> isNatIList proper X, proper U41(X1, X2) -> U41(proper X1, proper X2), proper U52 X -> U52 proper X, proper isNatList X -> isNatList proper X, proper U51(X1, X2) -> U51(proper X1, proper X2), proper U62(X1, X2) -> U62(proper X1, proper X2), proper isNat X -> isNat proper X, proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3), proper s X -> s proper X, proper length X -> length proper X, proper nil() -> ok nil(), top mark X -> top proper X, top ok X -> top active X} Open SCC (2): Strict: { U51#(mark X1, X2) -> U51#(X1, X2), U51#(ok X1, ok X2) -> U51#(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 U11 X -> U11 active X, active U11 tt() -> mark tt(), active U21 X -> U21 active X, active U21 tt() -> mark tt(), active U31 X -> U31 active X, active U31 tt() -> mark tt(), active U42 X -> U42 active X, active U42 tt() -> mark tt(), active isNatIList V -> mark U31 isNatList V, active isNatIList cons(V1, V2) -> mark U41(isNat V1, V2), active isNatIList zeros() -> mark tt(), active U41(X1, X2) -> U41(active X1, X2), active U41(tt(), V2) -> mark U42 isNatIList V2, active U52 X -> U52 active X, active U52 tt() -> mark tt(), active isNatList cons(V1, V2) -> mark U51(isNat V1, V2), active isNatList nil() -> mark tt(), active U51(X1, X2) -> U51(active X1, X2), active U51(tt(), V2) -> mark U52 isNatList V2, active U62(X1, X2) -> U62(active X1, X2), active U62(tt(), L) -> mark s length L, active isNat 0() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat length V1 -> mark U11 isNatList V1, active U61(X1, X2, X3) -> U61(active X1, X2, X3), active U61(tt(), L, N) -> mark U62(isNat N, L), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U61(isNatList L, L, N), active length nil() -> mark 0(), U11 mark X -> mark U11 X, U11 ok X -> ok U11 X, U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, U31 mark X -> mark U31 X, U31 ok X -> ok U31 X, U42 mark X -> mark U42 X, U42 ok X -> ok U42 X, isNatIList ok X -> ok isNatIList X, U41(mark X1, X2) -> mark U41(X1, X2), U41(ok X1, ok X2) -> ok U41(X1, X2), U52 mark X -> mark U52 X, U52 ok X -> ok U52 X, isNatList ok X -> ok isNatList X, U51(mark X1, X2) -> mark U51(X1, X2), U51(ok X1, ok X2) -> ok U51(X1, X2), U62(mark X1, X2) -> mark U62(X1, X2), U62(ok X1, ok X2) -> ok U62(X1, X2), isNat ok X -> ok isNat X, U61(mark X1, X2, X3) -> mark U61(X1, X2, X3), U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper tt() -> ok tt(), proper U11 X -> U11 proper X, proper U21 X -> U21 proper X, proper U31 X -> U31 proper X, proper U42 X -> U42 proper X, proper isNatIList X -> isNatIList proper X, proper U41(X1, X2) -> U41(proper X1, proper X2), proper U52 X -> U52 proper X, proper isNatList X -> isNatList proper X, proper U51(X1, X2) -> U51(proper X1, proper X2), proper U62(X1, X2) -> U62(proper X1, proper X2), proper isNat X -> isNat proper X, proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3), proper s X -> s proper X, proper length X -> length proper X, proper nil() -> ok nil(), 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 U11 X -> U11 active X, active U11 tt() -> mark tt(), active U21 X -> U21 active X, active U21 tt() -> mark tt(), active U31 X -> U31 active X, active U31 tt() -> mark tt(), active U42 X -> U42 active X, active U42 tt() -> mark tt(), active isNatIList V -> mark U31 isNatList V, active isNatIList cons(V1, V2) -> mark U41(isNat V1, V2), active isNatIList zeros() -> mark tt(), active U41(X1, X2) -> U41(active X1, X2), active U41(tt(), V2) -> mark U42 isNatIList V2, active U52 X -> U52 active X, active U52 tt() -> mark tt(), active isNatList cons(V1, V2) -> mark U51(isNat V1, V2), active isNatList nil() -> mark tt(), active U51(X1, X2) -> U51(active X1, X2), active U51(tt(), V2) -> mark U52 isNatList V2, active U62(X1, X2) -> U62(active X1, X2), active U62(tt(), L) -> mark s length L, active isNat 0() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat length V1 -> mark U11 isNatList V1, active U61(X1, X2, X3) -> U61(active X1, X2, X3), active U61(tt(), L, N) -> mark U62(isNat N, L), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U61(isNatList L, L, N), active length nil() -> mark 0(), U11 mark X -> mark U11 X, U11 ok X -> ok U11 X, U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, U31 mark X -> mark U31 X, U31 ok X -> ok U31 X, U42 mark X -> mark U42 X, U42 ok X -> ok U42 X, isNatIList ok X -> ok isNatIList X, U41(mark X1, X2) -> mark U41(X1, X2), U41(ok X1, ok X2) -> ok U41(X1, X2), U52 mark X -> mark U52 X, U52 ok X -> ok U52 X, isNatList ok X -> ok isNatList X, U51(mark X1, X2) -> mark U51(X1, X2), U51(ok X1, ok X2) -> ok U51(X1, X2), U62(mark X1, X2) -> mark U62(X1, X2), U62(ok X1, ok X2) -> ok U62(X1, X2), isNat ok X -> ok isNat X, U61(mark X1, X2, X3) -> mark U61(X1, X2, X3), U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper tt() -> ok tt(), proper U11 X -> U11 proper X, proper U21 X -> U21 proper X, proper U31 X -> U31 proper X, proper U42 X -> U42 proper X, proper isNatIList X -> isNatIList proper X, proper U41(X1, X2) -> U41(proper X1, proper X2), proper U52 X -> U52 proper X, proper isNatList X -> isNatList proper X, proper U51(X1, X2) -> U51(proper X1, proper X2), proper U62(X1, X2) -> U62(proper X1, proper X2), proper isNat X -> isNat proper X, proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3), proper s X -> s proper X, proper length X -> length proper X, proper nil() -> ok nil(), top mark X -> top proper X, top ok X -> top active X} Open SCC (2): Strict: {U52# mark X -> U52# X, U52# ok X -> U52# 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 U11 X -> U11 active X, active U11 tt() -> mark tt(), active U21 X -> U21 active X, active U21 tt() -> mark tt(), active U31 X -> U31 active X, active U31 tt() -> mark tt(), active U42 X -> U42 active X, active U42 tt() -> mark tt(), active isNatIList V -> mark U31 isNatList V, active isNatIList cons(V1, V2) -> mark U41(isNat V1, V2), active isNatIList zeros() -> mark tt(), active U41(X1, X2) -> U41(active X1, X2), active U41(tt(), V2) -> mark U42 isNatIList V2, active U52 X -> U52 active X, active U52 tt() -> mark tt(), active isNatList cons(V1, V2) -> mark U51(isNat V1, V2), active isNatList nil() -> mark tt(), active U51(X1, X2) -> U51(active X1, X2), active U51(tt(), V2) -> mark U52 isNatList V2, active U62(X1, X2) -> U62(active X1, X2), active U62(tt(), L) -> mark s length L, active isNat 0() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat length V1 -> mark U11 isNatList V1, active U61(X1, X2, X3) -> U61(active X1, X2, X3), active U61(tt(), L, N) -> mark U62(isNat N, L), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U61(isNatList L, L, N), active length nil() -> mark 0(), U11 mark X -> mark U11 X, U11 ok X -> ok U11 X, U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, U31 mark X -> mark U31 X, U31 ok X -> ok U31 X, U42 mark X -> mark U42 X, U42 ok X -> ok U42 X, isNatIList ok X -> ok isNatIList X, U41(mark X1, X2) -> mark U41(X1, X2), U41(ok X1, ok X2) -> ok U41(X1, X2), U52 mark X -> mark U52 X, U52 ok X -> ok U52 X, isNatList ok X -> ok isNatList X, U51(mark X1, X2) -> mark U51(X1, X2), U51(ok X1, ok X2) -> ok U51(X1, X2), U62(mark X1, X2) -> mark U62(X1, X2), U62(ok X1, ok X2) -> ok U62(X1, X2), isNat ok X -> ok isNat X, U61(mark X1, X2, X3) -> mark U61(X1, X2, X3), U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper tt() -> ok tt(), proper U11 X -> U11 proper X, proper U21 X -> U21 proper X, proper U31 X -> U31 proper X, proper U42 X -> U42 proper X, proper isNatIList X -> isNatIList proper X, proper U41(X1, X2) -> U41(proper X1, proper X2), proper U52 X -> U52 proper X, proper isNatList X -> isNatList proper X, proper U51(X1, X2) -> U51(proper X1, proper X2), proper U62(X1, X2) -> U62(proper X1, proper X2), proper isNat X -> isNat proper X, proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3), proper s X -> s proper X, proper length X -> length proper X, proper nil() -> ok nil(), top mark X -> top proper X, top ok X -> top active X} Open SCC (2): Strict: { U41#(mark X1, X2) -> U41#(X1, X2), U41#(ok X1, ok X2) -> U41#(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 U11 X -> U11 active X, active U11 tt() -> mark tt(), active U21 X -> U21 active X, active U21 tt() -> mark tt(), active U31 X -> U31 active X, active U31 tt() -> mark tt(), active U42 X -> U42 active X, active U42 tt() -> mark tt(), active isNatIList V -> mark U31 isNatList V, active isNatIList cons(V1, V2) -> mark U41(isNat V1, V2), active isNatIList zeros() -> mark tt(), active U41(X1, X2) -> U41(active X1, X2), active U41(tt(), V2) -> mark U42 isNatIList V2, active U52 X -> U52 active X, active U52 tt() -> mark tt(), active isNatList cons(V1, V2) -> mark U51(isNat V1, V2), active isNatList nil() -> mark tt(), active U51(X1, X2) -> U51(active X1, X2), active U51(tt(), V2) -> mark U52 isNatList V2, active U62(X1, X2) -> U62(active X1, X2), active U62(tt(), L) -> mark s length L, active isNat 0() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat length V1 -> mark U11 isNatList V1, active U61(X1, X2, X3) -> U61(active X1, X2, X3), active U61(tt(), L, N) -> mark U62(isNat N, L), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U61(isNatList L, L, N), active length nil() -> mark 0(), U11 mark X -> mark U11 X, U11 ok X -> ok U11 X, U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, U31 mark X -> mark U31 X, U31 ok X -> ok U31 X, U42 mark X -> mark U42 X, U42 ok X -> ok U42 X, isNatIList ok X -> ok isNatIList X, U41(mark X1, X2) -> mark U41(X1, X2), U41(ok X1, ok X2) -> ok U41(X1, X2), U52 mark X -> mark U52 X, U52 ok X -> ok U52 X, isNatList ok X -> ok isNatList X, U51(mark X1, X2) -> mark U51(X1, X2), U51(ok X1, ok X2) -> ok U51(X1, X2), U62(mark X1, X2) -> mark U62(X1, X2), U62(ok X1, ok X2) -> ok U62(X1, X2), isNat ok X -> ok isNat X, U61(mark X1, X2, X3) -> mark U61(X1, X2, X3), U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper tt() -> ok tt(), proper U11 X -> U11 proper X, proper U21 X -> U21 proper X, proper U31 X -> U31 proper X, proper U42 X -> U42 proper X, proper isNatIList X -> isNatIList proper X, proper U41(X1, X2) -> U41(proper X1, proper X2), proper U52 X -> U52 proper X, proper isNatList X -> isNatList proper X, proper U51(X1, X2) -> U51(proper X1, proper X2), proper U62(X1, X2) -> U62(proper X1, proper X2), proper isNat X -> isNat proper X, proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3), proper s X -> s proper X, proper length X -> length proper X, proper nil() -> ok nil(), 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 U11 X -> U11 active X, active U11 tt() -> mark tt(), active U21 X -> U21 active X, active U21 tt() -> mark tt(), active U31 X -> U31 active X, active U31 tt() -> mark tt(), active U42 X -> U42 active X, active U42 tt() -> mark tt(), active isNatIList V -> mark U31 isNatList V, active isNatIList cons(V1, V2) -> mark U41(isNat V1, V2), active isNatIList zeros() -> mark tt(), active U41(X1, X2) -> U41(active X1, X2), active U41(tt(), V2) -> mark U42 isNatIList V2, active U52 X -> U52 active X, active U52 tt() -> mark tt(), active isNatList cons(V1, V2) -> mark U51(isNat V1, V2), active isNatList nil() -> mark tt(), active U51(X1, X2) -> U51(active X1, X2), active U51(tt(), V2) -> mark U52 isNatList V2, active U62(X1, X2) -> U62(active X1, X2), active U62(tt(), L) -> mark s length L, active isNat 0() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat length V1 -> mark U11 isNatList V1, active U61(X1, X2, X3) -> U61(active X1, X2, X3), active U61(tt(), L, N) -> mark U62(isNat N, L), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U61(isNatList L, L, N), active length nil() -> mark 0(), U11 mark X -> mark U11 X, U11 ok X -> ok U11 X, U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, U31 mark X -> mark U31 X, U31 ok X -> ok U31 X, U42 mark X -> mark U42 X, U42 ok X -> ok U42 X, isNatIList ok X -> ok isNatIList X, U41(mark X1, X2) -> mark U41(X1, X2), U41(ok X1, ok X2) -> ok U41(X1, X2), U52 mark X -> mark U52 X, U52 ok X -> ok U52 X, isNatList ok X -> ok isNatList X, U51(mark X1, X2) -> mark U51(X1, X2), U51(ok X1, ok X2) -> ok U51(X1, X2), U62(mark X1, X2) -> mark U62(X1, X2), U62(ok X1, ok X2) -> ok U62(X1, X2), isNat ok X -> ok isNat X, U61(mark X1, X2, X3) -> mark U61(X1, X2, X3), U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper tt() -> ok tt(), proper U11 X -> U11 proper X, proper U21 X -> U21 proper X, proper U31 X -> U31 proper X, proper U42 X -> U42 proper X, proper isNatIList X -> isNatIList proper X, proper U41(X1, X2) -> U41(proper X1, proper X2), proper U52 X -> U52 proper X, proper isNatList X -> isNatList proper X, proper U51(X1, X2) -> U51(proper X1, proper X2), proper U62(X1, X2) -> U62(proper X1, proper X2), proper isNat X -> isNat proper X, proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3), proper s X -> s proper X, proper length X -> length proper X, proper nil() -> ok nil(), top mark X -> top proper X, top ok X -> top active X} Open SCC (2): Strict: {U42# mark X -> U42# X, U42# ok X -> U42# 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 U11 X -> U11 active X, active U11 tt() -> mark tt(), active U21 X -> U21 active X, active U21 tt() -> mark tt(), active U31 X -> U31 active X, active U31 tt() -> mark tt(), active U42 X -> U42 active X, active U42 tt() -> mark tt(), active isNatIList V -> mark U31 isNatList V, active isNatIList cons(V1, V2) -> mark U41(isNat V1, V2), active isNatIList zeros() -> mark tt(), active U41(X1, X2) -> U41(active X1, X2), active U41(tt(), V2) -> mark U42 isNatIList V2, active U52 X -> U52 active X, active U52 tt() -> mark tt(), active isNatList cons(V1, V2) -> mark U51(isNat V1, V2), active isNatList nil() -> mark tt(), active U51(X1, X2) -> U51(active X1, X2), active U51(tt(), V2) -> mark U52 isNatList V2, active U62(X1, X2) -> U62(active X1, X2), active U62(tt(), L) -> mark s length L, active isNat 0() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat length V1 -> mark U11 isNatList V1, active U61(X1, X2, X3) -> U61(active X1, X2, X3), active U61(tt(), L, N) -> mark U62(isNat N, L), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U61(isNatList L, L, N), active length nil() -> mark 0(), U11 mark X -> mark U11 X, U11 ok X -> ok U11 X, U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, U31 mark X -> mark U31 X, U31 ok X -> ok U31 X, U42 mark X -> mark U42 X, U42 ok X -> ok U42 X, isNatIList ok X -> ok isNatIList X, U41(mark X1, X2) -> mark U41(X1, X2), U41(ok X1, ok X2) -> ok U41(X1, X2), U52 mark X -> mark U52 X, U52 ok X -> ok U52 X, isNatList ok X -> ok isNatList X, U51(mark X1, X2) -> mark U51(X1, X2), U51(ok X1, ok X2) -> ok U51(X1, X2), U62(mark X1, X2) -> mark U62(X1, X2), U62(ok X1, ok X2) -> ok U62(X1, X2), isNat ok X -> ok isNat X, U61(mark X1, X2, X3) -> mark U61(X1, X2, X3), U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper tt() -> ok tt(), proper U11 X -> U11 proper X, proper U21 X -> U21 proper X, proper U31 X -> U31 proper X, proper U42 X -> U42 proper X, proper isNatIList X -> isNatIList proper X, proper U41(X1, X2) -> U41(proper X1, proper X2), proper U52 X -> U52 proper X, proper isNatList X -> isNatList proper X, proper U51(X1, X2) -> U51(proper X1, proper X2), proper U62(X1, X2) -> U62(proper X1, proper X2), proper isNat X -> isNat proper X, proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3), proper s X -> s proper X, proper length X -> length proper X, proper nil() -> ok nil(), top mark X -> top proper X, top ok X -> top active X} Open SCC (2): Strict: {U31# mark X -> U31# X, U31# ok X -> U31# 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 U11 X -> U11 active X, active U11 tt() -> mark tt(), active U21 X -> U21 active X, active U21 tt() -> mark tt(), active U31 X -> U31 active X, active U31 tt() -> mark tt(), active U42 X -> U42 active X, active U42 tt() -> mark tt(), active isNatIList V -> mark U31 isNatList V, active isNatIList cons(V1, V2) -> mark U41(isNat V1, V2), active isNatIList zeros() -> mark tt(), active U41(X1, X2) -> U41(active X1, X2), active U41(tt(), V2) -> mark U42 isNatIList V2, active U52 X -> U52 active X, active U52 tt() -> mark tt(), active isNatList cons(V1, V2) -> mark U51(isNat V1, V2), active isNatList nil() -> mark tt(), active U51(X1, X2) -> U51(active X1, X2), active U51(tt(), V2) -> mark U52 isNatList V2, active U62(X1, X2) -> U62(active X1, X2), active U62(tt(), L) -> mark s length L, active isNat 0() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat length V1 -> mark U11 isNatList V1, active U61(X1, X2, X3) -> U61(active X1, X2, X3), active U61(tt(), L, N) -> mark U62(isNat N, L), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U61(isNatList L, L, N), active length nil() -> mark 0(), U11 mark X -> mark U11 X, U11 ok X -> ok U11 X, U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, U31 mark X -> mark U31 X, U31 ok X -> ok U31 X, U42 mark X -> mark U42 X, U42 ok X -> ok U42 X, isNatIList ok X -> ok isNatIList X, U41(mark X1, X2) -> mark U41(X1, X2), U41(ok X1, ok X2) -> ok U41(X1, X2), U52 mark X -> mark U52 X, U52 ok X -> ok U52 X, isNatList ok X -> ok isNatList X, U51(mark X1, X2) -> mark U51(X1, X2), U51(ok X1, ok X2) -> ok U51(X1, X2), U62(mark X1, X2) -> mark U62(X1, X2), U62(ok X1, ok X2) -> ok U62(X1, X2), isNat ok X -> ok isNat X, U61(mark X1, X2, X3) -> mark U61(X1, X2, X3), U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper tt() -> ok tt(), proper U11 X -> U11 proper X, proper U21 X -> U21 proper X, proper U31 X -> U31 proper X, proper U42 X -> U42 proper X, proper isNatIList X -> isNatIList proper X, proper U41(X1, X2) -> U41(proper X1, proper X2), proper U52 X -> U52 proper X, proper isNatList X -> isNatList proper X, proper U51(X1, X2) -> U51(proper X1, proper X2), proper U62(X1, X2) -> U62(proper X1, proper X2), proper isNat X -> isNat proper X, proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3), proper s X -> s proper X, proper length X -> length proper X, proper nil() -> ok nil(), 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 U11 X -> U11 active X, active U11 tt() -> mark tt(), active U21 X -> U21 active X, active U21 tt() -> mark tt(), active U31 X -> U31 active X, active U31 tt() -> mark tt(), active U42 X -> U42 active X, active U42 tt() -> mark tt(), active isNatIList V -> mark U31 isNatList V, active isNatIList cons(V1, V2) -> mark U41(isNat V1, V2), active isNatIList zeros() -> mark tt(), active U41(X1, X2) -> U41(active X1, X2), active U41(tt(), V2) -> mark U42 isNatIList V2, active U52 X -> U52 active X, active U52 tt() -> mark tt(), active isNatList cons(V1, V2) -> mark U51(isNat V1, V2), active isNatList nil() -> mark tt(), active U51(X1, X2) -> U51(active X1, X2), active U51(tt(), V2) -> mark U52 isNatList V2, active U62(X1, X2) -> U62(active X1, X2), active U62(tt(), L) -> mark s length L, active isNat 0() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat length V1 -> mark U11 isNatList V1, active U61(X1, X2, X3) -> U61(active X1, X2, X3), active U61(tt(), L, N) -> mark U62(isNat N, L), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U61(isNatList L, L, N), active length nil() -> mark 0(), U11 mark X -> mark U11 X, U11 ok X -> ok U11 X, U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, U31 mark X -> mark U31 X, U31 ok X -> ok U31 X, U42 mark X -> mark U42 X, U42 ok X -> ok U42 X, isNatIList ok X -> ok isNatIList X, U41(mark X1, X2) -> mark U41(X1, X2), U41(ok X1, ok X2) -> ok U41(X1, X2), U52 mark X -> mark U52 X, U52 ok X -> ok U52 X, isNatList ok X -> ok isNatList X, U51(mark X1, X2) -> mark U51(X1, X2), U51(ok X1, ok X2) -> ok U51(X1, X2), U62(mark X1, X2) -> mark U62(X1, X2), U62(ok X1, ok X2) -> ok U62(X1, X2), isNat ok X -> ok isNat X, U61(mark X1, X2, X3) -> mark U61(X1, X2, X3), U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper tt() -> ok tt(), proper U11 X -> U11 proper X, proper U21 X -> U21 proper X, proper U31 X -> U31 proper X, proper U42 X -> U42 proper X, proper isNatIList X -> isNatIList proper X, proper U41(X1, X2) -> U41(proper X1, proper X2), proper U52 X -> U52 proper X, proper isNatList X -> isNatList proper X, proper U51(X1, X2) -> U51(proper X1, proper X2), proper U62(X1, X2) -> U62(proper X1, proper X2), proper isNat X -> isNat proper X, proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3), proper s X -> s proper X, proper length X -> length proper X, proper nil() -> ok nil(), top mark X -> top proper X, top ok X -> top active X} Open SCC (2): Strict: {U11# mark X -> U11# X, U11# ok X -> U11# 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 U11 X -> U11 active X, active U11 tt() -> mark tt(), active U21 X -> U21 active X, active U21 tt() -> mark tt(), active U31 X -> U31 active X, active U31 tt() -> mark tt(), active U42 X -> U42 active X, active U42 tt() -> mark tt(), active isNatIList V -> mark U31 isNatList V, active isNatIList cons(V1, V2) -> mark U41(isNat V1, V2), active isNatIList zeros() -> mark tt(), active U41(X1, X2) -> U41(active X1, X2), active U41(tt(), V2) -> mark U42 isNatIList V2, active U52 X -> U52 active X, active U52 tt() -> mark tt(), active isNatList cons(V1, V2) -> mark U51(isNat V1, V2), active isNatList nil() -> mark tt(), active U51(X1, X2) -> U51(active X1, X2), active U51(tt(), V2) -> mark U52 isNatList V2, active U62(X1, X2) -> U62(active X1, X2), active U62(tt(), L) -> mark s length L, active isNat 0() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat length V1 -> mark U11 isNatList V1, active U61(X1, X2, X3) -> U61(active X1, X2, X3), active U61(tt(), L, N) -> mark U62(isNat N, L), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U61(isNatList L, L, N), active length nil() -> mark 0(), U11 mark X -> mark U11 X, U11 ok X -> ok U11 X, U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, U31 mark X -> mark U31 X, U31 ok X -> ok U31 X, U42 mark X -> mark U42 X, U42 ok X -> ok U42 X, isNatIList ok X -> ok isNatIList X, U41(mark X1, X2) -> mark U41(X1, X2), U41(ok X1, ok X2) -> ok U41(X1, X2), U52 mark X -> mark U52 X, U52 ok X -> ok U52 X, isNatList ok X -> ok isNatList X, U51(mark X1, X2) -> mark U51(X1, X2), U51(ok X1, ok X2) -> ok U51(X1, X2), U62(mark X1, X2) -> mark U62(X1, X2), U62(ok X1, ok X2) -> ok U62(X1, X2), isNat ok X -> ok isNat X, U61(mark X1, X2, X3) -> mark U61(X1, X2, X3), U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper tt() -> ok tt(), proper U11 X -> U11 proper X, proper U21 X -> U21 proper X, proper U31 X -> U31 proper X, proper U42 X -> U42 proper X, proper isNatIList X -> isNatIList proper X, proper U41(X1, X2) -> U41(proper X1, proper X2), proper U52 X -> U52 proper X, proper isNatList X -> isNatList proper X, proper U51(X1, X2) -> U51(proper X1, proper X2), proper U62(X1, X2) -> U62(proper X1, proper X2), proper isNat X -> isNat proper X, proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3), proper s X -> s proper X, proper length X -> length proper X, proper nil() -> ok nil(), 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 U11 X -> U11 active X, active U11 tt() -> mark tt(), active U21 X -> U21 active X, active U21 tt() -> mark tt(), active U31 X -> U31 active X, active U31 tt() -> mark tt(), active U42 X -> U42 active X, active U42 tt() -> mark tt(), active isNatIList V -> mark U31 isNatList V, active isNatIList cons(V1, V2) -> mark U41(isNat V1, V2), active isNatIList zeros() -> mark tt(), active U41(X1, X2) -> U41(active X1, X2), active U41(tt(), V2) -> mark U42 isNatIList V2, active U52 X -> U52 active X, active U52 tt() -> mark tt(), active isNatList cons(V1, V2) -> mark U51(isNat V1, V2), active isNatList nil() -> mark tt(), active U51(X1, X2) -> U51(active X1, X2), active U51(tt(), V2) -> mark U52 isNatList V2, active U62(X1, X2) -> U62(active X1, X2), active U62(tt(), L) -> mark s length L, active isNat 0() -> mark tt(), active isNat s V1 -> mark U21 isNat V1, active isNat length V1 -> mark U11 isNatList V1, active U61(X1, X2, X3) -> U61(active X1, X2, X3), active U61(tt(), L, N) -> mark U62(isNat N, L), active s X -> s active X, active length X -> length active X, active length cons(N, L) -> mark U61(isNatList L, L, N), active length nil() -> mark 0(), U11 mark X -> mark U11 X, U11 ok X -> ok U11 X, U21 mark X -> mark U21 X, U21 ok X -> ok U21 X, U31 mark X -> mark U31 X, U31 ok X -> ok U31 X, U42 mark X -> mark U42 X, U42 ok X -> ok U42 X, isNatIList ok X -> ok isNatIList X, U41(mark X1, X2) -> mark U41(X1, X2), U41(ok X1, ok X2) -> ok U41(X1, X2), U52 mark X -> mark U52 X, U52 ok X -> ok U52 X, isNatList ok X -> ok isNatList X, U51(mark X1, X2) -> mark U51(X1, X2), U51(ok X1, ok X2) -> ok U51(X1, X2), U62(mark X1, X2) -> mark U62(X1, X2), U62(ok X1, ok X2) -> ok U62(X1, X2), isNat ok X -> ok isNat X, U61(mark X1, X2, X3) -> mark U61(X1, X2, X3), U61(ok X1, ok X2, ok X3) -> ok U61(X1, X2, X3), s mark X -> mark s X, s ok X -> ok s X, length mark X -> mark length X, length ok X -> ok length X, proper cons(X1, X2) -> cons(proper X1, proper X2), proper 0() -> ok 0(), proper zeros() -> ok zeros(), proper tt() -> ok tt(), proper U11 X -> U11 proper X, proper U21 X -> U21 proper X, proper U31 X -> U31 proper X, proper U42 X -> U42 proper X, proper isNatIList X -> isNatIList proper X, proper U41(X1, X2) -> U41(proper X1, proper X2), proper U52 X -> U52 proper X, proper isNatList X -> isNatList proper X, proper U51(X1, X2) -> U51(proper X1, proper X2), proper U62(X1, X2) -> U62(proper X1, proper X2), proper isNat X -> isNat proper X, proper U61(X1, X2, X3) -> U61(proper X1, proper X2, proper X3), proper s X -> s proper X, proper length X -> length proper X, proper nil() -> ok nil(), top mark X -> top proper X, top ok X -> top active X} Open