YES Time: 1.761694 TRS: { mark true() -> active true(), mark eq(X1, X2) -> active eq(X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark false() -> active false(), mark cons(X1, X2) -> active cons(X1, X2), mark inf X -> active inf mark X, mark nil() -> active nil(), mark take(X1, X2) -> active take(mark X1, mark X2), mark length X -> active length mark X, active eq(X, Y) -> mark false(), active eq(0(), 0()) -> mark true(), active eq(s X, s Y) -> mark eq(X, Y), active inf X -> mark cons(X, inf s X), active take(0(), X) -> mark nil(), active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)), active length cons(X, L) -> mark s length L, active length nil() -> mark 0(), eq(X1, mark X2) -> eq(X1, X2), eq(X1, active X2) -> eq(X1, X2), eq(mark X1, X2) -> eq(X1, X2), eq(active X1, X2) -> eq(X1, X2), s mark X -> s X, s active X -> s X, cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), inf mark X -> inf X, inf active X -> inf X, take(X1, mark X2) -> take(X1, X2), take(X1, active X2) -> take(X1, X2), take(mark X1, X2) -> take(X1, X2), take(active X1, X2) -> take(X1, X2), length mark X -> length X, length active X -> length X} DP: DP: { mark# true() -> active# true(), mark# eq(X1, X2) -> active# eq(X1, X2), mark# 0() -> active# 0(), mark# s X -> active# s X, mark# false() -> active# false(), mark# cons(X1, X2) -> active# cons(X1, X2), mark# inf X -> mark# X, mark# inf X -> active# inf mark X, mark# inf X -> inf# mark X, mark# nil() -> active# nil(), mark# take(X1, X2) -> mark# X1, mark# take(X1, X2) -> mark# X2, mark# take(X1, X2) -> active# take(mark X1, mark X2), mark# take(X1, X2) -> take#(mark X1, mark X2), mark# length X -> mark# X, mark# length X -> active# length mark X, mark# length X -> length# mark X, active# eq(X, Y) -> mark# false(), active# eq(0(), 0()) -> mark# true(), active# eq(s X, s Y) -> mark# eq(X, Y), active# eq(s X, s Y) -> eq#(X, Y), active# inf X -> mark# cons(X, inf s X), active# inf X -> s# X, active# inf X -> cons#(X, inf s X), active# inf X -> inf# s X, active# take(0(), X) -> mark# nil(), active# take(s X, cons(Y, L)) -> mark# cons(Y, take(X, L)), active# take(s X, cons(Y, L)) -> cons#(Y, take(X, L)), active# take(s X, cons(Y, L)) -> take#(X, L), active# length cons(X, L) -> mark# s length L, active# length cons(X, L) -> s# length L, active# length cons(X, L) -> length# L, active# length nil() -> mark# 0(), eq#(X1, mark X2) -> eq#(X1, X2), eq#(X1, active X2) -> eq#(X1, X2), eq#(mark X1, X2) -> eq#(X1, X2), eq#(active X1, X2) -> eq#(X1, X2), s# mark X -> s# X, s# active X -> s# X, cons#(X1, mark X2) -> cons#(X1, X2), cons#(X1, active X2) -> cons#(X1, X2), cons#(mark X1, X2) -> cons#(X1, X2), cons#(active X1, X2) -> cons#(X1, X2), inf# mark X -> inf# X, inf# active X -> inf# X, take#(X1, mark X2) -> take#(X1, X2), take#(X1, active X2) -> take#(X1, X2), take#(mark X1, X2) -> take#(X1, X2), take#(active X1, X2) -> take#(X1, X2), length# mark X -> length# X, length# active X -> length# X} TRS: { mark true() -> active true(), mark eq(X1, X2) -> active eq(X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark false() -> active false(), mark cons(X1, X2) -> active cons(X1, X2), mark inf X -> active inf mark X, mark nil() -> active nil(), mark take(X1, X2) -> active take(mark X1, mark X2), mark length X -> active length mark X, active eq(X, Y) -> mark false(), active eq(0(), 0()) -> mark true(), active eq(s X, s Y) -> mark eq(X, Y), active inf X -> mark cons(X, inf s X), active take(0(), X) -> mark nil(), active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)), active length cons(X, L) -> mark s length L, active length nil() -> mark 0(), eq(X1, mark X2) -> eq(X1, X2), eq(X1, active X2) -> eq(X1, X2), eq(mark X1, X2) -> eq(X1, X2), eq(active X1, X2) -> eq(X1, X2), s mark X -> s X, s active X -> s X, cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), inf mark X -> inf X, inf active X -> inf X, take(X1, mark X2) -> take(X1, X2), take(X1, active X2) -> take(X1, X2), take(mark X1, X2) -> take(X1, X2), take(active X1, X2) -> take(X1, X2), length mark X -> length X, length active X -> length X} EDG: { (mark# take(X1, X2) -> mark# X1, mark# length X -> length# mark X) (mark# take(X1, X2) -> mark# X1, mark# length X -> active# length mark X) (mark# take(X1, X2) -> mark# X1, mark# length X -> mark# X) (mark# take(X1, X2) -> mark# X1, mark# take(X1, X2) -> take#(mark X1, mark X2)) (mark# take(X1, X2) -> mark# X1, mark# take(X1, X2) -> active# take(mark X1, mark X2)) (mark# take(X1, X2) -> mark# X1, mark# take(X1, X2) -> mark# X2) (mark# take(X1, X2) -> mark# X1, mark# take(X1, X2) -> mark# X1) (mark# take(X1, X2) -> mark# X1, mark# nil() -> active# nil()) (mark# take(X1, X2) -> mark# X1, mark# inf X -> inf# mark X) (mark# take(X1, X2) -> mark# X1, mark# inf X -> active# inf mark X) (mark# take(X1, X2) -> mark# X1, mark# inf X -> mark# X) (mark# take(X1, X2) -> mark# X1, mark# cons(X1, X2) -> active# cons(X1, X2)) (mark# take(X1, X2) -> mark# X1, mark# false() -> active# false()) (mark# take(X1, X2) -> mark# X1, mark# s X -> active# s X) (mark# take(X1, X2) -> mark# X1, mark# 0() -> active# 0()) (mark# take(X1, X2) -> mark# X1, mark# eq(X1, X2) -> active# eq(X1, X2)) (mark# take(X1, X2) -> mark# X1, mark# true() -> active# true()) (mark# inf X -> mark# X, mark# length X -> length# mark X) (mark# inf X -> mark# X, mark# length X -> active# length mark X) (mark# inf X -> mark# X, mark# length X -> mark# X) (mark# inf X -> mark# X, mark# take(X1, X2) -> take#(mark X1, mark X2)) (mark# inf X -> mark# X, mark# take(X1, X2) -> active# take(mark X1, mark X2)) (mark# inf X -> mark# X, mark# take(X1, X2) -> mark# X2) (mark# inf X -> mark# X, mark# take(X1, X2) -> mark# X1) (mark# inf X -> mark# X, mark# nil() -> active# nil()) (mark# inf X -> mark# X, mark# inf X -> inf# mark X) (mark# inf X -> mark# X, mark# inf X -> active# inf mark X) (mark# inf X -> mark# X, mark# inf X -> mark# X) (mark# inf X -> mark# X, mark# cons(X1, X2) -> active# cons(X1, X2)) (mark# inf X -> mark# X, mark# false() -> active# false()) (mark# inf X -> mark# X, mark# s X -> active# s X) (mark# inf X -> mark# X, mark# 0() -> active# 0()) (mark# inf X -> mark# X, mark# eq(X1, X2) -> active# eq(X1, X2)) (mark# inf X -> mark# X, mark# true() -> active# true()) (active# inf X -> s# X, s# active X -> s# X) (active# inf X -> s# X, s# mark X -> s# X) (s# active X -> s# X, s# active X -> s# X) (s# active X -> s# X, s# mark X -> s# X) (inf# active X -> inf# X, inf# active X -> inf# X) (inf# active X -> inf# X, inf# mark X -> inf# X) (length# active X -> length# X, length# active X -> length# X) (length# active X -> length# X, length# mark X -> length# X) (mark# length X -> active# length mark X, active# length nil() -> mark# 0()) (mark# length X -> active# length mark X, active# length cons(X, L) -> length# L) (mark# length X -> active# length mark X, active# length cons(X, L) -> s# length L) (mark# length X -> active# length mark X, active# length cons(X, L) -> mark# s length L) (mark# length X -> active# length mark X, active# take(s X, cons(Y, L)) -> take#(X, L)) (mark# length X -> active# length mark X, active# take(s X, cons(Y, L)) -> cons#(Y, take(X, L))) (mark# length X -> active# length mark X, active# take(s X, cons(Y, L)) -> mark# cons(Y, take(X, L))) (mark# length X -> active# length mark X, active# take(0(), X) -> mark# nil()) (mark# length X -> active# length mark X, active# inf X -> inf# s X) (mark# length X -> active# length mark X, active# inf X -> cons#(X, inf s X)) (mark# length X -> active# length mark X, active# inf X -> s# X) (mark# length X -> active# length mark X, active# inf X -> mark# cons(X, inf s X)) (mark# length X -> active# length mark X, active# eq(s X, s Y) -> eq#(X, Y)) (mark# length X -> active# length mark X, active# eq(s X, s Y) -> mark# eq(X, Y)) (mark# length X -> active# length mark X, active# eq(0(), 0()) -> mark# true()) (mark# length X -> active# length mark X, active# eq(X, Y) -> mark# false()) (mark# eq(X1, X2) -> active# eq(X1, X2), active# length nil() -> mark# 0()) (mark# eq(X1, X2) -> active# eq(X1, X2), active# length cons(X, L) -> length# L) (mark# eq(X1, X2) -> active# eq(X1, X2), active# length cons(X, L) -> s# length L) (mark# eq(X1, X2) -> active# eq(X1, X2), active# length cons(X, L) -> mark# s length L) (mark# eq(X1, X2) -> active# eq(X1, X2), active# take(s X, cons(Y, L)) -> take#(X, L)) (mark# eq(X1, X2) -> active# eq(X1, X2), active# take(s X, cons(Y, L)) -> cons#(Y, take(X, L))) (mark# eq(X1, X2) -> active# eq(X1, X2), active# take(s X, cons(Y, L)) -> mark# cons(Y, take(X, L))) (mark# eq(X1, X2) -> active# eq(X1, X2), active# take(0(), X) -> mark# nil()) (mark# eq(X1, X2) -> active# eq(X1, X2), active# inf X -> inf# s X) (mark# eq(X1, X2) -> active# eq(X1, X2), active# inf X -> cons#(X, inf s X)) (mark# eq(X1, X2) -> active# eq(X1, X2), active# inf X -> s# X) (mark# eq(X1, X2) -> active# eq(X1, X2), active# inf X -> mark# cons(X, inf s X)) (mark# eq(X1, X2) -> active# eq(X1, X2), active# eq(s X, s Y) -> eq#(X, Y)) (mark# eq(X1, X2) -> active# eq(X1, X2), active# eq(s X, s Y) -> mark# eq(X, Y)) (mark# eq(X1, X2) -> active# eq(X1, X2), active# eq(0(), 0()) -> mark# true()) (mark# eq(X1, X2) -> active# eq(X1, X2), active# eq(X, Y) -> mark# false()) (active# eq(s X, s Y) -> mark# eq(X, Y), mark# length X -> length# mark X) (active# eq(s X, s Y) -> mark# eq(X, Y), mark# length X -> active# length mark X) (active# eq(s X, s Y) -> mark# eq(X, Y), mark# length X -> mark# X) (active# eq(s X, s Y) -> mark# eq(X, Y), mark# take(X1, X2) -> take#(mark X1, mark X2)) (active# eq(s X, s Y) -> mark# eq(X, Y), mark# take(X1, X2) -> active# take(mark X1, mark X2)) (active# eq(s X, s Y) -> mark# eq(X, Y), mark# take(X1, X2) -> mark# X2) (active# eq(s X, s Y) -> mark# eq(X, Y), mark# take(X1, X2) -> mark# X1) (active# eq(s X, s Y) -> mark# eq(X, Y), mark# nil() -> active# nil()) (active# eq(s X, s Y) -> mark# eq(X, Y), mark# inf X -> inf# mark X) (active# eq(s X, s Y) -> mark# eq(X, Y), mark# inf X -> active# inf mark X) (active# eq(s X, s Y) -> mark# eq(X, Y), mark# inf X -> mark# X) (active# eq(s X, s Y) -> mark# eq(X, Y), mark# cons(X1, X2) -> active# cons(X1, X2)) (active# eq(s X, s Y) -> mark# eq(X, Y), mark# false() -> active# false()) (active# eq(s X, s Y) -> mark# eq(X, Y), mark# s X -> active# s X) (active# eq(s X, s Y) -> mark# eq(X, Y), mark# 0() -> active# 0()) (active# eq(s X, s Y) -> mark# eq(X, Y), mark# eq(X1, X2) -> active# eq(X1, X2)) (active# eq(s X, s Y) -> mark# eq(X, Y), mark# true() -> active# true()) (mark# true() -> active# true(), active# length nil() -> mark# 0()) (mark# true() -> active# true(), active# length cons(X, L) -> length# L) (mark# true() -> active# true(), active# length cons(X, L) -> s# length L) (mark# true() -> active# true(), active# length cons(X, L) -> mark# s length L) (mark# true() -> active# true(), active# take(s X, cons(Y, L)) -> take#(X, L)) (mark# true() -> active# true(), active# take(s X, cons(Y, L)) -> cons#(Y, take(X, L))) (mark# true() -> active# true(), active# take(s X, cons(Y, L)) -> mark# cons(Y, take(X, L))) (mark# true() -> active# true(), active# take(0(), X) -> mark# nil()) (mark# true() -> active# true(), active# inf X -> inf# s X) (mark# true() -> active# true(), active# inf X -> cons#(X, inf s X)) (mark# true() -> active# true(), active# inf X -> s# X) (mark# true() -> active# true(), active# inf X -> mark# cons(X, inf s X)) (mark# true() -> active# true(), active# eq(s X, s Y) -> eq#(X, Y)) (mark# true() -> active# true(), active# eq(s X, s Y) -> mark# eq(X, Y)) (mark# true() -> active# true(), active# eq(0(), 0()) -> mark# true()) (mark# true() -> active# true(), active# eq(X, Y) -> mark# false()) (mark# false() -> active# false(), active# length nil() -> mark# 0()) (mark# false() -> active# false(), active# length cons(X, L) -> length# L) (mark# false() -> active# false(), active# length cons(X, L) -> s# length L) (mark# false() -> active# false(), active# length cons(X, L) -> mark# s length L) (mark# false() -> active# false(), active# take(s X, cons(Y, L)) -> take#(X, L)) (mark# false() -> active# false(), active# take(s X, cons(Y, L)) -> cons#(Y, take(X, L))) (mark# false() -> active# false(), active# take(s X, cons(Y, L)) -> mark# cons(Y, take(X, L))) (mark# false() -> active# false(), active# take(0(), X) -> mark# nil()) (mark# false() -> active# false(), active# inf X -> inf# s X) (mark# false() -> active# false(), active# inf X -> cons#(X, inf s X)) (mark# false() -> active# false(), active# inf X -> s# X) (mark# false() -> active# false(), active# inf X -> mark# cons(X, inf s X)) (mark# false() -> active# false(), active# eq(s X, s Y) -> eq#(X, Y)) (mark# false() -> active# false(), active# eq(s X, s Y) -> mark# eq(X, Y)) (mark# false() -> active# false(), active# eq(0(), 0()) -> mark# true()) (mark# false() -> active# false(), active# eq(X, Y) -> mark# false()) (active# eq(X, Y) -> mark# false(), mark# length X -> length# mark X) (active# eq(X, Y) -> mark# false(), mark# length X -> active# length mark X) (active# eq(X, Y) -> mark# false(), mark# length X -> mark# X) (active# eq(X, Y) -> mark# false(), mark# take(X1, X2) -> take#(mark X1, mark X2)) (active# eq(X, Y) -> mark# false(), mark# take(X1, X2) -> active# take(mark X1, mark X2)) (active# eq(X, Y) -> mark# false(), mark# take(X1, X2) -> mark# X2) (active# eq(X, Y) -> mark# false(), mark# take(X1, X2) -> mark# X1) (active# eq(X, Y) -> mark# false(), mark# nil() -> active# nil()) (active# eq(X, Y) -> mark# false(), mark# inf X -> inf# mark X) (active# eq(X, Y) -> mark# false(), mark# inf X -> active# inf mark X) (active# eq(X, Y) -> mark# false(), mark# inf X -> mark# X) (active# eq(X, Y) -> mark# false(), mark# cons(X1, X2) -> active# cons(X1, X2)) (active# eq(X, Y) -> mark# false(), mark# false() -> active# false()) (active# eq(X, Y) -> mark# false(), mark# s X -> active# s X) (active# eq(X, Y) -> mark# false(), mark# 0() -> active# 0()) (active# eq(X, Y) -> mark# false(), mark# eq(X1, X2) -> active# eq(X1, X2)) (active# eq(X, Y) -> mark# false(), mark# true() -> active# true()) (active# take(0(), X) -> mark# nil(), mark# length X -> length# mark X) (active# take(0(), X) -> mark# nil(), mark# length X -> active# length mark X) (active# take(0(), X) -> mark# nil(), mark# length X -> mark# X) (active# take(0(), X) -> mark# nil(), mark# take(X1, X2) -> take#(mark X1, mark X2)) (active# take(0(), X) -> mark# nil(), mark# take(X1, X2) -> active# take(mark X1, mark X2)) (active# take(0(), X) -> mark# nil(), mark# take(X1, X2) -> mark# X2) (active# take(0(), X) -> mark# nil(), mark# take(X1, X2) -> mark# X1) (active# take(0(), X) -> mark# nil(), mark# nil() -> active# nil()) (active# take(0(), X) -> mark# nil(), mark# inf X -> inf# mark X) (active# take(0(), X) -> mark# nil(), mark# inf X -> active# inf mark X) (active# take(0(), X) -> mark# nil(), mark# inf X -> mark# X) (active# take(0(), X) -> mark# nil(), mark# cons(X1, X2) -> active# cons(X1, X2)) (active# take(0(), X) -> mark# nil(), mark# false() -> active# false()) (active# take(0(), X) -> mark# nil(), mark# s X -> active# s X) (active# take(0(), X) -> mark# nil(), mark# 0() -> active# 0()) (active# take(0(), X) -> mark# nil(), mark# eq(X1, X2) -> active# eq(X1, X2)) (active# take(0(), X) -> mark# nil(), mark# true() -> active# true()) (mark# take(X1, X2) -> take#(mark X1, mark X2), take#(active X1, X2) -> take#(X1, X2)) (mark# take(X1, X2) -> take#(mark X1, mark X2), take#(mark X1, X2) -> take#(X1, X2)) (mark# take(X1, X2) -> take#(mark X1, mark X2), take#(X1, active X2) -> take#(X1, X2)) (mark# take(X1, X2) -> take#(mark X1, mark X2), take#(X1, mark X2) -> take#(X1, X2)) (mark# s X -> active# s X, active# length nil() -> mark# 0()) (mark# s X -> active# s X, active# length cons(X, L) -> length# L) (mark# s X -> active# s X, active# length cons(X, L) -> s# length L) (mark# s X -> active# s X, active# length cons(X, L) -> mark# s length L) (mark# s X -> active# s X, active# take(s X, cons(Y, L)) -> take#(X, L)) (mark# s X -> active# s X, active# take(s X, cons(Y, L)) -> cons#(Y, take(X, L))) (mark# s X -> active# s X, active# take(s X, cons(Y, L)) -> mark# cons(Y, take(X, L))) (mark# s X -> active# s X, active# take(0(), X) -> mark# nil()) (mark# s X -> active# s X, active# inf X -> inf# s X) (mark# s X -> active# s X, active# inf X -> cons#(X, inf s X)) (mark# s X -> active# s X, active# inf X -> s# X) (mark# s X -> active# s X, active# inf X -> mark# cons(X, inf s X)) (mark# s X -> active# s X, active# eq(s X, s Y) -> eq#(X, Y)) (mark# s X -> active# s X, active# eq(s X, s Y) -> mark# eq(X, Y)) (mark# s X -> active# s X, active# eq(0(), 0()) -> mark# true()) (mark# s X -> active# s X, active# eq(X, Y) -> mark# false()) (mark# length X -> length# mark X, length# active X -> 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active# take(s X, cons(Y, L)) -> take#(X, L)) (mark# take(X1, X2) -> active# take(mark X1, mark X2), active# length cons(X, L) -> mark# s length L) (mark# take(X1, X2) -> active# take(mark X1, mark X2), active# length cons(X, L) -> s# length L) (mark# take(X1, X2) -> active# take(mark X1, mark X2), active# length cons(X, L) -> length# L) (mark# take(X1, X2) -> active# take(mark X1, mark X2), active# length nil() -> mark# 0()) (take#(active X1, X2) -> take#(X1, X2), take#(X1, mark X2) -> take#(X1, X2)) (take#(active X1, X2) -> take#(X1, X2), take#(X1, active X2) -> take#(X1, X2)) (take#(active X1, X2) -> take#(X1, X2), take#(mark X1, X2) -> take#(X1, X2)) (take#(active X1, X2) -> take#(X1, X2), take#(active X1, X2) -> take#(X1, X2)) (take#(X1, active X2) -> take#(X1, X2), take#(X1, mark X2) -> take#(X1, X2)) (take#(X1, active X2) -> take#(X1, X2), take#(X1, active X2) -> take#(X1, X2)) (take#(X1, active X2) -> take#(X1, X2), take#(mark X1, X2) -> take#(X1, X2)) (take#(X1, active X2) -> take#(X1, X2), take#(active X1, X2) -> take#(X1, X2)) (cons#(active X1, X2) -> cons#(X1, X2), cons#(X1, mark X2) -> cons#(X1, X2)) (cons#(active X1, X2) -> cons#(X1, X2), cons#(X1, active X2) -> cons#(X1, X2)) (cons#(active X1, X2) -> cons#(X1, X2), cons#(mark X1, X2) -> cons#(X1, X2)) (cons#(active X1, X2) -> cons#(X1, X2), cons#(active X1, X2) -> cons#(X1, X2)) (cons#(X1, active X2) -> cons#(X1, X2), cons#(X1, mark X2) -> cons#(X1, X2)) (cons#(X1, active X2) -> cons#(X1, X2), cons#(X1, active X2) -> cons#(X1, X2)) (cons#(X1, active X2) -> cons#(X1, X2), cons#(mark X1, X2) -> cons#(X1, X2)) (cons#(X1, active X2) -> cons#(X1, X2), cons#(active X1, X2) -> cons#(X1, X2)) (eq#(active X1, X2) -> eq#(X1, X2), eq#(X1, mark X2) -> eq#(X1, X2)) (eq#(active X1, X2) -> eq#(X1, X2), eq#(X1, active X2) -> eq#(X1, X2)) (eq#(active X1, X2) -> eq#(X1, X2), eq#(mark X1, X2) -> eq#(X1, X2)) (eq#(active X1, X2) -> eq#(X1, X2), eq#(active X1, X2) -> eq#(X1, X2)) (eq#(X1, active X2) -> eq#(X1, X2), eq#(X1, mark X2) -> eq#(X1, X2)) (eq#(X1, active X2) -> eq#(X1, X2), eq#(X1, active X2) -> eq#(X1, X2)) (eq#(X1, active X2) -> eq#(X1, X2), eq#(mark X1, X2) -> eq#(X1, X2)) (eq#(X1, active X2) -> eq#(X1, X2), eq#(active X1, X2) -> eq#(X1, X2)) (active# take(s X, cons(Y, L)) -> mark# cons(Y, take(X, L)), mark# eq(X1, X2) -> active# eq(X1, X2)) (active# take(s X, cons(Y, L)) -> mark# cons(Y, take(X, L)), mark# s X -> active# s X) (active# take(s X, cons(Y, L)) -> mark# cons(Y, take(X, L)), mark# cons(X1, X2) -> active# cons(X1, X2)) (active# take(s X, cons(Y, L)) -> mark# cons(Y, take(X, L)), mark# inf X -> mark# X) (active# take(s X, cons(Y, L)) -> mark# cons(Y, take(X, L)), mark# inf X -> active# inf mark X) (active# take(s X, cons(Y, L)) -> mark# cons(Y, take(X, L)), mark# inf X -> inf# mark X) (active# take(s X, cons(Y, L)) -> mark# cons(Y, take(X, L)), mark# take(X1, X2) -> mark# X1) (active# take(s X, cons(Y, L)) -> mark# cons(Y, take(X, L)), mark# take(X1, X2) -> mark# X2) (active# take(s X, cons(Y, L)) -> mark# cons(Y, take(X, L)), mark# take(X1, X2) -> active# take(mark X1, mark X2)) (active# take(s X, cons(Y, L)) -> mark# cons(Y, take(X, L)), mark# take(X1, X2) -> take#(mark X1, mark X2)) (active# take(s X, cons(Y, L)) -> mark# cons(Y, take(X, L)), mark# length X -> mark# X) (active# take(s X, cons(Y, L)) -> mark# cons(Y, take(X, L)), mark# length X -> active# length mark X) (active# take(s X, cons(Y, L)) -> mark# cons(Y, take(X, L)), mark# length X -> length# mark X) (active# inf X -> inf# s X, inf# mark X -> inf# X) (active# inf X -> inf# s X, inf# active X -> inf# X) (mark# inf X -> inf# mark X, inf# mark X -> inf# X) (mark# inf X -> inf# mark X, inf# active X -> inf# X) (active# length cons(X, L) -> s# length L, s# mark X -> s# X) (active# length cons(X, L) -> s# length L, s# active X -> s# X) (active# length nil() -> mark# 0(), mark# 0() -> active# 0()) (active# eq(0(), 0()) -> mark# true(), mark# true() -> active# true()) (mark# cons(X1, X2) -> active# cons(X1, X2), active# eq(X, Y) -> mark# false()) (mark# cons(X1, X2) -> active# cons(X1, X2), active# eq(0(), 0()) -> mark# true()) (mark# cons(X1, X2) -> active# cons(X1, X2), active# eq(s X, s Y) -> mark# eq(X, Y)) (mark# cons(X1, X2) -> active# cons(X1, X2), active# eq(s X, s Y) -> eq#(X, Y)) (mark# cons(X1, X2) -> active# cons(X1, X2), active# inf X -> mark# cons(X, inf s X)) (mark# cons(X1, X2) -> active# cons(X1, X2), active# inf X -> s# X) (mark# cons(X1, X2) -> active# cons(X1, X2), active# inf X -> cons#(X, inf s X)) (mark# cons(X1, X2) -> active# cons(X1, X2), active# inf X -> inf# s X) (mark# cons(X1, X2) -> active# cons(X1, X2), active# take(0(), X) -> mark# nil()) (mark# cons(X1, X2) -> active# cons(X1, X2), active# take(s X, cons(Y, L)) -> mark# cons(Y, take(X, L))) (mark# cons(X1, X2) -> active# cons(X1, X2), active# take(s X, cons(Y, L)) -> cons#(Y, take(X, L))) (mark# cons(X1, X2) -> active# cons(X1, X2), active# take(s X, cons(Y, L)) -> take#(X, L)) (mark# cons(X1, X2) -> active# cons(X1, X2), active# length cons(X, L) -> mark# s length L) (mark# cons(X1, X2) -> active# cons(X1, X2), active# length cons(X, L) -> s# length L) (mark# cons(X1, X2) -> active# cons(X1, X2), active# length cons(X, L) -> length# L) (mark# cons(X1, X2) -> active# cons(X1, X2), active# length nil() -> mark# 0()) (active# length cons(X, L) -> mark# s length L, mark# eq(X1, X2) -> active# eq(X1, X2)) (active# length cons(X, L) -> mark# s length L, mark# s X -> active# s X) (active# length cons(X, L) -> mark# s length L, mark# cons(X1, X2) -> active# cons(X1, X2)) (active# length cons(X, L) -> mark# s length L, mark# inf X -> mark# X) (active# length cons(X, L) -> mark# s length L, mark# inf X -> active# inf mark X) (active# length cons(X, L) -> mark# s length L, mark# inf X -> inf# mark X) (active# length cons(X, L) -> mark# s length L, mark# take(X1, X2) -> mark# X1) (active# length cons(X, L) -> mark# s length L, mark# take(X1, X2) -> mark# X2) (active# length cons(X, L) -> mark# s length L, mark# take(X1, X2) -> active# take(mark X1, mark X2)) (active# length cons(X, L) -> mark# s length L, mark# take(X1, X2) -> take#(mark X1, mark X2)) (active# length cons(X, L) -> mark# s length L, mark# length X -> mark# X) (active# length cons(X, L) -> mark# s length L, mark# length X -> active# length mark X) (active# length cons(X, L) -> mark# s length L, mark# length X -> length# mark X) (mark# inf X -> active# inf mark X, active# eq(X, Y) -> mark# false()) (mark# inf X -> active# inf mark X, active# eq(0(), 0()) -> mark# true()) (mark# inf X -> active# inf mark X, active# eq(s X, s Y) -> mark# eq(X, Y)) (mark# inf X -> active# inf mark X, active# eq(s X, s Y) -> eq#(X, Y)) (mark# inf X -> active# inf mark X, active# inf X -> mark# cons(X, inf s X)) (mark# inf X -> active# inf mark X, active# inf X -> s# X) (mark# inf X -> active# inf mark X, active# inf X -> cons#(X, inf s X)) (mark# inf X -> active# inf mark X, active# inf X -> inf# s X) (mark# inf X -> active# inf mark X, active# take(0(), X) -> mark# nil()) (mark# inf X -> active# inf mark X, active# take(s X, cons(Y, L)) -> mark# cons(Y, take(X, L))) (mark# inf X -> active# inf mark X, active# take(s X, cons(Y, L)) -> cons#(Y, take(X, L))) (mark# inf X -> active# inf mark X, active# take(s X, cons(Y, L)) -> take#(X, L)) (mark# inf X -> active# inf mark X, active# length cons(X, L) -> mark# s length L) (mark# inf X -> active# inf mark X, active# length cons(X, L) -> s# length L) (mark# inf X -> active# inf mark X, active# length cons(X, L) -> length# L) (mark# inf X -> active# inf mark X, active# length nil() -> mark# 0()) (length# mark X -> length# X, length# mark X -> length# X) (length# mark X -> length# X, length# active X -> length# X) (inf# mark X -> inf# X, inf# mark X -> inf# X) (inf# mark X -> inf# X, inf# active X -> inf# X) (s# mark X -> s# X, s# mark X -> s# X) (s# mark X -> s# X, s# active X -> s# X) (mark# length X -> mark# X, mark# true() -> active# true()) (mark# length X -> mark# X, mark# eq(X1, X2) -> active# eq(X1, X2)) (mark# length X -> mark# X, mark# 0() -> active# 0()) (mark# length X -> mark# X, mark# s X -> active# s X) (mark# length X -> mark# X, mark# false() -> active# false()) (mark# length X -> mark# X, mark# cons(X1, X2) -> active# cons(X1, X2)) (mark# length X -> mark# X, mark# inf X -> mark# X) (mark# length X -> mark# X, mark# inf X -> active# inf mark X) (mark# length X -> mark# X, mark# inf X -> inf# mark X) (mark# length X -> mark# X, mark# nil() -> active# nil()) (mark# length X -> mark# X, mark# take(X1, X2) -> mark# X1) (mark# length X -> mark# X, mark# take(X1, X2) -> mark# X2) (mark# length X -> mark# X, mark# take(X1, X2) -> active# take(mark X1, mark X2)) (mark# length X -> mark# X, mark# take(X1, X2) -> take#(mark X1, mark X2)) (mark# length X -> mark# X, mark# length X -> mark# X) (mark# length X -> mark# X, mark# length X -> active# length mark X) (mark# length X -> mark# X, mark# length X -> length# mark X) (mark# take(X1, X2) -> mark# X2, mark# true() -> active# true()) (mark# take(X1, X2) -> mark# X2, mark# eq(X1, X2) -> active# eq(X1, X2)) (mark# take(X1, X2) -> mark# X2, mark# 0() -> active# 0()) (mark# take(X1, X2) -> mark# X2, mark# s X -> active# s X) (mark# take(X1, X2) -> mark# X2, mark# false() -> active# false()) (mark# take(X1, X2) -> mark# X2, mark# cons(X1, X2) -> active# cons(X1, X2)) (mark# take(X1, X2) -> mark# X2, mark# inf X -> mark# X) (mark# take(X1, X2) -> mark# X2, mark# inf X -> active# inf mark X) (mark# take(X1, X2) -> mark# X2, mark# inf X -> inf# mark X) (mark# take(X1, X2) -> mark# X2, mark# nil() -> active# nil()) (mark# take(X1, X2) -> mark# X2, mark# take(X1, X2) -> mark# X1) (mark# take(X1, X2) -> mark# X2, mark# take(X1, X2) -> mark# X2) (mark# take(X1, X2) -> mark# X2, mark# take(X1, X2) -> active# take(mark X1, mark X2)) (mark# take(X1, X2) -> mark# X2, mark# take(X1, X2) -> take#(mark X1, mark X2)) (mark# take(X1, X2) -> mark# X2, mark# length X -> mark# X) (mark# take(X1, X2) -> mark# X2, mark# length X -> active# length mark X) (mark# take(X1, X2) -> mark# X2, mark# length X -> length# mark X) } STATUS: arrows: 0.891580 SCCS (7): Scc: { eq#(X1, mark X2) -> eq#(X1, X2), eq#(X1, active X2) -> eq#(X1, X2), eq#(mark X1, X2) -> eq#(X1, X2), eq#(active X1, X2) -> eq#(X1, X2)} Scc: { mark# eq(X1, X2) -> active# eq(X1, X2), mark# s X -> active# s X, mark# cons(X1, X2) -> active# cons(X1, X2), mark# inf X -> mark# X, mark# inf X -> active# inf mark X, mark# take(X1, X2) -> mark# X1, mark# take(X1, X2) -> mark# X2, mark# take(X1, X2) -> active# take(mark X1, mark X2), mark# length X -> mark# X, mark# length X -> active# length mark X, active# eq(s X, s Y) -> mark# eq(X, Y), active# inf X -> mark# cons(X, inf s X), active# take(s X, cons(Y, L)) -> mark# cons(Y, take(X, L)), active# length cons(X, L) -> mark# s length L} Scc: { length# mark X -> length# X, length# active X -> length# X} Scc: { take#(X1, mark X2) -> take#(X1, X2), take#(X1, active X2) -> take#(X1, X2), take#(mark X1, X2) -> take#(X1, X2), take#(active X1, X2) -> take#(X1, X2)} Scc: { s# mark X -> s# X, s# active X -> s# X} Scc: { cons#(X1, mark X2) -> cons#(X1, X2), cons#(X1, active X2) -> cons#(X1, X2), cons#(mark X1, X2) -> cons#(X1, X2), cons#(active X1, X2) -> cons#(X1, X2)} Scc: { inf# mark X -> inf# X, inf# active X -> inf# X} SCC (4): Strict: { eq#(X1, mark X2) -> eq#(X1, X2), eq#(X1, active X2) -> eq#(X1, X2), eq#(mark X1, X2) -> eq#(X1, X2), eq#(active X1, X2) -> eq#(X1, X2)} Weak: { mark true() -> active true(), mark eq(X1, X2) -> active eq(X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark false() -> active false(), mark cons(X1, X2) -> active cons(X1, X2), mark inf X -> active inf mark X, mark nil() -> active nil(), mark take(X1, X2) -> active take(mark X1, mark X2), mark length X -> active length mark X, active eq(X, Y) -> mark false(), active eq(0(), 0()) -> mark true(), active eq(s X, s Y) -> mark eq(X, Y), active inf X -> mark cons(X, inf s X), active take(0(), X) -> mark nil(), active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)), active length cons(X, L) -> mark s length L, active length nil() -> mark 0(), eq(X1, mark X2) -> eq(X1, X2), eq(X1, active X2) -> eq(X1, X2), eq(mark X1, X2) -> eq(X1, X2), eq(active X1, X2) -> eq(X1, X2), s mark X -> s X, s active X -> s X, cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), inf mark X -> inf X, inf active X -> inf X, take(X1, mark X2) -> take(X1, X2), take(X1, active X2) -> take(X1, X2), take(mark X1, X2) -> take(X1, X2), take(active X1, X2) -> take(X1, X2), length mark X -> length X, length active X -> length X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [eq](x0, x1) = x0, [cons](x0, x1) = 0, [take](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [inf](x0) = 0, [length](x0) = 0, [true] = 0, [0] = 1, [false] = 1, [nil] = 1, [eq#](x0, x1) = x0 Strict: eq#(active X1, X2) -> eq#(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 eq#(mark X1, X2) -> eq#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 eq#(X1, active X2) -> eq#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 eq#(X1, mark X2) -> eq#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 Weak: length active X -> length X 0 + 0X >= 0 + 0X length mark X -> length X 0 + 0X >= 0 + 0X take(active X1, X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(mark X1, X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(X1, active X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(X1, mark X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 inf active X -> inf X 0 + 0X >= 0 + 0X inf mark X -> inf X 0 + 0X >= 0 + 0X cons(active X1, X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(mark X1, X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(X1, active X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(X1, mark X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X eq(active X1, X2) -> eq(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 eq(mark X1, X2) -> eq(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 eq(X1, active X2) -> eq(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 eq(X1, mark X2) -> eq(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 active length nil() -> mark 0() 1 >= 1 active length cons(X, L) -> mark s length L 1 + 0X + 0L >= 0 + 0L active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)) 1 + 0X + 0Y + 0L >= 0 + 0X + 0Y + 0L active take(0(), X) -> mark nil() 1 + 0X >= 1 active inf X -> mark cons(X, inf s X) 1 + 0X >= 0 + 0X active eq(s X, s Y) -> mark eq(X, Y) 1 + 0X + 0Y >= 0 + 1X + 0Y active eq(0(), 0()) -> mark true() 2 >= 0 active eq(X, Y) -> mark false() 1 + 1X + 0Y >= 1 mark length X -> active length mark X 0 + 0X >= 1 + 0X mark take(X1, X2) -> active take(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 2 mark inf X -> active inf mark X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark false() -> active false() 1 >= 2 mark s X -> active s X 0 + 0X >= 1 + 0X mark 0() -> active 0() 1 >= 2 mark eq(X1, X2) -> active eq(X1, X2) 0 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 mark true() -> active true() 0 >= 1 SCCS (1): Scc: { eq#(X1, mark X2) -> eq#(X1, X2), eq#(X1, active X2) -> eq#(X1, X2), eq#(mark X1, X2) -> eq#(X1, X2)} SCC (3): Strict: { eq#(X1, mark X2) -> eq#(X1, X2), eq#(X1, active X2) -> eq#(X1, X2), eq#(mark X1, X2) -> eq#(X1, X2)} Weak: { mark true() -> active true(), mark eq(X1, X2) -> active eq(X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark false() -> active false(), mark cons(X1, X2) -> active cons(X1, X2), mark inf X -> active inf mark X, mark nil() -> active nil(), mark take(X1, X2) -> active take(mark X1, mark X2), mark length X -> active length mark X, active eq(X, Y) -> mark false(), active eq(0(), 0()) -> mark true(), active eq(s X, s Y) -> mark eq(X, Y), active inf X -> mark cons(X, inf s X), active take(0(), X) -> mark nil(), active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)), active length cons(X, L) -> mark s length L, active length nil() -> mark 0(), eq(X1, mark X2) -> eq(X1, X2), eq(X1, active X2) -> eq(X1, X2), eq(mark X1, X2) -> eq(X1, X2), eq(active X1, X2) -> eq(X1, X2), s mark X -> s X, s active X -> s X, cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), inf mark X -> inf X, inf active X -> inf X, take(X1, mark X2) -> take(X1, X2), take(X1, active X2) -> take(X1, X2), take(mark X1, X2) -> take(X1, X2), take(active X1, X2) -> take(X1, X2), length mark X -> length X, length active X -> length X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [eq](x0, x1) = x0 + x1, [cons](x0, x1) = 1, [take](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [active](x0) = 0, [s](x0) = 1, [inf](x0) = x0 + 1, [length](x0) = 0, [true] = 0, [0] = 1, [false] = 0, [nil] = 1, [eq#](x0, x1) = x0 Strict: eq#(mark X1, X2) -> eq#(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 eq#(X1, active X2) -> eq#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 eq#(X1, mark X2) -> eq#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 Weak: length active X -> length X 0 + 0X >= 0 + 0X length mark X -> length X 0 + 0X >= 0 + 0X take(active X1, X2) -> take(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 take(mark X1, X2) -> take(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 take(X1, active X2) -> take(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 take(X1, mark X2) -> take(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 inf active X -> inf X 1 + 0X >= 1 + 1X inf mark X -> inf X 2 + 1X >= 1 + 1X cons(active X1, X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(mark X1, X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(X1, active X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(X1, mark X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 s active X -> s X 1 + 0X >= 1 + 0X s mark X -> s X 1 + 0X >= 1 + 0X eq(active X1, X2) -> eq(X1, X2) 0 + 0X1 + 1X2 >= 0 + 1X1 + 1X2 eq(mark X1, X2) -> eq(X1, X2) 1 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 eq(X1, active X2) -> eq(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 1X2 eq(X1, mark X2) -> eq(X1, X2) 1 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 active length nil() -> mark 0() 0 >= 2 active length cons(X, L) -> mark s length L 0 + 0X + 0L >= 2 + 0L active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)) 0 + 0X + 0Y + 0L >= 2 + 0X + 0Y + 0L active take(0(), X) -> mark nil() 0 + 0X >= 2 active inf X -> mark cons(X, inf s X) 0 + 0X >= 2 + 0X active eq(s X, s Y) -> mark eq(X, Y) 0 + 0X + 0Y >= 1 + 1X + 1Y active eq(0(), 0()) -> mark true() 0 >= 1 active eq(X, Y) -> mark false() 0 + 0X + 0Y >= 1 mark length X -> active length mark X 1 + 0X >= 0 + 0X mark take(X1, X2) -> active take(mark X1, mark X2) 2 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 mark nil() -> active nil() 2 >= 0 mark inf X -> active inf mark X 2 + 1X >= 0 + 0X mark cons(X1, X2) -> active cons(X1, X2) 2 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark false() -> active false() 1 >= 0 mark s X -> active s X 2 + 0X >= 0 + 0X mark 0() -> active 0() 2 >= 0 mark eq(X1, X2) -> active eq(X1, X2) 1 + 1X1 + 1X2 >= 0 + 0X1 + 0X2 mark true() -> active true() 1 >= 0 SCCS (1): Scc: { eq#(X1, mark X2) -> eq#(X1, X2), eq#(X1, active X2) -> eq#(X1, X2)} SCC (2): Strict: { eq#(X1, mark X2) -> eq#(X1, X2), eq#(X1, active X2) -> eq#(X1, X2)} Weak: { mark true() -> active true(), mark eq(X1, X2) -> active eq(X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark false() -> active false(), mark cons(X1, X2) -> active cons(X1, X2), mark inf X -> active inf mark X, mark nil() -> active nil(), mark take(X1, X2) -> active take(mark X1, mark X2), mark length X -> active length mark X, active eq(X, Y) -> mark false(), active eq(0(), 0()) -> mark true(), active eq(s X, s Y) -> mark eq(X, Y), active inf X -> mark cons(X, inf s X), active take(0(), X) -> mark nil(), active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)), active length cons(X, L) -> mark s length L, active length nil() -> mark 0(), eq(X1, mark X2) -> eq(X1, X2), eq(X1, active X2) -> eq(X1, X2), eq(mark X1, X2) -> eq(X1, X2), eq(active X1, X2) -> eq(X1, X2), s mark X -> s X, s active X -> s X, cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), inf mark X -> inf X, inf active X -> inf X, take(X1, mark X2) -> take(X1, X2), take(X1, active X2) -> take(X1, X2), take(mark X1, X2) -> take(X1, X2), take(active X1, X2) -> take(X1, X2), length mark X -> length X, length active X -> length X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [eq](x0, x1) = x0 + x1 + 1, [cons](x0, x1) = x0, [take](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [inf](x0) = 0, [length](x0) = 0, [true] = 1, [0] = 1, [false] = 1, [nil] = 1, [eq#](x0, x1) = x0 Strict: eq#(X1, active X2) -> eq#(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 eq#(X1, mark X2) -> eq#(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 Weak: length active X -> length X 0 + 0X >= 0 + 0X length mark X -> length X 0 + 0X >= 0 + 0X take(active X1, X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(mark X1, X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(X1, active X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(X1, mark X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 inf active X -> inf X 0 + 0X >= 0 + 0X inf mark X -> inf X 0 + 0X >= 0 + 0X cons(active X1, X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(mark X1, X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(X1, active X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(X1, mark X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X eq(active X1, X2) -> eq(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 eq(mark X1, X2) -> eq(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 eq(X1, active X2) -> eq(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 eq(X1, mark X2) -> eq(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active length nil() -> mark 0() 1 >= 1 active length cons(X, L) -> mark s length L 1 + 0X + 0L >= 0 + 0L active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)) 1 + 0X + 0Y + 0L >= 0 + 0X + 0Y + 0L active take(0(), X) -> mark nil() 1 + 0X >= 1 active inf X -> mark cons(X, inf s X) 1 + 0X >= 0 + 0X active eq(s X, s Y) -> mark eq(X, Y) 2 + 0X + 0Y >= 1 + 1X + 1Y active eq(0(), 0()) -> mark true() 4 >= 1 active eq(X, Y) -> mark false() 2 + 1X + 1Y >= 1 mark length X -> active length mark X 0 + 0X >= 1 + 0X mark take(X1, X2) -> active take(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 2 mark inf X -> active inf mark X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(X1, X2) 0 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 mark false() -> active false() 1 >= 2 mark s X -> active s X 0 + 0X >= 1 + 0X mark 0() -> active 0() 1 >= 2 mark eq(X1, X2) -> active eq(X1, X2) 1 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark true() -> active true() 1 >= 2 SCCS (1): Scc: {eq#(X1, mark X2) -> eq#(X1, X2)} SCC (1): Strict: {eq#(X1, mark X2) -> eq#(X1, X2)} Weak: { mark true() -> active true(), mark eq(X1, X2) -> active eq(X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark false() -> active false(), mark cons(X1, X2) -> active cons(X1, X2), mark inf X -> active inf mark X, mark nil() -> active nil(), mark take(X1, X2) -> active take(mark X1, mark X2), mark length X -> active length mark X, active eq(X, Y) -> mark false(), active eq(0(), 0()) -> mark true(), active eq(s X, s Y) -> mark eq(X, Y), active inf X -> mark cons(X, inf s X), active take(0(), X) -> mark nil(), active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)), active length cons(X, L) -> mark s length L, active length nil() -> mark 0(), eq(X1, mark X2) -> eq(X1, X2), eq(X1, active X2) -> eq(X1, X2), eq(mark X1, X2) -> eq(X1, X2), eq(active X1, X2) -> eq(X1, X2), s mark X -> s X, s active X -> s X, cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), inf mark X -> inf X, inf active X -> inf X, take(X1, mark X2) -> take(X1, X2), take(X1, active X2) -> take(X1, X2), take(mark X1, X2) -> take(X1, X2), take(active X1, X2) -> take(X1, X2), length mark X -> length X, length active X -> length X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [eq](x0, x1) = x0 + 1, [cons](x0, x1) = 1, [take](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [active](x0) = 0, [s](x0) = 1, [inf](x0) = x0 + 1, [length](x0) = x0 + 1, [true] = 0, [0] = 1, [false] = 0, [nil] = 1, [eq#](x0, x1) = x0 Strict: eq#(X1, mark X2) -> eq#(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 Weak: length active X -> length X 1 + 0X >= 1 + 1X length mark X -> length X 2 + 1X >= 1 + 1X take(active X1, X2) -> take(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 take(mark X1, X2) -> take(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 take(X1, active X2) -> take(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 take(X1, mark X2) -> take(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 inf active X -> inf X 1 + 0X >= 1 + 1X inf mark X -> inf X 2 + 1X >= 1 + 1X cons(active X1, X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(mark X1, X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(X1, active X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(X1, mark X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 s active X -> s X 1 + 0X >= 1 + 0X s mark X -> s X 1 + 0X >= 1 + 0X eq(active X1, X2) -> eq(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 eq(mark X1, X2) -> eq(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 eq(X1, active X2) -> eq(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 eq(X1, mark X2) -> eq(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active length nil() -> mark 0() 0 >= 2 active length cons(X, L) -> mark s length L 0 + 0X + 0L >= 2 + 0L active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)) 0 + 0X + 0Y + 0L >= 2 + 0X + 0Y + 0L active take(0(), X) -> mark nil() 0 + 0X >= 2 active inf X -> mark cons(X, inf s X) 0 + 0X >= 2 + 0X active eq(s X, s Y) -> mark eq(X, Y) 0 + 0X + 0Y >= 2 + 0X + 1Y active eq(0(), 0()) -> mark true() 0 >= 1 active eq(X, Y) -> mark false() 0 + 0X + 0Y >= 1 mark length X -> active length mark X 2 + 1X >= 0 + 0X mark take(X1, X2) -> active take(mark X1, mark X2) 2 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 mark nil() -> active nil() 2 >= 0 mark inf X -> active inf mark X 2 + 1X >= 0 + 0X mark cons(X1, X2) -> active cons(X1, X2) 2 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark false() -> active false() 1 >= 0 mark s X -> active s X 2 + 0X >= 0 + 0X mark 0() -> active 0() 2 >= 0 mark eq(X1, X2) -> active eq(X1, X2) 2 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 mark true() -> active true() 1 >= 0 Qed SCC (14): Strict: { mark# eq(X1, X2) -> active# eq(X1, X2), mark# s X -> active# s X, mark# cons(X1, X2) -> active# cons(X1, X2), mark# inf X -> mark# X, mark# inf X -> active# inf mark X, mark# take(X1, X2) -> mark# X1, mark# take(X1, X2) -> mark# X2, mark# take(X1, X2) -> active# take(mark X1, mark X2), mark# length X -> mark# X, mark# length X -> active# length mark X, active# eq(s X, s Y) -> mark# eq(X, Y), active# inf X -> mark# cons(X, inf s X), active# take(s X, cons(Y, L)) -> mark# cons(Y, take(X, L)), active# length cons(X, L) -> mark# s length L} Weak: { mark true() -> active true(), mark eq(X1, X2) -> active eq(X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark false() -> active false(), mark cons(X1, X2) -> active cons(X1, X2), mark inf X -> active inf mark X, mark nil() -> active nil(), mark take(X1, X2) -> active take(mark X1, mark X2), mark length X -> active length mark X, active eq(X, Y) -> mark false(), active eq(0(), 0()) -> mark true(), active eq(s X, s Y) -> mark eq(X, Y), active inf X -> mark cons(X, inf s X), active take(0(), X) -> mark nil(), active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)), active length cons(X, L) -> mark s length L, active length nil() -> mark 0(), eq(X1, mark X2) -> eq(X1, X2), eq(X1, active X2) -> eq(X1, X2), eq(mark X1, X2) -> eq(X1, X2), eq(active X1, X2) -> eq(X1, X2), s mark X -> s X, s active X -> s X, cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), inf mark X -> inf X, inf active X -> inf X, take(X1, mark X2) -> take(X1, X2), take(X1, active X2) -> take(X1, X2), take(mark X1, X2) -> take(X1, X2), take(active X1, X2) -> take(X1, X2), length mark X -> length X, length active X -> length X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [eq](x0, x1) = 0, [cons](x0, x1) = 0, [take](x0, x1) = x0 + x1 + 1, [mark](x0) = x0, [active](x0) = x0, [s](x0) = 1, [inf](x0) = x0 + 1, [length](x0) = x0 + 1, [true] = 0, [0] = 0, [false] = 0, [nil] = 0, [mark#](x0) = x0, [active#](x0) = x0 Strict: active# length cons(X, L) -> mark# s length L 1 + 0X + 0L >= 1 + 0L active# take(s X, cons(Y, L)) -> mark# cons(Y, take(X, L)) 2 + 0X + 0Y + 0L >= 0 + 0X + 0Y + 0L active# inf X -> mark# cons(X, inf s X) 1 + 1X >= 0 + 0X active# eq(s X, s Y) -> mark# eq(X, Y) 0 + 0X + 0Y >= 0 + 0X + 0Y mark# length X -> active# length mark X 1 + 1X >= 1 + 1X mark# length X -> mark# X 1 + 1X >= 0 + 1X mark# take(X1, X2) -> active# take(mark X1, mark X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 mark# take(X1, X2) -> mark# X2 1 + 1X1 + 1X2 >= 0 + 1X2 mark# take(X1, X2) -> mark# X1 1 + 1X1 + 1X2 >= 0 + 1X1 mark# inf X -> active# inf mark X 1 + 1X >= 1 + 1X mark# inf X -> mark# X 1 + 1X >= 0 + 1X mark# cons(X1, X2) -> active# cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark# s X -> active# s X 1 + 0X >= 1 + 0X mark# eq(X1, X2) -> active# eq(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 Weak: length active X -> length X 1 + 1X >= 1 + 1X length mark X -> length X 1 + 1X >= 1 + 1X take(active X1, X2) -> take(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 take(mark X1, X2) -> take(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 take(X1, active X2) -> take(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 take(X1, mark X2) -> take(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 inf active X -> inf X 1 + 1X >= 1 + 1X inf mark X -> inf X 1 + 1X >= 1 + 1X cons(active X1, X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(mark X1, X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(X1, active X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(X1, mark X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s active X -> s X 1 + 0X >= 1 + 0X s mark X -> s X 1 + 0X >= 1 + 0X eq(active X1, X2) -> eq(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 eq(mark X1, X2) -> eq(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 eq(X1, active X2) -> eq(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 eq(X1, mark X2) -> eq(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active length nil() -> mark 0() 1 >= 0 active length cons(X, L) -> mark s length L 1 + 0X + 0L >= 1 + 0L active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)) 2 + 0X + 0Y + 0L >= 0 + 0X + 0Y + 0L active take(0(), X) -> mark nil() 1 + 1X >= 0 active inf X -> mark cons(X, inf s X) 1 + 1X >= 0 + 0X active eq(s X, s Y) -> mark eq(X, Y) 0 + 0X + 0Y >= 0 + 0X + 0Y active eq(0(), 0()) -> mark true() 0 >= 0 active eq(X, Y) -> mark false() 0 + 0X + 0Y >= 0 mark length X -> active length mark X 1 + 1X >= 1 + 1X mark take(X1, X2) -> active take(mark X1, mark X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 mark nil() -> active nil() 0 >= 0 mark inf X -> active inf mark X 1 + 1X >= 1 + 1X mark cons(X1, X2) -> active cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark false() -> active false() 0 >= 0 mark s X -> active s X 1 + 0X >= 1 + 0X mark 0() -> active 0() 0 >= 0 mark eq(X1, X2) -> active eq(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark true() -> active true() 0 >= 0 SCCS (1): Scc: { mark# eq(X1, X2) -> active# eq(X1, X2), mark# s X -> active# s X, mark# cons(X1, X2) -> active# cons(X1, X2), mark# inf X -> active# inf mark X, mark# take(X1, X2) -> active# take(mark X1, mark X2), mark# length X -> active# length mark X, active# eq(s X, s Y) -> mark# eq(X, Y), active# length cons(X, L) -> mark# s length L} SCC (8): Strict: { mark# eq(X1, X2) -> active# eq(X1, X2), mark# s X -> active# s X, mark# cons(X1, X2) -> active# cons(X1, X2), mark# inf X -> active# inf mark X, mark# take(X1, X2) -> active# take(mark X1, mark X2), mark# length X -> active# length mark X, active# eq(s X, s Y) -> mark# eq(X, Y), active# length cons(X, L) -> mark# s length L} Weak: { mark true() -> active true(), mark eq(X1, X2) -> active eq(X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark false() -> active false(), mark cons(X1, X2) -> active cons(X1, X2), mark inf X -> active inf mark X, mark nil() -> active nil(), mark take(X1, X2) -> active take(mark X1, mark X2), mark length X -> active length mark X, active eq(X, Y) -> mark false(), active eq(0(), 0()) -> mark true(), active eq(s X, s Y) -> mark eq(X, Y), active inf X -> mark cons(X, inf s X), active take(0(), X) -> mark nil(), active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)), active length cons(X, L) -> mark s length L, active length nil() -> mark 0(), eq(X1, mark X2) -> eq(X1, X2), eq(X1, active X2) -> eq(X1, X2), eq(mark X1, X2) -> eq(X1, X2), eq(active X1, X2) -> eq(X1, X2), s mark X -> s X, s active X -> s X, cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), inf mark X -> inf X, inf active X -> inf X, take(X1, mark X2) -> take(X1, X2), take(X1, active X2) -> take(X1, X2), take(mark X1, X2) -> take(X1, X2), take(active X1, X2) -> take(X1, X2), length mark X -> length X, length active X -> length X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [eq](x0, x1) = 0, [cons](x0, x1) = 1, [take](x0, x1) = 1, [mark](x0) = x0, [active](x0) = x0, [s](x0) = 0, [inf](x0) = 1, [length](x0) = x0, [true] = 0, [0] = 0, [false] = 0, [nil] = 1, [mark#](x0) = x0, [active#](x0) = x0 Strict: active# length cons(X, L) -> mark# s length L 1 + 0X + 0L >= 0 + 0L active# eq(s X, s Y) -> mark# eq(X, Y) 0 + 0X + 0Y >= 0 + 0X + 0Y mark# length X -> active# length mark X 0 + 1X >= 0 + 1X mark# take(X1, X2) -> active# take(mark X1, mark X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark# inf X -> active# inf mark X 1 + 0X >= 1 + 0X mark# cons(X1, X2) -> active# cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark# s X -> active# s X 0 + 0X >= 0 + 0X mark# eq(X1, X2) -> active# eq(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 Weak: length active X -> length X 0 + 1X >= 0 + 1X length mark X -> length X 0 + 1X >= 0 + 1X take(active X1, X2) -> take(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 take(mark X1, X2) -> take(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 take(X1, active X2) -> take(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 take(X1, mark X2) -> take(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 inf active X -> inf X 1 + 0X >= 1 + 0X inf mark X -> inf X 1 + 0X >= 1 + 0X cons(active X1, X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(mark X1, X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(X1, active X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(X1, mark X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X eq(active X1, X2) -> eq(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 eq(mark X1, X2) -> eq(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 eq(X1, active X2) -> eq(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 eq(X1, mark X2) -> eq(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active length nil() -> mark 0() 1 >= 0 active length cons(X, L) -> mark s length L 1 + 0X + 0L >= 0 + 0L active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)) 1 + 0X + 0Y + 0L >= 1 + 0X + 0Y + 0L active take(0(), X) -> mark nil() 1 + 0X >= 1 active inf X -> mark cons(X, inf s X) 1 + 0X >= 1 + 0X active eq(s X, s Y) -> mark eq(X, Y) 0 + 0X + 0Y >= 0 + 0X + 0Y active eq(0(), 0()) -> mark true() 0 >= 0 active eq(X, Y) -> mark false() 0 + 0X + 0Y >= 0 mark length X -> active length mark X 0 + 1X >= 0 + 1X mark take(X1, X2) -> active take(mark X1, mark X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 1 mark inf X -> active inf mark X 1 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark false() -> active false() 0 >= 0 mark s X -> active s X 0 + 0X >= 0 + 0X mark 0() -> active 0() 0 >= 0 mark eq(X1, X2) -> active eq(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark true() -> active true() 0 >= 0 SCCS (1): Scc: { mark# eq(X1, X2) -> active# eq(X1, X2), mark# s X -> active# s X, mark# cons(X1, X2) -> active# cons(X1, X2), mark# inf X -> active# inf mark X, mark# take(X1, X2) -> active# take(mark X1, mark X2), mark# length X -> active# length mark X, active# eq(s X, s Y) -> mark# eq(X, Y)} SCC (7): Strict: { mark# eq(X1, X2) -> active# eq(X1, X2), mark# s X -> active# s X, mark# cons(X1, X2) -> active# cons(X1, X2), mark# inf X -> active# inf mark X, mark# take(X1, X2) -> active# take(mark X1, mark X2), mark# length X -> active# length mark X, active# eq(s X, s Y) -> mark# eq(X, Y)} Weak: { mark true() -> active true(), mark eq(X1, X2) -> active eq(X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark false() -> active false(), mark cons(X1, X2) -> active cons(X1, X2), mark inf X -> active inf mark X, mark nil() -> active nil(), mark take(X1, X2) -> active take(mark X1, mark X2), mark length X -> active length mark X, active eq(X, Y) -> mark false(), active eq(0(), 0()) -> mark true(), active eq(s X, s Y) -> mark eq(X, Y), active inf X -> mark cons(X, inf s X), active take(0(), X) -> mark nil(), active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)), active length cons(X, L) -> mark s length L, active length nil() -> mark 0(), eq(X1, mark X2) -> eq(X1, X2), eq(X1, active X2) -> eq(X1, X2), eq(mark X1, X2) -> eq(X1, X2), eq(active X1, X2) -> eq(X1, X2), s mark X -> s X, s active X -> s X, cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), inf mark X -> inf X, inf active X -> inf X, take(X1, mark X2) -> take(X1, X2), take(X1, active X2) -> take(X1, X2), take(mark X1, X2) -> take(X1, X2), take(active X1, X2) -> take(X1, X2), length mark X -> length X, length active X -> length X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [eq](x0, x1) = x0, [cons](x0, x1) = 1, [take](x0, x1) = 0, [mark](x0) = x0 + 1, [active](x0) = x0, [s](x0) = x0 + 1, [inf](x0) = 0, [length](x0) = 0, [true] = 0, [0] = 0, [false] = 0, [nil] = 0, [mark#](x0) = x0 + 1, [active#](x0) = x0 + 1 Strict: active# eq(s X, s Y) -> mark# eq(X, Y) 2 + 0X + 1Y >= 1 + 0X + 1Y mark# length X -> active# length mark X 1 + 0X >= 1 + 0X mark# take(X1, X2) -> active# take(mark X1, mark X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark# inf X -> active# inf mark X 1 + 0X >= 1 + 0X mark# cons(X1, X2) -> active# cons(X1, X2) 2 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 mark# s X -> active# s X 2 + 1X >= 2 + 1X mark# eq(X1, X2) -> active# eq(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 Weak: length active X -> length X 0 + 0X >= 0 + 0X length mark X -> length X 0 + 0X >= 0 + 0X take(active X1, X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(mark X1, X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(X1, active X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(X1, mark X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 inf active X -> inf X 0 + 0X >= 0 + 0X inf mark X -> inf X 0 + 0X >= 0 + 0X cons(active X1, X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(mark X1, X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(X1, active X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(X1, mark X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X eq(active X1, X2) -> eq(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 eq(mark X1, X2) -> eq(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 eq(X1, active X2) -> eq(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 eq(X1, mark X2) -> eq(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 active length nil() -> mark 0() 0 >= 1 active length cons(X, L) -> mark s length L 0 + 0X + 0L >= 2 + 0L active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)) 0 + 0X + 0Y + 0L >= 2 + 0X + 0Y + 0L active take(0(), X) -> mark nil() 0 + 0X >= 1 active inf X -> mark cons(X, inf s X) 0 + 0X >= 2 + 0X active eq(s X, s Y) -> mark eq(X, Y) 1 + 0X + 1Y >= 1 + 0X + 1Y active eq(0(), 0()) -> mark true() 0 >= 1 active eq(X, Y) -> mark false() 0 + 0X + 1Y >= 1 mark length X -> active length mark X 1 + 0X >= 0 + 0X mark take(X1, X2) -> active take(mark X1, mark X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 0 mark inf X -> active inf mark X 1 + 0X >= 0 + 0X mark cons(X1, X2) -> active cons(X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark false() -> active false() 1 >= 0 mark s X -> active s X 2 + 1X >= 1 + 1X mark 0() -> active 0() 1 >= 0 mark eq(X1, X2) -> active eq(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 mark true() -> active true() 1 >= 0 SCCS (0): SCC (2): Strict: { length# mark X -> length# X, length# active X -> length# X} Weak: { mark true() -> active true(), mark eq(X1, X2) -> active eq(X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark false() -> active false(), mark cons(X1, X2) -> active cons(X1, X2), mark inf X -> active inf mark X, mark nil() -> active nil(), mark take(X1, X2) -> active take(mark X1, mark X2), mark length X -> active length mark X, active eq(X, Y) -> mark false(), active eq(0(), 0()) -> mark true(), active eq(s X, s Y) -> mark eq(X, Y), active inf X -> mark cons(X, inf s X), active take(0(), X) -> mark nil(), active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)), active length cons(X, L) -> mark s length L, active length nil() -> mark 0(), eq(X1, mark X2) -> eq(X1, X2), eq(X1, active X2) -> eq(X1, X2), eq(mark X1, X2) -> eq(X1, X2), eq(active X1, X2) -> eq(X1, X2), s mark X -> s X, s active X -> s X, cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), inf mark X -> inf X, inf active X -> inf X, take(X1, mark X2) -> take(X1, X2), take(X1, active X2) -> take(X1, X2), take(mark X1, X2) -> take(X1, X2), take(active X1, X2) -> take(X1, X2), length mark X -> length X, length active X -> length X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [eq](x0, x1) = x0 + x1 + 1, [cons](x0, x1) = x0, [take](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [inf](x0) = 0, [length](x0) = 0, [true] = 1, [0] = 1, [false] = 1, [nil] = 1, [length#](x0) = x0 Strict: length# active X -> length# X 1 + 1X >= 0 + 1X length# mark X -> length# X 0 + 1X >= 0 + 1X Weak: length active X -> length X 0 + 0X >= 0 + 0X length mark X -> length X 0 + 0X >= 0 + 0X take(active X1, X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(mark X1, X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(X1, active X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(X1, mark X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 inf active X -> inf X 0 + 0X >= 0 + 0X inf mark X -> inf X 0 + 0X >= 0 + 0X cons(active X1, X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(mark X1, X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(X1, active X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(X1, mark X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X eq(active X1, X2) -> eq(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 eq(mark X1, X2) -> eq(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 eq(X1, active X2) -> eq(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 eq(X1, mark X2) -> eq(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active length nil() -> mark 0() 1 >= 1 active length cons(X, L) -> mark s length L 1 + 0X + 0L >= 0 + 0L active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)) 1 + 0X + 0Y + 0L >= 0 + 0X + 0Y + 0L active take(0(), X) -> mark nil() 1 + 0X >= 1 active inf X -> mark cons(X, inf s X) 1 + 0X >= 0 + 0X active eq(s X, s Y) -> mark eq(X, Y) 2 + 0X + 0Y >= 1 + 1X + 1Y active eq(0(), 0()) -> mark true() 4 >= 1 active eq(X, Y) -> mark false() 2 + 1X + 1Y >= 1 mark length X -> active length mark X 0 + 0X >= 1 + 0X mark take(X1, X2) -> active take(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 2 mark inf X -> active inf mark X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(X1, X2) 0 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 mark false() -> active false() 1 >= 2 mark s X -> active s X 0 + 0X >= 1 + 0X mark 0() -> active 0() 1 >= 2 mark eq(X1, X2) -> active eq(X1, X2) 1 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark true() -> active true() 1 >= 2 SCCS (1): Scc: {length# mark X -> length# X} SCC (1): Strict: {length# mark X -> length# X} Weak: { mark true() -> active true(), mark eq(X1, X2) -> active eq(X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark false() -> active false(), mark cons(X1, X2) -> active cons(X1, X2), mark inf X -> active inf mark X, mark nil() -> active nil(), mark take(X1, X2) -> active take(mark X1, mark X2), mark length X -> active length mark X, active eq(X, Y) -> mark false(), active eq(0(), 0()) -> mark true(), active eq(s X, s Y) -> mark eq(X, Y), active inf X -> mark cons(X, inf s X), active take(0(), X) -> mark nil(), active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)), active length cons(X, L) -> mark s length L, active length nil() -> mark 0(), eq(X1, mark X2) -> eq(X1, X2), eq(X1, active X2) -> eq(X1, X2), eq(mark X1, X2) -> eq(X1, X2), eq(active X1, X2) -> eq(X1, X2), s mark X -> s X, s active X -> s X, cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), inf mark X -> inf X, inf active X -> inf X, take(X1, mark X2) -> take(X1, X2), take(X1, active X2) -> take(X1, X2), take(mark X1, X2) -> take(X1, X2), take(active X1, X2) -> take(X1, X2), length mark X -> length X, length active X -> length X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [eq](x0, x1) = x0 + 1, [cons](x0, x1) = 1, [take](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [active](x0) = 0, [s](x0) = 1, [inf](x0) = x0 + 1, [length](x0) = x0 + 1, [true] = 0, [0] = 1, [false] = 0, [nil] = 1, [length#](x0) = x0 Strict: length# mark X -> length# X 1 + 1X >= 0 + 1X Weak: length active X -> length X 1 + 0X >= 1 + 1X length mark X -> length X 2 + 1X >= 1 + 1X take(active X1, X2) -> take(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 take(mark X1, X2) -> take(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 take(X1, active X2) -> take(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 take(X1, mark X2) -> take(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 inf active X -> inf X 1 + 0X >= 1 + 1X inf mark X -> inf X 2 + 1X >= 1 + 1X cons(active X1, X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(mark X1, X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(X1, active X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(X1, mark X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 s active X -> s X 1 + 0X >= 1 + 0X s mark X -> s X 1 + 0X >= 1 + 0X eq(active X1, X2) -> eq(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 eq(mark X1, X2) -> eq(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 eq(X1, active X2) -> eq(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 eq(X1, mark X2) -> eq(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active length nil() -> mark 0() 0 >= 2 active length cons(X, L) -> mark s length L 0 + 0X + 0L >= 2 + 0L active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)) 0 + 0X + 0Y + 0L >= 2 + 0X + 0Y + 0L active take(0(), X) -> mark nil() 0 + 0X >= 2 active inf X -> mark cons(X, inf s X) 0 + 0X >= 2 + 0X active eq(s X, s Y) -> mark eq(X, Y) 0 + 0X + 0Y >= 2 + 0X + 1Y active eq(0(), 0()) -> mark true() 0 >= 1 active eq(X, Y) -> mark false() 0 + 0X + 0Y >= 1 mark length X -> active length mark X 2 + 1X >= 0 + 0X mark take(X1, X2) -> active take(mark X1, mark X2) 2 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 mark nil() -> active nil() 2 >= 0 mark inf X -> active inf mark X 2 + 1X >= 0 + 0X mark cons(X1, X2) -> active cons(X1, X2) 2 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark false() -> active false() 1 >= 0 mark s X -> active s X 2 + 0X >= 0 + 0X mark 0() -> active 0() 2 >= 0 mark eq(X1, X2) -> active eq(X1, X2) 2 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 mark true() -> active true() 1 >= 0 Qed SCC (4): Strict: { take#(X1, mark X2) -> take#(X1, X2), take#(X1, active X2) -> take#(X1, X2), take#(mark X1, X2) -> take#(X1, X2), take#(active X1, X2) -> take#(X1, X2)} Weak: { mark true() -> active true(), mark eq(X1, X2) -> active eq(X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark false() -> active false(), mark cons(X1, X2) -> active cons(X1, X2), mark inf X -> active inf mark X, mark nil() -> active nil(), mark take(X1, X2) -> active take(mark X1, mark X2), mark length X -> active length mark X, active eq(X, Y) -> mark false(), active eq(0(), 0()) -> mark true(), active eq(s X, s Y) -> mark eq(X, Y), active inf X -> mark cons(X, inf s X), active take(0(), X) -> mark nil(), active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)), active length cons(X, L) -> mark s length L, active length nil() -> mark 0(), eq(X1, mark X2) -> eq(X1, X2), eq(X1, active X2) -> eq(X1, X2), eq(mark X1, X2) -> eq(X1, X2), eq(active X1, X2) -> eq(X1, X2), s mark X -> s X, s active X -> s X, cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), inf mark X -> inf X, inf active X -> inf X, take(X1, mark X2) -> take(X1, X2), take(X1, active X2) -> take(X1, X2), take(mark X1, X2) -> take(X1, X2), take(active X1, X2) -> take(X1, X2), length mark X -> length X, length active X -> length X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [eq](x0, x1) = x0, [cons](x0, x1) = 0, [take](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [inf](x0) = 0, [length](x0) = 0, [true] = 0, [0] = 1, [false] = 1, [nil] = 1, [take#](x0, x1) = x0 Strict: take#(active X1, X2) -> take#(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 take#(mark X1, X2) -> take#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 take#(X1, active X2) -> take#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 take#(X1, mark X2) -> take#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 Weak: length active X -> length X 0 + 0X >= 0 + 0X length mark X -> length X 0 + 0X >= 0 + 0X take(active X1, X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(mark X1, X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(X1, active X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(X1, mark X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 inf active X -> inf X 0 + 0X >= 0 + 0X inf mark X -> inf X 0 + 0X >= 0 + 0X cons(active X1, X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(mark X1, X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(X1, active X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(X1, mark X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X eq(active X1, X2) -> eq(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 eq(mark X1, X2) -> eq(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 eq(X1, active X2) -> eq(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 eq(X1, mark X2) -> eq(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 active length nil() -> mark 0() 1 >= 1 active length cons(X, L) -> mark s length L 1 + 0X + 0L >= 0 + 0L active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)) 1 + 0X + 0Y + 0L >= 0 + 0X + 0Y + 0L active take(0(), X) -> mark nil() 1 + 0X >= 1 active inf X -> mark cons(X, inf s X) 1 + 0X >= 0 + 0X active eq(s X, s Y) -> mark eq(X, Y) 1 + 0X + 0Y >= 0 + 1X + 0Y active eq(0(), 0()) -> mark true() 2 >= 0 active eq(X, Y) -> mark false() 1 + 1X + 0Y >= 1 mark length X -> active length mark X 0 + 0X >= 1 + 0X mark take(X1, X2) -> active take(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 2 mark inf X -> active inf mark X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark false() -> active false() 1 >= 2 mark s X -> active s X 0 + 0X >= 1 + 0X mark 0() -> active 0() 1 >= 2 mark eq(X1, X2) -> active eq(X1, X2) 0 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 mark true() -> active true() 0 >= 1 SCCS (1): Scc: { take#(X1, mark X2) -> take#(X1, X2), take#(X1, active X2) -> take#(X1, X2), take#(mark X1, X2) -> take#(X1, X2)} SCC (3): Strict: { take#(X1, mark X2) -> take#(X1, X2), take#(X1, active X2) -> take#(X1, X2), take#(mark X1, X2) -> take#(X1, X2)} Weak: { mark true() -> active true(), mark eq(X1, X2) -> active eq(X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark false() -> active false(), mark cons(X1, X2) -> active cons(X1, X2), mark inf X -> active inf mark X, mark nil() -> active nil(), mark take(X1, X2) -> active take(mark X1, mark X2), mark length X -> active length mark X, active eq(X, Y) -> mark false(), active eq(0(), 0()) -> mark true(), active eq(s X, s Y) -> mark eq(X, Y), active inf X -> mark cons(X, inf s X), active take(0(), X) -> mark nil(), active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)), active length cons(X, L) -> mark s length L, active length nil() -> mark 0(), eq(X1, mark X2) -> eq(X1, X2), eq(X1, active X2) -> eq(X1, X2), eq(mark X1, X2) -> eq(X1, X2), eq(active X1, X2) -> eq(X1, X2), s mark X -> s X, s active X -> s X, cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), inf mark X -> inf X, inf active X -> inf X, take(X1, mark X2) -> take(X1, X2), take(X1, active X2) -> take(X1, X2), take(mark X1, X2) -> take(X1, X2), take(active X1, X2) -> take(X1, X2), length mark X -> length X, length active X -> length X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [eq](x0, x1) = x0 + x1, [cons](x0, x1) = 1, [take](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [active](x0) = 0, [s](x0) = 1, [inf](x0) = x0 + 1, [length](x0) = 0, [true] = 0, [0] = 1, [false] = 0, [nil] = 1, [take#](x0, x1) = x0 Strict: take#(mark X1, X2) -> take#(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 take#(X1, active X2) -> take#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 take#(X1, mark X2) -> take#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 Weak: length active X -> length X 0 + 0X >= 0 + 0X length mark X -> length X 0 + 0X >= 0 + 0X take(active X1, X2) -> take(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 take(mark X1, X2) -> take(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 take(X1, active X2) -> take(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 take(X1, mark X2) -> take(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 inf active X -> inf X 1 + 0X >= 1 + 1X inf mark X -> inf X 2 + 1X >= 1 + 1X cons(active X1, X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(mark X1, X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(X1, active X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(X1, mark X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 s active X -> s X 1 + 0X >= 1 + 0X s mark X -> s X 1 + 0X >= 1 + 0X eq(active X1, X2) -> eq(X1, X2) 0 + 0X1 + 1X2 >= 0 + 1X1 + 1X2 eq(mark X1, X2) -> eq(X1, X2) 1 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 eq(X1, active X2) -> eq(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 1X2 eq(X1, mark X2) -> eq(X1, X2) 1 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 active length nil() -> mark 0() 0 >= 2 active length cons(X, L) -> mark s length L 0 + 0X + 0L >= 2 + 0L active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)) 0 + 0X + 0Y + 0L >= 2 + 0X + 0Y + 0L active take(0(), X) -> mark nil() 0 + 0X >= 2 active inf X -> mark cons(X, inf s X) 0 + 0X >= 2 + 0X active eq(s X, s Y) -> mark eq(X, Y) 0 + 0X + 0Y >= 1 + 1X + 1Y active eq(0(), 0()) -> mark true() 0 >= 1 active eq(X, Y) -> mark false() 0 + 0X + 0Y >= 1 mark length X -> active length mark X 1 + 0X >= 0 + 0X mark take(X1, X2) -> active take(mark X1, mark X2) 2 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 mark nil() -> active nil() 2 >= 0 mark inf X -> active inf mark X 2 + 1X >= 0 + 0X mark cons(X1, X2) -> active cons(X1, X2) 2 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark false() -> active false() 1 >= 0 mark s X -> active s X 2 + 0X >= 0 + 0X mark 0() -> active 0() 2 >= 0 mark eq(X1, X2) -> active eq(X1, X2) 1 + 1X1 + 1X2 >= 0 + 0X1 + 0X2 mark true() -> active true() 1 >= 0 SCCS (1): Scc: { take#(X1, mark X2) -> take#(X1, X2), take#(X1, active X2) -> take#(X1, X2)} SCC (2): Strict: { take#(X1, mark X2) -> take#(X1, X2), take#(X1, active X2) -> take#(X1, X2)} Weak: { mark true() -> active true(), mark eq(X1, X2) -> active eq(X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark false() -> active false(), mark cons(X1, X2) -> active cons(X1, X2), mark inf X -> active inf mark X, mark nil() -> active nil(), mark take(X1, X2) -> active take(mark X1, mark X2), mark length X -> active length mark X, active eq(X, Y) -> mark false(), active eq(0(), 0()) -> mark true(), active eq(s X, s Y) -> mark eq(X, Y), active inf X -> mark cons(X, inf s X), active take(0(), X) -> mark nil(), active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)), active length cons(X, L) -> mark s length L, active length nil() -> mark 0(), eq(X1, mark X2) -> eq(X1, X2), eq(X1, active X2) -> eq(X1, X2), eq(mark X1, X2) -> eq(X1, X2), eq(active X1, X2) -> eq(X1, X2), s mark X -> s X, s active X -> s X, cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), inf mark X -> inf X, inf active X -> inf X, take(X1, mark X2) -> take(X1, X2), take(X1, active X2) -> take(X1, X2), take(mark X1, X2) -> take(X1, X2), take(active X1, X2) -> take(X1, X2), length mark X -> length X, length active X -> length X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [eq](x0, x1) = x0 + x1 + 1, [cons](x0, x1) = x0, [take](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [inf](x0) = 0, [length](x0) = 0, [true] = 1, [0] = 1, [false] = 1, [nil] = 1, [take#](x0, x1) = x0 Strict: take#(X1, active X2) -> take#(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 take#(X1, mark X2) -> take#(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 Weak: length active X -> length X 0 + 0X >= 0 + 0X length mark X -> length X 0 + 0X >= 0 + 0X take(active X1, X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(mark X1, X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(X1, active X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(X1, mark X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 inf active X -> inf X 0 + 0X >= 0 + 0X inf mark X -> inf X 0 + 0X >= 0 + 0X cons(active X1, X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(mark X1, X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(X1, active X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(X1, mark X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X eq(active X1, X2) -> eq(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 eq(mark X1, X2) -> eq(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 eq(X1, active X2) -> eq(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 eq(X1, mark X2) -> eq(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active length nil() -> mark 0() 1 >= 1 active length cons(X, L) -> mark s length L 1 + 0X + 0L >= 0 + 0L active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)) 1 + 0X + 0Y + 0L >= 0 + 0X + 0Y + 0L active take(0(), X) -> mark nil() 1 + 0X >= 1 active inf X -> mark cons(X, inf s X) 1 + 0X >= 0 + 0X active eq(s X, s Y) -> mark eq(X, Y) 2 + 0X + 0Y >= 1 + 1X + 1Y active eq(0(), 0()) -> mark true() 4 >= 1 active eq(X, Y) -> mark false() 2 + 1X + 1Y >= 1 mark length X -> active length mark X 0 + 0X >= 1 + 0X mark take(X1, X2) -> active take(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 2 mark inf X -> active inf mark X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(X1, X2) 0 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 mark false() -> active false() 1 >= 2 mark s X -> active s X 0 + 0X >= 1 + 0X mark 0() -> active 0() 1 >= 2 mark eq(X1, X2) -> active eq(X1, X2) 1 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark true() -> active true() 1 >= 2 SCCS (1): Scc: {take#(X1, mark X2) -> take#(X1, X2)} SCC (1): Strict: {take#(X1, mark X2) -> take#(X1, X2)} Weak: { mark true() -> active true(), mark eq(X1, X2) -> active eq(X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark false() -> active false(), mark cons(X1, X2) -> active cons(X1, X2), mark inf X -> active inf mark X, mark nil() -> active nil(), mark take(X1, X2) -> active take(mark X1, mark X2), mark length X -> active length mark X, active eq(X, Y) -> mark false(), active eq(0(), 0()) -> mark true(), active eq(s X, s Y) -> mark eq(X, Y), active inf X -> mark cons(X, inf s X), active take(0(), X) -> mark nil(), active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)), active length cons(X, L) -> mark s length L, active length nil() -> mark 0(), eq(X1, mark X2) -> eq(X1, X2), eq(X1, active X2) -> eq(X1, X2), eq(mark X1, X2) -> eq(X1, X2), eq(active X1, X2) -> eq(X1, X2), s mark X -> s X, s active X -> s X, cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), inf mark X -> inf X, inf active X -> inf X, take(X1, mark X2) -> take(X1, X2), take(X1, active X2) -> take(X1, X2), take(mark X1, X2) -> take(X1, X2), take(active X1, X2) -> take(X1, X2), length mark X -> length X, length active X -> length X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [eq](x0, x1) = x0 + 1, [cons](x0, x1) = 1, [take](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [active](x0) = 0, [s](x0) = 1, [inf](x0) = x0 + 1, [length](x0) = x0 + 1, [true] = 0, [0] = 1, [false] = 0, [nil] = 1, [take#](x0, x1) = x0 Strict: take#(X1, mark X2) -> take#(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 Weak: length active X -> length X 1 + 0X >= 1 + 1X length mark X -> length X 2 + 1X >= 1 + 1X take(active X1, X2) -> take(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 take(mark X1, X2) -> take(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 take(X1, active X2) -> take(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 take(X1, mark X2) -> take(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 inf active X -> inf X 1 + 0X >= 1 + 1X inf mark X -> inf X 2 + 1X >= 1 + 1X cons(active X1, X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(mark X1, X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(X1, active X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(X1, mark X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 s active X -> s X 1 + 0X >= 1 + 0X s mark X -> s X 1 + 0X >= 1 + 0X eq(active X1, X2) -> eq(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 eq(mark X1, X2) -> eq(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 eq(X1, active X2) -> eq(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 eq(X1, mark X2) -> eq(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active length nil() -> mark 0() 0 >= 2 active length cons(X, L) -> mark s length L 0 + 0X + 0L >= 2 + 0L active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)) 0 + 0X + 0Y + 0L >= 2 + 0X + 0Y + 0L active take(0(), X) -> mark nil() 0 + 0X >= 2 active inf X -> mark cons(X, inf s X) 0 + 0X >= 2 + 0X active eq(s X, s Y) -> mark eq(X, Y) 0 + 0X + 0Y >= 2 + 0X + 1Y active eq(0(), 0()) -> mark true() 0 >= 1 active eq(X, Y) -> mark false() 0 + 0X + 0Y >= 1 mark length X -> active length mark X 2 + 1X >= 0 + 0X mark take(X1, X2) -> active take(mark X1, mark X2) 2 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 mark nil() -> active nil() 2 >= 0 mark inf X -> active inf mark X 2 + 1X >= 0 + 0X mark cons(X1, X2) -> active cons(X1, X2) 2 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark false() -> active false() 1 >= 0 mark s X -> active s X 2 + 0X >= 0 + 0X mark 0() -> active 0() 2 >= 0 mark eq(X1, X2) -> active eq(X1, X2) 2 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 mark true() -> active true() 1 >= 0 Qed SCC (2): Strict: { s# mark X -> s# X, s# active X -> s# X} Weak: { mark true() -> active true(), mark eq(X1, X2) -> active eq(X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark false() -> active false(), mark cons(X1, X2) -> active cons(X1, X2), mark inf X -> active inf mark X, mark nil() -> active nil(), mark take(X1, X2) -> active take(mark X1, mark X2), mark length X -> active length mark X, active eq(X, Y) -> mark false(), active eq(0(), 0()) -> mark true(), active eq(s X, s Y) -> mark eq(X, Y), active inf X -> mark cons(X, inf s X), active take(0(), X) -> mark nil(), active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)), active length cons(X, L) -> mark s length L, active length nil() -> mark 0(), eq(X1, mark X2) -> eq(X1, X2), eq(X1, active X2) -> eq(X1, X2), eq(mark X1, X2) -> eq(X1, X2), eq(active X1, X2) -> eq(X1, X2), s mark X -> s X, s active X -> s X, cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), inf mark X -> inf X, inf active X -> inf X, take(X1, mark X2) -> take(X1, X2), take(X1, active X2) -> take(X1, X2), take(mark X1, X2) -> take(X1, X2), take(active X1, X2) -> take(X1, X2), length mark X -> length X, length active X -> length X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [eq](x0, x1) = x0 + x1 + 1, [cons](x0, x1) = x0, [take](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [inf](x0) = 0, [length](x0) = 0, [true] = 1, [0] = 1, [false] = 1, [nil] = 1, [s#](x0) = x0 Strict: s# active X -> s# X 1 + 1X >= 0 + 1X s# mark X -> s# X 0 + 1X >= 0 + 1X Weak: length active X -> length X 0 + 0X >= 0 + 0X length mark X -> length X 0 + 0X >= 0 + 0X take(active X1, X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(mark X1, X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(X1, active X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(X1, mark X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 inf active X -> inf X 0 + 0X >= 0 + 0X inf mark X -> inf X 0 + 0X >= 0 + 0X cons(active X1, X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(mark X1, X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(X1, active X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(X1, mark X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X eq(active X1, X2) -> eq(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 eq(mark X1, X2) -> eq(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 eq(X1, active X2) -> eq(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 eq(X1, mark X2) -> eq(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active length nil() -> mark 0() 1 >= 1 active length cons(X, L) -> mark s length L 1 + 0X + 0L >= 0 + 0L active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)) 1 + 0X + 0Y + 0L >= 0 + 0X + 0Y + 0L active take(0(), X) -> mark nil() 1 + 0X >= 1 active inf X -> mark cons(X, inf s X) 1 + 0X >= 0 + 0X active eq(s X, s Y) -> mark eq(X, Y) 2 + 0X + 0Y >= 1 + 1X + 1Y active eq(0(), 0()) -> mark true() 4 >= 1 active eq(X, Y) -> mark false() 2 + 1X + 1Y >= 1 mark length X -> active length mark X 0 + 0X >= 1 + 0X mark take(X1, X2) -> active take(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 2 mark inf X -> active inf mark X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(X1, X2) 0 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 mark false() -> active false() 1 >= 2 mark s X -> active s X 0 + 0X >= 1 + 0X mark 0() -> active 0() 1 >= 2 mark eq(X1, X2) -> active eq(X1, X2) 1 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark true() -> active true() 1 >= 2 SCCS (1): Scc: {s# mark X -> s# X} SCC (1): Strict: {s# mark X -> s# X} Weak: { mark true() -> active true(), mark eq(X1, X2) -> active eq(X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark false() -> active false(), mark cons(X1, X2) -> active cons(X1, X2), mark inf X -> active inf mark X, mark nil() -> active nil(), mark take(X1, X2) -> active take(mark X1, mark X2), mark length X -> active length mark X, active eq(X, Y) -> mark false(), active eq(0(), 0()) -> mark true(), active eq(s X, s Y) -> mark eq(X, Y), active inf X -> mark cons(X, inf s X), active take(0(), X) -> mark nil(), active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)), active length cons(X, L) -> mark s length L, active length nil() -> mark 0(), eq(X1, mark X2) -> eq(X1, X2), eq(X1, active X2) -> eq(X1, X2), eq(mark X1, X2) -> eq(X1, X2), eq(active X1, X2) -> eq(X1, X2), s mark X -> s X, s active X -> s X, cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), inf mark X -> inf X, inf active X -> inf X, take(X1, mark X2) -> take(X1, X2), take(X1, active X2) -> take(X1, X2), take(mark X1, X2) -> take(X1, X2), take(active X1, X2) -> take(X1, X2), length mark X -> length X, length active X -> length X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [eq](x0, x1) = x0 + 1, [cons](x0, x1) = 1, [take](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [active](x0) = 0, [s](x0) = 1, [inf](x0) = x0 + 1, [length](x0) = x0 + 1, [true] = 0, [0] = 1, [false] = 0, [nil] = 1, [s#](x0) = x0 Strict: s# mark X -> s# X 1 + 1X >= 0 + 1X Weak: length active X -> length X 1 + 0X >= 1 + 1X length mark X -> length X 2 + 1X >= 1 + 1X take(active X1, X2) -> take(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 take(mark X1, X2) -> take(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 take(X1, active X2) -> take(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 take(X1, mark X2) -> take(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 inf active X -> inf X 1 + 0X >= 1 + 1X inf mark X -> inf X 2 + 1X >= 1 + 1X cons(active X1, X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(mark X1, X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(X1, active X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(X1, mark X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 s active X -> s X 1 + 0X >= 1 + 0X s mark X -> s X 1 + 0X >= 1 + 0X eq(active X1, X2) -> eq(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 eq(mark X1, X2) -> eq(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 eq(X1, active X2) -> eq(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 eq(X1, mark X2) -> eq(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active length nil() -> mark 0() 0 >= 2 active length cons(X, L) -> mark s length L 0 + 0X + 0L >= 2 + 0L active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)) 0 + 0X + 0Y + 0L >= 2 + 0X + 0Y + 0L active take(0(), X) -> mark nil() 0 + 0X >= 2 active inf X -> mark cons(X, inf s X) 0 + 0X >= 2 + 0X active eq(s X, s Y) -> mark eq(X, Y) 0 + 0X + 0Y >= 2 + 0X + 1Y active eq(0(), 0()) -> mark true() 0 >= 1 active eq(X, Y) -> mark false() 0 + 0X + 0Y >= 1 mark length X -> active length mark X 2 + 1X >= 0 + 0X mark take(X1, X2) -> active take(mark X1, mark X2) 2 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 mark nil() -> active nil() 2 >= 0 mark inf X -> active inf mark X 2 + 1X >= 0 + 0X mark cons(X1, X2) -> active cons(X1, X2) 2 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark false() -> active false() 1 >= 0 mark s X -> active s X 2 + 0X >= 0 + 0X mark 0() -> active 0() 2 >= 0 mark eq(X1, X2) -> active eq(X1, X2) 2 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 mark true() -> active true() 1 >= 0 Qed SCC (4): Strict: { cons#(X1, mark X2) -> cons#(X1, X2), cons#(X1, active X2) -> cons#(X1, X2), cons#(mark X1, X2) -> cons#(X1, X2), cons#(active X1, X2) -> cons#(X1, X2)} Weak: { mark true() -> active true(), mark eq(X1, X2) -> active eq(X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark false() -> active false(), mark cons(X1, X2) -> active cons(X1, X2), mark inf X -> active inf mark X, mark nil() -> active nil(), mark take(X1, X2) -> active take(mark X1, mark X2), mark length X -> active length mark X, active eq(X, Y) -> mark false(), active eq(0(), 0()) -> mark true(), active eq(s X, s Y) -> mark eq(X, Y), active inf X -> mark cons(X, inf s X), active take(0(), X) -> mark nil(), active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)), active length cons(X, L) -> mark s length L, active length nil() -> mark 0(), eq(X1, mark X2) -> eq(X1, X2), eq(X1, active X2) -> eq(X1, X2), eq(mark X1, X2) -> eq(X1, X2), eq(active X1, X2) -> eq(X1, X2), s mark X -> s X, s active X -> s X, cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), inf mark X -> inf X, inf active X -> inf X, take(X1, mark X2) -> take(X1, X2), take(X1, active X2) -> take(X1, X2), take(mark X1, X2) -> take(X1, X2), take(active X1, X2) -> take(X1, X2), length mark X -> length X, length active X -> length X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [eq](x0, x1) = x0, [cons](x0, x1) = 0, [take](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [inf](x0) = 0, [length](x0) = 0, [true] = 0, [0] = 1, [false] = 1, [nil] = 1, [cons#](x0, x1) = x0 Strict: cons#(active X1, X2) -> cons#(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 cons#(mark X1, X2) -> cons#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 cons#(X1, active X2) -> cons#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 cons#(X1, mark X2) -> cons#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 Weak: length active X -> length X 0 + 0X >= 0 + 0X length mark X -> length X 0 + 0X >= 0 + 0X take(active X1, X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(mark X1, X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(X1, active X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(X1, mark X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 inf active X -> inf X 0 + 0X >= 0 + 0X inf mark X -> inf X 0 + 0X >= 0 + 0X cons(active X1, X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(mark X1, X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(X1, active X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(X1, mark X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X eq(active X1, X2) -> eq(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 eq(mark X1, X2) -> eq(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 eq(X1, active X2) -> eq(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 eq(X1, mark X2) -> eq(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 active length nil() -> mark 0() 1 >= 1 active length cons(X, L) -> mark s length L 1 + 0X + 0L >= 0 + 0L active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)) 1 + 0X + 0Y + 0L >= 0 + 0X + 0Y + 0L active take(0(), X) -> mark nil() 1 + 0X >= 1 active inf X -> mark cons(X, inf s X) 1 + 0X >= 0 + 0X active eq(s X, s Y) -> mark eq(X, Y) 1 + 0X + 0Y >= 0 + 1X + 0Y active eq(0(), 0()) -> mark true() 2 >= 0 active eq(X, Y) -> mark false() 1 + 1X + 0Y >= 1 mark length X -> active length mark X 0 + 0X >= 1 + 0X mark take(X1, X2) -> active take(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 2 mark inf X -> active inf mark X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark false() -> active false() 1 >= 2 mark s X -> active s X 0 + 0X >= 1 + 0X mark 0() -> active 0() 1 >= 2 mark eq(X1, X2) -> active eq(X1, X2) 0 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 mark true() -> active true() 0 >= 1 SCCS (1): Scc: { cons#(X1, mark X2) -> cons#(X1, X2), cons#(X1, active X2) -> cons#(X1, X2), cons#(mark X1, X2) -> cons#(X1, X2)} SCC (3): Strict: { cons#(X1, mark X2) -> cons#(X1, X2), cons#(X1, active X2) -> cons#(X1, X2), cons#(mark X1, X2) -> cons#(X1, X2)} Weak: { mark true() -> active true(), mark eq(X1, X2) -> active eq(X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark false() -> active false(), mark cons(X1, X2) -> active cons(X1, X2), mark inf X -> active inf mark X, mark nil() -> active nil(), mark take(X1, X2) -> active take(mark X1, mark X2), mark length X -> active length mark X, active eq(X, Y) -> mark false(), active eq(0(), 0()) -> mark true(), active eq(s X, s Y) -> mark eq(X, Y), active inf X -> mark cons(X, inf s X), active take(0(), X) -> mark nil(), active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)), active length cons(X, L) -> mark s length L, active length nil() -> mark 0(), eq(X1, mark X2) -> eq(X1, X2), eq(X1, active X2) -> eq(X1, X2), eq(mark X1, X2) -> eq(X1, X2), eq(active X1, X2) -> eq(X1, X2), s mark X -> s X, s active X -> s X, cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), inf mark X -> inf X, inf active X -> inf X, take(X1, mark X2) -> take(X1, X2), take(X1, active X2) -> take(X1, X2), take(mark X1, X2) -> take(X1, X2), take(active X1, X2) -> take(X1, X2), length mark X -> length X, length active X -> length X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [eq](x0, x1) = x0 + x1, [cons](x0, x1) = 1, [take](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [active](x0) = 0, [s](x0) = 1, [inf](x0) = x0 + 1, [length](x0) = 0, [true] = 0, [0] = 1, [false] = 0, [nil] = 1, [cons#](x0, x1) = x0 Strict: cons#(mark X1, X2) -> cons#(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 cons#(X1, active X2) -> cons#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 cons#(X1, mark X2) -> cons#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 Weak: length active X -> length X 0 + 0X >= 0 + 0X length mark X -> length X 0 + 0X >= 0 + 0X take(active X1, X2) -> take(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 take(mark X1, X2) -> take(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 take(X1, active X2) -> take(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 take(X1, mark X2) -> take(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 inf active X -> inf X 1 + 0X >= 1 + 1X inf mark X -> inf X 2 + 1X >= 1 + 1X cons(active X1, X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(mark X1, X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(X1, active X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(X1, mark X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 s active X -> s X 1 + 0X >= 1 + 0X s mark X -> s X 1 + 0X >= 1 + 0X eq(active X1, X2) -> eq(X1, X2) 0 + 0X1 + 1X2 >= 0 + 1X1 + 1X2 eq(mark X1, X2) -> eq(X1, X2) 1 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 eq(X1, active X2) -> eq(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 1X2 eq(X1, mark X2) -> eq(X1, X2) 1 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 active length nil() -> mark 0() 0 >= 2 active length cons(X, L) -> mark s length L 0 + 0X + 0L >= 2 + 0L active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)) 0 + 0X + 0Y + 0L >= 2 + 0X + 0Y + 0L active take(0(), X) -> mark nil() 0 + 0X >= 2 active inf X -> mark cons(X, inf s X) 0 + 0X >= 2 + 0X active eq(s X, s Y) -> mark eq(X, Y) 0 + 0X + 0Y >= 1 + 1X + 1Y active eq(0(), 0()) -> mark true() 0 >= 1 active eq(X, Y) -> mark false() 0 + 0X + 0Y >= 1 mark length X -> active length mark X 1 + 0X >= 0 + 0X mark take(X1, X2) -> active take(mark X1, mark X2) 2 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 mark nil() -> active nil() 2 >= 0 mark inf X -> active inf mark X 2 + 1X >= 0 + 0X mark cons(X1, X2) -> active cons(X1, X2) 2 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark false() -> active false() 1 >= 0 mark s X -> active s X 2 + 0X >= 0 + 0X mark 0() -> active 0() 2 >= 0 mark eq(X1, X2) -> active eq(X1, X2) 1 + 1X1 + 1X2 >= 0 + 0X1 + 0X2 mark true() -> active true() 1 >= 0 SCCS (1): Scc: { cons#(X1, mark X2) -> cons#(X1, X2), cons#(X1, active X2) -> cons#(X1, X2)} SCC (2): Strict: { cons#(X1, mark X2) -> cons#(X1, X2), cons#(X1, active X2) -> cons#(X1, X2)} Weak: { mark true() -> active true(), mark eq(X1, X2) -> active eq(X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark false() -> active false(), mark cons(X1, X2) -> active cons(X1, X2), mark inf X -> active inf mark X, mark nil() -> active nil(), mark take(X1, X2) -> active take(mark X1, mark X2), mark length X -> active length mark X, active eq(X, Y) -> mark false(), active eq(0(), 0()) -> mark true(), active eq(s X, s Y) -> mark eq(X, Y), active inf X -> mark cons(X, inf s X), active take(0(), X) -> mark nil(), active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)), active length cons(X, L) -> mark s length L, active length nil() -> mark 0(), eq(X1, mark X2) -> eq(X1, X2), eq(X1, active X2) -> eq(X1, X2), eq(mark X1, X2) -> eq(X1, X2), eq(active X1, X2) -> eq(X1, X2), s mark X -> s X, s active X -> s X, cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), inf mark X -> inf X, inf active X -> inf X, take(X1, mark X2) -> take(X1, X2), take(X1, active X2) -> take(X1, X2), take(mark X1, X2) -> take(X1, X2), take(active X1, X2) -> take(X1, X2), length mark X -> length X, length active X -> length X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [eq](x0, x1) = x0 + x1 + 1, [cons](x0, x1) = x0, [take](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [inf](x0) = 0, [length](x0) = 0, [true] = 1, [0] = 1, [false] = 1, [nil] = 1, [cons#](x0, x1) = x0 Strict: cons#(X1, active X2) -> cons#(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons#(X1, mark X2) -> cons#(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 Weak: length active X -> length X 0 + 0X >= 0 + 0X length mark X -> length X 0 + 0X >= 0 + 0X take(active X1, X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(mark X1, X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(X1, active X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(X1, mark X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 inf active X -> inf X 0 + 0X >= 0 + 0X inf mark X -> inf X 0 + 0X >= 0 + 0X cons(active X1, X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(mark X1, X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(X1, active X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(X1, mark X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X eq(active X1, X2) -> eq(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 eq(mark X1, X2) -> eq(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 eq(X1, active X2) -> eq(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 eq(X1, mark X2) -> eq(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active length nil() -> mark 0() 1 >= 1 active length cons(X, L) -> mark s length L 1 + 0X + 0L >= 0 + 0L active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)) 1 + 0X + 0Y + 0L >= 0 + 0X + 0Y + 0L active take(0(), X) -> mark nil() 1 + 0X >= 1 active inf X -> mark cons(X, inf s X) 1 + 0X >= 0 + 0X active eq(s X, s Y) -> mark eq(X, Y) 2 + 0X + 0Y >= 1 + 1X + 1Y active eq(0(), 0()) -> mark true() 4 >= 1 active eq(X, Y) -> mark false() 2 + 1X + 1Y >= 1 mark length X -> active length mark X 0 + 0X >= 1 + 0X mark take(X1, X2) -> active take(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 2 mark inf X -> active inf mark X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(X1, X2) 0 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 mark false() -> active false() 1 >= 2 mark s X -> active s X 0 + 0X >= 1 + 0X mark 0() -> active 0() 1 >= 2 mark eq(X1, X2) -> active eq(X1, X2) 1 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark true() -> active true() 1 >= 2 SCCS (1): Scc: {cons#(X1, mark X2) -> cons#(X1, X2)} SCC (1): Strict: {cons#(X1, mark X2) -> cons#(X1, X2)} Weak: { mark true() -> active true(), mark eq(X1, X2) -> active eq(X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark false() -> active false(), mark cons(X1, X2) -> active cons(X1, X2), mark inf X -> active inf mark X, mark nil() -> active nil(), mark take(X1, X2) -> active take(mark X1, mark X2), mark length X -> active length mark X, active eq(X, Y) -> mark false(), active eq(0(), 0()) -> mark true(), active eq(s X, s Y) -> mark eq(X, Y), active inf X -> mark cons(X, inf s X), active take(0(), X) -> mark nil(), active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)), active length cons(X, L) -> mark s length L, active length nil() -> mark 0(), eq(X1, mark X2) -> eq(X1, X2), eq(X1, active X2) -> eq(X1, X2), eq(mark X1, X2) -> eq(X1, X2), eq(active X1, X2) -> eq(X1, X2), s mark X -> s X, s active X -> s X, cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), inf mark X -> inf X, inf active X -> inf X, take(X1, mark X2) -> take(X1, X2), take(X1, active X2) -> take(X1, X2), take(mark X1, X2) -> take(X1, X2), take(active X1, X2) -> take(X1, X2), length mark X -> length X, length active X -> length X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [eq](x0, x1) = x0 + 1, [cons](x0, x1) = 1, [take](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [active](x0) = 0, [s](x0) = 1, [inf](x0) = x0 + 1, [length](x0) = x0 + 1, [true] = 0, [0] = 1, [false] = 0, [nil] = 1, [cons#](x0, x1) = x0 Strict: cons#(X1, mark X2) -> cons#(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 Weak: length active X -> length X 1 + 0X >= 1 + 1X length mark X -> length X 2 + 1X >= 1 + 1X take(active X1, X2) -> take(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 take(mark X1, X2) -> take(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 take(X1, active X2) -> take(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 take(X1, mark X2) -> take(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 inf active X -> inf X 1 + 0X >= 1 + 1X inf mark X -> inf X 2 + 1X >= 1 + 1X cons(active X1, X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(mark X1, X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(X1, active X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(X1, mark X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 s active X -> s X 1 + 0X >= 1 + 0X s mark X -> s X 1 + 0X >= 1 + 0X eq(active X1, X2) -> eq(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 eq(mark X1, X2) -> eq(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 eq(X1, active X2) -> eq(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 eq(X1, mark X2) -> eq(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active length nil() -> mark 0() 0 >= 2 active length cons(X, L) -> mark s length L 0 + 0X + 0L >= 2 + 0L active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)) 0 + 0X + 0Y + 0L >= 2 + 0X + 0Y + 0L active take(0(), X) -> mark nil() 0 + 0X >= 2 active inf X -> mark cons(X, inf s X) 0 + 0X >= 2 + 0X active eq(s X, s Y) -> mark eq(X, Y) 0 + 0X + 0Y >= 2 + 0X + 1Y active eq(0(), 0()) -> mark true() 0 >= 1 active eq(X, Y) -> mark false() 0 + 0X + 0Y >= 1 mark length X -> active length mark X 2 + 1X >= 0 + 0X mark take(X1, X2) -> active take(mark X1, mark X2) 2 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 mark nil() -> active nil() 2 >= 0 mark inf X -> active inf mark X 2 + 1X >= 0 + 0X mark cons(X1, X2) -> active cons(X1, X2) 2 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark false() -> active false() 1 >= 0 mark s X -> active s X 2 + 0X >= 0 + 0X mark 0() -> active 0() 2 >= 0 mark eq(X1, X2) -> active eq(X1, X2) 2 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 mark true() -> active true() 1 >= 0 Qed SCC (2): Strict: { inf# mark X -> inf# X, inf# active X -> inf# X} Weak: { mark true() -> active true(), mark eq(X1, X2) -> active eq(X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark false() -> active false(), mark cons(X1, X2) -> active cons(X1, X2), mark inf X -> active inf mark X, mark nil() -> active nil(), mark take(X1, X2) -> active take(mark X1, mark X2), mark length X -> active length mark X, active eq(X, Y) -> mark false(), active eq(0(), 0()) -> mark true(), active eq(s X, s Y) -> mark eq(X, Y), active inf X -> mark cons(X, inf s X), active take(0(), X) -> mark nil(), active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)), active length cons(X, L) -> mark s length L, active length nil() -> mark 0(), eq(X1, mark X2) -> eq(X1, X2), eq(X1, active X2) -> eq(X1, X2), eq(mark X1, X2) -> eq(X1, X2), eq(active X1, X2) -> eq(X1, X2), s mark X -> s X, s active X -> s X, cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), inf mark X -> inf X, inf active X -> inf X, take(X1, mark X2) -> take(X1, X2), take(X1, active X2) -> take(X1, X2), take(mark X1, X2) -> take(X1, X2), take(active X1, X2) -> take(X1, X2), length mark X -> length X, length active X -> length X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [eq](x0, x1) = x0 + x1 + 1, [cons](x0, x1) = x0, [take](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [inf](x0) = 0, [length](x0) = 0, [true] = 1, [0] = 1, [false] = 1, [nil] = 1, [inf#](x0) = x0 Strict: inf# active X -> inf# X 1 + 1X >= 0 + 1X inf# mark X -> inf# X 0 + 1X >= 0 + 1X Weak: length active X -> length X 0 + 0X >= 0 + 0X length mark X -> length X 0 + 0X >= 0 + 0X take(active X1, X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(mark X1, X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(X1, active X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 take(X1, mark X2) -> take(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 inf active X -> inf X 0 + 0X >= 0 + 0X inf mark X -> inf X 0 + 0X >= 0 + 0X cons(active X1, X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(mark X1, X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(X1, active X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(X1, mark X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X eq(active X1, X2) -> eq(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 eq(mark X1, X2) -> eq(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 eq(X1, active X2) -> eq(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 eq(X1, mark X2) -> eq(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active length nil() -> mark 0() 1 >= 1 active length cons(X, L) -> mark s length L 1 + 0X + 0L >= 0 + 0L active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)) 1 + 0X + 0Y + 0L >= 0 + 0X + 0Y + 0L active take(0(), X) -> mark nil() 1 + 0X >= 1 active inf X -> mark cons(X, inf s X) 1 + 0X >= 0 + 0X active eq(s X, s Y) -> mark eq(X, Y) 2 + 0X + 0Y >= 1 + 1X + 1Y active eq(0(), 0()) -> mark true() 4 >= 1 active eq(X, Y) -> mark false() 2 + 1X + 1Y >= 1 mark length X -> active length mark X 0 + 0X >= 1 + 0X mark take(X1, X2) -> active take(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 2 mark inf X -> active inf mark X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(X1, X2) 0 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 mark false() -> active false() 1 >= 2 mark s X -> active s X 0 + 0X >= 1 + 0X mark 0() -> active 0() 1 >= 2 mark eq(X1, X2) -> active eq(X1, X2) 1 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark true() -> active true() 1 >= 2 SCCS (1): Scc: {inf# mark X -> inf# X} SCC (1): Strict: {inf# mark X -> inf# X} Weak: { mark true() -> active true(), mark eq(X1, X2) -> active eq(X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark false() -> active false(), mark cons(X1, X2) -> active cons(X1, X2), mark inf X -> active inf mark X, mark nil() -> active nil(), mark take(X1, X2) -> active take(mark X1, mark X2), mark length X -> active length mark X, active eq(X, Y) -> mark false(), active eq(0(), 0()) -> mark true(), active eq(s X, s Y) -> mark eq(X, Y), active inf X -> mark cons(X, inf s X), active take(0(), X) -> mark nil(), active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)), active length cons(X, L) -> mark s length L, active length nil() -> mark 0(), eq(X1, mark X2) -> eq(X1, X2), eq(X1, active X2) -> eq(X1, X2), eq(mark X1, X2) -> eq(X1, X2), eq(active X1, X2) -> eq(X1, X2), s mark X -> s X, s active X -> s X, cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), inf mark X -> inf X, inf active X -> inf X, take(X1, mark X2) -> take(X1, X2), take(X1, active X2) -> take(X1, X2), take(mark X1, X2) -> take(X1, X2), take(active X1, X2) -> take(X1, X2), length mark X -> length X, length active X -> length X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [eq](x0, x1) = x0 + 1, [cons](x0, x1) = 1, [take](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [active](x0) = 0, [s](x0) = 1, [inf](x0) = x0 + 1, [length](x0) = x0 + 1, [true] = 0, [0] = 1, [false] = 0, [nil] = 1, [inf#](x0) = x0 Strict: inf# mark X -> inf# X 1 + 1X >= 0 + 1X Weak: length active X -> length X 1 + 0X >= 1 + 1X length mark X -> length X 2 + 1X >= 1 + 1X take(active X1, X2) -> take(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 take(mark X1, X2) -> take(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 take(X1, active X2) -> take(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 take(X1, mark X2) -> take(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 inf active X -> inf X 1 + 0X >= 1 + 1X inf mark X -> inf X 2 + 1X >= 1 + 1X cons(active X1, X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(mark X1, X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(X1, active X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 cons(X1, mark X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 s active X -> s X 1 + 0X >= 1 + 0X s mark X -> s X 1 + 0X >= 1 + 0X eq(active X1, X2) -> eq(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 eq(mark X1, X2) -> eq(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 eq(X1, active X2) -> eq(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 eq(X1, mark X2) -> eq(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active length nil() -> mark 0() 0 >= 2 active length cons(X, L) -> mark s length L 0 + 0X + 0L >= 2 + 0L active take(s X, cons(Y, L)) -> mark cons(Y, take(X, L)) 0 + 0X + 0Y + 0L >= 2 + 0X + 0Y + 0L active take(0(), X) -> mark nil() 0 + 0X >= 2 active inf X -> mark cons(X, inf s X) 0 + 0X >= 2 + 0X active eq(s X, s Y) -> mark eq(X, Y) 0 + 0X + 0Y >= 2 + 0X + 1Y active eq(0(), 0()) -> mark true() 0 >= 1 active eq(X, Y) -> mark false() 0 + 0X + 0Y >= 1 mark length X -> active length mark X 2 + 1X >= 0 + 0X mark take(X1, X2) -> active take(mark X1, mark X2) 2 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 mark nil() -> active nil() 2 >= 0 mark inf X -> active inf mark X 2 + 1X >= 0 + 0X mark cons(X1, X2) -> active cons(X1, X2) 2 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark false() -> active false() 1 >= 0 mark s X -> active s X 2 + 0X >= 0 + 0X mark 0() -> active 0() 2 >= 0 mark eq(X1, X2) -> active eq(X1, X2) 2 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 mark true() -> active true() 1 >= 0 Qed