YES Time: 55.677575 TRS: { mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s mark X, mark from X -> active from mark X, active first(0(), X) -> mark nil(), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active from X -> mark cons(X, from s X), first(X1, mark X2) -> first(X1, X2), first(X1, active X2) -> first(X1, X2), first(mark X1, X2) -> first(X1, X2), first(active X1, X2) -> first(X1, X2), 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), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X} DP: DP: { mark# nil() -> active# nil(), mark# first(X1, X2) -> mark# X1, mark# first(X1, X2) -> mark# X2, mark# first(X1, X2) -> active# first(mark X1, mark X2), mark# first(X1, X2) -> first#(mark X1, mark X2), mark# 0() -> active# 0(), mark# cons(X1, X2) -> mark# X1, mark# cons(X1, X2) -> active# cons(mark X1, X2), mark# cons(X1, X2) -> cons#(mark X1, X2), mark# s X -> mark# X, mark# s X -> active# s mark X, mark# s X -> s# mark X, mark# from X -> mark# X, mark# from X -> active# from mark X, mark# from X -> from# mark X, active# first(0(), X) -> mark# nil(), active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z)), active# first(s X, cons(Y, Z)) -> first#(X, Z), active# first(s X, cons(Y, Z)) -> cons#(Y, first(X, Z)), active# from X -> mark# cons(X, from s X), active# from X -> cons#(X, from s X), active# from X -> s# X, active# from X -> from# s X, first#(X1, mark X2) -> first#(X1, X2), first#(X1, active X2) -> first#(X1, X2), first#(mark X1, X2) -> first#(X1, X2), first#(active X1, X2) -> first#(X1, X2), 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), s# mark X -> s# X, s# active X -> s# X, from# mark X -> from# X, from# active X -> from# X} TRS: { mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s mark X, mark from X -> active from mark X, active first(0(), X) -> mark nil(), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active from X -> mark cons(X, from s X), first(X1, mark X2) -> first(X1, X2), first(X1, active X2) -> first(X1, X2), first(mark X1, X2) -> first(X1, X2), first(active X1, X2) -> first(X1, X2), 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), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X} UR: { mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s mark X, mark from X -> active from mark X, active first(0(), X) -> mark nil(), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active from X -> mark cons(X, from s X), first(X1, mark X2) -> first(X1, X2), first(X1, active X2) -> first(X1, X2), first(mark X1, X2) -> first(X1, X2), first(active X1, X2) -> first(X1, X2), 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), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X} EDG: { (mark# first(X1, X2) -> mark# X1, mark# from X -> from# mark X) (mark# first(X1, X2) -> mark# X1, mark# from X -> active# from mark X) (mark# first(X1, X2) -> mark# X1, mark# from X -> mark# X) (mark# first(X1, X2) -> mark# X1, mark# s X -> s# mark X) (mark# first(X1, X2) -> mark# X1, mark# s X -> active# s mark X) (mark# first(X1, X2) -> mark# X1, mark# s X -> mark# X) (mark# first(X1, X2) -> mark# X1, mark# cons(X1, X2) -> cons#(mark X1, X2)) (mark# first(X1, X2) -> mark# X1, mark# cons(X1, X2) -> active# cons(mark X1, X2)) (mark# first(X1, X2) -> mark# X1, mark# cons(X1, X2) -> mark# X1) (mark# first(X1, X2) -> mark# X1, mark# 0() -> active# 0()) (mark# first(X1, X2) -> mark# X1, mark# first(X1, X2) -> first#(mark X1, mark X2)) (mark# first(X1, X2) -> mark# X1, mark# first(X1, X2) -> active# first(mark X1, mark X2)) (mark# first(X1, X2) -> mark# X1, mark# first(X1, X2) -> mark# X2) (mark# first(X1, X2) -> mark# X1, mark# first(X1, X2) -> mark# X1) (mark# first(X1, X2) -> mark# X1, mark# nil() -> active# nil()) (active# first(s X, cons(Y, Z)) -> first#(X, Z), first#(active X1, X2) -> first#(X1, X2)) (active# first(s X, cons(Y, Z)) -> first#(X, Z), first#(mark X1, X2) -> first#(X1, X2)) (active# first(s X, cons(Y, Z)) -> first#(X, Z), first#(X1, active X2) -> first#(X1, X2)) (active# first(s X, cons(Y, Z)) -> first#(X, Z), first#(X1, mark X2) -> first#(X1, X2)) (active# from X -> cons#(X, from s X), cons#(active X1, X2) -> cons#(X1, X2)) (active# from X -> cons#(X, from s X), cons#(mark X1, X2) -> cons#(X1, X2)) (mark# s X -> mark# X, mark# from X -> from# mark X) (mark# s X -> mark# X, mark# from X -> active# from mark X) (mark# s X -> mark# X, mark# from X -> mark# X) (mark# s X -> mark# X, mark# s X -> s# mark X) (mark# s X -> mark# X, mark# s X -> active# s mark X) (mark# s X -> mark# X, mark# s X -> mark# X) (mark# s X -> mark# X, mark# cons(X1, X2) -> cons#(mark X1, X2)) (mark# s X -> mark# X, mark# cons(X1, X2) -> active# cons(mark X1, X2)) (mark# s X -> mark# X, mark# cons(X1, X2) -> mark# X1) (mark# s X -> mark# X, mark# 0() -> active# 0()) (mark# s X -> mark# X, mark# first(X1, X2) -> first#(mark X1, mark X2)) (mark# s X -> mark# X, mark# first(X1, X2) -> active# first(mark X1, mark X2)) (mark# s X -> mark# X, mark# first(X1, X2) -> mark# X2) (mark# s X -> mark# X, mark# first(X1, X2) -> mark# X1) (mark# s X -> mark# X, mark# nil() -> active# nil()) (active# from X -> s# X, s# active X -> s# X) (active# from 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) (from# active X -> from# X, from# active X -> from# X) (from# active X -> from# X, from# mark X -> from# X) (mark# cons(X1, X2) -> cons#(mark X1, X2), cons#(active X1, X2) -> cons#(X1, X2)) (mark# cons(X1, X2) -> cons#(mark X1, X2), cons#(mark X1, X2) -> cons#(X1, X2)) (mark# cons(X1, X2) -> cons#(mark X1, X2), cons#(X1, active X2) -> cons#(X1, X2)) (mark# cons(X1, X2) -> cons#(mark X1, X2), cons#(X1, mark X2) -> cons#(X1, X2)) (mark# first(X1, X2) -> first#(mark X1, mark X2), first#(active X1, X2) -> first#(X1, X2)) (mark# first(X1, X2) -> first#(mark X1, mark X2), first#(mark X1, X2) -> first#(X1, X2)) (mark# first(X1, X2) -> first#(mark X1, mark X2), first#(X1, active X2) -> first#(X1, X2)) (mark# first(X1, X2) -> first#(mark X1, mark X2), first#(X1, mark X2) -> first#(X1, X2)) (active# from X -> mark# cons(X, from s X), mark# cons(X1, X2) -> cons#(mark X1, X2)) (active# from X -> mark# cons(X, from s X), mark# cons(X1, X2) -> active# cons(mark X1, X2)) (active# from X -> mark# cons(X, from s X), mark# cons(X1, X2) -> mark# X1) (mark# from X -> active# from mark X, active# from X -> from# s X) (mark# from X -> active# from mark X, active# from X -> s# X) (mark# from X -> active# from mark X, active# from X -> cons#(X, from s X)) (mark# from X -> active# from mark X, active# from X -> mark# cons(X, from s X)) (first#(X1, active X2) -> first#(X1, X2), first#(active X1, X2) -> first#(X1, X2)) (first#(X1, active X2) -> first#(X1, X2), first#(mark X1, X2) -> first#(X1, X2)) (first#(X1, active X2) -> first#(X1, X2), first#(X1, active X2) -> first#(X1, X2)) (first#(X1, active X2) -> first#(X1, X2), first#(X1, mark X2) -> first#(X1, X2)) (first#(active X1, X2) -> first#(X1, X2), first#(active X1, X2) -> first#(X1, X2)) (first#(active X1, X2) -> first#(X1, X2), first#(mark X1, X2) -> first#(X1, X2)) (first#(active X1, X2) -> first#(X1, X2), first#(X1, active X2) -> first#(X1, X2)) (first#(active X1, X2) -> first#(X1, X2), first#(X1, mark X2) -> first#(X1, X2)) (cons#(X1, active X2) -> cons#(X1, X2), cons#(active X1, 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#(X1, active X2) -> cons#(X1, X2)) (cons#(X1, active X2) -> cons#(X1, X2), cons#(X1, mark X2) -> cons#(X1, X2)) (cons#(active X1, X2) -> cons#(X1, X2), cons#(active X1, 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#(X1, active X2) -> cons#(X1, X2)) (cons#(active X1, X2) -> cons#(X1, X2), cons#(X1, mark X2) -> cons#(X1, X2)) (mark# from X -> from# mark X, from# active X -> from# X) (mark# from X -> from# mark X, from# mark X -> from# X) (mark# s X -> s# mark X, s# mark X -> s# X) (mark# s X -> s# mark X, s# active X -> s# X) (cons#(mark X1, X2) -> cons#(X1, X2), cons#(X1, mark X2) -> cons#(X1, X2)) (cons#(mark X1, X2) -> cons#(X1, X2), cons#(X1, active X2) -> cons#(X1, X2)) (cons#(mark X1, X2) -> cons#(X1, X2), cons#(mark X1, X2) -> cons#(X1, X2)) (cons#(mark X1, X2) -> cons#(X1, X2), cons#(active X1, X2) -> cons#(X1, X2)) (cons#(X1, mark X2) -> cons#(X1, X2), cons#(X1, mark X2) -> cons#(X1, X2)) (cons#(X1, mark X2) -> cons#(X1, X2), cons#(X1, active X2) -> cons#(X1, X2)) (cons#(X1, mark X2) -> cons#(X1, X2), cons#(mark X1, X2) -> cons#(X1, X2)) (cons#(X1, mark X2) -> cons#(X1, X2), cons#(active X1, X2) -> cons#(X1, X2)) (first#(mark X1, X2) -> first#(X1, X2), first#(X1, mark X2) -> first#(X1, X2)) (first#(mark X1, X2) -> first#(X1, X2), first#(X1, active X2) -> first#(X1, X2)) (first#(mark X1, X2) -> first#(X1, X2), first#(mark X1, X2) -> first#(X1, X2)) (first#(mark X1, X2) -> first#(X1, X2), first#(active X1, X2) -> first#(X1, X2)) (first#(X1, mark X2) -> first#(X1, X2), first#(X1, mark X2) -> first#(X1, X2)) (first#(X1, mark X2) -> first#(X1, X2), first#(X1, active X2) -> first#(X1, X2)) (first#(X1, mark X2) -> first#(X1, X2), first#(mark X1, X2) -> first#(X1, X2)) (first#(X1, mark X2) -> first#(X1, X2), first#(active X1, X2) -> first#(X1, X2)) (mark# first(X1, X2) -> active# first(mark X1, mark X2), active# first(0(), X) -> mark# nil()) (mark# first(X1, X2) -> active# first(mark X1, mark X2), active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z))) (mark# first(X1, X2) -> active# first(mark X1, mark X2), active# first(s X, cons(Y, Z)) -> first#(X, Z)) (mark# first(X1, X2) -> active# first(mark X1, mark X2), active# first(s X, cons(Y, Z)) -> cons#(Y, first(X, Z))) (mark# first(X1, X2) -> mark# X2, mark# nil() -> active# nil()) (mark# first(X1, X2) -> mark# X2, mark# first(X1, X2) -> mark# X1) (mark# first(X1, X2) -> mark# X2, mark# first(X1, X2) -> mark# X2) (mark# first(X1, X2) -> mark# X2, mark# first(X1, X2) -> active# first(mark X1, mark X2)) (mark# first(X1, X2) -> mark# X2, mark# first(X1, X2) -> first#(mark X1, mark X2)) (mark# first(X1, X2) -> mark# X2, mark# 0() -> active# 0()) (mark# first(X1, X2) -> mark# X2, mark# cons(X1, X2) -> mark# X1) (mark# first(X1, X2) -> mark# X2, mark# cons(X1, X2) -> active# cons(mark X1, X2)) (mark# first(X1, X2) -> mark# X2, mark# cons(X1, X2) -> cons#(mark X1, X2)) (mark# first(X1, X2) -> mark# X2, mark# s X -> mark# X) (mark# first(X1, X2) -> mark# X2, mark# s X -> active# s mark X) (mark# first(X1, X2) -> mark# X2, mark# s X -> s# mark X) (mark# first(X1, X2) -> mark# X2, mark# from X -> mark# X) (mark# first(X1, X2) -> mark# X2, mark# from X -> active# from mark X) (mark# first(X1, X2) -> mark# X2, mark# from X -> from# mark X) (active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z)), mark# cons(X1, X2) -> mark# X1) (active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z)), mark# cons(X1, X2) -> active# cons(mark X1, X2)) (active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z)), mark# cons(X1, X2) -> cons#(mark X1, X2)) (from# mark X -> from# X, from# mark X -> from# X) (from# mark X -> from# X, from# active X -> from# X) (s# mark X -> s# X, s# mark X -> s# X) (s# mark X -> s# X, s# active X -> s# X) (mark# from X -> mark# X, mark# nil() -> active# nil()) (mark# from X -> mark# X, mark# first(X1, X2) -> mark# X1) (mark# from X -> mark# X, mark# first(X1, X2) -> mark# X2) (mark# from X -> mark# X, mark# first(X1, X2) -> active# first(mark X1, mark X2)) (mark# from X -> mark# X, mark# first(X1, X2) -> first#(mark X1, mark X2)) (mark# from X -> mark# X, mark# 0() -> active# 0()) (mark# from X -> mark# X, mark# cons(X1, X2) -> mark# X1) (mark# from X -> mark# X, mark# cons(X1, X2) -> active# cons(mark X1, X2)) (mark# from X -> mark# X, mark# cons(X1, X2) -> cons#(mark X1, X2)) (mark# from X -> mark# X, mark# s X -> mark# X) (mark# from X -> mark# X, mark# s X -> active# s mark X) (mark# from X -> mark# X, mark# s X -> s# mark X) (mark# from X -> mark# X, mark# from X -> mark# X) (mark# from X -> mark# X, mark# from X -> active# from mark X) (mark# from X -> mark# X, mark# from X -> from# mark X) (active# first(0(), X) -> mark# nil(), mark# nil() -> active# nil()) (mark# cons(X1, X2) -> mark# X1, mark# nil() -> active# nil()) (mark# cons(X1, X2) -> mark# X1, mark# first(X1, X2) -> mark# X1) (mark# cons(X1, X2) -> mark# X1, mark# first(X1, X2) -> mark# X2) (mark# cons(X1, X2) -> mark# X1, mark# first(X1, X2) -> active# first(mark X1, mark X2)) (mark# cons(X1, X2) -> mark# X1, mark# first(X1, X2) -> first#(mark X1, mark X2)) (mark# cons(X1, X2) -> mark# X1, mark# 0() -> active# 0()) (mark# cons(X1, X2) -> mark# X1, mark# cons(X1, X2) -> mark# X1) (mark# cons(X1, X2) -> mark# X1, mark# cons(X1, X2) -> active# cons(mark X1, X2)) (mark# cons(X1, X2) -> mark# X1, mark# cons(X1, X2) -> cons#(mark X1, X2)) (mark# cons(X1, X2) -> mark# X1, mark# s X -> mark# X) (mark# cons(X1, X2) -> mark# X1, mark# s X -> active# s mark X) (mark# cons(X1, X2) -> mark# X1, mark# s X -> s# mark X) (mark# cons(X1, X2) -> mark# X1, mark# from X -> mark# X) (mark# cons(X1, X2) -> mark# X1, mark# from X -> active# from mark X) (mark# cons(X1, X2) -> mark# X1, mark# from X -> from# mark X) (active# first(s X, cons(Y, Z)) -> cons#(Y, first(X, Z)), cons#(mark X1, X2) -> cons#(X1, X2)) (active# first(s X, cons(Y, Z)) -> cons#(Y, first(X, Z)), cons#(active X1, X2) -> cons#(X1, X2)) } STATUS: arrows: 0.875918 SCCS (5): Scc: { mark# first(X1, X2) -> mark# X1, mark# first(X1, X2) -> mark# X2, mark# first(X1, X2) -> active# first(mark X1, mark X2), mark# cons(X1, X2) -> mark# X1, mark# s X -> mark# X, mark# from X -> mark# X, mark# from X -> active# from mark X, active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z)), active# from X -> mark# cons(X, from s X)} Scc: { from# mark X -> from# X, from# active X -> from# X} Scc: { s# mark X -> s# X, s# active X -> s# X} Scc: { first#(X1, mark X2) -> first#(X1, X2), first#(X1, active X2) -> first#(X1, X2), first#(mark X1, X2) -> first#(X1, X2), first#(active X1, X2) -> first#(X1, X2)} 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 (9): Strict: { mark# first(X1, X2) -> mark# X1, mark# first(X1, X2) -> mark# X2, mark# first(X1, X2) -> active# first(mark X1, mark X2), mark# cons(X1, X2) -> mark# X1, mark# s X -> mark# X, mark# from X -> mark# X, mark# from X -> active# from mark X, active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z)), active# from X -> mark# cons(X, from s X)} Weak: { mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s mark X, mark from X -> active from mark X, active first(0(), X) -> mark nil(), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active from X -> mark cons(X, from s X), first(X1, mark X2) -> first(X1, X2), first(X1, active X2) -> first(X1, X2), first(mark X1, X2) -> first(X1, X2), first(active X1, X2) -> first(X1, X2), 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), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [first](x0, x1) = x0 + x1 + 1, [cons](x0, x1) = x0, [mark](x0) = x0, [active](x0) = x0, [s](x0) = x0 + 1, [from](x0) = x0, [nil] = 1, [0] = 0, [mark#](x0) = x0, [active#](x0) = x0 Strict: active# from X -> mark# cons(X, from s X) 0 + 1X >= 0 + 1X active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z)) 2 + 1X + 1Y + 0Z >= 0 + 0X + 1Y + 0Z mark# from X -> active# from mark X 0 + 1X >= 0 + 1X mark# from X -> mark# X 0 + 1X >= 0 + 1X mark# s X -> mark# X 1 + 1X >= 0 + 1X mark# cons(X1, X2) -> mark# X1 0 + 1X1 + 0X2 >= 0 + 1X1 mark# first(X1, X2) -> active# first(mark X1, mark X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 mark# first(X1, X2) -> mark# X2 1 + 1X1 + 1X2 >= 0 + 1X2 mark# first(X1, X2) -> mark# X1 1 + 1X1 + 1X2 >= 0 + 1X1 Weak: from active X -> from X 0 + 1X >= 0 + 1X from mark X -> from X 0 + 1X >= 0 + 1X s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 1 + 1X >= 1 + 1X cons(active X1, X2) -> cons(X1, X2) 0 + 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 first(active X1, X2) -> first(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 first(mark X1, X2) -> first(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 first(X1, active X2) -> first(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 first(X1, mark X2) -> first(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active from X -> mark cons(X, from s X) 0 + 1X >= 0 + 1X active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 2 + 1X + 1Y + 0Z >= 0 + 0X + 1Y + 0Z active first(0(), X) -> mark nil() 1 + 1X >= 1 mark from X -> active from mark X 0 + 1X >= 0 + 1X mark s X -> active s mark X 1 + 1X >= 1 + 1X mark cons(X1, X2) -> active cons(mark X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 mark 0() -> active 0() 0 >= 0 mark first(X1, X2) -> active first(mark X1, mark X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 mark nil() -> active nil() 1 >= 1 SCCS (1): Scc: {mark# cons(X1, X2) -> mark# X1, mark# from X -> mark# X, mark# from X -> active# from mark X, active# from X -> mark# cons(X, from s X)} SCC (4): Strict: {mark# cons(X1, X2) -> mark# X1, mark# from X -> mark# X, mark# from X -> active# from mark X, active# from X -> mark# cons(X, from s X)} Weak: { mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s mark X, mark from X -> active from mark X, active first(0(), X) -> mark nil(), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active from X -> mark cons(X, from s X), first(X1, mark X2) -> first(X1, X2), first(X1, active X2) -> first(X1, X2), first(mark X1, X2) -> first(X1, X2), first(active X1, X2) -> first(X1, X2), 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), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [first](x0, x1) = x0, [cons](x0, x1) = x0, [mark](x0) = x0, [active](x0) = x0, [s](x0) = 0, [from](x0) = x0 + 1, [nil] = 0, [0] = 0, [mark#](x0) = x0, [active#](x0) = x0 Strict: active# from X -> mark# cons(X, from s X) 1 + 1X >= 0 + 1X mark# from X -> active# from mark X 1 + 1X >= 1 + 1X mark# from X -> mark# X 1 + 1X >= 0 + 1X mark# cons(X1, X2) -> mark# X1 0 + 1X1 + 0X2 >= 0 + 1X1 Weak: from active X -> from X 1 + 1X >= 1 + 1X from mark X -> from X 1 + 1X >= 1 + 1X s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X cons(active X1, X2) -> cons(X1, X2) 0 + 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 first(active X1, X2) -> first(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 first(mark X1, X2) -> first(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 first(X1, active X2) -> first(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 first(X1, mark X2) -> first(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 active from X -> mark cons(X, from s X) 1 + 1X >= 0 + 1X active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 0 + 0X + 1Y + 0Z >= 0 + 0X + 1Y + 0Z active first(0(), X) -> mark nil() 0 + 1X >= 0 mark from X -> active from mark X 1 + 1X >= 1 + 1X mark s X -> active s mark X 0 + 0X >= 0 + 0X mark cons(X1, X2) -> active cons(mark X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 mark 0() -> active 0() 0 >= 0 mark first(X1, X2) -> active first(mark X1, mark X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 mark nil() -> active nil() 0 >= 0 SCCS (1): Scc: {mark# cons(X1, X2) -> mark# X1} SCC (1): Strict: {mark# cons(X1, X2) -> mark# X1} Weak: { mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s mark X, mark from X -> active from mark X, active first(0(), X) -> mark nil(), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active from X -> mark cons(X, from s X), first(X1, mark X2) -> first(X1, X2), first(X1, active X2) -> first(X1, X2), first(mark X1, X2) -> first(X1, X2), first(active X1, X2) -> first(X1, X2), 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), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [first](x0, x1) = x0 + 1, [cons](x0, x1) = x0 + x1 + 1, [mark](x0) = x0 + 1, [active](x0) = x0, [s](x0) = x0 + 1, [from](x0) = x0 + 1, [nil] = 0, [0] = 1, [mark#](x0) = x0 Strict: mark# cons(X1, X2) -> mark# X1 1 + 1X1 + 1X2 >= 0 + 1X1 Weak: from active X -> from X 1 + 1X >= 1 + 1X from mark X -> from X 2 + 1X >= 1 + 1X s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X cons(active X1, X2) -> cons(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(X1, active X2) -> cons(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(X1, mark X2) -> cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 first(active X1, X2) -> first(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 first(mark X1, X2) -> first(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 first(X1, active X2) -> first(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 first(X1, mark X2) -> first(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 active from X -> mark cons(X, from s X) 1 + 1X >= 4 + 2X active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 2 + 1X + 0Y + 0Z >= 3 + 1X + 1Y + 0Z active first(0(), X) -> mark nil() 2 + 0X >= 1 mark from X -> active from mark X 2 + 1X >= 2 + 1X mark s X -> active s mark X 2 + 1X >= 2 + 1X mark cons(X1, X2) -> active cons(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark 0() -> active 0() 2 >= 1 mark first(X1, X2) -> active first(mark X1, mark X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark nil() -> active nil() 1 >= 0 Qed SCC (2): Strict: { from# mark X -> from# X, from# active X -> from# X} Weak: { mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s mark X, mark from X -> active from mark X, active first(0(), X) -> mark nil(), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active from X -> mark cons(X, from s X), first(X1, mark X2) -> first(X1, X2), first(X1, active X2) -> first(X1, X2), first(mark X1, X2) -> first(X1, X2), first(active X1, X2) -> first(X1, X2), 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), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [first](x0, x1) = 0, [cons](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [from](x0) = 0, [nil] = 1, [0] = 0, [from#](x0) = x0 Strict: from# active X -> from# X 1 + 1X >= 0 + 1X from# mark X -> from# X 0 + 1X >= 0 + 1X Weak: from active X -> from X 0 + 0X >= 0 + 0X from mark X -> from X 0 + 0X >= 0 + 0X s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s 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 first(active X1, X2) -> first(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 first(mark X1, X2) -> first(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 first(X1, active X2) -> first(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 first(X1, mark X2) -> first(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active from X -> mark cons(X, from s X) 1 + 0X >= 0 + 0X active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 1 + 0X + 0Y + 0Z >= 0 + 0X + 0Y + 0Z active first(0(), X) -> mark nil() 1 + 0X >= 1 mark from X -> active from mark X 0 + 0X >= 1 + 0X mark s X -> active s mark X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark 0() -> active 0() 0 >= 1 mark first(X1, X2) -> active first(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 2 SCCS (1): Scc: {from# mark X -> from# X} SCC (1): Strict: {from# mark X -> from# X} Weak: { mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s mark X, mark from X -> active from mark X, active first(0(), X) -> mark nil(), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active from X -> mark cons(X, from s X), first(X1, mark X2) -> first(X1, X2), first(X1, active X2) -> first(X1, X2), first(mark X1, X2) -> first(X1, X2), first(active X1, X2) -> first(X1, X2), 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), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [first](x0, x1) = x0 + 1, [cons](x0, x1) = x0 + x1 + 1, [mark](x0) = x0 + 1, [active](x0) = x0, [s](x0) = x0 + 1, [from](x0) = x0 + 1, [nil] = 0, [0] = 1, [from#](x0) = x0 Strict: from# mark X -> from# X 1 + 1X >= 0 + 1X Weak: from active X -> from X 1 + 1X >= 1 + 1X from mark X -> from X 2 + 1X >= 1 + 1X s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X cons(active X1, X2) -> cons(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(X1, active X2) -> cons(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(X1, mark X2) -> cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 first(active X1, X2) -> first(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 first(mark X1, X2) -> first(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 first(X1, active X2) -> first(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 first(X1, mark X2) -> first(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 active from X -> mark cons(X, from s X) 1 + 1X >= 4 + 2X active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 2 + 1X + 0Y + 0Z >= 3 + 1X + 1Y + 0Z active first(0(), X) -> mark nil() 2 + 0X >= 1 mark from X -> active from mark X 2 + 1X >= 2 + 1X mark s X -> active s mark X 2 + 1X >= 2 + 1X mark cons(X1, X2) -> active cons(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark 0() -> active 0() 2 >= 1 mark first(X1, X2) -> active first(mark X1, mark X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark nil() -> active nil() 1 >= 0 Qed SCC (2): Strict: { s# mark X -> s# X, s# active X -> s# X} Weak: { mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s mark X, mark from X -> active from mark X, active first(0(), X) -> mark nil(), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active from X -> mark cons(X, from s X), first(X1, mark X2) -> first(X1, X2), first(X1, active X2) -> first(X1, X2), first(mark X1, X2) -> first(X1, X2), first(active X1, X2) -> first(X1, X2), 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), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [first](x0, x1) = 0, [cons](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [from](x0) = 0, [nil] = 1, [0] = 0, [s#](x0) = x0 Strict: s# active X -> s# X 1 + 1X >= 0 + 1X s# mark X -> s# X 0 + 1X >= 0 + 1X Weak: from active X -> from X 0 + 0X >= 0 + 0X from mark X -> from X 0 + 0X >= 0 + 0X s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s 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 first(active X1, X2) -> first(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 first(mark X1, X2) -> first(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 first(X1, active X2) -> first(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 first(X1, mark X2) -> first(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active from X -> mark cons(X, from s X) 1 + 0X >= 0 + 0X active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 1 + 0X + 0Y + 0Z >= 0 + 0X + 0Y + 0Z active first(0(), X) -> mark nil() 1 + 0X >= 1 mark from X -> active from mark X 0 + 0X >= 1 + 0X mark s X -> active s mark X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark 0() -> active 0() 0 >= 1 mark first(X1, X2) -> active first(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 2 SCCS (1): Scc: {s# mark X -> s# X} SCC (1): Strict: {s# mark X -> s# X} Weak: { mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s mark X, mark from X -> active from mark X, active first(0(), X) -> mark nil(), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active from X -> mark cons(X, from s X), first(X1, mark X2) -> first(X1, X2), first(X1, active X2) -> first(X1, X2), first(mark X1, X2) -> first(X1, X2), first(active X1, X2) -> first(X1, X2), 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), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [first](x0, x1) = x0 + 1, [cons](x0, x1) = x0 + x1 + 1, [mark](x0) = x0 + 1, [active](x0) = x0, [s](x0) = x0 + 1, [from](x0) = x0 + 1, [nil] = 0, [0] = 1, [s#](x0) = x0 Strict: s# mark X -> s# X 1 + 1X >= 0 + 1X Weak: from active X -> from X 1 + 1X >= 1 + 1X from mark X -> from X 2 + 1X >= 1 + 1X s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X cons(active X1, X2) -> cons(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(X1, active X2) -> cons(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(X1, mark X2) -> cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 first(active X1, X2) -> first(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 first(mark X1, X2) -> first(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 first(X1, active X2) -> first(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 first(X1, mark X2) -> first(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 active from X -> mark cons(X, from s X) 1 + 1X >= 4 + 2X active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 2 + 1X + 0Y + 0Z >= 3 + 1X + 1Y + 0Z active first(0(), X) -> mark nil() 2 + 0X >= 1 mark from X -> active from mark X 2 + 1X >= 2 + 1X mark s X -> active s mark X 2 + 1X >= 2 + 1X mark cons(X1, X2) -> active cons(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark 0() -> active 0() 2 >= 1 mark first(X1, X2) -> active first(mark X1, mark X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark nil() -> active nil() 1 >= 0 Qed SCC (4): Strict: { first#(X1, mark X2) -> first#(X1, X2), first#(X1, active X2) -> first#(X1, X2), first#(mark X1, X2) -> first#(X1, X2), first#(active X1, X2) -> first#(X1, X2)} Weak: { mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s mark X, mark from X -> active from mark X, active first(0(), X) -> mark nil(), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active from X -> mark cons(X, from s X), first(X1, mark X2) -> first(X1, X2), first(X1, active X2) -> first(X1, X2), first(mark X1, X2) -> first(X1, X2), first(active X1, X2) -> first(X1, X2), 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), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [first](x0, x1) = 0, [cons](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [from](x0) = 0, [nil] = 1, [0] = 0, [first#](x0, x1) = x0 Strict: first#(active X1, X2) -> first#(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 first#(mark X1, X2) -> first#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 first#(X1, active X2) -> first#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 first#(X1, mark X2) -> first#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 Weak: from active X -> from X 0 + 0X >= 0 + 0X from mark X -> from X 0 + 0X >= 0 + 0X s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s 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 first(active X1, X2) -> first(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 first(mark X1, X2) -> first(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 first(X1, active X2) -> first(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 first(X1, mark X2) -> first(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active from X -> mark cons(X, from s X) 1 + 0X >= 0 + 0X active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 1 + 0X + 0Y + 0Z >= 0 + 0X + 0Y + 0Z active first(0(), X) -> mark nil() 1 + 0X >= 1 mark from X -> active from mark X 0 + 0X >= 1 + 0X mark s X -> active s mark X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark 0() -> active 0() 0 >= 1 mark first(X1, X2) -> active first(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 2 SCCS (1): Scc: { first#(X1, mark X2) -> first#(X1, X2), first#(X1, active X2) -> first#(X1, X2), first#(mark X1, X2) -> first#(X1, X2)} SCC (3): Strict: { first#(X1, mark X2) -> first#(X1, X2), first#(X1, active X2) -> first#(X1, X2), first#(mark X1, X2) -> first#(X1, X2)} Weak: { mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s mark X, mark from X -> active from mark X, active first(0(), X) -> mark nil(), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active from X -> mark cons(X, from s X), first(X1, mark X2) -> first(X1, X2), first(X1, active X2) -> first(X1, X2), first(mark X1, X2) -> first(X1, X2), first(active X1, X2) -> first(X1, X2), 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), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [first](x0, x1) = x0 + 1, [cons](x0, x1) = x0 + x1 + 1, [mark](x0) = x0 + 1, [active](x0) = x0, [s](x0) = x0 + 1, [from](x0) = 0, [nil] = 0, [0] = 1, [first#](x0, x1) = x0 Strict: first#(mark X1, X2) -> first#(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 first#(X1, active X2) -> first#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 first#(X1, mark X2) -> first#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 Weak: from active X -> from X 0 + 0X >= 0 + 0X from mark X -> from X 0 + 0X >= 0 + 0X s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X cons(active X1, X2) -> cons(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(X1, active X2) -> cons(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(X1, mark X2) -> cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 first(active X1, X2) -> first(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 first(mark X1, X2) -> first(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 first(X1, active X2) -> first(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 first(X1, mark X2) -> first(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 active from X -> mark cons(X, from s X) 0 + 0X >= 2 + 1X active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 2 + 1X + 0Y + 0Z >= 3 + 1X + 1Y + 0Z active first(0(), X) -> mark nil() 2 + 0X >= 1 mark from X -> active from mark X 1 + 0X >= 0 + 0X mark s X -> active s mark X 2 + 1X >= 2 + 1X mark cons(X1, X2) -> active cons(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark 0() -> active 0() 2 >= 1 mark first(X1, X2) -> active first(mark X1, mark X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark nil() -> active nil() 1 >= 0 SCCS (1): Scc: { first#(X1, mark X2) -> first#(X1, X2), first#(X1, active X2) -> first#(X1, X2)} SCC (2): Strict: { first#(X1, mark X2) -> first#(X1, X2), first#(X1, active X2) -> first#(X1, X2)} Weak: { mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s mark X, mark from X -> active from mark X, active first(0(), X) -> mark nil(), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active from X -> mark cons(X, from s X), first(X1, mark X2) -> first(X1, X2), first(X1, active X2) -> first(X1, X2), first(mark X1, X2) -> first(X1, X2), first(active X1, X2) -> first(X1, X2), 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), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [first](x0, x1) = 0, [cons](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [from](x0) = 0, [nil] = 1, [0] = 0, [first#](x0, x1) = x0 Strict: first#(X1, active X2) -> first#(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 first#(X1, mark X2) -> first#(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 Weak: from active X -> from X 0 + 0X >= 0 + 0X from mark X -> from X 0 + 0X >= 0 + 0X s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s 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 first(active X1, X2) -> first(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 first(mark X1, X2) -> first(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 first(X1, active X2) -> first(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 first(X1, mark X2) -> first(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active from X -> mark cons(X, from s X) 1 + 0X >= 0 + 0X active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 1 + 0X + 0Y + 0Z >= 0 + 0X + 0Y + 0Z active first(0(), X) -> mark nil() 1 + 0X >= 1 mark from X -> active from mark X 0 + 0X >= 1 + 0X mark s X -> active s mark X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark 0() -> active 0() 0 >= 1 mark first(X1, X2) -> active first(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 2 SCCS (1): Scc: {first#(X1, mark X2) -> first#(X1, X2)} SCC (1): Strict: {first#(X1, mark X2) -> first#(X1, X2)} Weak: { mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s mark X, mark from X -> active from mark X, active first(0(), X) -> mark nil(), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active from X -> mark cons(X, from s X), first(X1, mark X2) -> first(X1, X2), first(X1, active X2) -> first(X1, X2), first(mark X1, X2) -> first(X1, X2), first(active X1, X2) -> first(X1, X2), 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), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [first](x0, x1) = x0 + 1, [cons](x0, x1) = x0 + x1 + 1, [mark](x0) = x0 + 1, [active](x0) = x0, [s](x0) = x0 + 1, [from](x0) = x0 + 1, [nil] = 0, [0] = 1, [first#](x0, x1) = x0 Strict: first#(X1, mark X2) -> first#(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 Weak: from active X -> from X 1 + 1X >= 1 + 1X from mark X -> from X 2 + 1X >= 1 + 1X s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X cons(active X1, X2) -> cons(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(X1, active X2) -> cons(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(X1, mark X2) -> cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 first(active X1, X2) -> first(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 first(mark X1, X2) -> first(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 first(X1, active X2) -> first(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 first(X1, mark X2) -> first(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 active from X -> mark cons(X, from s X) 1 + 1X >= 4 + 2X active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 2 + 1X + 0Y + 0Z >= 3 + 1X + 1Y + 0Z active first(0(), X) -> mark nil() 2 + 0X >= 1 mark from X -> active from mark X 2 + 1X >= 2 + 1X mark s X -> active s mark X 2 + 1X >= 2 + 1X mark cons(X1, X2) -> active cons(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark 0() -> active 0() 2 >= 1 mark first(X1, X2) -> active first(mark X1, mark X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark nil() -> active nil() 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 nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s mark X, mark from X -> active from mark X, active first(0(), X) -> mark nil(), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active from X -> mark cons(X, from s X), first(X1, mark X2) -> first(X1, X2), first(X1, active X2) -> first(X1, X2), first(mark X1, X2) -> first(X1, X2), first(active X1, X2) -> first(X1, X2), 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), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [first](x0, x1) = 0, [cons](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [from](x0) = 0, [nil] = 1, [0] = 0, [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: from active X -> from X 0 + 0X >= 0 + 0X from mark X -> from X 0 + 0X >= 0 + 0X s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s 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 first(active X1, X2) -> first(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 first(mark X1, X2) -> first(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 first(X1, active X2) -> first(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 first(X1, mark X2) -> first(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active from X -> mark cons(X, from s X) 1 + 0X >= 0 + 0X active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 1 + 0X + 0Y + 0Z >= 0 + 0X + 0Y + 0Z active first(0(), X) -> mark nil() 1 + 0X >= 1 mark from X -> active from mark X 0 + 0X >= 1 + 0X mark s X -> active s mark X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark 0() -> active 0() 0 >= 1 mark first(X1, X2) -> active first(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 2 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 nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s mark X, mark from X -> active from mark X, active first(0(), X) -> mark nil(), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active from X -> mark cons(X, from s X), first(X1, mark X2) -> first(X1, X2), first(X1, active X2) -> first(X1, X2), first(mark X1, X2) -> first(X1, X2), first(active X1, X2) -> first(X1, X2), 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), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [first](x0, x1) = x0 + 1, [cons](x0, x1) = x0 + x1 + 1, [mark](x0) = x0 + 1, [active](x0) = x0, [s](x0) = x0 + 1, [from](x0) = 0, [nil] = 0, [0] = 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: from active X -> from X 0 + 0X >= 0 + 0X from mark X -> from X 0 + 0X >= 0 + 0X s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X cons(active X1, X2) -> cons(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(X1, active X2) -> cons(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(X1, mark X2) -> cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 first(active X1, X2) -> first(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 first(mark X1, X2) -> first(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 first(X1, active X2) -> first(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 first(X1, mark X2) -> first(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 active from X -> mark cons(X, from s X) 0 + 0X >= 2 + 1X active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 2 + 1X + 0Y + 0Z >= 3 + 1X + 1Y + 0Z active first(0(), X) -> mark nil() 2 + 0X >= 1 mark from X -> active from mark X 1 + 0X >= 0 + 0X mark s X -> active s mark X 2 + 1X >= 2 + 1X mark cons(X1, X2) -> active cons(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark 0() -> active 0() 2 >= 1 mark first(X1, X2) -> active first(mark X1, mark X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark nil() -> active nil() 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 nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s mark X, mark from X -> active from mark X, active first(0(), X) -> mark nil(), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active from X -> mark cons(X, from s X), first(X1, mark X2) -> first(X1, X2), first(X1, active X2) -> first(X1, X2), first(mark X1, X2) -> first(X1, X2), first(active X1, X2) -> first(X1, X2), 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), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [first](x0, x1) = 0, [cons](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [from](x0) = 0, [nil] = 1, [0] = 0, [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: from active X -> from X 0 + 0X >= 0 + 0X from mark X -> from X 0 + 0X >= 0 + 0X s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s 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 first(active X1, X2) -> first(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 first(mark X1, X2) -> first(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 first(X1, active X2) -> first(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 first(X1, mark X2) -> first(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active from X -> mark cons(X, from s X) 1 + 0X >= 0 + 0X active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 1 + 0X + 0Y + 0Z >= 0 + 0X + 0Y + 0Z active first(0(), X) -> mark nil() 1 + 0X >= 1 mark from X -> active from mark X 0 + 0X >= 1 + 0X mark s X -> active s mark X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark 0() -> active 0() 0 >= 1 mark first(X1, X2) -> active first(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 2 SCCS (1): Scc: {cons#(X1, mark X2) -> cons#(X1, X2)} SCC (1): Strict: {cons#(X1, mark X2) -> cons#(X1, X2)} Weak: { mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s mark X, mark from X -> active from mark X, active first(0(), X) -> mark nil(), active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)), active from X -> mark cons(X, from s X), first(X1, mark X2) -> first(X1, X2), first(X1, active X2) -> first(X1, X2), first(mark X1, X2) -> first(X1, X2), first(active X1, X2) -> first(X1, X2), 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), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [first](x0, x1) = x0 + 1, [cons](x0, x1) = x0 + x1 + 1, [mark](x0) = x0 + 1, [active](x0) = x0, [s](x0) = x0 + 1, [from](x0) = x0 + 1, [nil] = 0, [0] = 1, [cons#](x0, x1) = x0 Strict: cons#(X1, mark X2) -> cons#(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 Weak: from active X -> from X 1 + 1X >= 1 + 1X from mark X -> from X 2 + 1X >= 1 + 1X s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X cons(active X1, X2) -> cons(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(X1, active X2) -> cons(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(X1, mark X2) -> cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 first(active X1, X2) -> first(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 first(mark X1, X2) -> first(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 first(X1, active X2) -> first(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 first(X1, mark X2) -> first(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 active from X -> mark cons(X, from s X) 1 + 1X >= 4 + 2X active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 2 + 1X + 0Y + 0Z >= 3 + 1X + 1Y + 0Z active first(0(), X) -> mark nil() 2 + 0X >= 1 mark from X -> active from mark X 2 + 1X >= 2 + 1X mark s X -> active s mark X 2 + 1X >= 2 + 1X mark cons(X1, X2) -> active cons(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark 0() -> active 0() 2 >= 1 mark first(X1, X2) -> active first(mark X1, mark X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark nil() -> active nil() 1 >= 0 Qed