YES Time: 1.689456 TRS: { mark and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} DP: DP: { mark# and(X1, X2) -> mark# X1, mark# and(X1, X2) -> active# and(mark X1, X2), mark# and(X1, X2) -> and#(mark X1, X2), mark# true() -> active# true(), mark# false() -> active# false(), mark# if(X1, X2, X3) -> mark# X1, mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3), mark# if(X1, X2, X3) -> if#(mark X1, X2, X3), mark# add(X1, X2) -> mark# X1, mark# add(X1, X2) -> active# add(mark X1, X2), mark# add(X1, X2) -> add#(mark X1, X2), mark# 0() -> active# 0(), mark# s X -> active# s X, 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# cons(X1, X2) -> active# cons(X1, X2), mark# from X -> active# from X, active# and(true(), X) -> mark# X, active# and(false(), Y) -> mark# false(), active# if(true(), X, Y) -> mark# X, active# if(false(), X, Y) -> mark# Y, active# add(0(), X) -> mark# X, active# add(s X, Y) -> mark# s add(X, Y), active# add(s X, Y) -> add#(X, Y), active# add(s X, Y) -> s# add(X, Y), 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 -> s# X, active# from X -> cons#(X, from s X), active# from X -> from# s X, and#(X1, mark X2) -> and#(X1, X2), and#(X1, active X2) -> and#(X1, X2), and#(mark X1, X2) -> and#(X1, X2), and#(active X1, X2) -> and#(X1, X2), if#(X1, X2, mark X3) -> if#(X1, X2, X3), if#(X1, X2, active X3) -> if#(X1, X2, X3), if#(X1, mark X2, X3) -> if#(X1, X2, X3), if#(X1, active X2, X3) -> if#(X1, X2, X3), if#(mark X1, X2, X3) -> if#(X1, X2, X3), if#(active X1, X2, X3) -> if#(X1, X2, X3), add#(X1, mark X2) -> add#(X1, X2), add#(X1, active X2) -> add#(X1, X2), add#(mark X1, X2) -> add#(X1, X2), add#(active X1, X2) -> add#(X1, X2), s# mark X -> s# X, s# active X -> 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), from# mark X -> from# X, from# active X -> from# X} TRS: { mark and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} EDG: { (active# add(s X, Y) -> mark# s add(X, Y), mark# from X -> active# from X) (active# add(s X, Y) -> mark# s add(X, Y), mark# cons(X1, X2) -> active# cons(X1, X2)) (active# add(s X, Y) -> mark# s add(X, Y), mark# first(X1, X2) -> first#(mark X1, mark X2)) (active# add(s X, Y) -> mark# s add(X, Y), mark# first(X1, X2) -> active# first(mark X1, mark X2)) (active# add(s X, Y) -> mark# s add(X, Y), mark# first(X1, X2) -> mark# X2) (active# add(s X, Y) -> mark# s add(X, Y), mark# first(X1, X2) -> mark# X1) (active# add(s X, Y) -> mark# s add(X, Y), mark# s X -> active# s X) (active# add(s X, Y) -> mark# s add(X, Y), mark# add(X1, X2) -> add#(mark X1, X2)) (active# add(s X, Y) -> mark# s add(X, Y), mark# add(X1, X2) -> active# add(mark X1, X2)) (active# add(s X, Y) -> mark# s add(X, Y), mark# add(X1, X2) -> mark# X1) (active# add(s X, Y) -> mark# s add(X, Y), mark# if(X1, X2, X3) -> if#(mark X1, X2, X3)) (active# add(s X, Y) -> mark# s add(X, Y), mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3)) (active# add(s X, Y) -> mark# s add(X, Y), mark# if(X1, X2, X3) -> mark# X1) (active# add(s X, Y) -> mark# s add(X, Y), mark# and(X1, X2) -> and#(mark X1, X2)) (active# add(s X, Y) -> mark# s add(X, Y), mark# and(X1, X2) -> active# and(mark X1, X2)) (active# add(s X, Y) -> mark# s add(X, Y), mark# and(X1, X2) -> mark# X1) (mark# if(X1, X2, X3) -> mark# X1, mark# from X -> active# from X) (mark# if(X1, X2, X3) -> mark# X1, mark# cons(X1, X2) -> active# cons(X1, X2)) (mark# if(X1, X2, X3) -> mark# X1, mark# first(X1, X2) -> first#(mark X1, mark X2)) (mark# if(X1, X2, X3) -> mark# X1, mark# first(X1, X2) -> active# first(mark X1, mark X2)) (mark# if(X1, X2, X3) -> mark# X1, mark# first(X1, X2) -> mark# X2) (mark# if(X1, X2, X3) -> mark# X1, mark# first(X1, X2) -> mark# X1) (mark# if(X1, X2, X3) -> mark# X1, mark# nil() -> active# nil()) (mark# if(X1, X2, X3) -> mark# X1, mark# s X -> active# s X) (mark# if(X1, X2, X3) -> mark# X1, mark# 0() -> active# 0()) (mark# if(X1, X2, X3) -> mark# X1, mark# add(X1, X2) -> add#(mark X1, X2)) (mark# if(X1, X2, X3) -> mark# X1, mark# add(X1, X2) -> active# add(mark X1, X2)) (mark# if(X1, X2, X3) -> mark# X1, mark# add(X1, X2) -> mark# X1) (mark# if(X1, X2, X3) -> mark# X1, mark# if(X1, X2, X3) -> if#(mark X1, X2, X3)) (mark# if(X1, X2, X3) -> mark# X1, mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3)) (mark# if(X1, X2, X3) -> mark# X1, mark# if(X1, X2, X3) -> mark# X1) (mark# if(X1, X2, X3) -> mark# X1, mark# false() -> active# false()) (mark# if(X1, X2, X3) -> mark# X1, mark# true() -> active# true()) (mark# if(X1, X2, X3) -> mark# X1, mark# and(X1, X2) -> and#(mark X1, X2)) (mark# if(X1, X2, X3) -> mark# X1, mark# and(X1, X2) -> active# and(mark X1, X2)) (mark# if(X1, X2, X3) -> mark# X1, mark# and(X1, X2) -> mark# X1) (mark# add(X1, X2) -> mark# X1, mark# from X -> active# from X) (mark# add(X1, X2) -> mark# X1, mark# cons(X1, X2) -> active# cons(X1, X2)) (mark# add(X1, X2) -> mark# X1, mark# first(X1, X2) -> first#(mark X1, mark X2)) (mark# add(X1, X2) -> mark# X1, mark# first(X1, X2) -> active# first(mark X1, mark X2)) (mark# add(X1, X2) -> mark# X1, mark# first(X1, X2) -> mark# X2) (mark# add(X1, X2) -> mark# X1, mark# first(X1, X2) -> mark# X1) (mark# add(X1, X2) -> mark# X1, mark# nil() -> active# nil()) (mark# add(X1, X2) -> mark# X1, mark# s X -> active# s X) (mark# add(X1, X2) -> mark# X1, mark# 0() -> active# 0()) (mark# add(X1, X2) -> mark# X1, mark# add(X1, X2) -> add#(mark X1, X2)) (mark# add(X1, X2) -> mark# X1, mark# add(X1, X2) -> active# add(mark X1, X2)) (mark# add(X1, X2) -> mark# X1, mark# add(X1, X2) -> mark# X1) (mark# add(X1, X2) -> mark# X1, mark# if(X1, X2, X3) -> if#(mark X1, X2, X3)) (mark# add(X1, X2) -> mark# X1, mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3)) (mark# add(X1, X2) -> mark# X1, mark# if(X1, X2, X3) -> mark# X1) (mark# add(X1, X2) -> mark# X1, mark# false() -> active# false()) (mark# add(X1, X2) -> mark# X1, mark# true() -> active# true()) (mark# add(X1, X2) -> mark# X1, mark# and(X1, X2) -> and#(mark X1, X2)) (mark# add(X1, X2) -> mark# X1, mark# and(X1, X2) -> active# and(mark X1, X2)) (mark# add(X1, X2) -> mark# X1, mark# and(X1, X2) -> mark# X1) (if#(X1, X2, mark X3) -> if#(X1, X2, X3), if#(active X1, X2, X3) -> if#(X1, X2, X3)) (if#(X1, X2, mark X3) -> if#(X1, X2, X3), if#(mark X1, X2, X3) -> if#(X1, X2, X3)) (if#(X1, X2, mark X3) -> if#(X1, X2, X3), if#(X1, active X2, X3) -> if#(X1, X2, X3)) (if#(X1, X2, mark X3) -> if#(X1, X2, X3), if#(X1, mark X2, X3) -> if#(X1, X2, X3)) (if#(X1, X2, mark X3) -> if#(X1, X2, X3), if#(X1, X2, active X3) -> if#(X1, X2, X3)) (if#(X1, X2, mark X3) -> if#(X1, X2, X3), if#(X1, X2, mark X3) -> if#(X1, X2, X3)) (if#(X1, mark X2, X3) -> if#(X1, X2, X3), if#(active X1, X2, X3) -> if#(X1, X2, X3)) (if#(X1, mark X2, X3) -> if#(X1, X2, X3), if#(mark X1, X2, X3) -> if#(X1, X2, X3)) (if#(X1, mark X2, X3) -> if#(X1, X2, X3), if#(X1, active X2, X3) -> if#(X1, X2, X3)) (if#(X1, mark X2, X3) -> if#(X1, X2, X3), if#(X1, mark X2, X3) -> if#(X1, X2, X3)) (if#(X1, mark X2, X3) -> if#(X1, X2, X3), if#(X1, X2, active X3) -> if#(X1, X2, X3)) (if#(X1, mark X2, X3) -> if#(X1, X2, X3), if#(X1, X2, mark X3) -> if#(X1, X2, X3)) (if#(mark X1, X2, X3) -> if#(X1, X2, X3), if#(active X1, X2, X3) -> if#(X1, X2, X3)) (if#(mark X1, X2, X3) -> if#(X1, X2, X3), if#(mark X1, X2, X3) -> if#(X1, X2, X3)) (if#(mark X1, X2, X3) -> if#(X1, X2, X3), if#(X1, active X2, X3) -> if#(X1, X2, X3)) (if#(mark X1, X2, X3) -> if#(X1, X2, X3), if#(X1, mark X2, X3) -> if#(X1, X2, X3)) (if#(mark X1, X2, X3) -> if#(X1, X2, X3), if#(X1, X2, active X3) -> if#(X1, X2, X3)) (if#(mark X1, X2, X3) -> if#(X1, X2, X3), if#(X1, X2, mark X3) -> if#(X1, X2, X3)) (active# first(s X, cons(Y, Z)) -> cons#(Y, first(X, Z)), cons#(X1, active X2) -> cons#(X1, X2)) (active# first(s X, cons(Y, Z)) -> cons#(Y, first(X, Z)), cons#(X1, mark X2) -> cons#(X1, X2)) (mark# first(X1, X2) -> active# first(mark X1, mark X2), active# from X -> from# s X) (mark# first(X1, X2) -> active# first(mark X1, mark X2), active# from X -> cons#(X, from s X)) (mark# first(X1, X2) -> active# first(mark X1, mark X2), active# from X -> s# X) (mark# first(X1, X2) -> active# first(mark X1, mark X2), active# from X -> mark# cons(X, from s X)) (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) -> 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)) -> mark# cons(Y, first(X, Z))) (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# add(s X, Y) -> s# add(X, Y)) (mark# first(X1, X2) -> active# first(mark X1, mark X2), active# add(s X, Y) -> add#(X, Y)) (mark# first(X1, X2) -> active# first(mark X1, mark X2), active# add(s X, Y) -> mark# s add(X, Y)) (mark# first(X1, X2) -> active# first(mark X1, mark X2), active# add(0(), X) -> mark# X) (mark# first(X1, X2) -> active# first(mark X1, mark X2), active# if(false(), X, Y) -> mark# Y) (mark# first(X1, X2) -> active# first(mark X1, mark X2), active# if(true(), X, Y) -> mark# X) (mark# first(X1, X2) -> active# first(mark X1, mark X2), active# and(false(), Y) -> mark# false()) (mark# first(X1, X2) -> active# first(mark X1, mark X2), active# and(true(), X) -> mark# X) (active# if(true(), X, Y) -> mark# X, mark# from X -> active# from X) (active# if(true(), X, Y) -> mark# X, mark# cons(X1, X2) -> active# cons(X1, X2)) (active# if(true(), X, Y) -> mark# X, mark# first(X1, X2) -> first#(mark X1, mark X2)) (active# if(true(), X, Y) -> mark# X, mark# first(X1, X2) -> active# first(mark X1, mark X2)) (active# if(true(), X, Y) -> mark# X, mark# first(X1, X2) -> mark# X2) (active# if(true(), X, Y) -> mark# X, mark# first(X1, X2) -> mark# X1) (active# if(true(), X, Y) -> mark# X, mark# nil() -> active# nil()) (active# if(true(), X, Y) -> mark# X, mark# s X -> active# s X) (active# if(true(), X, Y) -> mark# X, mark# 0() -> active# 0()) (active# if(true(), X, Y) -> mark# X, mark# add(X1, X2) -> add#(mark X1, X2)) (active# if(true(), X, Y) -> mark# X, mark# add(X1, X2) -> active# add(mark X1, X2)) (active# if(true(), X, Y) -> mark# X, mark# add(X1, X2) -> mark# X1) (active# if(true(), X, Y) -> mark# X, mark# if(X1, X2, X3) -> if#(mark X1, X2, X3)) (active# if(true(), X, Y) -> mark# X, mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3)) (active# if(true(), X, Y) -> mark# X, mark# if(X1, X2, X3) -> mark# X1) (active# if(true(), X, Y) -> mark# X, mark# false() -> active# false()) (active# if(true(), X, Y) -> mark# X, mark# true() -> active# true()) (active# if(true(), X, Y) -> mark# X, mark# and(X1, X2) -> and#(mark X1, X2)) (active# if(true(), X, Y) -> mark# X, mark# and(X1, X2) -> active# and(mark X1, X2)) (active# if(true(), X, Y) -> mark# X, mark# and(X1, X2) -> mark# X1) (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# add(X1, X2) -> add#(mark X1, X2), add#(active X1, X2) -> add#(X1, X2)) (mark# add(X1, X2) -> add#(mark X1, X2), add#(mark X1, X2) -> add#(X1, X2)) (active# from X -> cons#(X, from s X), cons#(X1, active X2) -> cons#(X1, X2)) (active# from X -> cons#(X, from s X), cons#(X1, mark X2) -> cons#(X1, X2)) (and#(X1, active X2) -> and#(X1, X2), and#(active X1, X2) -> and#(X1, X2)) (and#(X1, active X2) -> and#(X1, X2), and#(mark X1, X2) -> and#(X1, X2)) (and#(X1, active X2) -> and#(X1, X2), and#(X1, active X2) -> and#(X1, X2)) (and#(X1, active X2) -> and#(X1, X2), and#(X1, mark X2) -> and#(X1, X2)) (and#(active X1, X2) -> and#(X1, X2), and#(active X1, X2) -> and#(X1, X2)) (and#(active X1, X2) -> and#(X1, X2), and#(mark X1, X2) -> and#(X1, X2)) (and#(active X1, X2) -> and#(X1, X2), and#(X1, active X2) -> and#(X1, X2)) (and#(active X1, X2) -> and#(X1, X2), and#(X1, mark X2) -> and#(X1, X2)) (add#(X1, active X2) -> add#(X1, X2), add#(active X1, X2) -> add#(X1, X2)) (add#(X1, active X2) -> add#(X1, X2), add#(mark X1, X2) -> add#(X1, X2)) (add#(X1, active X2) -> add#(X1, X2), add#(X1, active X2) -> add#(X1, X2)) (add#(X1, active X2) -> add#(X1, X2), add#(X1, mark X2) -> add#(X1, X2)) (add#(active X1, X2) -> add#(X1, X2), add#(active X1, X2) -> add#(X1, X2)) (add#(active X1, X2) -> add#(X1, X2), add#(mark X1, X2) -> add#(X1, X2)) (add#(active X1, X2) -> add#(X1, X2), add#(X1, active X2) -> add#(X1, X2)) (add#(active X1, X2) -> add#(X1, X2), add#(X1, mark X2) -> add#(X1, X2)) (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# if(X1, X2, X3) -> active# if(mark X1, X2, X3), active# from X -> from# s X) (mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3), active# from X -> cons#(X, from s X)) (mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3), active# from X -> s# X) (mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3), active# from X -> mark# cons(X, from s X)) (mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3), active# first(s X, cons(Y, Z)) -> cons#(Y, first(X, Z))) (mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3), active# first(s X, cons(Y, Z)) -> first#(X, Z)) (mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3), active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z))) (mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3), active# first(0(), X) -> mark# nil()) (mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3), active# add(s X, Y) -> s# add(X, Y)) (mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3), active# add(s X, Y) -> add#(X, Y)) (mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3), active# add(s X, Y) -> mark# s add(X, Y)) (mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3), active# add(0(), X) -> mark# X) (mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3), active# if(false(), X, Y) -> mark# Y) (mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3), active# if(true(), X, Y) -> mark# X) (mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3), active# and(false(), Y) -> mark# false()) (mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3), active# and(true(), X) -> mark# X) (active# first(0(), X) -> mark# nil(), mark# nil() -> active# nil()) (mark# and(X1, X2) -> active# and(mark X1, X2), active# from X -> from# s X) (mark# and(X1, X2) -> active# and(mark X1, X2), active# from X -> cons#(X, from s X)) (mark# and(X1, X2) -> active# and(mark X1, X2), active# from X -> s# X) (mark# and(X1, X2) -> active# and(mark X1, X2), active# from X -> mark# cons(X, from s X)) (mark# and(X1, X2) -> active# and(mark X1, X2), active# first(s X, cons(Y, Z)) -> cons#(Y, first(X, Z))) (mark# and(X1, X2) -> active# and(mark X1, X2), active# first(s X, cons(Y, Z)) -> first#(X, Z)) (mark# and(X1, X2) -> active# and(mark X1, X2), active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z))) (mark# and(X1, X2) -> active# and(mark X1, X2), active# first(0(), X) -> mark# nil()) (mark# and(X1, X2) -> active# and(mark X1, X2), active# add(s X, Y) -> s# add(X, Y)) (mark# and(X1, X2) -> active# and(mark X1, X2), active# add(s X, Y) -> add#(X, Y)) (mark# and(X1, X2) -> active# and(mark X1, X2), active# add(s X, Y) -> mark# s add(X, Y)) (mark# and(X1, X2) -> active# and(mark X1, X2), active# add(0(), X) -> mark# X) (mark# and(X1, X2) -> active# and(mark X1, X2), active# if(false(), X, Y) -> mark# Y) (mark# and(X1, X2) -> active# and(mark X1, X2), active# if(true(), X, Y) -> mark# X) (mark# and(X1, X2) -> active# and(mark X1, X2), active# and(false(), Y) -> mark# false()) (mark# and(X1, X2) -> active# and(mark X1, X2), active# and(true(), X) -> mark# X) (mark# cons(X1, X2) -> active# cons(X1, X2), active# from X -> from# s X) (mark# cons(X1, X2) -> active# cons(X1, X2), active# from X -> cons#(X, from s X)) (mark# cons(X1, X2) -> active# cons(X1, X2), active# from X -> s# X) (mark# cons(X1, X2) -> active# cons(X1, X2), active# from X -> mark# cons(X, from s X)) (mark# cons(X1, X2) -> active# 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-> mark# X) (mark# s X -> active# s X, active# from X -> from# s X) (mark# s X -> active# s X, active# from X -> cons#(X, from s X)) (mark# s X -> active# s X, active# from X -> s# X) (mark# s X -> active# s X, active# from X -> mark# cons(X, from s X)) (mark# s X -> active# s X, active# first(s X, cons(Y, Z)) -> cons#(Y, first(X, Z))) (mark# s X -> active# s X, active# first(s X, cons(Y, Z)) -> first#(X, Z)) (mark# s X -> active# s X, active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z))) (mark# s X -> active# s X, active# first(0(), X) -> mark# nil()) (mark# s X -> active# s X, active# add(s X, Y) -> s# add(X, Y)) (mark# s X -> active# s X, active# add(s X, Y) -> add#(X, Y)) (mark# s X -> active# s X, active# add(s X, Y) -> mark# s add(X, Y)) (mark# s X -> active# s X, active# add(0(), X) -> mark# X) (mark# s X -> active# s X, active# if(false(), X, Y) -> mark# Y) (mark# s X -> active# s X, active# if(true(), X, Y) -> mark# X) (mark# s X -> active# s X, active# and(false(), Y) -> mark# false()) (mark# s X -> active# s X, active# and(true(), X) -> mark# X) (active# from X -> from# s X, from# active X -> from# X) (active# from X -> from# s X, from# mark X -> from# X) (mark# from X -> active# from X, active# and(true(), X) -> mark# X) (mark# from X -> active# from X, active# and(false(), Y) -> mark# false()) (mark# from X -> active# from X, active# if(true(), X, Y) -> mark# X) (mark# from X -> active# from X, active# if(false(), X, Y) -> mark# Y) (mark# from X -> active# from X, active# add(0(), X) -> mark# X) (mark# from X -> active# from X, active# add(s X, Y) -> mark# s add(X, Y)) (mark# from X -> active# from X, active# add(s X, Y) -> add#(X, Y)) (mark# from X -> active# from X, active# add(s X, Y) -> s# add(X, Y)) (mark# from X -> active# from X, active# first(0(), X) -> mark# nil()) (mark# from X -> active# from X, active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z))) (mark# from X -> active# from X, active# first(s X, cons(Y, Z)) -> first#(X, Z)) (mark# from X -> active# from X, active# first(s X, cons(Y, Z)) -> cons#(Y, first(X, Z))) (mark# from X -> active# from X, active# from X -> mark# cons(X, from s X)) (mark# from X -> active# from X, active# from X -> s# X) (mark# from X -> active# from X, active# from X -> cons#(X, from s X)) (mark# from X -> active# from X, active# from X -> from# s X) (active# add(s X, Y) -> s# add(X, Y), s# mark X -> s# X) (active# add(s X, Y) -> s# add(X, Y), s# active X -> s# X) (mark# add(X1, X2) -> active# add(mark X1, X2), active# and(true(), X) -> mark# X) (mark# add(X1, X2) -> active# add(mark X1, X2), active# and(false(), Y) -> mark# false()) (mark# add(X1, X2) -> active# add(mark X1, X2), active# if(true(), X, Y) -> mark# X) (mark# add(X1, X2) -> active# add(mark X1, X2), active# if(false(), X, Y) -> mark# Y) (mark# add(X1, X2) -> active# add(mark X1, X2), active# add(0(), X) -> mark# X) (mark# add(X1, X2) -> active# add(mark X1, X2), active# add(s X, Y) -> mark# s add(X, Y)) (mark# add(X1, X2) -> active# add(mark X1, X2), active# add(s X, Y) -> add#(X, Y)) (mark# add(X1, X2) -> active# add(mark X1, X2), active# add(s X, Y) -> s# add(X, Y)) (mark# add(X1, X2) -> active# add(mark X1, X2), active# first(0(), X) -> mark# nil()) (mark# add(X1, X2) -> active# add(mark X1, X2), active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z))) (mark# add(X1, X2) -> active# add(mark X1, X2), active# first(s X, cons(Y, Z)) -> first#(X, Z)) (mark# add(X1, X2) -> active# add(mark X1, X2), active# first(s X, cons(Y, Z)) -> cons#(Y, first(X, Z))) (mark# add(X1, X2) -> active# add(mark X1, X2), active# from X -> mark# cons(X, from s X)) (mark# add(X1, X2) -> active# add(mark X1, X2), active# from X -> s# X) (mark# add(X1, X2) -> active# add(mark X1, X2), active# from X -> cons#(X, from s X)) (mark# add(X1, X2) -> active# add(mark X1, X2), active# from X -> from# s X) (active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z)), mark# and(X1, X2) -> mark# X1) (active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z)), mark# and(X1, X2) -> active# and(mark X1, X2)) (active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z)), mark# and(X1, X2) -> and#(mark X1, X2)) (active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z)), mark# if(X1, X2, X3) -> mark# X1) (active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z)), mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3)) (active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z)), mark# if(X1, X2, X3) -> if#(mark X1, X2, X3)) (active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z)), mark# add(X1, X2) -> mark# X1) (active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z)), mark# add(X1, X2) -> active# add(mark X1, X2)) (active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z)), mark# add(X1, X2) -> add#(mark X1, X2)) (active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z)), mark# s X -> active# s X) (active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z)), mark# first(X1, X2) -> mark# X1) (active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z)), mark# first(X1, X2) -> 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)) -> mark# cons(Y, first(X, Z)), mark# first(X1, X2) -> first#(mark X1, mark X2)) (active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z)), mark# cons(X1, X2) -> active# cons(X1, X2)) (active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z)), mark# from X -> active# from X) (active# and(false(), Y) -> mark# false(), mark# false() -> active# false()) (active# if(false(), X, Y) -> mark# Y, mark# and(X1, X2) -> mark# X1) (active# if(false(), X, Y) -> mark# Y, mark# and(X1, X2) -> active# and(mark X1, X2)) (active# if(false(), X, Y) -> mark# Y, mark# and(X1, X2) -> and#(mark X1, X2)) (active# if(false(), X, Y) -> mark# Y, mark# true() -> active# true()) (active# if(false(), X, Y) -> mark# Y, mark# false() -> active# false()) (active# if(false(), X, Y) -> mark# Y, mark# if(X1, X2, X3) -> mark# X1) (active# if(false(), X, Y) -> mark# Y, mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3)) (active# if(false(), X, Y) -> mark# Y, mark# if(X1, X2, X3) -> if#(mark X1, X2, X3)) (active# if(false(), X, Y) -> mark# Y, mark# add(X1, X2) -> mark# X1) (active# if(false(), X, Y) -> mark# Y, mark# add(X1, X2) -> active# add(mark X1, X2)) (active# if(false(), X, Y) -> mark# Y, mark# add(X1, X2) -> add#(mark X1, X2)) (active# if(false(), X, Y) -> mark# Y, mark# 0() -> active# 0()) (active# if(false(), X, Y) -> mark# Y, mark# s X -> active# s X) (active# if(false(), X, Y) -> mark# Y, mark# nil() -> active# nil()) (active# if(false(), X, Y) -> mark# Y, mark# first(X1, X2) -> mark# X1) (active# if(false(), X, Y) -> mark# Y, mark# first(X1, X2) -> mark# X2) (active# if(false(), X, Y) -> mark# Y, mark# first(X1, X2) -> active# first(mark X1, mark X2)) (active# if(false(), X, Y) -> mark# Y, mark# first(X1, X2) -> first#(mark X1, mark X2)) (active# if(false(), X, Y) -> mark# Y, mark# cons(X1, X2) -> active# cons(X1, X2)) (active# if(false(), X, Y) -> mark# Y, mark# from X -> active# from 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)) (add#(mark X1, X2) -> add#(X1, X2), add#(X1, mark X2) -> add#(X1, X2)) (add#(mark X1, X2) -> add#(X1, X2), add#(X1, active X2) -> add#(X1, X2)) (add#(mark X1, X2) -> add#(X1, X2), add#(mark X1, X2) -> add#(X1, X2)) (add#(mark X1, X2) -> add#(X1, X2), add#(active X1, X2) -> add#(X1, X2)) (add#(X1, mark X2) -> add#(X1, X2), add#(X1, mark X2) -> add#(X1, X2)) (add#(X1, mark X2) -> add#(X1, X2), add#(X1, active X2) -> add#(X1, X2)) (add#(X1, mark X2) -> add#(X1, X2), add#(mark X1, X2) -> add#(X1, X2)) (add#(X1, mark X2) -> add#(X1, X2), add#(active X1, X2) -> add#(X1, X2)) (and#(mark X1, X2) -> and#(X1, X2), and#(X1, mark X2) -> and#(X1, X2)) (and#(mark X1, X2) -> and#(X1, X2), and#(X1, active X2) -> and#(X1, X2)) (and#(mark X1, X2) -> and#(X1, X2), and#(mark X1, X2) -> and#(X1, X2)) (and#(mark X1, X2) -> and#(X1, X2), and#(active X1, X2) -> and#(X1, X2)) (and#(X1, mark X2) -> and#(X1, X2), and#(X1, mark X2) -> and#(X1, X2)) (and#(X1, mark X2) -> and#(X1, X2), and#(X1, active X2) -> and#(X1, X2)) (and#(X1, mark X2) -> and#(X1, X2), and#(mark X1, X2) -> and#(X1, X2)) (and#(X1, mark X2) -> and#(X1, X2), and#(active X1, X2) -> and#(X1, X2)) (mark# first(X1, X2) -> mark# X2, mark# and(X1, X2) -> mark# X1) (mark# first(X1, X2) -> mark# X2, mark# and(X1, X2) -> active# and(mark X1, X2)) (mark# first(X1, X2) -> mark# X2, mark# and(X1, X2) -> and#(mark X1, X2)) (mark# first(X1, X2) -> mark# X2, mark# true() -> active# true()) (mark# first(X1, X2) -> mark# X2, mark# false() -> active# false()) (mark# first(X1, X2) -> mark# X2, mark# if(X1, X2, X3) -> mark# X1) (mark# first(X1, X2) -> mark# X2, mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3)) (mark# first(X1, X2) -> mark# X2, mark# if(X1, X2, X3) -> if#(mark X1, X2, X3)) (mark# first(X1, X2) -> mark# X2, mark# add(X1, X2) -> mark# X1) (mark# first(X1, X2) -> mark# X2, mark# add(X1, X2) -> active# add(mark X1, X2)) (mark# first(X1, X2) -> mark# X2, mark# add(X1, X2) -> add#(mark X1, X2)) (mark# first(X1, X2) -> mark# X2, mark# 0() -> active# 0()) (mark# first(X1, X2) -> mark# X2, mark# s X -> active# s X) (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# cons(X1, X2) -> active# cons(X1, X2)) (mark# first(X1, X2) -> mark# X2, mark# from X -> active# from X) (mark# and(X1, X2) -> and#(mark X1, X2), and#(mark X1, X2) -> and#(X1, X2)) (mark# and(X1, X2) -> and#(mark X1, X2), and#(active X1, X2) -> and#(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) (active# add(0(), X) -> mark# X, mark# and(X1, X2) -> mark# X1) (active# add(0(), X) -> mark# X, mark# and(X1, X2) -> active# and(mark X1, X2)) (active# add(0(), X) -> mark# X, mark# and(X1, X2) -> and#(mark X1, X2)) (active# add(0(), X) -> mark# X, mark# true() -> active# true()) (active# add(0(), X) -> mark# X, mark# false() -> active# false()) (active# add(0(), X) -> mark# X, mark# if(X1, X2, X3) -> mark# X1) (active# add(0(), X) -> mark# X, mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3)) (active# add(0(), X) -> mark# X, mark# if(X1, X2, X3) -> if#(mark X1, X2, X3)) (active# add(0(), X) -> mark# X, mark# add(X1, X2) -> mark# X1) (active# add(0(), X) -> mark# X, mark# add(X1, X2) -> active# add(mark X1, X2)) (active# add(0(), X) -> mark# X, mark# add(X1, X2) -> add#(mark X1, X2)) (active# add(0(), X) -> mark# X, mark# 0() -> active# 0()) (active# add(0(), X) -> mark# X, mark# s X -> active# s X) (active# add(0(), X) -> mark# X, mark# nil() -> active# nil()) (active# add(0(), X) -> mark# X, mark# first(X1, X2) -> mark# X1) (active# add(0(), X) -> mark# X, mark# first(X1, X2) -> mark# X2) (active# add(0(), X) -> mark# X, mark# first(X1, X2) -> active# first(mark X1, mark X2)) (active# add(0(), X) -> mark# X, mark# first(X1, X2) -> first#(mark X1, mark X2)) (active# add(0(), X) -> mark# X, mark# cons(X1, X2) -> active# cons(X1, X2)) (active# add(0(), X) -> mark# X, mark# from X -> active# from X) (active# and(true(), X) -> mark# X, mark# and(X1, X2) -> mark# X1) (active# and(true(), X) -> mark# X, mark# and(X1, X2) -> active# and(mark X1, X2)) (active# and(true(), X) -> mark# X, mark# and(X1, X2) -> and#(mark X1, X2)) (active# and(true(), X) -> mark# X, mark# true() -> active# true()) (active# and(true(), X) -> mark# X, mark# false() -> active# false()) (active# and(true(), X) -> mark# X, mark# if(X1, X2, X3) -> mark# X1) (active# and(true(), X) -> mark# X, mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3)) (active# and(true(), X) -> mark# X, mark# if(X1, X2, X3) -> if#(mark X1, X2, X3)) (active# and(true(), X) -> mark# X, mark# add(X1, X2) -> mark# X1) (active# and(true(), X) -> mark# X, mark# add(X1, X2) -> active# add(mark X1, X2)) (active# and(true(), X) -> mark# X, mark# add(X1, X2) -> add#(mark X1, X2)) (active# and(true(), X) -> mark# X, mark# 0() -> active# 0()) (active# and(true(), X) -> mark# X, mark# s X -> active# s X) (active# and(true(), X) -> mark# X, mark# nil() -> active# nil()) (active# and(true(), X) -> mark# X, mark# first(X1, X2) -> mark# X1) (active# and(true(), X) -> mark# X, mark# first(X1, X2) -> mark# X2) (active# and(true(), X) -> mark# X, mark# first(X1, X2) -> active# first(mark X1, mark X2)) (active# and(true(), X) -> mark# X, mark# first(X1, X2) -> first#(mark X1, mark X2)) (active# and(true(), X) -> mark# X, mark# cons(X1, X2) -> active# cons(X1, X2)) (active# and(true(), X) -> mark# X, mark# from X -> active# from X) (active# from X -> mark# cons(X, from s X), mark# and(X1, X2) -> mark# X1) (active# from X -> mark# cons(X, from s X), mark# and(X1, X2) -> active# and(mark X1, X2)) (active# from X -> mark# cons(X, from s X), mark# and(X1, X2) -> and#(mark X1, X2)) (active# from X -> mark# cons(X, from s X), mark# if(X1, X2, X3) -> mark# X1) (active# from X -> mark# cons(X, from s X), mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3)) (active# from X -> mark# cons(X, from s X), mark# if(X1, X2, X3) -> if#(mark X1, X2, X3)) (active# from X -> mark# cons(X, from s X), mark# add(X1, X2) -> mark# X1) (active# from X -> mark# cons(X, from s X), mark# add(X1, X2) -> active# add(mark X1, X2)) (active# from X -> mark# cons(X, from s X), mark# add(X1, X2) -> add#(mark X1, X2)) (active# from X -> mark# cons(X, from s X), mark# s X -> active# s X) (active# from X -> mark# cons(X, from s X), mark# first(X1, X2) -> mark# X1) (active# from X -> mark# cons(X, from s X), mark# first(X1, X2) -> mark# X2) (active# from X -> mark# cons(X, from s X), mark# first(X1, X2) -> active# first(mark X1, mark X2)) (active# from X -> mark# cons(X, from s X), mark# first(X1, X2) -> first#(mark X1, mark X2)) (active# from X -> mark# cons(X, from s X), mark# cons(X1, X2) -> active# cons(X1, X2)) (active# from X -> mark# cons(X, from s X), mark# from X -> active# from X) (if#(active X1, X2, X3) -> if#(X1, X2, X3), if#(X1, X2, mark X3) -> if#(X1, X2, X3)) (if#(active X1, X2, X3) -> if#(X1, X2, X3), if#(X1, X2, active X3) -> if#(X1, X2, X3)) (if#(active X1, X2, X3) -> if#(X1, X2, X3), if#(X1, mark X2, X3) -> if#(X1, X2, X3)) (if#(active X1, X2, X3) -> if#(X1, X2, X3), if#(X1, active X2, X3) -> if#(X1, X2, X3)) (if#(active X1, X2, X3) -> if#(X1, X2, X3), if#(mark X1, X2, X3) -> if#(X1, X2, X3)) (if#(active X1, X2, X3) -> if#(X1, X2, X3), if#(active X1, X2, X3) -> if#(X1, X2, X3)) (if#(X1, active X2, X3) -> if#(X1, X2, X3), if#(X1, X2, mark X3) -> if#(X1, X2, X3)) (if#(X1, active X2, X3) -> if#(X1, X2, X3), if#(X1, X2, active X3) -> if#(X1, X2, X3)) (if#(X1, active X2, X3) -> if#(X1, X2, X3), if#(X1, mark X2, X3) -> if#(X1, X2, X3)) (if#(X1, active X2, X3) -> if#(X1, X2, X3), if#(X1, active X2, X3) -> if#(X1, X2, X3)) (if#(X1, active X2, X3) -> if#(X1, X2, X3), if#(mark X1, X2, X3) -> if#(X1, X2, X3)) (if#(X1, active X2, X3) -> if#(X1, X2, X3), if#(active X1, X2, X3) -> if#(X1, X2, X3)) (if#(X1, X2, active X3) -> if#(X1, X2, X3), if#(X1, X2, mark X3) -> if#(X1, X2, X3)) (if#(X1, X2, active X3) -> if#(X1, X2, X3), if#(X1, X2, active X3) -> if#(X1, X2, X3)) (if#(X1, X2, active X3) -> if#(X1, X2, X3), if#(X1, mark X2, X3) -> if#(X1, X2, X3)) (if#(X1, X2, active X3) -> if#(X1, X2, X3), if#(X1, active X2, X3) -> if#(X1, X2, X3)) (if#(X1, X2, active X3) -> if#(X1, X2, X3), if#(mark X1, X2, X3) -> if#(X1, X2, X3)) (if#(X1, X2, active X3) -> if#(X1, X2, X3), if#(active X1, X2, X3) -> if#(X1, X2, X3)) (mark# first(X1, X2) -> mark# X1, mark# and(X1, X2) -> mark# X1) (mark# first(X1, X2) -> mark# X1, mark# and(X1, X2) -> active# and(mark X1, X2)) (mark# first(X1, X2) -> mark# X1, mark# and(X1, X2) -> and#(mark X1, X2)) (mark# first(X1, X2) -> mark# X1, mark# true() -> active# true()) (mark# first(X1, X2) -> mark# X1, mark# false() -> active# false()) (mark# first(X1, X2) -> mark# X1, mark# if(X1, X2, X3) -> mark# X1) (mark# first(X1, X2) -> mark# X1, mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3)) (mark# first(X1, X2) -> mark# X1, mark# if(X1, X2, X3) -> if#(mark X1, X2, X3)) (mark# first(X1, X2) -> mark# X1, mark# add(X1, X2) -> mark# X1) (mark# first(X1, X2) -> mark# X1, mark# add(X1, X2) -> active# add(mark X1, X2)) (mark# first(X1, X2) -> mark# X1, mark# add(X1, X2) -> add#(mark X1, X2)) (mark# first(X1, X2) -> mark# X1, mark# 0() -> active# 0()) (mark# first(X1, X2) -> mark# X1, mark# s X -> active# s X) (mark# first(X1, X2) -> mark# X1, mark# nil() -> active# nil()) (mark# first(X1, X2) -> mark# X1, mark# first(X1, X2) -> mark# X1) (mark# first(X1, X2) -> mark# X1, mark# first(X1, X2) -> 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) -> first#(mark X1, mark X2)) (mark# first(X1, X2) -> mark# X1, mark# cons(X1, X2) -> active# cons(X1, X2)) (mark# first(X1, X2) -> mark# X1, mark# from X -> active# from X) (mark# if(X1, X2, X3) -> if#(mark X1, X2, X3), if#(mark X1, X2, X3) -> if#(X1, X2, X3)) (mark# if(X1, X2, X3) -> if#(mark X1, X2, X3), if#(active X1, X2, X3) -> if#(X1, X2, X3)) (mark# and(X1, X2) -> mark# X1, mark# and(X1, X2) -> mark# X1) (mark# and(X1, X2) -> mark# X1, mark# and(X1, X2) -> active# and(mark X1, X2)) (mark# and(X1, X2) -> mark# X1, mark# and(X1, X2) -> and#(mark X1, X2)) (mark# and(X1, X2) -> mark# X1, mark# true() -> active# true()) (mark# and(X1, X2) -> mark# X1, mark# false() -> active# false()) (mark# and(X1, X2) -> mark# X1, mark# if(X1, X2, X3) -> mark# X1) (mark# and(X1, X2) -> mark# X1, mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3)) (mark# and(X1, X2) -> mark# X1, mark# if(X1, X2, X3) -> if#(mark X1, X2, X3)) (mark# and(X1, X2) -> mark# X1, mark# add(X1, X2) -> mark# X1) (mark# and(X1, X2) -> mark# X1, mark# add(X1, X2) -> active# add(mark X1, X2)) (mark# and(X1, X2) -> mark# X1, mark# add(X1, X2) -> add#(mark X1, X2)) (mark# and(X1, X2) -> mark# X1, mark# 0() -> active# 0()) (mark# and(X1, X2) -> mark# X1, mark# s X -> active# s X) (mark# and(X1, X2) -> mark# X1, mark# nil() -> active# nil()) (mark# and(X1, X2) -> mark# X1, mark# first(X1, X2) -> mark# X1) (mark# and(X1, X2) -> mark# X1, mark# first(X1, X2) -> mark# X2) (mark# and(X1, X2) -> mark# X1, mark# first(X1, X2) -> active# first(mark X1, mark X2)) (mark# and(X1, X2) -> mark# X1, mark# first(X1, X2) -> first#(mark X1, mark X2)) (mark# and(X1, X2) -> mark# X1, mark# cons(X1, X2) -> active# cons(X1, X2)) (mark# and(X1, X2) -> mark# X1, mark# from X -> active# from X) (mark# first(X1, X2) -> first#(mark X1, mark X2), first#(X1, mark 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#(mark X1, X2) -> first#(X1, X2)) (mark# first(X1, X2) -> first#(mark X1, mark X2), first#(active X1, X2) -> first#(X1, X2)) } STATUS: arrows: 0.878252 SCCS (8): Scc: { mark# and(X1, X2) -> mark# X1, mark# and(X1, X2) -> active# and(mark X1, X2), mark# if(X1, X2, X3) -> mark# X1, mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3), mark# add(X1, X2) -> mark# X1, mark# add(X1, X2) -> active# add(mark X1, X2), mark# s X -> active# s X, 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) -> active# cons(X1, X2), mark# from X -> active# from X, active# and(true(), X) -> mark# X, active# if(true(), X, Y) -> mark# X, active# if(false(), X, Y) -> mark# Y, active# add(0(), X) -> mark# X, active# add(s X, Y) -> mark# s add(X, Y), 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: { 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: { s# mark X -> s# X, s# active X -> s# X} Scc: { add#(X1, mark X2) -> add#(X1, X2), add#(X1, active X2) -> add#(X1, X2), add#(mark X1, X2) -> add#(X1, X2), add#(active X1, X2) -> add#(X1, X2)} Scc: { if#(X1, X2, mark X3) -> if#(X1, X2, X3), if#(X1, X2, active X3) -> if#(X1, X2, X3), if#(X1, mark X2, X3) -> if#(X1, X2, X3), if#(X1, active X2, X3) -> if#(X1, X2, X3), if#(mark X1, X2, X3) -> if#(X1, X2, X3), if#(active X1, X2, X3) -> if#(X1, X2, X3)} Scc: { and#(X1, mark X2) -> and#(X1, X2), and#(X1, active X2) -> and#(X1, X2), and#(mark X1, X2) -> and#(X1, X2), and#(active X1, X2) -> and#(X1, X2)} 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 (19): Strict: { mark# and(X1, X2) -> mark# X1, mark# and(X1, X2) -> active# and(mark X1, X2), mark# if(X1, X2, X3) -> mark# X1, mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3), mark# add(X1, X2) -> mark# X1, mark# add(X1, X2) -> active# add(mark X1, X2), mark# s X -> active# s X, 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) -> active# cons(X1, X2), mark# from X -> active# from X, active# and(true(), X) -> mark# X, active# if(true(), X, Y) -> mark# X, active# if(false(), X, Y) -> mark# Y, active# add(0(), X) -> mark# X, active# add(s X, Y) -> mark# s add(X, Y), active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z)), active# from X -> mark# cons(X, from s X)} Weak: { mark and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [if](x0, x1, x2) = 1, [and](x0, x1) = 1, [add](x0, x1) = 1, [first](x0, x1) = 1, [cons](x0, x1) = 1, [mark](x0) = 0, [active](x0) = 0, [s](x0) = 0, [from](x0) = 1, [true] = 0, [false] = 0, [0] = 0, [nil] = 0, [mark#](x0) = 1, [active#](x0) = x0 Strict: active# from X -> mark# cons(X, from s X) 1 + 0X >= 1 + 0X active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z)) 1 + 0X + 0Y + 0Z >= 1 + 0X + 0Y + 0Z active# add(s X, Y) -> mark# s add(X, Y) 1 + 0X + 0Y >= 1 + 0X + 0Y active# add(0(), X) -> mark# X 1 + 0X >= 1 + 0X active# if(false(), X, Y) -> mark# Y 1 + 0X + 0Y >= 1 + 0Y active# if(true(), X, Y) -> mark# X 1 + 0X + 0Y >= 1 + 0X active# and(true(), X) -> mark# X 1 + 0X >= 1 + 0X mark# from X -> active# from X 1 + 0X >= 1 + 0X mark# cons(X1, X2) -> active# cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark# first(X1, X2) -> active# first(mark X1, mark X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark# first(X1, X2) -> mark# X2 1 + 0X1 + 0X2 >= 1 + 0X2 mark# first(X1, X2) -> mark# X1 1 + 0X1 + 0X2 >= 1 + 0X1 mark# s X -> active# s X 1 + 0X >= 0 + 0X mark# add(X1, X2) -> active# add(mark X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark# add(X1, X2) -> mark# X1 1 + 0X1 + 0X2 >= 1 + 0X1 mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark# if(X1, X2, X3) -> mark# X1 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 mark# and(X1, X2) -> active# and(mark X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark# and(X1, X2) -> mark# X1 1 + 0X1 + 0X2 >= 1 + 0X1 Weak: from active X -> from X 1 + 0X >= 1 + 0X from mark X -> from 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 first(active X1, X2) -> first(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 first(mark X1, X2) -> first(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 first(X1, active X2) -> first(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 first(X1, mark X2) -> first(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 add(active X1, X2) -> add(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 add(mark X1, X2) -> add(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 add(X1, active X2) -> add(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 add(X1, mark X2) -> add(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 if(active X1, X2, X3) -> if(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 if(mark X1, X2, X3) -> if(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 if(X1, active X2, X3) -> if(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 if(X1, mark X2, X3) -> if(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 if(X1, X2, active X3) -> if(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 if(X1, X2, mark X3) -> if(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 and(active X1, X2) -> and(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 and(mark X1, X2) -> and(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 and(X1, active X2) -> and(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 and(X1, mark X2) -> and(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active from X -> mark cons(X, from s X) 0 + 0X >= 0 + 0X active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Y + 0Z active first(0(), X) -> mark nil() 0 + 0X >= 0 active add(s X, Y) -> mark s add(X, Y) 0 + 0X + 0Y >= 0 + 0X + 0Y active add(0(), X) -> mark X 0 + 0X >= 0 + 0X active if(false(), X, Y) -> mark Y 0 + 0X + 0Y >= 0 + 0Y active if(true(), X, Y) -> mark X 0 + 0X + 0Y >= 0 + 0X active and(false(), Y) -> mark false() 0 + 0Y >= 0 active and(true(), X) -> mark X 0 + 0X >= 0 + 0X mark from X -> active from X 0 + 0X >= 0 + 0X mark cons(X1, X2) -> active cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark first(X1, X2) -> active first(mark X1, mark X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark nil() -> active nil() 0 >= 0 mark s X -> active s X 0 + 0X >= 0 + 0X mark 0() -> active 0() 0 >= 0 mark add(X1, X2) -> active add(mark X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark if(X1, X2, X3) -> active if(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 mark false() -> active false() 0 >= 0 mark true() -> active true() 0 >= 0 mark and(X1, X2) -> active and(mark X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: { mark# and(X1, X2) -> mark# X1, mark# and(X1, X2) -> active# and(mark X1, X2), mark# if(X1, X2, X3) -> mark# X1, mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3), mark# add(X1, X2) -> mark# X1, mark# add(X1, X2) -> active# add(mark X1, X2), 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) -> active# cons(X1, X2), mark# from X -> active# from X, active# and(true(), X) -> mark# X, active# if(true(), X, Y) -> mark# X, active# if(false(), X, Y) -> mark# Y, active# add(0(), X) -> mark# X, active# add(s X, Y) -> mark# s add(X, Y), active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z)), active# from X -> mark# cons(X, from s X)} SCC (18): Strict: { mark# and(X1, X2) -> mark# X1, mark# and(X1, X2) -> active# and(mark X1, X2), mark# if(X1, X2, X3) -> mark# X1, mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3), mark# add(X1, X2) -> mark# X1, mark# add(X1, X2) -> active# add(mark X1, X2), 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) -> active# cons(X1, X2), mark# from X -> active# from X, active# and(true(), X) -> mark# X, active# if(true(), X, Y) -> mark# X, active# if(false(), X, Y) -> mark# Y, active# add(0(), X) -> mark# X, active# add(s X, Y) -> mark# s add(X, Y), active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z)), active# from X -> mark# cons(X, from s X)} Weak: { mark and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [if](x0, x1, x2) = x0 + x1 + x2 + 1, [and](x0, x1) = x0 + x1, [add](x0, x1) = x0 + x1, [first](x0, x1) = x0 + x1, [cons](x0, x1) = x0, [mark](x0) = x0, [active](x0) = x0, [s](x0) = x0, [from](x0) = 1, [true] = 0, [false] = 1, [0] = 0, [nil] = 0, [mark#](x0) = x0, [active#](x0) = x0 Strict: active# from X -> mark# cons(X, from s X) 1 + 0X >= 1 + 0X active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z)) 0 + 1X + 0Y + 1Z >= 0 + 1X + 0Y + 1Z active# add(s X, Y) -> mark# s add(X, Y) 0 + 1X + 1Y >= 0 + 1X + 1Y active# add(0(), X) -> mark# X 0 + 1X >= 0 + 1X active# if(false(), X, Y) -> mark# Y 2 + 1X + 1Y >= 0 + 1Y active# if(true(), X, Y) -> mark# X 1 + 1X + 1Y >= 0 + 1X active# and(true(), X) -> mark# X 0 + 1X >= 0 + 1X mark# from X -> active# from X 1 + 0X >= 1 + 0X mark# cons(X1, X2) -> active# cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 mark# first(X1, X2) -> active# first(mark X1, mark X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 mark# first(X1, X2) -> mark# X2 0 + 1X1 + 1X2 >= 0 + 1X2 mark# first(X1, X2) -> mark# X1 0 + 1X1 + 1X2 >= 0 + 1X1 mark# add(X1, X2) -> active# add(mark X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 mark# add(X1, X2) -> mark# X1 0 + 1X1 + 1X2 >= 0 + 1X1 mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 mark# if(X1, X2, X3) -> mark# X1 1 + 1X1 + 1X2 + 1X3 >= 0 + 1X1 mark# and(X1, X2) -> active# and(mark X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 mark# and(X1, X2) -> mark# X1 0 + 1X1 + 1X2 >= 0 + 1X1 Weak: from active X -> from X 1 + 0X >= 1 + 0X from mark X -> from X 1 + 0X >= 1 + 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) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(X1, mark X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 first(active X1, X2) -> first(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 first(mark X1, X2) -> first(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 first(X1, active X2) -> first(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 first(X1, mark X2) -> first(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 s active X -> s X 0 + 1X >= 0 + 1X s mark X -> s X 0 + 1X >= 0 + 1X add(active X1, X2) -> add(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 add(mark X1, X2) -> add(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 add(X1, active X2) -> add(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 add(X1, mark X2) -> add(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 if(active X1, X2, X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(mark X1, X2, X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, active X2, X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, mark X2, X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, X2, active X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, X2, mark X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 and(active X1, X2) -> and(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 and(mark X1, X2) -> and(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 and(X1, active X2) -> and(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 and(X1, mark X2) -> and(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 active from X -> mark cons(X, from s X) 1 + 0X >= 1 + 0X active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 0 + 1X + 0Y + 1Z >= 0 + 1X + 0Y + 1Z active first(0(), X) -> mark nil() 0 + 1X >= 0 active add(s X, Y) -> mark s add(X, Y) 0 + 1X + 1Y >= 0 + 1X + 1Y active add(0(), X) -> mark X 0 + 1X >= 0 + 1X active if(false(), X, Y) -> mark Y 2 + 1X + 1Y >= 0 + 1Y active if(true(), X, Y) -> mark X 1 + 1X + 1Y >= 0 + 1X active and(false(), Y) -> mark false() 1 + 1Y >= 1 active and(true(), X) -> mark X 0 + 1X >= 0 + 1X mark from X -> active from X 1 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 mark first(X1, X2) -> active first(mark X1, mark X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 mark nil() -> active nil() 0 >= 0 mark s X -> active s X 0 + 1X >= 0 + 1X mark 0() -> active 0() 0 >= 0 mark add(X1, X2) -> active add(mark X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 mark if(X1, X2, X3) -> active if(mark X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 mark false() -> active false() 1 >= 1 mark true() -> active true() 0 >= 0 mark and(X1, X2) -> active and(mark X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 SCCS (1): Scc: { mark# and(X1, X2) -> mark# X1, mark# and(X1, X2) -> active# and(mark X1, X2), mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3), mark# add(X1, X2) -> mark# X1, mark# add(X1, X2) -> active# add(mark X1, X2), 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) -> active# cons(X1, X2), mark# from X -> active# from X, active# and(true(), X) -> mark# X, active# add(0(), X) -> mark# X, active# add(s X, Y) -> mark# s add(X, Y), active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z)), active# from X -> mark# cons(X, from s X)} SCC (15): Strict: { mark# and(X1, X2) -> mark# X1, mark# and(X1, X2) -> active# and(mark X1, X2), mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3), mark# add(X1, X2) -> mark# X1, mark# add(X1, X2) -> active# add(mark X1, X2), 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) -> active# cons(X1, X2), mark# from X -> active# from X, active# and(true(), X) -> mark# X, active# add(0(), X) -> mark# X, active# add(s X, Y) -> mark# s add(X, Y), active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z)), active# from X -> mark# cons(X, from s X)} Weak: { mark and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [if](x0, x1, x2) = 1, [and](x0, x1) = 1, [add](x0, x1) = 1, [first](x0, x1) = 1, [cons](x0, x1) = 0, [mark](x0) = x0 + 1, [active](x0) = 0, [s](x0) = x0 + 1, [from](x0) = 1, [true] = 1, [false] = 1, [0] = 1, [nil] = 0, [mark#](x0) = 1, [active#](x0) = x0 Strict: active# from X -> mark# cons(X, from s X) 1 + 0X >= 1 + 0X active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z)) 1 + 0X + 0Y + 0Z >= 1 + 0X + 0Y + 0Z active# add(s X, Y) -> mark# s add(X, Y) 1 + 0X + 0Y >= 1 + 0X + 0Y active# add(0(), X) -> mark# X 1 + 0X >= 1 + 0X active# and(true(), X) -> mark# X 1 + 0X >= 1 + 0X mark# from X -> active# from X 1 + 0X >= 1 + 0X mark# cons(X1, X2) -> active# cons(X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark# first(X1, X2) -> active# first(mark X1, mark X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark# first(X1, X2) -> mark# X2 1 + 0X1 + 0X2 >= 1 + 0X2 mark# first(X1, X2) -> mark# X1 1 + 0X1 + 0X2 >= 1 + 0X1 mark# add(X1, X2) -> active# add(mark X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark# add(X1, X2) -> mark# X1 1 + 0X1 + 0X2 >= 1 + 0X1 mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark# and(X1, X2) -> active# and(mark X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark# and(X1, X2) -> mark# X1 1 + 0X1 + 0X2 >= 1 + 0X1 Weak: from active X -> from X 1 + 0X >= 1 + 0X from mark X -> from X 1 + 0X >= 1 + 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) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 first(mark X1, X2) -> first(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 first(X1, active X2) -> first(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 first(X1, mark X2) -> first(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 s active X -> s X 1 + 0X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X add(active X1, X2) -> add(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 add(mark X1, X2) -> add(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 add(X1, active X2) -> add(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 add(X1, mark X2) -> add(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 if(active X1, X2, X3) -> if(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 if(mark X1, X2, X3) -> if(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 if(X1, active X2, X3) -> if(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 if(X1, mark X2, X3) -> if(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 if(X1, X2, active X3) -> if(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 if(X1, X2, mark X3) -> if(X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 and(active X1, X2) -> and(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 and(mark X1, X2) -> and(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 and(X1, active X2) -> and(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 and(X1, mark X2) -> and(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active from X -> mark cons(X, from s X) 0 + 0X >= 1 + 0X active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 0 + 0X + 0Y + 0Z >= 1 + 0X + 0Y + 0Z active first(0(), X) -> mark nil() 0 + 0X >= 1 active add(s X, Y) -> mark s add(X, Y) 0 + 0X + 0Y >= 3 + 0X + 0Y active add(0(), X) -> mark X 0 + 0X >= 1 + 1X active if(false(), X, Y) -> mark Y 0 + 0X + 0Y >= 1 + 1Y active if(true(), X, Y) -> mark X 0 + 0X + 0Y >= 1 + 1X active and(false(), Y) -> mark false() 0 + 0Y >= 2 active and(true(), X) -> mark X 0 + 0X >= 1 + 1X mark from X -> active from X 2 + 0X >= 0 + 0X mark cons(X1, X2) -> active cons(X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark first(X1, X2) -> active first(mark X1, mark X2) 2 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 0 mark s X -> active s X 2 + 1X >= 0 + 0X mark 0() -> active 0() 2 >= 0 mark add(X1, X2) -> active add(mark X1, X2) 2 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark if(X1, X2, X3) -> active if(mark X1, X2, X3) 2 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 mark false() -> active false() 2 >= 0 mark true() -> active true() 2 >= 0 mark and(X1, X2) -> active and(mark X1, X2) 2 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: { mark# and(X1, X2) -> mark# X1, mark# and(X1, X2) -> active# and(mark X1, X2), mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3), mark# add(X1, X2) -> mark# X1, mark# add(X1, X2) -> active# add(mark X1, X2), mark# first(X1, X2) -> mark# X1, mark# first(X1, X2) -> mark# X2, mark# first(X1, X2) -> active# first(mark X1, mark X2), mark# from X -> active# from X, active# and(true(), X) -> mark# X, active# add(0(), X) -> mark# X, active# add(s X, Y) -> mark# s add(X, Y), active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z)), active# from X -> mark# cons(X, from s X)} SCC (14): Strict: { mark# and(X1, X2) -> mark# X1, mark# and(X1, X2) -> active# and(mark X1, X2), mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3), mark# add(X1, X2) -> mark# X1, mark# add(X1, X2) -> active# add(mark X1, X2), mark# first(X1, X2) -> mark# X1, mark# first(X1, X2) -> mark# X2, mark# first(X1, X2) -> active# first(mark X1, mark X2), mark# from X -> active# from X, active# and(true(), X) -> mark# X, active# add(0(), X) -> mark# X, active# add(s X, Y) -> mark# s add(X, Y), active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z)), active# from X -> mark# cons(X, from s X)} Weak: { mark and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [if](x0, x1, x2) = 0, [and](x0, x1) = 1, [add](x0, x1) = 1, [first](x0, x1) = 1, [cons](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [active](x0) = 0, [s](x0) = x0 + 1, [from](x0) = 1, [true] = 1, [false] = 1, [0] = 1, [nil] = 0, [mark#](x0) = 1, [active#](x0) = x0 Strict: active# from X -> mark# cons(X, from s X) 1 + 0X >= 1 + 0X active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z)) 1 + 0X + 0Y + 0Z >= 1 + 0X + 0Y + 0Z active# add(s X, Y) -> mark# s add(X, Y) 1 + 0X + 0Y >= 1 + 0X + 0Y active# add(0(), X) -> mark# X 1 + 0X >= 1 + 0X active# and(true(), X) -> mark# X 1 + 0X >= 1 + 0X mark# from X -> active# from X 1 + 0X >= 1 + 0X mark# first(X1, X2) -> active# first(mark X1, mark X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark# first(X1, X2) -> mark# X2 1 + 0X1 + 0X2 >= 1 + 0X2 mark# first(X1, X2) -> mark# X1 1 + 0X1 + 0X2 >= 1 + 0X1 mark# add(X1, X2) -> active# add(mark X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark# add(X1, X2) -> mark# X1 1 + 0X1 + 0X2 >= 1 + 0X1 mark# if(X1, X2, X3) -> active# if(mark X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 mark# and(X1, X2) -> active# and(mark X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark# and(X1, X2) -> mark# X1 1 + 0X1 + 0X2 >= 1 + 0X1 Weak: from active X -> from X 1 + 0X >= 1 + 0X from mark X -> from X 1 + 0X >= 1 + 0X cons(active X1, X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 cons(mark X1, X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 cons(X1, active X2) -> cons(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 cons(X1, mark X2) -> cons(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(active X1, X2) -> first(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 first(mark X1, X2) -> first(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 first(X1, active X2) -> first(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 first(X1, mark X2) -> first(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 s active X -> s X 1 + 0X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X add(active X1, X2) -> add(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 add(mark X1, X2) -> add(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 add(X1, active X2) -> add(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 add(X1, mark X2) -> add(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 if(active X1, X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(mark X1, X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, active X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, mark X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, X2, active X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, X2, mark X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 and(active X1, X2) -> and(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 and(mark X1, X2) -> and(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 and(X1, active X2) -> and(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 and(X1, mark X2) -> and(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active from X -> mark cons(X, from s X) 0 + 0X >= 3 + 0X active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 0 + 0X + 0Y + 0Z >= 3 + 0X + 0Y + 0Z active first(0(), X) -> mark nil() 0 + 0X >= 1 active add(s X, Y) -> mark s add(X, Y) 0 + 0X + 0Y >= 3 + 0X + 0Y active add(0(), X) -> mark X 0 + 0X >= 1 + 1X active if(false(), X, Y) -> mark Y 0 + 0X + 0Y >= 1 + 1Y active if(true(), X, Y) -> mark X 0 + 0X + 0Y >= 1 + 1X active and(false(), Y) -> mark false() 0 + 0Y >= 2 active and(true(), X) -> mark X 0 + 0X >= 1 + 1X mark from X -> active from X 2 + 0X >= 0 + 0X mark cons(X1, X2) -> active cons(X1, X2) 2 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 mark first(X1, X2) -> active first(mark X1, mark X2) 2 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 0 mark s X -> active s X 2 + 1X >= 0 + 0X mark 0() -> active 0() 2 >= 0 mark add(X1, X2) -> active add(mark X1, X2) 2 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark if(X1, X2, X3) -> active if(mark X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 mark false() -> active false() 2 >= 0 mark true() -> active true() 2 >= 0 mark and(X1, X2) -> active and(mark X1, X2) 2 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 SCCS (1): Scc: { mark# and(X1, X2) -> mark# X1, mark# and(X1, X2) -> active# and(mark X1, X2), mark# add(X1, X2) -> mark# X1, mark# add(X1, X2) -> active# add(mark X1, X2), mark# first(X1, X2) -> mark# X1, mark# first(X1, X2) -> mark# X2, mark# first(X1, X2) -> active# first(mark X1, mark X2), mark# from X -> active# from X, active# and(true(), X) -> mark# X, active# add(0(), X) -> mark# X, active# add(s X, Y) -> mark# s add(X, Y), active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z)), active# from X -> mark# cons(X, from s X)} SCC (13): Strict: { mark# and(X1, X2) -> mark# X1, mark# and(X1, X2) -> active# and(mark X1, X2), mark# add(X1, X2) -> mark# X1, mark# add(X1, X2) -> active# add(mark X1, X2), mark# first(X1, X2) -> mark# X1, mark# first(X1, X2) -> mark# X2, mark# first(X1, X2) -> active# first(mark X1, mark X2), mark# from X -> active# from X, active# and(true(), X) -> mark# X, active# add(0(), X) -> mark# X, active# add(s X, Y) -> mark# s add(X, Y), active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z)), active# from X -> mark# cons(X, from s X)} Weak: { mark and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [if](x0, x1, x2) = x0 + x1, [and](x0, x1) = x0 + x1, [add](x0, x1) = x0 + x1, [first](x0, x1) = x0 + x1 + 1, [cons](x0, x1) = x0, [mark](x0) = x0, [active](x0) = x0, [s](x0) = x0 + 1, [from](x0) = 0, [true] = 0, [false] = 0, [0] = 0, [nil] = 0, [mark#](x0) = x0, [active#](x0) = x0 Strict: active# from X -> mark# cons(X, from s X) 0 + 0X >= 0 + 0X active# first(s X, cons(Y, Z)) -> mark# cons(Y, first(X, Z)) 2 + 1X + 0Y + 1Z >= 1 + 1X + 0Y + 1Z active# add(s X, Y) -> mark# s add(X, Y) 1 + 1X + 1Y >= 1 + 1X + 1Y active# add(0(), X) -> mark# X 0 + 1X >= 0 + 1X active# and(true(), X) -> mark# X 0 + 1X >= 0 + 1X mark# from X -> active# from X 0 + 0X >= 0 + 0X 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 mark# add(X1, X2) -> active# add(mark X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 mark# add(X1, X2) -> mark# X1 0 + 1X1 + 1X2 >= 0 + 1X1 mark# and(X1, X2) -> active# and(mark X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 mark# and(X1, X2) -> mark# X1 0 + 1X1 + 1X2 >= 0 + 1X1 Weak: from active X -> from X 0 + 0X >= 0 + 0X from mark X -> from 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) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(X1, mark X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 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 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 1 + 1X >= 1 + 1X add(active X1, X2) -> add(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 add(mark X1, X2) -> add(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 add(X1, active X2) -> add(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 add(X1, mark X2) -> add(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 if(active X1, X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 if(mark X1, X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 if(X1, active X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 if(X1, mark X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 if(X1, X2, active X3) -> if(X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 if(X1, X2, mark X3) -> if(X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 and(active X1, X2) -> and(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 and(mark X1, X2) -> and(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 and(X1, active X2) -> and(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 and(X1, mark X2) -> and(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 active from X -> mark cons(X, from s X) 0 + 0X >= 0 + 0X active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 2 + 1X + 0Y + 1Z >= 1 + 1X + 0Y + 1Z active first(0(), X) -> mark nil() 1 + 1X >= 0 active add(s X, Y) -> mark s add(X, Y) 1 + 1X + 1Y >= 1 + 1X + 1Y active add(0(), X) -> mark X 0 + 1X >= 0 + 1X active if(false(), X, Y) -> mark Y 0 + 1X + 1Y >= 0 + 1Y active if(true(), X, Y) -> mark X 0 + 1X + 1Y >= 0 + 1X active and(false(), Y) -> mark false() 0 + 1Y >= 0 active and(true(), X) -> mark X 0 + 1X >= 0 + 1X mark from X -> active from X 0 + 0X >= 0 + 0X mark cons(X1, X2) -> active cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 mark first(X1, X2) -> active first(mark X1, mark X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 mark nil() -> active nil() 0 >= 0 mark s X -> active s X 1 + 1X >= 1 + 1X mark 0() -> active 0() 0 >= 0 mark add(X1, X2) -> active add(mark X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 mark if(X1, X2, X3) -> active if(mark X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 mark false() -> active false() 0 >= 0 mark true() -> active true() 0 >= 0 mark and(X1, X2) -> active and(mark X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 SCCS (1): Scc: { mark# and(X1, X2) -> mark# X1, mark# and(X1, X2) -> active# and(mark X1, X2), mark# add(X1, X2) -> mark# X1, mark# add(X1, X2) -> active# add(mark X1, X2), mark# first(X1, X2) -> active# first(mark X1, mark X2), mark# from X -> active# from X, active# and(true(), X) -> mark# X, active# add(0(), X) -> mark# X, active# add(s X, Y) -> mark# s add(X, Y), active# from X -> mark# cons(X, from s X)} SCC (10): Strict: { mark# and(X1, X2) -> mark# X1, mark# and(X1, X2) -> active# and(mark X1, X2), mark# add(X1, X2) -> mark# X1, mark# add(X1, X2) -> active# add(mark X1, X2), mark# first(X1, X2) -> active# first(mark X1, mark X2), mark# from X -> active# from X, active# and(true(), X) -> mark# X, active# add(0(), X) -> mark# X, active# add(s X, Y) -> mark# s add(X, Y), active# from X -> mark# cons(X, from s X)} Weak: { mark and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [if](x0, x1, x2) = x0 + x1, [and](x0, x1) = x0 + x1, [add](x0, x1) = x0 + x1, [first](x0, x1) = 0, [cons](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0, [s](x0) = 0, [from](x0) = x0 + 1, [true] = 1, [false] = 0, [0] = 0, [nil] = 0, [mark#](x0) = x0, [active#](x0) = x0 Strict: active# from X -> mark# cons(X, from s X) 1 + 1X >= 0 + 0X active# add(s X, Y) -> mark# s add(X, Y) 0 + 0X + 1Y >= 0 + 0X + 0Y active# add(0(), X) -> mark# X 0 + 1X >= 0 + 1X active# and(true(), X) -> mark# X 1 + 1X >= 0 + 1X mark# from X -> active# from X 1 + 1X >= 1 + 1X mark# first(X1, X2) -> active# first(mark X1, mark X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark# add(X1, X2) -> active# add(mark X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 mark# add(X1, X2) -> mark# X1 0 + 1X1 + 1X2 >= 0 + 1X1 mark# and(X1, X2) -> active# and(mark X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 mark# and(X1, X2) -> mark# X1 0 + 1X1 + 1X2 >= 0 + 1X1 Weak: from active X -> from X 1 + 1X >= 1 + 1X from mark X -> from 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 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 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X add(active X1, X2) -> add(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 add(mark X1, X2) -> add(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 add(X1, active X2) -> add(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 add(X1, mark X2) -> add(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 if(active X1, X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 if(mark X1, X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 if(X1, active X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 if(X1, mark X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 if(X1, X2, active X3) -> if(X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 if(X1, X2, mark X3) -> if(X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 and(active X1, X2) -> and(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 and(mark X1, X2) -> and(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 and(X1, active X2) -> and(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 and(X1, mark X2) -> and(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 active from X -> mark cons(X, from s X) 1 + 1X >= 0 + 0X active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Y + 0Z active first(0(), X) -> mark nil() 0 + 0X >= 0 active add(s X, Y) -> mark s add(X, Y) 0 + 0X + 1Y >= 0 + 0X + 0Y active add(0(), X) -> mark X 0 + 1X >= 0 + 1X active if(false(), X, Y) -> mark Y 0 + 1X + 1Y >= 0 + 1Y active if(true(), X, Y) -> mark X 0 + 1X + 1Y >= 0 + 1X active and(false(), Y) -> mark false() 0 + 1Y >= 0 active and(true(), X) -> mark X 1 + 1X >= 0 + 1X mark from X -> active from X 1 + 1X >= 1 + 1X mark cons(X1, X2) -> active cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark first(X1, X2) -> active first(mark X1, mark X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark nil() -> active nil() 0 >= 0 mark s X -> active s X 0 + 0X >= 0 + 0X mark 0() -> active 0() 0 >= 0 mark add(X1, X2) -> active add(mark X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 mark if(X1, X2, X3) -> active if(mark X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 mark false() -> active false() 0 >= 0 mark true() -> active true() 1 >= 1 mark and(X1, X2) -> active and(mark X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 SCCS (1): Scc: { mark# and(X1, X2) -> mark# X1, mark# and(X1, X2) -> active# and(mark X1, X2), mark# add(X1, X2) -> mark# X1, mark# add(X1, X2) -> active# add(mark X1, X2), mark# first(X1, X2) -> active# first(mark X1, mark X2), mark# from X -> active# from X, active# add(0(), X) -> mark# X, active# add(s X, Y) -> mark# s add(X, Y)} SCC (8): Strict: { mark# and(X1, X2) -> mark# X1, mark# and(X1, X2) -> active# and(mark X1, X2), mark# add(X1, X2) -> mark# X1, mark# add(X1, X2) -> active# add(mark X1, X2), mark# first(X1, X2) -> active# first(mark X1, mark X2), mark# from X -> active# from X, active# add(0(), X) -> mark# X, active# add(s X, Y) -> mark# s add(X, Y)} Weak: { mark and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [if](x0, x1, x2) = x0 + x1 + 1, [and](x0, x1) = 0, [add](x0, x1) = 1, [first](x0, x1) = 0, [cons](x0, x1) = x0 + x1 + 1, [mark](x0) = 1, [active](x0) = x0 + 1, [s](x0) = x0 + 1, [from](x0) = 1, [true] = 1, [false] = 1, [0] = 1, [nil] = 1, [mark#](x0) = 1, [active#](x0) = x0 Strict: active# add(s X, Y) -> mark# s add(X, Y) 1 + 0X + 0Y >= 1 + 0X + 0Y active# add(0(), X) -> mark# X 1 + 0X >= 1 + 0X mark# from X -> active# from X 1 + 0X >= 1 + 0X mark# first(X1, X2) -> active# first(mark X1, mark X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark# add(X1, X2) -> active# add(mark X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark# add(X1, X2) -> mark# X1 1 + 0X1 + 0X2 >= 1 + 0X1 mark# and(X1, X2) -> active# and(mark X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark# and(X1, X2) -> mark# X1 1 + 0X1 + 0X2 >= 1 + 0X1 Weak: from active X -> from X 1 + 0X >= 1 + 0X from mark X -> from X 1 + 0X >= 1 + 0X cons(active X1, X2) -> cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(mark X1, X2) -> cons(X1, X2) 2 + 0X1 + 1X2 >= 1 + 1X1 + 1X2 cons(X1, active X2) -> cons(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 cons(X1, mark X2) -> cons(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 1X2 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 s active X -> s X 2 + 1X >= 1 + 1X s mark X -> s X 2 + 0X >= 1 + 1X add(active X1, X2) -> add(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 add(mark X1, X2) -> add(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 add(X1, active X2) -> add(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 add(X1, mark X2) -> add(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 if(active X1, X2, X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 if(mark X1, X2, X3) -> if(X1, X2, X3) 2 + 0X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 if(X1, active X2, X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 if(X1, mark X2, X3) -> if(X1, X2, X3) 2 + 1X1 + 0X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 if(X1, X2, active X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 if(X1, X2, mark X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 and(active X1, X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(mark X1, X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(X1, active X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(X1, mark X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active from X -> mark cons(X, from s X) 2 + 0X >= 1 + 0X active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 1 + 0X + 0Y + 0Z >= 1 + 0X + 0Y + 0Z active first(0(), X) -> mark nil() 1 + 0X >= 1 active add(s X, Y) -> mark s add(X, Y) 2 + 0X + 0Y >= 1 + 0X + 0Y active add(0(), X) -> mark X 2 + 0X >= 1 + 0X active if(false(), X, Y) -> mark Y 3 + 1X + 0Y >= 1 + 0Y active if(true(), X, Y) -> mark X 3 + 1X + 0Y >= 1 + 0X active and(false(), Y) -> mark false() 1 + 0Y >= 1 active and(true(), X) -> mark X 1 + 0X >= 1 + 0X mark from X -> active from X 1 + 0X >= 2 + 0X mark cons(X1, X2) -> active cons(X1, X2) 1 + 0X1 + 0X2 >= 2 + 1X1 + 1X2 mark first(X1, X2) -> active first(mark X1, mark X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 2 mark s X -> active s X 1 + 0X >= 2 + 1X mark 0() -> active 0() 1 >= 2 mark add(X1, X2) -> active add(mark X1, X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 mark if(X1, X2, X3) -> active if(mark X1, X2, X3) 1 + 0X1 + 0X2 + 0X3 >= 3 + 0X1 + 1X2 + 0X3 mark false() -> active false() 1 >= 2 mark true() -> active true() 1 >= 2 mark and(X1, X2) -> active and(mark X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 SCCS (1): Scc: { mark# and(X1, X2) -> mark# X1, mark# add(X1, X2) -> mark# X1, mark# add(X1, X2) -> active# add(mark X1, X2), mark# from X -> active# from X, active# add(0(), X) -> mark# X, active# add(s X, Y) -> mark# s add(X, Y)} SCC (6): Strict: { mark# and(X1, X2) -> mark# X1, mark# add(X1, X2) -> mark# X1, mark# add(X1, X2) -> active# add(mark X1, X2), mark# from X -> active# from X, active# add(0(), X) -> mark# X, active# add(s X, Y) -> mark# s add(X, Y)} Weak: { mark and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [if](x0, x1, x2) = x0 + x1, [and](x0, x1) = x0 + x1, [add](x0, x1) = x0 + x1, [first](x0, x1) = 0, [cons](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0, [s](x0) = 1, [from](x0) = 0, [true] = 0, [false] = 0, [0] = 1, [nil] = 0, [mark#](x0) = x0, [active#](x0) = x0 Strict: active# add(s X, Y) -> mark# s add(X, Y) 1 + 0X + 1Y >= 1 + 0X + 0Y active# add(0(), X) -> mark# X 1 + 1X >= 0 + 1X mark# from X -> active# from X 0 + 0X >= 0 + 0X mark# add(X1, X2) -> active# add(mark X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 mark# add(X1, X2) -> mark# X1 0 + 1X1 + 1X2 >= 0 + 1X1 mark# and(X1, X2) -> mark# X1 0 + 1X1 + 1X2 >= 0 + 1X1 Weak: from active X -> from X 0 + 0X >= 0 + 0X from mark X -> from 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 s active X -> s X 1 + 0X >= 1 + 0X s mark X -> s X 1 + 0X >= 1 + 0X add(active X1, X2) -> add(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 add(mark X1, X2) -> add(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 add(X1, active X2) -> add(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 add(X1, mark X2) -> add(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 if(active X1, X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 if(mark X1, X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 if(X1, active X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 if(X1, mark X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 if(X1, X2, active X3) -> if(X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 if(X1, X2, mark X3) -> if(X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 and(active X1, X2) -> and(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 and(mark X1, X2) -> and(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 and(X1, active X2) -> and(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 and(X1, mark X2) -> and(X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 active from X -> mark cons(X, from s X) 0 + 0X >= 0 + 0X active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 0 + 0X + 0Y + 0Z >= 0 + 0X + 0Y + 0Z active first(0(), X) -> mark nil() 0 + 0X >= 0 active add(s X, Y) -> mark s add(X, Y) 1 + 0X + 1Y >= 1 + 0X + 0Y active add(0(), X) -> mark X 1 + 1X >= 0 + 1X active if(false(), X, Y) -> mark Y 0 + 1X + 1Y >= 0 + 1Y active if(true(), X, Y) -> mark X 0 + 1X + 1Y >= 0 + 1X active and(false(), Y) -> mark false() 0 + 1Y >= 0 active and(true(), X) -> mark X 0 + 1X >= 0 + 1X mark from X -> active from X 0 + 0X >= 0 + 0X mark cons(X1, X2) -> active cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark first(X1, X2) -> active first(mark X1, mark X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark nil() -> active nil() 0 >= 0 mark s X -> active s X 1 + 0X >= 1 + 0X mark 0() -> active 0() 1 >= 1 mark add(X1, X2) -> active add(mark X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 mark if(X1, X2, X3) -> active if(mark X1, X2, X3) 0 + 0X1 + 1X2 + 1X3 >= 0 + 0X1 + 1X2 + 1X3 mark false() -> active false() 0 >= 0 mark true() -> active true() 0 >= 0 mark and(X1, X2) -> active and(mark X1, X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 SCCS (1): Scc: { mark# and(X1, X2) -> mark# X1, mark# add(X1, X2) -> mark# X1, mark# add(X1, X2) -> active# add(mark X1, X2), mark# from X -> active# from X, active# add(s X, Y) -> mark# s add(X, Y)} SCC (5): Strict: { mark# and(X1, X2) -> mark# X1, mark# add(X1, X2) -> mark# X1, mark# add(X1, X2) -> active# add(mark X1, X2), mark# from X -> active# from X, active# add(s X, Y) -> mark# s add(X, Y)} Weak: { mark and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [if](x0, x1, x2) = x0 + x1 + x2 + 1, [and](x0, x1) = x0 + x1 + 1, [add](x0, x1) = x0 + x1 + 1, [first](x0, x1) = x0 + x1, [cons](x0, x1) = 1, [mark](x0) = 0, [active](x0) = 1, [s](x0) = 1, [from](x0) = 1, [true] = 1, [false] = 1, [0] = 1, [nil] = 0, [mark#](x0) = x0, [active#](x0) = 1 Strict: active# add(s X, Y) -> mark# s add(X, Y) 1 + 0X + 0Y >= 1 + 0X + 0Y mark# from X -> active# from X 1 + 0X >= 1 + 0X mark# add(X1, X2) -> active# add(mark X1, X2) 1 + 1X1 + 1X2 >= 1 + 0X1 + 0X2 mark# add(X1, X2) -> mark# X1 1 + 1X1 + 1X2 >= 0 + 1X1 mark# and(X1, X2) -> mark# X1 1 + 1X1 + 1X2 >= 0 + 1X1 Weak: from active X -> from X 1 + 0X >= 1 + 0X from mark X -> from 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 first(active X1, X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 0 + 1X1 + 1X2 first(mark X1, X2) -> first(X1, X2) 0 + 0X1 + 1X2 >= 0 + 1X1 + 1X2 first(X1, active X2) -> first(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 1X2 first(X1, mark X2) -> first(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 1X2 s active X -> s X 1 + 0X >= 1 + 0X s mark X -> s X 1 + 0X >= 1 + 0X add(active X1, X2) -> add(X1, X2) 2 + 0X1 + 1X2 >= 1 + 1X1 + 1X2 add(mark X1, X2) -> add(X1, X2) 1 + 0X1 + 1X2 >= 1 + 1X1 + 1X2 add(X1, active X2) -> add(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 1X2 add(X1, mark X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 1X2 if(active X1, X2, X3) -> if(X1, X2, X3) 2 + 0X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(mark X1, X2, X3) -> if(X1, X2, X3) 1 + 0X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, active X2, X3) -> if(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, mark X2, X3) -> if(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, X2, active X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, X2, mark X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 1X3 and(active X1, X2) -> and(X1, X2) 2 + 0X1 + 1X2 >= 1 + 1X1 + 1X2 and(mark X1, X2) -> and(X1, X2) 1 + 0X1 + 1X2 >= 1 + 1X1 + 1X2 and(X1, active X2) -> and(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 1X2 and(X1, mark X2) -> and(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 1X2 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 >= 0 active add(s X, Y) -> mark s add(X, Y) 1 + 0X + 0Y >= 0 + 0X + 0Y active add(0(), X) -> mark X 1 + 0X >= 0 + 0X active if(false(), X, Y) -> mark Y 1 + 0X + 0Y >= 0 + 0Y active if(true(), X, Y) -> mark X 1 + 0X + 0Y >= 0 + 0X active and(false(), Y) -> mark false() 1 + 0Y >= 0 active and(true(), X) -> mark X 1 + 0X >= 0 + 0X mark from X -> active from X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark first(X1, X2) -> active first(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark nil() -> active nil() 0 >= 1 mark s X -> active s X 0 + 0X >= 1 + 0X mark 0() -> active 0() 0 >= 1 mark add(X1, X2) -> active add(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark if(X1, X2, X3) -> active if(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark false() -> active false() 0 >= 1 mark true() -> active true() 0 >= 1 mark and(X1, X2) -> active and(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 SCCS (1): Scc: { mark# add(X1, X2) -> active# add(mark X1, X2), mark# from X -> active# from X, active# add(s X, Y) -> mark# s add(X, Y)} SCC (3): Strict: { mark# add(X1, X2) -> active# add(mark X1, X2), mark# from X -> active# from X, active# add(s X, Y) -> mark# s add(X, Y)} Weak: { mark and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [if](x0, x1, x2) = x0 + x1 + x2 + 1, [and](x0, x1) = 0, [add](x0, x1) = 1, [first](x0, x1) = 0, [cons](x0, x1) = 0, [mark](x0) = 0, [active](x0) = 1, [s](x0) = 0, [from](x0) = 0, [true] = 1, [false] = 1, [0] = 0, [nil] = 0, [mark#](x0) = x0, [active#](x0) = x0 Strict: active# add(s X, Y) -> mark# s add(X, Y) 1 + 0X + 0Y >= 0 + 0X + 0Y mark# from X -> active# from X 0 + 0X >= 0 + 0X mark# add(X1, X2) -> active# add(mark X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 Weak: from active X -> from X 0 + 0X >= 0 + 0X from mark X -> from 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 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X add(active X1, X2) -> add(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 add(mark X1, X2) -> add(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 add(X1, active X2) -> add(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 add(X1, mark X2) -> add(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 if(active X1, X2, X3) -> if(X1, X2, X3) 2 + 0X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(mark X1, X2, X3) -> if(X1, X2, X3) 1 + 0X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, active X2, X3) -> if(X1, X2, X3) 2 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, mark X2, X3) -> if(X1, X2, X3) 1 + 1X1 + 0X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, X2, active X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, X2, mark X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 1X3 and(active X1, X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(mark X1, X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(X1, active X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(X1, mark X2) -> and(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 >= 0 active add(s X, Y) -> mark s add(X, Y) 1 + 0X + 0Y >= 0 + 0X + 0Y active add(0(), X) -> mark X 1 + 0X >= 0 + 0X active if(false(), X, Y) -> mark Y 1 + 0X + 0Y >= 0 + 0Y active if(true(), X, Y) -> mark X 1 + 0X + 0Y >= 0 + 0X active and(false(), Y) -> mark false() 1 + 0Y >= 0 active and(true(), X) -> mark X 1 + 0X >= 0 + 0X mark from X -> active from X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark first(X1, X2) -> active first(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark nil() -> active nil() 0 >= 1 mark s X -> active s X 0 + 0X >= 1 + 0X mark 0() -> active 0() 0 >= 1 mark add(X1, X2) -> active add(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark if(X1, X2, X3) -> active if(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark false() -> active false() 0 >= 1 mark true() -> active true() 0 >= 1 mark and(X1, X2) -> active and(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 SCCS (0): SCC (2): Strict: { from# mark X -> from# X, from# active X -> from# X} Weak: { mark and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [if](x0, x1, x2) = 0, [and](x0, x1) = 0, [add](x0, x1) = 0, [first](x0, x1) = 0, [cons](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [from](x0) = 0, [true] = 0, [false] = 1, [0] = 0, [nil] = 1, [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 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 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X add(active X1, X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(mark X1, X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(X1, active X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(X1, mark X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 if(active X1, X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(mark X1, X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, active X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, mark X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, X2, active X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, X2, mark X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 and(active X1, X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(mark X1, X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(X1, active X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(X1, mark X2) -> and(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 active add(s X, Y) -> mark s add(X, Y) 1 + 0X + 0Y >= 0 + 0X + 0Y active add(0(), X) -> mark X 1 + 0X >= 0 + 1X active if(false(), X, Y) -> mark Y 1 + 0X + 0Y >= 0 + 1Y active if(true(), X, Y) -> mark X 1 + 0X + 0Y >= 0 + 1X active and(false(), Y) -> mark false() 1 + 0Y >= 1 active and(true(), X) -> mark X 1 + 0X >= 0 + 1X mark from X -> active from X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark first(X1, X2) -> active first(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 2 mark s X -> active s X 0 + 0X >= 1 + 0X mark 0() -> active 0() 0 >= 1 mark add(X1, X2) -> active add(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark if(X1, X2, X3) -> active if(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark false() -> active false() 1 >= 2 mark true() -> active true() 0 >= 1 mark and(X1, X2) -> active and(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 SCCS (1): Scc: {from# mark X -> from# X} SCC (1): Strict: {from# mark X -> from# X} Weak: { mark and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [if](x0, x1, x2) = x0 + x1 + x2 + 1, [and](x0, x1) = x0 + x1 + 1, [add](x0, x1) = x0 + 1, [first](x0, x1) = x0 + 1, [cons](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [active](x0) = x0, [s](x0) = x0 + 1, [from](x0) = 1, [true] = 1, [false] = 0, [0] = 1, [nil] = 0, [from#](x0) = x0 Strict: from# mark X -> from# X 1 + 1X >= 0 + 1X Weak: from active X -> from X 1 + 0X >= 1 + 0X from mark X -> from X 1 + 0X >= 1 + 0X cons(active X1, X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 cons(mark X1, X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 cons(X1, active X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 cons(X1, mark X2) -> cons(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(active X1, X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(mark X1, X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(X1, active X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(X1, mark X2) -> first(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X add(active X1, X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 add(mark X1, X2) -> add(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 add(X1, active X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 add(X1, mark X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 if(active X1, X2, X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(mark X1, X2, X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, active X2, X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, mark X2, X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, X2, active X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, X2, mark X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 and(active X1, X2) -> and(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(mark X1, X2) -> and(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(X1, active X2) -> and(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(X1, mark X2) -> and(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active from X -> mark cons(X, from s X) 1 + 0X >= 3 + 0X active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 2 + 0X + 0Y + 1Z >= 3 + 0X + 0Y + 1Z active first(0(), X) -> mark nil() 1 + 1X >= 1 active add(s X, Y) -> mark s add(X, Y) 2 + 1X + 0Y >= 3 + 1X + 0Y active add(0(), X) -> mark X 2 + 0X >= 1 + 1X active if(false(), X, Y) -> mark Y 1 + 1X + 1Y >= 1 + 1Y active if(true(), X, Y) -> mark X 2 + 1X + 1Y >= 1 + 1X active and(false(), Y) -> mark false() 1 + 1Y >= 1 active and(true(), X) -> mark X 2 + 1X >= 1 + 1X mark from X -> active from X 2 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 mark first(X1, X2) -> active first(mark X1, mark X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 mark nil() -> active nil() 1 >= 0 mark s X -> active s X 2 + 1X >= 1 + 1X mark 0() -> active 0() 2 >= 1 mark add(X1, X2) -> active add(mark X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark if(X1, X2, X3) -> active if(mark X1, X2, X3) 2 + 1X1 + 1X2 + 1X3 >= 2 + 1X1 + 1X2 + 1X3 mark false() -> active false() 1 >= 0 mark true() -> active true() 2 >= 1 mark and(X1, X2) -> active and(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 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 and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [if](x0, x1, x2) = 0, [and](x0, x1) = 0, [add](x0, x1) = 0, [first](x0, x1) = 0, [cons](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [from](x0) = 0, [true] = 0, [false] = 1, [0] = 0, [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: from active X -> from X 0 + 0X >= 0 + 0X from mark X -> from 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 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X add(active X1, X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(mark X1, X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(X1, active X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(X1, mark X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 if(active X1, X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(mark X1, X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, active X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, mark X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, X2, active X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, X2, mark X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 and(active X1, X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(mark X1, X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(X1, active X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(X1, mark X2) -> and(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 active add(s X, Y) -> mark s add(X, Y) 1 + 0X + 0Y >= 0 + 0X + 0Y active add(0(), X) -> mark X 1 + 0X >= 0 + 1X active if(false(), X, Y) -> mark Y 1 + 0X + 0Y >= 0 + 1Y active if(true(), X, Y) -> mark X 1 + 0X + 0Y >= 0 + 1X active and(false(), Y) -> mark false() 1 + 0Y >= 1 active and(true(), X) -> mark X 1 + 0X >= 0 + 1X mark from X -> active from X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark first(X1, X2) -> active first(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 2 mark s X -> active s X 0 + 0X >= 1 + 0X mark 0() -> active 0() 0 >= 1 mark add(X1, X2) -> active add(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark if(X1, X2, X3) -> active if(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark false() -> active false() 1 >= 2 mark true() -> active true() 0 >= 1 mark and(X1, X2) -> active and(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 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 and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [if](x0, x1, x2) = x0 + x1 + 1, [and](x0, x1) = x0 + x1 + 1, [add](x0, x1) = x0 + 1, [first](x0, x1) = x0 + 1, [cons](x0, x1) = 1, [mark](x0) = x0 + 1, [active](x0) = x0, [s](x0) = x0 + 1, [from](x0) = 0, [true] = 1, [false] = 0, [0] = 1, [nil] = 0, [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 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 first(active X1, X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(mark X1, X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(X1, active X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(X1, mark X2) -> first(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X add(active X1, X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 add(mark X1, X2) -> add(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 add(X1, active X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 add(X1, mark X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 if(active X1, X2, X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 if(mark X1, X2, X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 if(X1, active X2, X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 if(X1, mark X2, X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 if(X1, X2, active X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 if(X1, X2, mark X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 and(active X1, X2) -> and(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(mark X1, X2) -> and(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(X1, active X2) -> and(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(X1, mark X2) -> and(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active from X -> mark cons(X, from s X) 0 + 0X >= 2 + 0X active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 2 + 0X + 0Y + 0Z >= 2 + 0X + 0Y + 0Z active first(0(), X) -> mark nil() 1 + 1X >= 1 active add(s X, Y) -> mark s add(X, Y) 2 + 1X + 0Y >= 3 + 1X + 0Y active add(0(), X) -> mark X 2 + 0X >= 1 + 1X active if(false(), X, Y) -> mark Y 1 + 1X + 0Y >= 1 + 1Y active if(true(), X, Y) -> mark X 2 + 1X + 0Y >= 1 + 1X active and(false(), Y) -> mark false() 1 + 1Y >= 1 active and(true(), X) -> mark X 2 + 1X >= 1 + 1X mark from X -> active from X 1 + 0X >= 0 + 0X mark cons(X1, X2) -> active cons(X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark first(X1, X2) -> active first(mark X1, mark X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 mark nil() -> active nil() 1 >= 0 mark s X -> active s X 2 + 1X >= 1 + 1X mark 0() -> active 0() 2 >= 1 mark add(X1, X2) -> active add(mark X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark if(X1, X2, X3) -> active if(mark X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 2 + 1X1 + 1X2 + 0X3 mark false() -> active false() 1 >= 0 mark true() -> active true() 2 >= 1 mark and(X1, X2) -> active and(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 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 and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [if](x0, x1, x2) = 0, [and](x0, x1) = 0, [add](x0, x1) = 0, [first](x0, x1) = 0, [cons](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [from](x0) = 0, [true] = 0, [false] = 1, [0] = 0, [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: from active X -> from X 0 + 0X >= 0 + 0X from mark X -> from 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 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X add(active X1, X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(mark X1, X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(X1, active X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(X1, mark X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 if(active X1, X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(mark X1, X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, active X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, mark X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, X2, active X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, X2, mark X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 and(active X1, X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(mark X1, X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(X1, active X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(X1, mark X2) -> and(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 active add(s X, Y) -> mark s add(X, Y) 1 + 0X + 0Y >= 0 + 0X + 0Y active add(0(), X) -> mark X 1 + 0X >= 0 + 1X active if(false(), X, Y) -> mark Y 1 + 0X + 0Y >= 0 + 1Y active if(true(), X, Y) -> mark X 1 + 0X + 0Y >= 0 + 1X active and(false(), Y) -> mark false() 1 + 0Y >= 1 active and(true(), X) -> mark X 1 + 0X >= 0 + 1X mark from X -> active from X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark first(X1, X2) -> active first(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 2 mark s X -> active s X 0 + 0X >= 1 + 0X mark 0() -> active 0() 0 >= 1 mark add(X1, X2) -> active add(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark if(X1, X2, X3) -> active if(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark false() -> active false() 1 >= 2 mark true() -> active true() 0 >= 1 mark and(X1, X2) -> active and(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 SCCS (1): Scc: {cons#(X1, mark X2) -> cons#(X1, X2)} SCC (1): Strict: {cons#(X1, mark X2) -> cons#(X1, X2)} Weak: { mark and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [if](x0, x1, x2) = x0 + x1 + x2 + 1, [and](x0, x1) = x0 + x1 + 1, [add](x0, x1) = x0 + 1, [first](x0, x1) = x0 + 1, [cons](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [active](x0) = x0, [s](x0) = x0 + 1, [from](x0) = 1, [true] = 1, [false] = 0, [0] = 1, [nil] = 0, [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 + 0X >= 1 + 0X from mark X -> from X 1 + 0X >= 1 + 0X cons(active X1, X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 cons(mark X1, X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 cons(X1, active X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 cons(X1, mark X2) -> cons(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(active X1, X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(mark X1, X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(X1, active X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(X1, mark X2) -> first(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X add(active X1, X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 add(mark X1, X2) -> add(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 add(X1, active X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 add(X1, mark X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 if(active X1, X2, X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(mark X1, X2, X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, active X2, X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, mark X2, X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, X2, active X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, X2, mark X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 and(active X1, X2) -> and(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(mark X1, X2) -> and(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(X1, active X2) -> and(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(X1, mark X2) -> and(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active from X -> mark cons(X, from s X) 1 + 0X >= 3 + 0X active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 2 + 0X + 0Y + 1Z >= 3 + 0X + 0Y + 1Z active first(0(), X) -> mark nil() 1 + 1X >= 1 active add(s X, Y) -> mark s add(X, Y) 2 + 1X + 0Y >= 3 + 1X + 0Y active add(0(), X) -> mark X 2 + 0X >= 1 + 1X active if(false(), X, Y) -> mark Y 1 + 1X + 1Y >= 1 + 1Y active if(true(), X, Y) -> mark X 2 + 1X + 1Y >= 1 + 1X active and(false(), Y) -> mark false() 1 + 1Y >= 1 active and(true(), X) -> mark X 2 + 1X >= 1 + 1X mark from X -> active from X 2 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 mark first(X1, X2) -> active first(mark X1, mark X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 mark nil() -> active nil() 1 >= 0 mark s X -> active s X 2 + 1X >= 1 + 1X mark 0() -> active 0() 2 >= 1 mark add(X1, X2) -> active add(mark X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark if(X1, X2, X3) -> active if(mark X1, X2, X3) 2 + 1X1 + 1X2 + 1X3 >= 2 + 1X1 + 1X2 + 1X3 mark false() -> active false() 1 >= 0 mark true() -> active true() 2 >= 1 mark and(X1, X2) -> active and(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 Qed SCC (2): Strict: { s# mark X -> s# X, s# active X -> s# X} Weak: { mark and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [if](x0, x1, x2) = 0, [and](x0, x1) = 0, [add](x0, x1) = 0, [first](x0, x1) = 0, [cons](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [from](x0) = 0, [true] = 0, [false] = 1, [0] = 0, [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: from active X -> from X 0 + 0X >= 0 + 0X from mark X -> from 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 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X add(active X1, X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(mark X1, X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(X1, active X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(X1, mark X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 if(active X1, X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(mark X1, X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, active X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, mark X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, X2, active X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, X2, mark X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 and(active X1, X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(mark X1, X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(X1, active X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(X1, mark X2) -> and(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 active add(s X, Y) -> mark s add(X, Y) 1 + 0X + 0Y >= 0 + 0X + 0Y active add(0(), X) -> mark X 1 + 0X >= 0 + 1X active if(false(), X, Y) -> mark Y 1 + 0X + 0Y >= 0 + 1Y active if(true(), X, Y) -> mark X 1 + 0X + 0Y >= 0 + 1X active and(false(), Y) -> mark false() 1 + 0Y >= 1 active and(true(), X) -> mark X 1 + 0X >= 0 + 1X mark from X -> active from X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark first(X1, X2) -> active first(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 2 mark s X -> active s X 0 + 0X >= 1 + 0X mark 0() -> active 0() 0 >= 1 mark add(X1, X2) -> active add(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark if(X1, X2, X3) -> active if(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark false() -> active false() 1 >= 2 mark true() -> active true() 0 >= 1 mark and(X1, X2) -> active and(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 SCCS (1): Scc: {s# mark X -> s# X} SCC (1): Strict: {s# mark X -> s# X} Weak: { mark and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [if](x0, x1, x2) = x0 + x1 + x2 + 1, [and](x0, x1) = x0 + x1 + 1, [add](x0, x1) = x0 + 1, [first](x0, x1) = x0 + 1, [cons](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [active](x0) = x0, [s](x0) = x0 + 1, [from](x0) = 1, [true] = 1, [false] = 0, [0] = 1, [nil] = 0, [s#](x0) = x0 Strict: s# mark X -> s# X 1 + 1X >= 0 + 1X Weak: from active X -> from X 1 + 0X >= 1 + 0X from mark X -> from X 1 + 0X >= 1 + 0X cons(active X1, X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 cons(mark X1, X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 cons(X1, active X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 cons(X1, mark X2) -> cons(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(active X1, X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(mark X1, X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(X1, active X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(X1, mark X2) -> first(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X add(active X1, X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 add(mark X1, X2) -> add(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 add(X1, active X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 add(X1, mark X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 if(active X1, X2, X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(mark X1, X2, X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, active X2, X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, mark X2, X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, X2, active X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, X2, mark X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 and(active X1, X2) -> and(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(mark X1, X2) -> and(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(X1, active X2) -> and(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(X1, mark X2) -> and(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active from X -> mark cons(X, from s X) 1 + 0X >= 3 + 0X active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 2 + 0X + 0Y + 1Z >= 3 + 0X + 0Y + 1Z active first(0(), X) -> mark nil() 1 + 1X >= 1 active add(s X, Y) -> mark s add(X, Y) 2 + 1X + 0Y >= 3 + 1X + 0Y active add(0(), X) -> mark X 2 + 0X >= 1 + 1X active if(false(), X, Y) -> mark Y 1 + 1X + 1Y >= 1 + 1Y active if(true(), X, Y) -> mark X 2 + 1X + 1Y >= 1 + 1X active and(false(), Y) -> mark false() 1 + 1Y >= 1 active and(true(), X) -> mark X 2 + 1X >= 1 + 1X mark from X -> active from X 2 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 mark first(X1, X2) -> active first(mark X1, mark X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 mark nil() -> active nil() 1 >= 0 mark s X -> active s X 2 + 1X >= 1 + 1X mark 0() -> active 0() 2 >= 1 mark add(X1, X2) -> active add(mark X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark if(X1, X2, X3) -> active if(mark X1, X2, X3) 2 + 1X1 + 1X2 + 1X3 >= 2 + 1X1 + 1X2 + 1X3 mark false() -> active false() 1 >= 0 mark true() -> active true() 2 >= 1 mark and(X1, X2) -> active and(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 Qed SCC (4): Strict: { add#(X1, mark X2) -> add#(X1, X2), add#(X1, active X2) -> add#(X1, X2), add#(mark X1, X2) -> add#(X1, X2), add#(active X1, X2) -> add#(X1, X2)} Weak: { mark and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [if](x0, x1, x2) = 0, [and](x0, x1) = 0, [add](x0, x1) = 0, [first](x0, x1) = 0, [cons](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [from](x0) = 0, [true] = 0, [false] = 1, [0] = 0, [nil] = 1, [add#](x0, x1) = x0 Strict: add#(active X1, X2) -> add#(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 add#(mark X1, X2) -> add#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 add#(X1, active X2) -> add#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 add#(X1, mark X2) -> add#(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 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 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X add(active X1, X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(mark X1, X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(X1, active X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(X1, mark X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 if(active X1, X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(mark X1, X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, active X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, mark X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, X2, active X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, X2, mark X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 and(active X1, X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(mark X1, X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(X1, active X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(X1, mark X2) -> and(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 active add(s X, Y) -> mark s add(X, Y) 1 + 0X + 0Y >= 0 + 0X + 0Y active add(0(), X) -> mark X 1 + 0X >= 0 + 1X active if(false(), X, Y) -> mark Y 1 + 0X + 0Y >= 0 + 1Y active if(true(), X, Y) -> mark X 1 + 0X + 0Y >= 0 + 1X active and(false(), Y) -> mark false() 1 + 0Y >= 1 active and(true(), X) -> mark X 1 + 0X >= 0 + 1X mark from X -> active from X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark first(X1, X2) -> active first(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 2 mark s X -> active s X 0 + 0X >= 1 + 0X mark 0() -> active 0() 0 >= 1 mark add(X1, X2) -> active add(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark if(X1, X2, X3) -> active if(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark false() -> active false() 1 >= 2 mark true() -> active true() 0 >= 1 mark and(X1, X2) -> active and(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 SCCS (1): Scc: { add#(X1, mark X2) -> add#(X1, X2), add#(X1, active X2) -> add#(X1, X2), add#(mark X1, X2) -> add#(X1, X2)} SCC (3): Strict: { add#(X1, mark X2) -> add#(X1, X2), add#(X1, active X2) -> add#(X1, X2), add#(mark X1, X2) -> add#(X1, X2)} Weak: { mark and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [if](x0, x1, x2) = x0 + x1 + 1, [and](x0, x1) = x0 + x1 + 1, [add](x0, x1) = x0 + 1, [first](x0, x1) = x0 + 1, [cons](x0, x1) = 1, [mark](x0) = x0 + 1, [active](x0) = x0, [s](x0) = x0 + 1, [from](x0) = 0, [true] = 1, [false] = 0, [0] = 1, [nil] = 0, [add#](x0, x1) = x0 Strict: add#(mark X1, X2) -> add#(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 add#(X1, active X2) -> add#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 add#(X1, mark X2) -> add#(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 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 first(active X1, X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(mark X1, X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(X1, active X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(X1, mark X2) -> first(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X add(active X1, X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 add(mark X1, X2) -> add(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 add(X1, active X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 add(X1, mark X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 if(active X1, X2, X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 if(mark X1, X2, X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 if(X1, active X2, X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 if(X1, mark X2, X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 if(X1, X2, active X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 if(X1, X2, mark X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 and(active X1, X2) -> and(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(mark X1, X2) -> and(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(X1, active X2) -> and(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(X1, mark X2) -> and(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active from X -> mark cons(X, from s X) 0 + 0X >= 2 + 0X active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 2 + 0X + 0Y + 0Z >= 2 + 0X + 0Y + 0Z active first(0(), X) -> mark nil() 1 + 1X >= 1 active add(s X, Y) -> mark s add(X, Y) 2 + 1X + 0Y >= 3 + 1X + 0Y active add(0(), X) -> mark X 2 + 0X >= 1 + 1X active if(false(), X, Y) -> mark Y 1 + 1X + 0Y >= 1 + 1Y active if(true(), X, Y) -> mark X 2 + 1X + 0Y >= 1 + 1X active and(false(), Y) -> mark false() 1 + 1Y >= 1 active and(true(), X) -> mark X 2 + 1X >= 1 + 1X mark from X -> active from X 1 + 0X >= 0 + 0X mark cons(X1, X2) -> active cons(X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark first(X1, X2) -> active first(mark X1, mark X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 mark nil() -> active nil() 1 >= 0 mark s X -> active s X 2 + 1X >= 1 + 1X mark 0() -> active 0() 2 >= 1 mark add(X1, X2) -> active add(mark X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark if(X1, X2, X3) -> active if(mark X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 2 + 1X1 + 1X2 + 0X3 mark false() -> active false() 1 >= 0 mark true() -> active true() 2 >= 1 mark and(X1, X2) -> active and(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 SCCS (1): Scc: { add#(X1, mark X2) -> add#(X1, X2), add#(X1, active X2) -> add#(X1, X2)} SCC (2): Strict: { add#(X1, mark X2) -> add#(X1, X2), add#(X1, active X2) -> add#(X1, X2)} Weak: { mark and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [if](x0, x1, x2) = 0, [and](x0, x1) = 0, [add](x0, x1) = 0, [first](x0, x1) = 0, [cons](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [from](x0) = 0, [true] = 0, [false] = 1, [0] = 0, [nil] = 1, [add#](x0, x1) = x0 Strict: add#(X1, active X2) -> add#(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 add#(X1, mark X2) -> add#(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 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 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X add(active X1, X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(mark X1, X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(X1, active X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(X1, mark X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 if(active X1, X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(mark X1, X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, active X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, mark X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, X2, active X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, X2, mark X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 and(active X1, X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(mark X1, X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(X1, active X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(X1, mark X2) -> and(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 active add(s X, Y) -> mark s add(X, Y) 1 + 0X + 0Y >= 0 + 0X + 0Y active add(0(), X) -> mark X 1 + 0X >= 0 + 1X active if(false(), X, Y) -> mark Y 1 + 0X + 0Y >= 0 + 1Y active if(true(), X, Y) -> mark X 1 + 0X + 0Y >= 0 + 1X active and(false(), Y) -> mark false() 1 + 0Y >= 1 active and(true(), X) -> mark X 1 + 0X >= 0 + 1X mark from X -> active from X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark first(X1, X2) -> active first(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 2 mark s X -> active s X 0 + 0X >= 1 + 0X mark 0() -> active 0() 0 >= 1 mark add(X1, X2) -> active add(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark if(X1, X2, X3) -> active if(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark false() -> active false() 1 >= 2 mark true() -> active true() 0 >= 1 mark and(X1, X2) -> active and(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 SCCS (1): Scc: {add#(X1, mark X2) -> add#(X1, X2)} SCC (1): Strict: {add#(X1, mark X2) -> add#(X1, X2)} Weak: { mark and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [if](x0, x1, x2) = x0 + x1 + x2 + 1, [and](x0, x1) = x0 + x1 + 1, [add](x0, x1) = x0 + 1, [first](x0, x1) = x0 + 1, [cons](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [active](x0) = x0, [s](x0) = x0 + 1, [from](x0) = 1, [true] = 1, [false] = 0, [0] = 1, [nil] = 0, [add#](x0, x1) = x0 Strict: add#(X1, mark X2) -> add#(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 Weak: from active X -> from X 1 + 0X >= 1 + 0X from mark X -> from X 1 + 0X >= 1 + 0X cons(active X1, X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 cons(mark X1, X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 cons(X1, active X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 cons(X1, mark X2) -> cons(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(active X1, X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(mark X1, X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(X1, active X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(X1, mark X2) -> first(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X add(active X1, X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 add(mark X1, X2) -> add(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 add(X1, active X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 add(X1, mark X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 if(active X1, X2, X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(mark X1, X2, X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, active X2, X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, mark X2, X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, X2, active X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, X2, mark X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 and(active X1, X2) -> and(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(mark X1, X2) -> and(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(X1, active X2) -> and(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(X1, mark X2) -> and(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active from X -> mark cons(X, from s X) 1 + 0X >= 3 + 0X active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 2 + 0X + 0Y + 1Z >= 3 + 0X + 0Y + 1Z active first(0(), X) -> mark nil() 1 + 1X >= 1 active add(s X, Y) -> mark s add(X, Y) 2 + 1X + 0Y >= 3 + 1X + 0Y active add(0(), X) -> mark X 2 + 0X >= 1 + 1X active if(false(), X, Y) -> mark Y 1 + 1X + 1Y >= 1 + 1Y active if(true(), X, Y) -> mark X 2 + 1X + 1Y >= 1 + 1X active and(false(), Y) -> mark false() 1 + 1Y >= 1 active and(true(), X) -> mark X 2 + 1X >= 1 + 1X mark from X -> active from X 2 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 mark first(X1, X2) -> active first(mark X1, mark X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 mark nil() -> active nil() 1 >= 0 mark s X -> active s X 2 + 1X >= 1 + 1X mark 0() -> active 0() 2 >= 1 mark add(X1, X2) -> active add(mark X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark if(X1, X2, X3) -> active if(mark X1, X2, X3) 2 + 1X1 + 1X2 + 1X3 >= 2 + 1X1 + 1X2 + 1X3 mark false() -> active false() 1 >= 0 mark true() -> active true() 2 >= 1 mark and(X1, X2) -> active and(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 Qed SCC (6): Strict: { if#(X1, X2, mark X3) -> if#(X1, X2, X3), if#(X1, X2, active X3) -> if#(X1, X2, X3), if#(X1, mark X2, X3) -> if#(X1, X2, X3), if#(X1, active X2, X3) -> if#(X1, X2, X3), if#(mark X1, X2, X3) -> if#(X1, X2, X3), if#(active X1, X2, X3) -> if#(X1, X2, X3)} Weak: { mark and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [if](x0, x1, x2) = 0, [and](x0, x1) = x0, [add](x0, x1) = 0, [first](x0, x1) = 1, [cons](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [from](x0) = 0, [true] = 0, [false] = 1, [0] = 0, [nil] = 1, [if#](x0, x1, x2) = x0 Strict: if#(active X1, X2, X3) -> if#(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 if#(mark X1, X2, X3) -> if#(X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 if#(X1, active X2, X3) -> if#(X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 if#(X1, mark X2, X3) -> if#(X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 if#(X1, X2, active X3) -> if#(X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 if#(X1, X2, mark X3) -> if#(X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 Weak: from active X -> from X 0 + 0X >= 0 + 0X from mark X -> from 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) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 first(mark X1, X2) -> first(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 first(X1, active X2) -> first(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 first(X1, mark X2) -> first(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 add(active X1, X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(mark X1, X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(X1, active X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(X1, mark X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 if(active X1, X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(mark X1, X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, active X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, mark X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, X2, active X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, X2, mark X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 and(active X1, X2) -> and(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 and(mark X1, X2) -> and(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 and(X1, active X2) -> and(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 and(X1, mark X2) -> and(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 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)) 2 + 0X + 0Y + 0Z >= 0 + 0X + 0Y + 0Z active first(0(), X) -> mark nil() 2 + 0X >= 1 active add(s X, Y) -> mark s add(X, Y) 1 + 0X + 0Y >= 0 + 0X + 0Y active add(0(), X) -> mark X 1 + 0X >= 0 + 1X active if(false(), X, Y) -> mark Y 1 + 0X + 0Y >= 0 + 1Y active if(true(), X, Y) -> mark X 1 + 0X + 0Y >= 0 + 1X active and(false(), Y) -> mark false() 2 + 0Y >= 1 active and(true(), X) -> mark X 1 + 0X >= 0 + 1X mark from X -> active from X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark first(X1, X2) -> active first(mark X1, mark X2) 1 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 2 mark s X -> active s X 0 + 0X >= 1 + 0X mark 0() -> active 0() 0 >= 1 mark add(X1, X2) -> active add(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark if(X1, X2, X3) -> active if(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark false() -> active false() 1 >= 2 mark true() -> active true() 0 >= 1 mark and(X1, X2) -> active and(mark X1, X2) 0 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 SCCS (1): Scc: { if#(X1, X2, mark X3) -> if#(X1, X2, X3), if#(X1, X2, active X3) -> if#(X1, X2, X3), if#(X1, mark X2, X3) -> if#(X1, X2, X3), if#(X1, active X2, X3) -> if#(X1, X2, X3), if#(mark X1, X2, X3) -> if#(X1, X2, X3)} SCC (5): Strict: { if#(X1, X2, mark X3) -> if#(X1, X2, X3), if#(X1, X2, active X3) -> if#(X1, X2, X3), if#(X1, mark X2, X3) -> if#(X1, X2, X3), if#(X1, active X2, X3) -> if#(X1, X2, X3), if#(mark X1, X2, X3) -> if#(X1, X2, X3)} Weak: { mark and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [if](x0, x1, x2) = 0, [and](x0, x1) = 0, [add](x0, x1) = 0, [first](x0, x1) = 0, [cons](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [from](x0) = 0, [true] = 0, [false] = 1, [0] = 0, [nil] = 1, [if#](x0, x1, x2) = x0 Strict: if#(mark X1, X2, X3) -> if#(X1, X2, X3) 0 + 0X1 + 1X2 + 0X3 >= 0 + 0X1 + 1X2 + 0X3 if#(X1, active X2, X3) -> if#(X1, X2, X3) 1 + 0X1 + 1X2 + 0X3 >= 0 + 0X1 + 1X2 + 0X3 if#(X1, mark X2, X3) -> if#(X1, X2, X3) 0 + 0X1 + 1X2 + 0X3 >= 0 + 0X1 + 1X2 + 0X3 if#(X1, X2, active X3) -> if#(X1, X2, X3) 0 + 0X1 + 1X2 + 0X3 >= 0 + 0X1 + 1X2 + 0X3 if#(X1, X2, mark X3) -> if#(X1, X2, X3) 0 + 0X1 + 1X2 + 0X3 >= 0 + 0X1 + 1X2 + 0X3 Weak: from active X -> from X 0 + 0X >= 0 + 0X from mark X -> from 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 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X add(active X1, X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(mark X1, X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(X1, active X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(X1, mark X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 if(active X1, X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(mark X1, X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, active X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, mark X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, X2, active X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, X2, mark X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 and(active X1, X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(mark X1, X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(X1, active X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(X1, mark X2) -> and(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 active add(s X, Y) -> mark s add(X, Y) 1 + 0X + 0Y >= 0 + 0X + 0Y active add(0(), X) -> mark X 1 + 0X >= 0 + 1X active if(false(), X, Y) -> mark Y 1 + 0X + 0Y >= 0 + 1Y active if(true(), X, Y) -> mark X 1 + 0X + 0Y >= 0 + 1X active and(false(), Y) -> mark false() 1 + 0Y >= 1 active and(true(), X) -> mark X 1 + 0X >= 0 + 1X mark from X -> active from X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark first(X1, X2) -> active first(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 2 mark s X -> active s X 0 + 0X >= 1 + 0X mark 0() -> active 0() 0 >= 1 mark add(X1, X2) -> active add(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark if(X1, X2, X3) -> active if(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark false() -> active false() 1 >= 2 mark true() -> active true() 0 >= 1 mark and(X1, X2) -> active and(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 SCCS (1): Scc: { if#(X1, X2, mark X3) -> if#(X1, X2, X3), if#(X1, X2, active X3) -> if#(X1, X2, X3), if#(X1, mark X2, X3) -> if#(X1, X2, X3), if#(mark X1, X2, X3) -> if#(X1, X2, X3)} SCC (4): Strict: { if#(X1, X2, mark X3) -> if#(X1, X2, X3), if#(X1, X2, active X3) -> if#(X1, X2, X3), if#(X1, mark X2, X3) -> if#(X1, X2, X3), if#(mark X1, X2, X3) -> if#(X1, X2, X3)} Weak: { mark and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [if](x0, x1, x2) = x0 + x1 + 1, [and](x0, x1) = x0 + x1 + 1, [add](x0, x1) = x0 + x1 + 1, [first](x0, x1) = x0 + 1, [cons](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [active](x0) = x0, [s](x0) = 1, [from](x0) = x0, [true] = 1, [false] = 0, [0] = 1, [nil] = 0, [if#](x0, x1, x2) = x0 Strict: if#(mark X1, X2, X3) -> if#(X1, X2, X3) 1 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 if#(X1, mark X2, X3) -> if#(X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 if#(X1, X2, active X3) -> if#(X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 if#(X1, X2, mark X3) -> if#(X1, X2, X3) 0 + 1X1 + 0X2 + 0X3 >= 0 + 1X1 + 0X2 + 0X3 Weak: from active X -> from X 0 + 1X >= 0 + 1X from mark X -> from X 1 + 1X >= 0 + 1X cons(active X1, X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 cons(mark X1, X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 cons(X1, active X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 cons(X1, mark X2) -> cons(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(active X1, X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(mark X1, X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(X1, active X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(X1, mark X2) -> first(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 s active X -> s X 1 + 0X >= 1 + 0X s mark X -> s X 1 + 0X >= 1 + 0X add(active X1, X2) -> add(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 add(mark X1, X2) -> add(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 add(X1, active X2) -> add(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 add(X1, mark X2) -> add(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 if(active X1, X2, X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 if(mark X1, X2, X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 if(X1, active X2, X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 if(X1, mark X2, X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 if(X1, X2, active X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 if(X1, X2, mark X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 and(active X1, X2) -> and(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(mark X1, X2) -> and(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(X1, active X2) -> and(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(X1, mark X2) -> and(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active from X -> mark cons(X, from s X) 0 + 1X >= 3 + 0X active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 2 + 0X + 0Y + 1Z >= 3 + 0X + 0Y + 1Z active first(0(), X) -> mark nil() 1 + 1X >= 1 active add(s X, Y) -> mark s add(X, Y) 2 + 0X + 1Y >= 2 + 0X + 0Y active add(0(), X) -> mark X 2 + 1X >= 1 + 1X active if(false(), X, Y) -> mark Y 1 + 1X + 0Y >= 1 + 1Y active if(true(), X, Y) -> mark X 2 + 1X + 0Y >= 1 + 1X active and(false(), Y) -> mark false() 1 + 1Y >= 1 active and(true(), X) -> mark X 2 + 1X >= 1 + 1X mark from X -> active from X 1 + 1X >= 0 + 1X mark cons(X1, X2) -> active cons(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 mark first(X1, X2) -> active first(mark X1, mark X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 mark nil() -> active nil() 1 >= 0 mark s X -> active s X 2 + 0X >= 1 + 0X mark 0() -> active 0() 2 >= 1 mark add(X1, X2) -> active add(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 mark if(X1, X2, X3) -> active if(mark X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 2 + 1X1 + 1X2 + 0X3 mark false() -> active false() 1 >= 0 mark true() -> active true() 2 >= 1 mark and(X1, X2) -> active and(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 SCCS (1): Scc: { if#(X1, X2, mark X3) -> if#(X1, X2, X3), if#(X1, X2, active X3) -> if#(X1, X2, X3), if#(X1, mark X2, X3) -> if#(X1, X2, X3)} SCC (3): Strict: { if#(X1, X2, mark X3) -> if#(X1, X2, X3), if#(X1, X2, active X3) -> if#(X1, X2, X3), if#(X1, mark X2, X3) -> if#(X1, X2, X3)} Weak: { mark and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [if](x0, x1, x2) = x0 + x1 + 1, [and](x0, x1) = x0 + x1 + 1, [add](x0, x1) = x0 + 1, [first](x0, x1) = x0 + 1, [cons](x0, x1) = 1, [mark](x0) = x0 + 1, [active](x0) = x0, [s](x0) = x0 + 1, [from](x0) = 0, [true] = 1, [false] = 0, [0] = 1, [nil] = 0, [if#](x0, x1, x2) = x0 Strict: if#(X1, mark X2, X3) -> if#(X1, X2, X3) 1 + 0X1 + 1X2 + 0X3 >= 0 + 0X1 + 1X2 + 0X3 if#(X1, X2, active X3) -> if#(X1, X2, X3) 0 + 0X1 + 1X2 + 0X3 >= 0 + 0X1 + 1X2 + 0X3 if#(X1, X2, mark X3) -> if#(X1, X2, X3) 0 + 0X1 + 1X2 + 0X3 >= 0 + 0X1 + 1X2 + 0X3 Weak: from active X -> from X 0 + 0X >= 0 + 0X from mark X -> from 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 first(active X1, X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(mark X1, X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(X1, active X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(X1, mark X2) -> first(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X add(active X1, X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 add(mark X1, X2) -> add(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 add(X1, active X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 add(X1, mark X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 if(active X1, X2, X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 if(mark X1, X2, X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 if(X1, active X2, X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 if(X1, mark X2, X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 if(X1, X2, active X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 if(X1, X2, mark X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 and(active X1, X2) -> and(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(mark X1, X2) -> and(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(X1, active X2) -> and(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(X1, mark X2) -> and(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active from X -> mark cons(X, from s X) 0 + 0X >= 2 + 0X active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 2 + 0X + 0Y + 0Z >= 2 + 0X + 0Y + 0Z active first(0(), X) -> mark nil() 1 + 1X >= 1 active add(s X, Y) -> mark s add(X, Y) 2 + 1X + 0Y >= 3 + 1X + 0Y active add(0(), X) -> mark X 2 + 0X >= 1 + 1X active if(false(), X, Y) -> mark Y 1 + 1X + 0Y >= 1 + 1Y active if(true(), X, Y) -> mark X 2 + 1X + 0Y >= 1 + 1X active and(false(), Y) -> mark false() 1 + 1Y >= 1 active and(true(), X) -> mark X 2 + 1X >= 1 + 1X mark from X -> active from X 1 + 0X >= 0 + 0X mark cons(X1, X2) -> active cons(X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark first(X1, X2) -> active first(mark X1, mark X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 mark nil() -> active nil() 1 >= 0 mark s X -> active s X 2 + 1X >= 1 + 1X mark 0() -> active 0() 2 >= 1 mark add(X1, X2) -> active add(mark X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark if(X1, X2, X3) -> active if(mark X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 2 + 1X1 + 1X2 + 0X3 mark false() -> active false() 1 >= 0 mark true() -> active true() 2 >= 1 mark and(X1, X2) -> active and(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 SCCS (1): Scc: { if#(X1, X2, mark X3) -> if#(X1, X2, X3), if#(X1, X2, active X3) -> if#(X1, X2, X3)} SCC (2): Strict: { if#(X1, X2, mark X3) -> if#(X1, X2, X3), if#(X1, X2, active X3) -> if#(X1, X2, X3)} Weak: { mark and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [if](x0, x1, x2) = 0, [and](x0, x1) = 0, [add](x0, x1) = 0, [first](x0, x1) = 0, [cons](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [from](x0) = 0, [true] = 0, [false] = 1, [0] = 0, [nil] = 1, [if#](x0, x1, x2) = x0 Strict: if#(X1, X2, active X3) -> if#(X1, X2, X3) 1 + 0X1 + 0X2 + 1X3 >= 0 + 0X1 + 0X2 + 1X3 if#(X1, X2, mark X3) -> if#(X1, X2, X3) 0 + 0X1 + 0X2 + 1X3 >= 0 + 0X1 + 0X2 + 1X3 Weak: from active X -> from X 0 + 0X >= 0 + 0X from mark X -> from 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 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X add(active X1, X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(mark X1, X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(X1, active X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(X1, mark X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 if(active X1, X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(mark X1, X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, active X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, mark X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, X2, active X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, X2, mark X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 and(active X1, X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(mark X1, X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(X1, active X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(X1, mark X2) -> and(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 active add(s X, Y) -> mark s add(X, Y) 1 + 0X + 0Y >= 0 + 0X + 0Y active add(0(), X) -> mark X 1 + 0X >= 0 + 1X active if(false(), X, Y) -> mark Y 1 + 0X + 0Y >= 0 + 1Y active if(true(), X, Y) -> mark X 1 + 0X + 0Y >= 0 + 1X active and(false(), Y) -> mark false() 1 + 0Y >= 1 active and(true(), X) -> mark X 1 + 0X >= 0 + 1X mark from X -> active from X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark first(X1, X2) -> active first(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 2 mark s X -> active s X 0 + 0X >= 1 + 0X mark 0() -> active 0() 0 >= 1 mark add(X1, X2) -> active add(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark if(X1, X2, X3) -> active if(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark false() -> active false() 1 >= 2 mark true() -> active true() 0 >= 1 mark and(X1, X2) -> active and(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 SCCS (1): Scc: {if#(X1, X2, mark X3) -> if#(X1, X2, X3)} SCC (1): Strict: {if#(X1, X2, mark X3) -> if#(X1, X2, X3)} Weak: { mark and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [if](x0, x1, x2) = x0 + x1 + x2 + 1, [and](x0, x1) = x0 + x1 + 1, [add](x0, x1) = x0 + 1, [first](x0, x1) = x0 + 1, [cons](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [active](x0) = x0, [s](x0) = x0 + 1, [from](x0) = 1, [true] = 1, [false] = 0, [0] = 1, [nil] = 0, [if#](x0, x1, x2) = x0 Strict: if#(X1, X2, mark X3) -> if#(X1, X2, X3) 1 + 0X1 + 0X2 + 1X3 >= 0 + 0X1 + 0X2 + 1X3 Weak: from active X -> from X 1 + 0X >= 1 + 0X from mark X -> from X 1 + 0X >= 1 + 0X cons(active X1, X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 cons(mark X1, X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 cons(X1, active X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 cons(X1, mark X2) -> cons(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(active X1, X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(mark X1, X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(X1, active X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(X1, mark X2) -> first(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X add(active X1, X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 add(mark X1, X2) -> add(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 add(X1, active X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 add(X1, mark X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 if(active X1, X2, X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(mark X1, X2, X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, active X2, X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, mark X2, X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, X2, active X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, X2, mark X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 and(active X1, X2) -> and(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(mark X1, X2) -> and(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(X1, active X2) -> and(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(X1, mark X2) -> and(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active from X -> mark cons(X, from s X) 1 + 0X >= 3 + 0X active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 2 + 0X + 0Y + 1Z >= 3 + 0X + 0Y + 1Z active first(0(), X) -> mark nil() 1 + 1X >= 1 active add(s X, Y) -> mark s add(X, Y) 2 + 1X + 0Y >= 3 + 1X + 0Y active add(0(), X) -> mark X 2 + 0X >= 1 + 1X active if(false(), X, Y) -> mark Y 1 + 1X + 1Y >= 1 + 1Y active if(true(), X, Y) -> mark X 2 + 1X + 1Y >= 1 + 1X active and(false(), Y) -> mark false() 1 + 1Y >= 1 active and(true(), X) -> mark X 2 + 1X >= 1 + 1X mark from X -> active from X 2 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 mark first(X1, X2) -> active first(mark X1, mark X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 mark nil() -> active nil() 1 >= 0 mark s X -> active s X 2 + 1X >= 1 + 1X mark 0() -> active 0() 2 >= 1 mark add(X1, X2) -> active add(mark X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark if(X1, X2, X3) -> active if(mark X1, X2, X3) 2 + 1X1 + 1X2 + 1X3 >= 2 + 1X1 + 1X2 + 1X3 mark false() -> active false() 1 >= 0 mark true() -> active true() 2 >= 1 mark and(X1, X2) -> active and(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 Qed SCC (4): Strict: { and#(X1, mark X2) -> and#(X1, X2), and#(X1, active X2) -> and#(X1, X2), and#(mark X1, X2) -> and#(X1, X2), and#(active X1, X2) -> and#(X1, X2)} Weak: { mark and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [if](x0, x1, x2) = 0, [and](x0, x1) = 0, [add](x0, x1) = 0, [first](x0, x1) = 0, [cons](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [from](x0) = 0, [true] = 0, [false] = 1, [0] = 0, [nil] = 1, [and#](x0, x1) = x0 Strict: and#(active X1, X2) -> and#(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 and#(mark X1, X2) -> and#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 and#(X1, active X2) -> and#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 and#(X1, mark X2) -> and#(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 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 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X add(active X1, X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(mark X1, X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(X1, active X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(X1, mark X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 if(active X1, X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(mark X1, X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, active X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, mark X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, X2, active X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, X2, mark X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 and(active X1, X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(mark X1, X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(X1, active X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(X1, mark X2) -> and(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 active add(s X, Y) -> mark s add(X, Y) 1 + 0X + 0Y >= 0 + 0X + 0Y active add(0(), X) -> mark X 1 + 0X >= 0 + 1X active if(false(), X, Y) -> mark Y 1 + 0X + 0Y >= 0 + 1Y active if(true(), X, Y) -> mark X 1 + 0X + 0Y >= 0 + 1X active and(false(), Y) -> mark false() 1 + 0Y >= 1 active and(true(), X) -> mark X 1 + 0X >= 0 + 1X mark from X -> active from X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark first(X1, X2) -> active first(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 2 mark s X -> active s X 0 + 0X >= 1 + 0X mark 0() -> active 0() 0 >= 1 mark add(X1, X2) -> active add(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark if(X1, X2, X3) -> active if(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark false() -> active false() 1 >= 2 mark true() -> active true() 0 >= 1 mark and(X1, X2) -> active and(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 SCCS (1): Scc: { and#(X1, mark X2) -> and#(X1, X2), and#(X1, active X2) -> and#(X1, X2), and#(mark X1, X2) -> and#(X1, X2)} SCC (3): Strict: { and#(X1, mark X2) -> and#(X1, X2), and#(X1, active X2) -> and#(X1, X2), and#(mark X1, X2) -> and#(X1, X2)} Weak: { mark and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [if](x0, x1, x2) = x0 + x1 + 1, [and](x0, x1) = x0 + x1 + 1, [add](x0, x1) = x0 + 1, [first](x0, x1) = x0 + 1, [cons](x0, x1) = 1, [mark](x0) = x0 + 1, [active](x0) = x0, [s](x0) = x0 + 1, [from](x0) = 0, [true] = 1, [false] = 0, [0] = 1, [nil] = 0, [and#](x0, x1) = x0 Strict: and#(mark X1, X2) -> and#(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 and#(X1, active X2) -> and#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 and#(X1, mark X2) -> and#(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 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 first(active X1, X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(mark X1, X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(X1, active X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(X1, mark X2) -> first(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X add(active X1, X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 add(mark X1, X2) -> add(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 add(X1, active X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 add(X1, mark X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 if(active X1, X2, X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 if(mark X1, X2, X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 if(X1, active X2, X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 if(X1, mark X2, X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 if(X1, X2, active X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 if(X1, X2, mark X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 and(active X1, X2) -> and(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(mark X1, X2) -> and(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(X1, active X2) -> and(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(X1, mark X2) -> and(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active from X -> mark cons(X, from s X) 0 + 0X >= 2 + 0X active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 2 + 0X + 0Y + 0Z >= 2 + 0X + 0Y + 0Z active first(0(), X) -> mark nil() 1 + 1X >= 1 active add(s X, Y) -> mark s add(X, Y) 2 + 1X + 0Y >= 3 + 1X + 0Y active add(0(), X) -> mark X 2 + 0X >= 1 + 1X active if(false(), X, Y) -> mark Y 1 + 1X + 0Y >= 1 + 1Y active if(true(), X, Y) -> mark X 2 + 1X + 0Y >= 1 + 1X active and(false(), Y) -> mark false() 1 + 1Y >= 1 active and(true(), X) -> mark X 2 + 1X >= 1 + 1X mark from X -> active from X 1 + 0X >= 0 + 0X mark cons(X1, X2) -> active cons(X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark first(X1, X2) -> active first(mark X1, mark X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 mark nil() -> active nil() 1 >= 0 mark s X -> active s X 2 + 1X >= 1 + 1X mark 0() -> active 0() 2 >= 1 mark add(X1, X2) -> active add(mark X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark if(X1, X2, X3) -> active if(mark X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 2 + 1X1 + 1X2 + 0X3 mark false() -> active false() 1 >= 0 mark true() -> active true() 2 >= 1 mark and(X1, X2) -> active and(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 SCCS (1): Scc: { and#(X1, mark X2) -> and#(X1, X2), and#(X1, active X2) -> and#(X1, X2)} SCC (2): Strict: { and#(X1, mark X2) -> and#(X1, X2), and#(X1, active X2) -> and#(X1, X2)} Weak: { mark and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [if](x0, x1, x2) = 0, [and](x0, x1) = 0, [add](x0, x1) = 0, [first](x0, x1) = 0, [cons](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [from](x0) = 0, [true] = 0, [false] = 1, [0] = 0, [nil] = 1, [and#](x0, x1) = x0 Strict: and#(X1, active X2) -> and#(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 and#(X1, mark X2) -> and#(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 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 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X add(active X1, X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(mark X1, X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(X1, active X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(X1, mark X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 if(active X1, X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(mark X1, X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, active X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, mark X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, X2, active X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, X2, mark X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 and(active X1, X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(mark X1, X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(X1, active X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(X1, mark X2) -> and(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 active add(s X, Y) -> mark s add(X, Y) 1 + 0X + 0Y >= 0 + 0X + 0Y active add(0(), X) -> mark X 1 + 0X >= 0 + 1X active if(false(), X, Y) -> mark Y 1 + 0X + 0Y >= 0 + 1Y active if(true(), X, Y) -> mark X 1 + 0X + 0Y >= 0 + 1X active and(false(), Y) -> mark false() 1 + 0Y >= 1 active and(true(), X) -> mark X 1 + 0X >= 0 + 1X mark from X -> active from X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark first(X1, X2) -> active first(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 2 mark s X -> active s X 0 + 0X >= 1 + 0X mark 0() -> active 0() 0 >= 1 mark add(X1, X2) -> active add(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark if(X1, X2, X3) -> active if(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark false() -> active false() 1 >= 2 mark true() -> active true() 0 >= 1 mark and(X1, X2) -> active and(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 SCCS (1): Scc: {and#(X1, mark X2) -> and#(X1, X2)} SCC (1): Strict: {and#(X1, mark X2) -> and#(X1, X2)} Weak: { mark and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [if](x0, x1, x2) = x0 + x1 + x2 + 1, [and](x0, x1) = x0 + x1 + 1, [add](x0, x1) = x0 + 1, [first](x0, x1) = x0 + 1, [cons](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [active](x0) = x0, [s](x0) = x0 + 1, [from](x0) = 1, [true] = 1, [false] = 0, [0] = 1, [nil] = 0, [and#](x0, x1) = x0 Strict: and#(X1, mark X2) -> and#(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 Weak: from active X -> from X 1 + 0X >= 1 + 0X from mark X -> from X 1 + 0X >= 1 + 0X cons(active X1, X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 cons(mark X1, X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 cons(X1, active X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 cons(X1, mark X2) -> cons(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(active X1, X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(mark X1, X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(X1, active X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(X1, mark X2) -> first(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X add(active X1, X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 add(mark X1, X2) -> add(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 add(X1, active X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 add(X1, mark X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 if(active X1, X2, X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(mark X1, X2, X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, active X2, X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, mark X2, X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, X2, active X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, X2, mark X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 and(active X1, X2) -> and(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(mark X1, X2) -> and(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(X1, active X2) -> and(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(X1, mark X2) -> and(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active from X -> mark cons(X, from s X) 1 + 0X >= 3 + 0X active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 2 + 0X + 0Y + 1Z >= 3 + 0X + 0Y + 1Z active first(0(), X) -> mark nil() 1 + 1X >= 1 active add(s X, Y) -> mark s add(X, Y) 2 + 1X + 0Y >= 3 + 1X + 0Y active add(0(), X) -> mark X 2 + 0X >= 1 + 1X active if(false(), X, Y) -> mark Y 1 + 1X + 1Y >= 1 + 1Y active if(true(), X, Y) -> mark X 2 + 1X + 1Y >= 1 + 1X active and(false(), Y) -> mark false() 1 + 1Y >= 1 active and(true(), X) -> mark X 2 + 1X >= 1 + 1X mark from X -> active from X 2 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 mark first(X1, X2) -> active first(mark X1, mark X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 mark nil() -> active nil() 1 >= 0 mark s X -> active s X 2 + 1X >= 1 + 1X mark 0() -> active 0() 2 >= 1 mark add(X1, X2) -> active add(mark X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark if(X1, X2, X3) -> active if(mark X1, X2, X3) 2 + 1X1 + 1X2 + 1X3 >= 2 + 1X1 + 1X2 + 1X3 mark false() -> active false() 1 >= 0 mark true() -> active true() 2 >= 1 mark and(X1, X2) -> active and(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 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 and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [if](x0, x1, x2) = 0, [and](x0, x1) = 0, [add](x0, x1) = 0, [first](x0, x1) = 0, [cons](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [from](x0) = 0, [true] = 0, [false] = 1, [0] = 0, [nil] = 1, [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 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 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X add(active X1, X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(mark X1, X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(X1, active X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(X1, mark X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 if(active X1, X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(mark X1, X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, active X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, mark X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, X2, active X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, X2, mark X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 and(active X1, X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(mark X1, X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(X1, active X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(X1, mark X2) -> and(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 active add(s X, Y) -> mark s add(X, Y) 1 + 0X + 0Y >= 0 + 0X + 0Y active add(0(), X) -> mark X 1 + 0X >= 0 + 1X active if(false(), X, Y) -> mark Y 1 + 0X + 0Y >= 0 + 1Y active if(true(), X, Y) -> mark X 1 + 0X + 0Y >= 0 + 1X active and(false(), Y) -> mark false() 1 + 0Y >= 1 active and(true(), X) -> mark X 1 + 0X >= 0 + 1X mark from X -> active from X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark first(X1, X2) -> active first(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 2 mark s X -> active s X 0 + 0X >= 1 + 0X mark 0() -> active 0() 0 >= 1 mark add(X1, X2) -> active add(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark if(X1, X2, X3) -> active if(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark false() -> active false() 1 >= 2 mark true() -> active true() 0 >= 1 mark and(X1, X2) -> active and(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 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 and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [if](x0, x1, x2) = x0 + x1 + 1, [and](x0, x1) = x0 + x1 + 1, [add](x0, x1) = x0 + 1, [first](x0, x1) = x0 + 1, [cons](x0, x1) = 1, [mark](x0) = x0 + 1, [active](x0) = x0, [s](x0) = x0 + 1, [from](x0) = 0, [true] = 1, [false] = 0, [0] = 1, [nil] = 0, [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 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 first(active X1, X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(mark X1, X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(X1, active X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(X1, mark X2) -> first(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X add(active X1, X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 add(mark X1, X2) -> add(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 add(X1, active X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 add(X1, mark X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 if(active X1, X2, X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 if(mark X1, X2, X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 if(X1, active X2, X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 if(X1, mark X2, X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 if(X1, X2, active X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 if(X1, X2, mark X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 0X3 >= 1 + 1X1 + 1X2 + 0X3 and(active X1, X2) -> and(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(mark X1, X2) -> and(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(X1, active X2) -> and(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(X1, mark X2) -> and(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active from X -> mark cons(X, from s X) 0 + 0X >= 2 + 0X active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 2 + 0X + 0Y + 0Z >= 2 + 0X + 0Y + 0Z active first(0(), X) -> mark nil() 1 + 1X >= 1 active add(s X, Y) -> mark s add(X, Y) 2 + 1X + 0Y >= 3 + 1X + 0Y active add(0(), X) -> mark X 2 + 0X >= 1 + 1X active if(false(), X, Y) -> mark Y 1 + 1X + 0Y >= 1 + 1Y active if(true(), X, Y) -> mark X 2 + 1X + 0Y >= 1 + 1X active and(false(), Y) -> mark false() 1 + 1Y >= 1 active and(true(), X) -> mark X 2 + 1X >= 1 + 1X mark from X -> active from X 1 + 0X >= 0 + 0X mark cons(X1, X2) -> active cons(X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark first(X1, X2) -> active first(mark X1, mark X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 mark nil() -> active nil() 1 >= 0 mark s X -> active s X 2 + 1X >= 1 + 1X mark 0() -> active 0() 2 >= 1 mark add(X1, X2) -> active add(mark X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark if(X1, X2, X3) -> active if(mark X1, X2, X3) 2 + 1X1 + 1X2 + 0X3 >= 2 + 1X1 + 1X2 + 0X3 mark false() -> active false() 1 >= 0 mark true() -> active true() 2 >= 1 mark and(X1, X2) -> active and(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 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 and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [if](x0, x1, x2) = 0, [and](x0, x1) = 0, [add](x0, x1) = 0, [first](x0, x1) = 0, [cons](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [from](x0) = 0, [true] = 0, [false] = 1, [0] = 0, [nil] = 1, [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 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 s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X add(active X1, X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(mark X1, X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(X1, active X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 add(X1, mark X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 if(active X1, X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(mark X1, X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, active X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, mark X2, X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, X2, active X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 if(X1, X2, mark X3) -> if(X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 0 + 0X1 + 0X2 + 0X3 and(active X1, X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(mark X1, X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(X1, active X2) -> and(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 and(X1, mark X2) -> and(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 active add(s X, Y) -> mark s add(X, Y) 1 + 0X + 0Y >= 0 + 0X + 0Y active add(0(), X) -> mark X 1 + 0X >= 0 + 1X active if(false(), X, Y) -> mark Y 1 + 0X + 0Y >= 0 + 1Y active if(true(), X, Y) -> mark X 1 + 0X + 0Y >= 0 + 1X active and(false(), Y) -> mark false() 1 + 0Y >= 1 active and(true(), X) -> mark X 1 + 0X >= 0 + 1X mark from X -> active from X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark first(X1, X2) -> active first(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 2 mark s X -> active s X 0 + 0X >= 1 + 0X mark 0() -> active 0() 0 >= 1 mark add(X1, X2) -> active add(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark if(X1, X2, X3) -> active if(mark X1, X2, X3) 0 + 0X1 + 0X2 + 0X3 >= 1 + 0X1 + 0X2 + 0X3 mark false() -> active false() 1 >= 2 mark true() -> active true() 0 >= 1 mark and(X1, X2) -> active and(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 SCCS (1): Scc: {first#(X1, mark X2) -> first#(X1, X2)} SCC (1): Strict: {first#(X1, mark X2) -> first#(X1, X2)} Weak: { mark and(X1, X2) -> active and(mark X1, X2), mark true() -> active true(), mark false() -> active false(), mark if(X1, X2, X3) -> active if(mark X1, X2, X3), mark add(X1, X2) -> active add(mark X1, X2), mark 0() -> active 0(), mark s X -> active s X, mark nil() -> active nil(), mark first(X1, X2) -> active first(mark X1, mark X2), mark cons(X1, X2) -> active cons(X1, X2), mark from X -> active from X, active and(true(), X) -> mark X, active and(false(), Y) -> mark false(), active if(true(), X, Y) -> mark X, active if(false(), X, Y) -> mark Y, active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), 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), and(X1, mark X2) -> and(X1, X2), and(X1, active X2) -> and(X1, X2), and(mark X1, X2) -> and(X1, X2), and(active X1, X2) -> and(X1, X2), if(X1, X2, mark X3) -> if(X1, X2, X3), if(X1, X2, active X3) -> if(X1, X2, X3), if(X1, mark X2, X3) -> if(X1, X2, X3), if(X1, active X2, X3) -> if(X1, X2, X3), if(mark X1, X2, X3) -> if(X1, X2, X3), if(active X1, X2, X3) -> if(X1, X2, X3), add(X1, mark X2) -> add(X1, X2), add(X1, active X2) -> add(X1, X2), add(mark X1, X2) -> add(X1, X2), add(active X1, X2) -> add(X1, X2), s mark X -> s X, s active X -> 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), from mark X -> from X, from active X -> from X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [if](x0, x1, x2) = x0 + x1 + x2 + 1, [and](x0, x1) = x0 + x1 + 1, [add](x0, x1) = x0 + 1, [first](x0, x1) = x0 + 1, [cons](x0, x1) = x0 + 1, [mark](x0) = x0 + 1, [active](x0) = x0, [s](x0) = x0 + 1, [from](x0) = 1, [true] = 1, [false] = 0, [0] = 1, [nil] = 0, [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 + 0X >= 1 + 0X from mark X -> from X 1 + 0X >= 1 + 0X cons(active X1, X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 cons(mark X1, X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 cons(X1, active X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 cons(X1, mark X2) -> cons(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(active X1, X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(mark X1, X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(X1, active X2) -> first(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 first(X1, mark X2) -> first(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 s active X -> s X 1 + 1X >= 1 + 1X s mark X -> s X 2 + 1X >= 1 + 1X add(active X1, X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 add(mark X1, X2) -> add(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 add(X1, active X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 add(X1, mark X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 if(active X1, X2, X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(mark X1, X2, X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, active X2, X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, mark X2, X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, X2, active X3) -> if(X1, X2, X3) 1 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 if(X1, X2, mark X3) -> if(X1, X2, X3) 2 + 1X1 + 1X2 + 1X3 >= 1 + 1X1 + 1X2 + 1X3 and(active X1, X2) -> and(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(mark X1, X2) -> and(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(X1, active X2) -> and(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 and(X1, mark X2) -> and(X1, X2) 2 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active from X -> mark cons(X, from s X) 1 + 0X >= 3 + 0X active first(s X, cons(Y, Z)) -> mark cons(Y, first(X, Z)) 2 + 0X + 0Y + 1Z >= 3 + 0X + 0Y + 1Z active first(0(), X) -> mark nil() 1 + 1X >= 1 active add(s X, Y) -> mark s add(X, Y) 2 + 1X + 0Y >= 3 + 1X + 0Y active add(0(), X) -> mark X 2 + 0X >= 1 + 1X active if(false(), X, Y) -> mark Y 1 + 1X + 1Y >= 1 + 1Y active if(true(), X, Y) -> mark X 2 + 1X + 1Y >= 1 + 1X active and(false(), Y) -> mark false() 1 + 1Y >= 1 active and(true(), X) -> mark X 2 + 1X >= 1 + 1X mark from X -> active from X 2 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 mark first(X1, X2) -> active first(mark X1, mark X2) 2 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 mark nil() -> active nil() 1 >= 0 mark s X -> active s X 2 + 1X >= 1 + 1X mark 0() -> active 0() 2 >= 1 mark add(X1, X2) -> active add(mark X1, X2) 2 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark if(X1, X2, X3) -> active if(mark X1, X2, X3) 2 + 1X1 + 1X2 + 1X3 >= 2 + 1X1 + 1X2 + 1X3 mark false() -> active false() 1 >= 0 mark true() -> active true() 2 >= 1 mark and(X1, X2) -> active and(mark X1, X2) 2 + 1X1 + 1X2 >= 2 + 1X1 + 1X2 Qed