YES Time: 1.080696 TRS: { mark nil() -> active nil(), mark fst(X1, X2) -> active fst(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s X, mark from X -> active from mark X, mark add(X1, X2) -> active add(mark X1, mark X2), mark len X -> active len mark X, active fst(0(), Z) -> mark nil(), active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)), active from X -> mark cons(X, from s X), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active len nil() -> mark 0(), active len cons(X, Z) -> mark s len Z, fst(X1, mark X2) -> fst(X1, X2), fst(X1, active X2) -> fst(X1, X2), fst(mark X1, X2) -> fst(X1, X2), fst(active X1, X2) -> fst(X1, X2), cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X, 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), len mark X -> len X, len active X -> len X} DP: DP: { mark# nil() -> active# nil(), mark# fst(X1, X2) -> mark# X1, mark# fst(X1, X2) -> mark# X2, mark# fst(X1, X2) -> active# fst(mark X1, mark X2), mark# fst(X1, X2) -> fst#(mark X1, mark X2), mark# 0() -> active# 0(), mark# cons(X1, X2) -> mark# X1, mark# cons(X1, X2) -> active# cons(mark X1, X2), mark# cons(X1, X2) -> cons#(mark X1, X2), mark# s X -> active# s X, mark# from X -> mark# X, mark# from X -> active# from mark X, mark# from X -> from# mark X, mark# add(X1, X2) -> mark# X1, mark# add(X1, X2) -> mark# X2, mark# add(X1, X2) -> active# add(mark X1, mark X2), mark# add(X1, X2) -> add#(mark X1, mark X2), mark# len X -> mark# X, mark# len X -> active# len mark X, mark# len X -> len# mark X, active# fst(0(), Z) -> mark# nil(), active# fst(s X, cons(Y, Z)) -> mark# cons(Y, fst(X, Z)), active# fst(s X, cons(Y, Z)) -> fst#(X, Z), active# fst(s X, cons(Y, Z)) -> cons#(Y, fst(X, Z)), active# from X -> mark# cons(X, from s X), active# from X -> cons#(X, from s X), active# from X -> s# X, active# from X -> from# s X, active# add(0(), X) -> mark# X, active# add(s X, Y) -> mark# s add(X, Y), active# add(s X, Y) -> s# add(X, Y), active# add(s X, Y) -> add#(X, Y), active# len nil() -> mark# 0(), active# len cons(X, Z) -> mark# s len Z, active# len cons(X, Z) -> s# len Z, active# len cons(X, Z) -> len# Z, fst#(X1, mark X2) -> fst#(X1, X2), fst#(X1, active X2) -> fst#(X1, X2), fst#(mark X1, X2) -> fst#(X1, X2), fst#(active X1, X2) -> fst#(X1, X2), cons#(X1, mark X2) -> cons#(X1, X2), cons#(X1, active X2) -> cons#(X1, X2), cons#(mark X1, X2) -> cons#(X1, X2), cons#(active X1, X2) -> cons#(X1, X2), s# mark X -> s# X, s# active X -> s# X, from# mark X -> from# X, from# active X -> from# X, 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), len# mark X -> len# X, len# active X -> len# X} TRS: { mark nil() -> active nil(), mark fst(X1, X2) -> active fst(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s X, mark from X -> active from mark X, mark add(X1, X2) -> active add(mark X1, mark X2), mark len X -> active len mark X, active fst(0(), Z) -> mark nil(), active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)), active from X -> mark cons(X, from s X), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active len nil() -> mark 0(), active len cons(X, Z) -> mark s len Z, fst(X1, mark X2) -> fst(X1, X2), fst(X1, active X2) -> fst(X1, X2), fst(mark X1, X2) -> fst(X1, X2), fst(active X1, X2) -> fst(X1, X2), cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X, 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), len mark X -> len X, len active X -> len X} UR: { mark nil() -> active nil(), mark fst(X1, X2) -> active fst(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s X, mark from X -> active from mark X, mark add(X1, X2) -> active add(mark X1, mark X2), mark len X -> active len mark X, active fst(0(), Z) -> mark nil(), active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)), active from X -> mark cons(X, from s X), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active len nil() -> mark 0(), active len cons(X, Z) -> mark s len Z, fst(X1, mark X2) -> fst(X1, X2), fst(X1, active X2) -> fst(X1, X2), fst(mark X1, X2) -> fst(X1, X2), fst(active X1, X2) -> fst(X1, X2), cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X, 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), len mark X -> len X, len active X -> len X, a(x, y) -> x, a(x, y) -> y} EDG: { (mark# nil() -> active# nil(), active# len cons(X, Z) -> len# Z) (mark# nil() -> active# nil(), active# len cons(X, Z) -> s# len Z) (mark# nil() -> active# nil(), active# len cons(X, Z) -> mark# s len Z) (mark# nil() -> active# nil(), active# len nil() -> mark# 0()) (mark# nil() -> active# nil(), active# add(s X, Y) -> add#(X, Y)) (mark# nil() -> active# nil(), active# add(s X, Y) -> s# add(X, Y)) (mark# nil() -> active# nil(), active# add(s X, Y) -> mark# s add(X, Y)) (mark# nil() -> active# nil(), active# add(0(), X) -> mark# X) (mark# nil() -> active# nil(), active# from X -> from# s X) (mark# nil() -> active# nil(), active# from X -> s# X) (mark# nil() -> active# nil(), active# from X -> cons#(X, from s X)) (mark# nil() -> active# nil(), active# from X -> mark# cons(X, from s X)) (mark# nil() -> active# nil(), active# fst(s X, cons(Y, Z)) -> cons#(Y, fst(X, Z))) (mark# nil() -> active# nil(), active# fst(s X, cons(Y, Z)) -> fst#(X, Z)) (mark# nil() -> active# nil(), active# fst(s X, cons(Y, Z)) -> mark# cons(Y, fst(X, Z))) (mark# nil() -> active# nil(), active# fst(0(), Z) -> mark# nil()) (active# fst(0(), Z) -> mark# nil(), mark# len X -> len# mark X) (active# fst(0(), Z) -> mark# nil(), mark# len X -> active# len mark X) (active# fst(0(), Z) -> mark# nil(), mark# len X -> mark# X) (active# fst(0(), Z) -> mark# nil(), mark# add(X1, X2) -> add#(mark X1, mark X2)) (active# fst(0(), Z) -> mark# nil(), mark# add(X1, X2) -> active# add(mark X1, mark X2)) (active# fst(0(), Z) -> mark# nil(), mark# add(X1, X2) -> mark# X2) (active# fst(0(), Z) -> mark# nil(), mark# add(X1, X2) -> mark# X1) (active# fst(0(), Z) -> mark# nil(), mark# from X -> from# mark X) (active# fst(0(), Z) -> mark# nil(), mark# from X -> active# from mark X) (active# fst(0(), Z) -> mark# nil(), mark# from X -> mark# X) (active# fst(0(), Z) -> mark# nil(), mark# s X -> active# s X) (active# fst(0(), Z) -> mark# nil(), mark# cons(X1, X2) -> cons#(mark X1, X2)) (active# fst(0(), Z) -> mark# nil(), mark# cons(X1, X2) -> active# cons(mark X1, X2)) (active# fst(0(), Z) -> mark# nil(), mark# cons(X1, X2) -> mark# X1) (active# fst(0(), Z) -> mark# nil(), mark# 0() -> active# 0()) (active# fst(0(), Z) -> mark# nil(), mark# fst(X1, X2) -> fst#(mark X1, mark X2)) (active# fst(0(), Z) -> mark# nil(), mark# fst(X1, X2) -> active# fst(mark X1, mark X2)) (active# fst(0(), Z) -> mark# nil(), mark# fst(X1, X2) -> mark# X2) (active# fst(0(), Z) -> mark# nil(), mark# fst(X1, X2) -> mark# X1) (active# fst(0(), Z) -> mark# nil(), mark# nil() -> active# nil()) (mark# fst(X1, X2) -> fst#(mark X1, mark X2), fst#(active X1, X2) -> fst#(X1, X2)) (mark# fst(X1, X2) -> fst#(mark X1, mark X2), fst#(mark X1, X2) -> fst#(X1, X2)) (mark# fst(X1, X2) -> fst#(mark X1, mark X2), fst#(X1, active X2) -> fst#(X1, X2)) (mark# fst(X1, X2) -> fst#(mark X1, mark X2), fst#(X1, mark X2) -> fst#(X1, X2)) (active# len cons(X, Z) -> len# Z, len# active X -> len# X) (active# len cons(X, Z) -> len# Z, len# mark X -> len# X) (fst#(X1, active X2) -> fst#(X1, X2), fst#(active X1, X2) -> fst#(X1, X2)) (fst#(X1, active X2) -> fst#(X1, X2), fst#(mark X1, X2) -> fst#(X1, X2)) (fst#(X1, active X2) -> fst#(X1, X2), fst#(X1, active X2) -> fst#(X1, X2)) (fst#(X1, active X2) -> fst#(X1, X2), fst#(X1, mark X2) -> fst#(X1, X2)) (fst#(active X1, X2) -> fst#(X1, X2), fst#(active X1, X2) -> fst#(X1, X2)) (fst#(active X1, X2) -> fst#(X1, X2), fst#(mark X1, X2) -> fst#(X1, X2)) (fst#(active X1, X2) -> fst#(X1, X2), fst#(X1, active X2) -> fst#(X1, X2)) (fst#(active X1, X2) -> fst#(X1, X2), fst#(X1, mark X2) -> fst#(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)) (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)) (mark# fst(X1, X2) -> mark# X2, mark# len X -> len# mark X) (mark# fst(X1, X2) -> mark# X2, mark# len X -> active# len mark X) (mark# fst(X1, X2) -> mark# X2, mark# len X -> mark# X) (mark# fst(X1, X2) -> mark# X2, mark# add(X1, X2) -> add#(mark X1, mark X2)) (mark# fst(X1, X2) -> mark# X2, mark# add(X1, X2) -> active# add(mark X1, mark X2)) (mark# fst(X1, X2) -> mark# X2, mark# add(X1, X2) -> mark# X2) (mark# fst(X1, X2) -> mark# X2, mark# add(X1, X2) -> mark# X1) (mark# fst(X1, X2) -> mark# X2, mark# from X -> from# mark X) (mark# fst(X1, X2) -> mark# X2, mark# from X -> active# from mark X) (mark# fst(X1, X2) -> mark# X2, mark# from X -> mark# X) (mark# fst(X1, X2) -> mark# X2, mark# s X -> active# s X) (mark# fst(X1, X2) -> mark# X2, mark# cons(X1, X2) -> cons#(mark X1, X2)) (mark# fst(X1, X2) -> mark# X2, mark# cons(X1, X2) -> active# cons(mark X1, X2)) (mark# fst(X1, X2) -> mark# X2, mark# cons(X1, X2) -> mark# X1) (mark# fst(X1, X2) -> mark# X2, mark# 0() -> active# 0()) (mark# fst(X1, X2) -> mark# X2, mark# fst(X1, X2) -> fst#(mark X1, mark X2)) (mark# fst(X1, X2) -> mark# X2, mark# fst(X1, X2) -> active# fst(mark X1, mark X2)) (mark# fst(X1, X2) -> mark# X2, mark# fst(X1, X2) -> mark# X2) (mark# fst(X1, X2) -> mark# X2, mark# fst(X1, X2) -> mark# X1) (mark# fst(X1, X2) -> mark# X2, mark# nil() -> active# nil()) (active# fst(s X, cons(Y, Z)) -> mark# cons(Y, fst(X, Z)), mark# len X -> len# mark X) (active# fst(s X, cons(Y, Z)) -> mark# cons(Y, fst(X, Z)), mark# len X -> active# len mark X) (active# fst(s X, cons(Y, Z)) -> mark# cons(Y, fst(X, Z)), mark# len X -> mark# X) (active# fst(s X, cons(Y, Z)) -> mark# cons(Y, fst(X, Z)), mark# add(X1, X2) -> add#(mark X1, mark X2)) (active# fst(s X, cons(Y, Z)) -> mark# cons(Y, fst(X, Z)), mark# add(X1, X2) -> active# add(mark X1, mark X2)) (active# fst(s X, cons(Y, Z)) -> mark# cons(Y, fst(X, Z)), mark# add(X1, X2) -> mark# X2) (active# fst(s X, cons(Y, Z)) -> mark# cons(Y, fst(X, Z)), mark# add(X1, X2) -> mark# X1) (active# fst(s X, cons(Y, Z)) -> mark# cons(Y, fst(X, Z)), mark# from X -> from# mark X) (active# fst(s X, cons(Y, Z)) -> mark# cons(Y, fst(X, Z)), mark# from X -> active# from mark X) (active# fst(s X, cons(Y, Z)) -> mark# cons(Y, fst(X, Z)), mark# from X -> mark# X) (active# fst(s X, cons(Y, Z)) -> mark# cons(Y, fst(X, Z)), mark# s X -> active# s X) (active# fst(s X, cons(Y, Z)) -> mark# cons(Y, fst(X, Z)), mark# cons(X1, X2) -> cons#(mark X1, X2)) (active# fst(s X, cons(Y, Z)) -> mark# cons(Y, fst(X, Z)), mark# cons(X1, X2) -> active# cons(mark X1, X2)) (active# fst(s X, cons(Y, Z)) -> mark# cons(Y, fst(X, Z)), mark# cons(X1, X2) -> mark# X1) (active# fst(s X, cons(Y, Z)) -> mark# cons(Y, fst(X, Z)), mark# 0() -> active# 0()) (active# fst(s X, cons(Y, Z)) -> mark# cons(Y, fst(X, Z)), mark# fst(X1, X2) -> fst#(mark X1, mark X2)) (active# fst(s X, cons(Y, Z)) -> mark# cons(Y, fst(X, Z)), mark# fst(X1, X2) -> active# fst(mark X1, mark X2)) (active# fst(s X, cons(Y, Z)) -> mark# cons(Y, fst(X, Z)), mark# fst(X1, X2) -> mark# X2) (active# fst(s X, cons(Y, Z)) -> mark# cons(Y, fst(X, Z)), mark# fst(X1, X2) -> mark# X1) (active# fst(s X, cons(Y, Z)) -> mark# cons(Y, fst(X, Z)), mark# nil() -> active# nil()) (active# add(s X, Y) -> s# add(X, Y), s# active X -> s# X) (active# add(s X, Y) -> s# add(X, Y), s# mark X -> s# X) (mark# from X -> active# from mark X, active# len cons(X, Z) -> len# Z) (mark# from X -> active# from mark X, active# len cons(X, Z) -> s# len Z) (mark# from X -> active# from mark X, active# len cons(X, Z) -> mark# s len Z) (mark# from X -> active# from mark X, active# len nil() -> mark# 0()) (mark# from X -> active# from mark X, active# add(s X, Y) -> add#(X, Y)) (mark# from X -> active# from mark X, active# add(s X, Y) -> s# add(X, Y)) (mark# from X -> active# from mark X, active# add(s X, Y) -> mark# s add(X, Y)) (mark# from X -> active# from mark X, active# add(0(), X) -> mark# X) (mark# from X -> active# from mark X, active# from X -> from# s X) (mark# from X -> active# from mark X, active# from X -> s# X) (mark# from X -> active# from mark X, active# from X -> cons#(X, from s X)) (mark# from X -> active# from mark X, active# from X -> mark# cons(X, from s X)) (mark# from X -> active# from mark X, active# fst(s X, cons(Y, Z)) -> cons#(Y, fst(X, Z))) (mark# from X -> active# from mark X, active# fst(s X, cons(Y, Z)) -> fst#(X, Z)) (mark# from X -> active# from mark X, active# fst(s X, cons(Y, Z)) -> mark# cons(Y, fst(X, Z))) (mark# from X -> active# from mark X, active# fst(0(), Z) -> mark# nil()) (active# add(s X, Y) -> mark# s add(X, Y), mark# len X -> len# mark X) (active# add(s X, Y) -> mark# s add(X, Y), mark# len X -> active# len mark X) (active# add(s X, Y) -> mark# s add(X, Y), mark# len X -> mark# X) (active# add(s X, Y) -> mark# s add(X, Y), mark# add(X1, X2) -> add#(mark X1, mark X2)) (active# add(s X, Y) -> mark# s add(X, Y), mark# add(X1, X2) -> active# add(mark X1, mark X2)) (active# add(s X, Y) -> mark# s add(X, Y), mark# add(X1, X2) -> mark# 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# from X -> from# mark X) (active# add(s X, Y) -> mark# s add(X, Y), mark# from X -> active# from mark X) (active# add(s X, Y) -> mark# s add(X, Y), mark# from X -> mark# X) (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# cons(X1, X2) -> cons#(mark X1, X2)) (active# add(s X, Y) -> mark# s add(X, Y), mark# cons(X1, X2) -> active# cons(mark X1, X2)) (active# add(s X, Y) -> mark# s add(X, Y), mark# cons(X1, X2) -> mark# X1) (active# add(s X, Y) -> mark# s add(X, Y), mark# 0() -> active# 0()) (active# add(s X, Y) -> mark# s add(X, Y), mark# fst(X1, X2) -> fst#(mark X1, mark X2)) (active# add(s X, Y) -> mark# s add(X, Y), mark# fst(X1, X2) -> active# fst(mark X1, mark X2)) (active# add(s X, Y) -> mark# s add(X, Y), mark# fst(X1, X2) -> mark# X2) (active# add(s X, Y) -> mark# s add(X, Y), mark# fst(X1, X2) -> mark# X1) (active# add(s X, Y) -> mark# s add(X, Y), mark# nil() -> active# nil()) (active# fst(s X, cons(Y, Z)) -> fst#(X, Z), fst#(active X1, X2) -> fst#(X1, X2)) (active# fst(s X, cons(Y, Z)) -> fst#(X, Z), fst#(mark X1, X2) -> fst#(X1, X2)) (active# fst(s X, cons(Y, Z)) -> fst#(X, Z), fst#(X1, active X2) -> fst#(X1, X2)) (active# fst(s X, cons(Y, Z)) -> fst#(X, Z), fst#(X1, mark X2) -> fst#(X1, X2)) (mark# from X -> mark# X, mark# len X -> len# mark X) (mark# from X -> mark# X, mark# len X -> active# len mark X) (mark# from X -> mark# X, mark# len X -> mark# X) (mark# from X -> mark# X, mark# add(X1, X2) -> add#(mark X1, mark X2)) (mark# from X -> mark# X, mark# add(X1, X2) -> active# add(mark X1, mark X2)) (mark# from X -> mark# X, mark# add(X1, X2) -> mark# X2) (mark# from X -> mark# X, mark# add(X1, X2) -> mark# X1) 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-> mark# X2) (mark# add(X1, X2) -> mark# X1, mark# fst(X1, X2) -> mark# X1) (mark# add(X1, X2) -> mark# X1, mark# nil() -> active# nil()) (mark# cons(X1, X2) -> mark# X1, mark# nil() -> active# nil()) (mark# cons(X1, X2) -> mark# X1, mark# fst(X1, X2) -> mark# X1) (mark# cons(X1, X2) -> mark# X1, mark# fst(X1, X2) -> mark# X2) (mark# cons(X1, X2) -> mark# X1, mark# fst(X1, X2) -> active# fst(mark X1, mark X2)) (mark# cons(X1, X2) -> mark# X1, mark# fst(X1, X2) -> fst#(mark X1, mark X2)) (mark# cons(X1, X2) -> mark# X1, mark# 0() -> active# 0()) (mark# cons(X1, X2) -> mark# X1, mark# cons(X1, X2) -> mark# X1) (mark# cons(X1, X2) -> mark# X1, mark# cons(X1, X2) -> active# cons(mark X1, X2)) (mark# cons(X1, X2) -> mark# X1, mark# cons(X1, X2) -> cons#(mark X1, X2)) (mark# cons(X1, X2) -> mark# X1, mark# s X -> active# s X) (mark# cons(X1, X2) -> mark# X1, mark# from X -> mark# X) (mark# cons(X1, X2) -> mark# X1, mark# from X -> active# from mark X) (mark# cons(X1, X2) -> mark# X1, mark# 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X, mark# len X -> active# len mark X) (mark# len X -> mark# X, mark# len X -> len# mark X) (active# from X -> cons#(X, from s X), cons#(X1, mark X2) -> cons#(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#(mark X1, X2) -> cons#(X1, X2)) (active# from X -> cons#(X, from s X), cons#(active X1, X2) -> cons#(X1, X2)) (active# len cons(X, Z) -> mark# s len Z, mark# nil() -> active# nil()) (active# len cons(X, Z) -> mark# s len Z, mark# fst(X1, X2) -> mark# X1) (active# len cons(X, Z) -> mark# s len Z, mark# fst(X1, X2) -> mark# X2) (active# len cons(X, Z) -> mark# s len Z, mark# fst(X1, X2) -> active# fst(mark X1, mark X2)) (active# len cons(X, Z) -> mark# s len Z, mark# fst(X1, X2) -> fst#(mark X1, mark X2)) (active# len cons(X, Z) -> mark# s len Z, mark# 0() -> active# 0()) (active# len cons(X, Z) -> mark# s len Z, mark# cons(X1, X2) -> mark# X1) (active# len cons(X, Z) -> mark# s len Z, mark# cons(X1, X2) -> active# cons(mark X1, X2)) (active# len cons(X, Z) -> mark# s len Z, mark# cons(X1, X2) -> cons#(mark X1, X2)) (active# len cons(X, Z) -> mark# s len Z, mark# s X -> active# s X) (active# len cons(X, Z) -> mark# s len Z, mark# from X -> mark# X) (active# len cons(X, Z) -> mark# s len Z, mark# from X -> active# from mark X) (active# len cons(X, Z) -> mark# s len Z, mark# from X -> from# mark X) (active# len cons(X, Z) -> mark# s len Z, mark# add(X1, X2) -> mark# X1) (active# len cons(X, Z) -> mark# s len Z, mark# add(X1, X2) -> mark# X2) (active# len cons(X, Z) -> mark# s len Z, mark# add(X1, X2) -> active# add(mark X1, mark X2)) (active# len cons(X, Z) -> mark# s len Z, mark# add(X1, X2) -> add#(mark X1, mark X2)) (active# len cons(X, Z) -> mark# s len Z, mark# len X -> mark# X) (active# len cons(X, Z) -> mark# s len Z, mark# len X -> active# len mark X) (active# len cons(X, Z) -> mark# s len Z, mark# len X -> len# mark X) (mark# len X -> active# len mark X, active# fst(0(), Z) -> mark# nil()) (mark# len X -> active# len mark X, active# fst(s X, cons(Y, Z)) -> mark# cons(Y, fst(X, Z))) (mark# len X -> active# len mark X, active# fst(s X, cons(Y, Z)) -> fst#(X, Z)) (mark# len X -> active# len mark X, active# fst(s X, cons(Y, Z)) -> cons#(Y, fst(X, Z))) (mark# len X -> active# len mark X, active# from X -> mark# cons(X, from s X)) (mark# len X -> active# len mark X, active# from X -> cons#(X, from s X)) (mark# len X -> active# len mark X, active# from X -> s# X) (mark# len X -> active# len mark X, active# from X -> from# s X) (mark# len X -> active# len mark X, active# add(0(), X) -> mark# X) (mark# len X -> active# len mark X, active# add(s X, Y) -> mark# s add(X, Y)) (mark# len X -> active# len mark X, active# add(s X, Y) -> s# add(X, Y)) (mark# len X -> active# len mark X, active# add(s X, Y) -> add#(X, Y)) (mark# len X -> active# len mark X, active# len nil() -> mark# 0()) (mark# len X -> active# len mark X, active# len cons(X, Z) -> mark# s len Z) (mark# len X -> active# len mark X, active# len cons(X, Z) -> s# len Z) (mark# len X -> active# len mark X, active# len cons(X, Z) -> len# Z) (active# fst(s X, cons(Y, Z)) -> cons#(Y, fst(X, Z)), cons#(X1, mark X2) -> cons#(X1, X2)) (active# fst(s X, cons(Y, Z)) -> cons#(Y, fst(X, Z)), cons#(X1, active X2) -> cons#(X1, X2)) (active# fst(s X, cons(Y, Z)) -> cons#(Y, fst(X, Z)), cons#(mark X1, X2) -> cons#(X1, X2)) (active# fst(s X, cons(Y, Z)) -> cons#(Y, fst(X, Z)), cons#(active X1, X2) -> cons#(X1, X2)) (mark# cons(X1, X2) -> active# cons(mark X1, X2), active# fst(0(), Z) -> mark# nil()) (mark# cons(X1, X2) -> active# cons(mark X1, X2), active# fst(s X, cons(Y, Z)) -> mark# cons(Y, fst(X, Z))) (mark# cons(X1, X2) -> active# cons(mark X1, X2), active# fst(s X, cons(Y, Z)) -> fst#(X, Z)) (mark# cons(X1, X2) -> active# cons(mark X1, X2), active# fst(s X, cons(Y, Z)) -> cons#(Y, fst(X, Z))) (mark# cons(X1, X2) -> active# cons(mark X1, X2), active# from X -> mark# cons(X, from s X)) (mark# cons(X1, X2) -> active# cons(mark X1, X2), active# from X -> cons#(X, from s X)) (mark# cons(X1, X2) -> active# cons(mark X1, X2), active# from X -> s# X) (mark# cons(X1, X2) -> active# cons(mark X1, X2), active# from X -> from# s X) (mark# cons(X1, X2) -> active# cons(mark X1, X2), active# add(0(), X) -> mark# X) (mark# cons(X1, X2) -> active# cons(mark X1, X2), active# add(s X, Y) -> mark# s add(X, Y)) (mark# cons(X1, X2) -> active# cons(mark X1, X2), active# add(s X, Y) -> s# add(X, Y)) (mark# cons(X1, X2) -> active# cons(mark X1, X2), active# add(s X, Y) -> add#(X, Y)) (mark# cons(X1, X2) -> active# cons(mark X1, X2), active# len nil() -> mark# 0()) (mark# cons(X1, X2) -> active# cons(mark X1, X2), active# len cons(X, Z) -> mark# s len Z) (mark# cons(X1, X2) -> active# cons(mark X1, X2), active# len cons(X, Z) -> s# len Z) (mark# cons(X1, X2) -> active# cons(mark X1, X2), active# len cons(X, Z) -> len# Z) (mark# add(X1, X2) -> mark# X2, mark# nil() -> active# nil()) (mark# add(X1, X2) -> mark# X2, mark# fst(X1, X2) -> mark# X1) (mark# add(X1, X2) -> mark# X2, mark# fst(X1, X2) -> mark# X2) (mark# add(X1, X2) -> mark# X2, mark# fst(X1, X2) -> active# fst(mark X1, mark X2)) (mark# add(X1, X2) -> mark# X2, mark# fst(X1, X2) -> fst#(mark X1, mark X2)) (mark# add(X1, X2) -> mark# X2, mark# 0() -> active# 0()) (mark# add(X1, X2) -> mark# X2, mark# cons(X1, X2) -> mark# X1) (mark# add(X1, X2) -> mark# X2, mark# cons(X1, X2) -> active# cons(mark X1, X2)) (mark# add(X1, X2) -> mark# X2, mark# cons(X1, X2) -> cons#(mark X1, X2)) (mark# add(X1, X2) -> mark# X2, mark# s X -> active# s X) (mark# add(X1, X2) -> mark# X2, mark# from X -> mark# X) (mark# add(X1, X2) -> mark# X2, mark# from X -> active# from mark X) (mark# add(X1, X2) -> mark# X2, mark# from X -> from# mark X) (mark# add(X1, X2) -> mark# X2, mark# add(X1, X2) -> mark# X1) (mark# add(X1, X2) -> mark# X2, mark# add(X1, X2) -> mark# X2) (mark# add(X1, X2) -> mark# X2, mark# add(X1, X2) -> active# add(mark X1, mark X2)) (mark# add(X1, X2) -> mark# X2, mark# add(X1, X2) -> add#(mark X1, mark X2)) (mark# add(X1, X2) -> mark# X2, mark# len X -> mark# X) (mark# add(X1, X2) -> mark# X2, mark# len X -> active# len mark X) (mark# add(X1, X2) -> mark# X2, mark# len X -> len# mark X) (active# add(s X, Y) -> add#(X, Y), add#(X1, mark X2) -> add#(X1, X2)) (active# add(s X, Y) -> add#(X, Y), add#(X1, active X2) -> add#(X1, X2)) (active# add(s X, Y) -> add#(X, Y), add#(mark X1, X2) -> add#(X1, X2)) (active# add(s X, Y) -> add#(X, Y), add#(active X1, X2) -> add#(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)) (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)) (fst#(mark X1, X2) -> fst#(X1, X2), fst#(X1, mark X2) -> fst#(X1, X2)) (fst#(mark X1, X2) -> fst#(X1, X2), fst#(X1, active X2) -> fst#(X1, X2)) (fst#(mark X1, X2) -> fst#(X1, X2), fst#(mark X1, X2) -> fst#(X1, X2)) (fst#(mark X1, X2) -> fst#(X1, X2), fst#(active X1, X2) -> fst#(X1, X2)) (fst#(X1, mark X2) -> fst#(X1, X2), fst#(X1, mark X2) -> fst#(X1, X2)) (fst#(X1, mark X2) -> fst#(X1, X2), fst#(X1, active X2) -> fst#(X1, X2)) (fst#(X1, mark X2) -> fst#(X1, X2), fst#(mark X1, X2) -> fst#(X1, X2)) (fst#(X1, mark X2) -> fst#(X1, X2), fst#(active X1, X2) -> fst#(X1, X2)) (mark# add(X1, X2) -> add#(mark X1, mark X2), add#(X1, mark X2) -> add#(X1, X2)) (mark# add(X1, X2) -> add#(mark X1, mark X2), add#(X1, active X2) -> add#(X1, X2)) (mark# add(X1, X2) -> add#(mark X1, mark X2), add#(mark X1, X2) -> add#(X1, X2)) (mark# add(X1, X2) -> add#(mark X1, mark X2), add#(active X1, X2) -> add#(X1, X2)) (active# len nil() -> mark# 0(), mark# nil() -> active# nil()) (active# len nil() -> mark# 0(), mark# fst(X1, X2) -> mark# X1) (active# len nil() -> mark# 0(), mark# fst(X1, X2) -> mark# X2) (active# len nil() -> mark# 0(), mark# fst(X1, X2) -> active# fst(mark X1, mark X2)) (active# len nil() -> mark# 0(), mark# fst(X1, X2) -> fst#(mark X1, mark X2)) (active# len nil() -> mark# 0(), mark# 0() -> active# 0()) (active# len nil() -> mark# 0(), mark# cons(X1, X2) -> mark# X1) (active# len nil() -> mark# 0(), mark# cons(X1, X2) -> active# cons(mark X1, X2)) (active# len nil() -> mark# 0(), mark# cons(X1, X2) -> cons#(mark X1, X2)) (active# len nil() -> mark# 0(), mark# s X -> active# s X) (active# len nil() -> mark# 0(), mark# from X -> mark# X) (active# len nil() -> mark# 0(), mark# from X -> active# from mark X) (active# len nil() -> mark# 0(), mark# from X -> from# mark X) (active# len nil() -> mark# 0(), mark# add(X1, X2) -> mark# X1) (active# len nil() -> mark# 0(), mark# add(X1, X2) -> mark# X2) (active# len nil() -> mark# 0(), mark# add(X1, X2) -> active# add(mark X1, mark X2)) (active# len nil() -> mark# 0(), mark# add(X1, X2) -> add#(mark X1, mark X2)) (active# len nil() -> mark# 0(), mark# len X -> mark# X) (active# len nil() -> mark# 0(), mark# len X -> active# len mark X) (active# len nil() -> mark# 0(), mark# len X -> len# mark X) (mark# 0() -> active# 0(), active# fst(0(), Z) -> mark# nil()) (mark# 0() -> active# 0(), active# fst(s X, cons(Y, Z)) -> mark# cons(Y, fst(X, Z))) (mark# 0() -> active# 0(), active# fst(s X, cons(Y, Z)) -> fst#(X, Z)) (mark# 0() -> active# 0(), active# fst(s X, cons(Y, Z)) -> cons#(Y, fst(X, Z))) (mark# 0() -> active# 0(), active# from X -> mark# cons(X, from s X)) (mark# 0() -> active# 0(), active# from X -> cons#(X, from s X)) (mark# 0() -> active# 0(), active# from X -> s# X) (mark# 0() -> active# 0(), active# from X -> from# s X) (mark# 0() -> active# 0(), active# add(0(), X) -> mark# X) (mark# 0() -> active# 0(), active# add(s X, Y) -> mark# s add(X, Y)) (mark# 0() -> active# 0(), active# add(s X, Y) -> s# add(X, Y)) (mark# 0() -> active# 0(), active# add(s X, Y) -> add#(X, Y)) (mark# 0() -> active# 0(), active# len nil() -> mark# 0()) (mark# 0() -> active# 0(), active# len cons(X, Z) -> mark# s len Z) (mark# 0() -> active# 0(), active# len cons(X, Z) -> s# len Z) (mark# 0() -> active# 0(), active# len cons(X, Z) -> len# Z) (mark# cons(X1, X2) -> cons#(mark X1, X2), cons#(X1, mark X2) -> cons#(X1, X2)) (mark# cons(X1, X2) -> cons#(mark X1, X2), cons#(X1, active X2) -> cons#(X1, X2)) (mark# cons(X1, X2) -> cons#(mark X1, X2), cons#(mark X1, X2) -> cons#(X1, X2)) (mark# cons(X1, X2) -> cons#(mark X1, X2), cons#(active X1, X2) -> cons#(X1, X2)) } STATUS: arrows: 0.825103 SCCS (7): Scc: { mark# nil() -> active# nil(), mark# fst(X1, X2) -> mark# X1, mark# fst(X1, X2) -> mark# X2, mark# fst(X1, X2) -> active# fst(mark X1, mark X2), mark# 0() -> active# 0(), mark# cons(X1, X2) -> mark# X1, mark# cons(X1, X2) -> active# cons(mark X1, X2), mark# s X -> active# s X, mark# from X -> mark# X, mark# from X -> active# from mark X, mark# add(X1, X2) -> mark# X1, mark# add(X1, X2) -> mark# X2, mark# add(X1, X2) -> active# add(mark X1, mark X2), mark# len X -> mark# X, mark# len X -> active# len mark X, active# fst(0(), Z) -> mark# nil(), active# fst(s X, cons(Y, Z)) -> mark# cons(Y, fst(X, Z)), active# from X -> mark# cons(X, from s X), active# add(0(), X) -> mark# X, active# add(s X, Y) -> mark# s add(X, Y), active# len nil() -> mark# 0(), active# len cons(X, Z) -> mark# s len Z} Scc: { len# mark X -> len# X, len# active X -> len# 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: { from# mark X -> from# X, from# active X -> from# X} Scc: { s# mark X -> s# X, s# active X -> s# X} Scc: { fst#(X1, mark X2) -> fst#(X1, X2), fst#(X1, active X2) -> fst#(X1, X2), fst#(mark X1, X2) -> fst#(X1, X2), fst#(active X1, X2) -> fst#(X1, X2)} Scc: { cons#(X1, mark X2) -> cons#(X1, X2), cons#(X1, active X2) -> cons#(X1, X2), cons#(mark X1, X2) -> cons#(X1, X2), cons#(active X1, X2) -> cons#(X1, X2)} SCC (22): Strict: { mark# nil() -> active# nil(), mark# fst(X1, X2) -> mark# X1, mark# fst(X1, X2) -> mark# X2, mark# fst(X1, X2) -> active# fst(mark X1, mark X2), mark# 0() -> active# 0(), mark# cons(X1, X2) -> mark# X1, mark# cons(X1, X2) -> active# cons(mark X1, X2), mark# s X -> active# s X, mark# from X -> mark# X, mark# from X -> active# from mark X, mark# add(X1, X2) -> mark# X1, mark# add(X1, X2) -> mark# X2, mark# add(X1, X2) -> active# add(mark X1, mark X2), mark# len X -> mark# X, mark# len X -> active# len mark X, active# fst(0(), Z) -> mark# nil(), active# fst(s X, cons(Y, Z)) -> mark# cons(Y, fst(X, Z)), active# from X -> mark# cons(X, from s X), active# add(0(), X) -> mark# X, active# add(s X, Y) -> mark# s add(X, Y), active# len nil() -> mark# 0(), active# len cons(X, Z) -> mark# s len Z} Weak: { mark nil() -> active nil(), mark fst(X1, X2) -> active fst(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s X, mark from X -> active from mark X, mark add(X1, X2) -> active add(mark X1, mark X2), mark len X -> active len mark X, active fst(0(), Z) -> mark nil(), active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)), active from X -> mark cons(X, from s X), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active len nil() -> mark 0(), active len cons(X, Z) -> mark s len Z, fst(X1, mark X2) -> fst(X1, X2), fst(X1, active X2) -> fst(X1, X2), fst(mark X1, X2) -> fst(X1, X2), fst(active X1, X2) -> fst(X1, X2), cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X, 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), len mark X -> len X, len active X -> len X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [fst](x0, x1) = x0 + x1 + 1, [cons](x0, x1) = x0 + 1, [add](x0, x1) = x0 + x1, [mark](x0) = x0, [active](x0) = x0, [s](x0) = 0, [from](x0) = x0 + 1, [len](x0) = x0 + 1, [nil] = 1, [0] = 0, [mark#](x0) = x0, [active#](x0) = x0 Strict: active# len cons(X, Z) -> mark# s len Z 2 + 0Z + 1X >= 0 + 0Z active# len nil() -> mark# 0() 2 >= 0 active# add(s X, Y) -> mark# s add(X, Y) 0 + 1Y + 0X >= 0 + 0Y + 0X active# add(0(), X) -> mark# X 0 + 1X >= 0 + 1X active# from X -> mark# cons(X, from s X) 1 + 1X >= 1 + 1X active# fst(s X, cons(Y, Z)) -> mark# cons(Y, fst(X, Z)) 2 + 0Z + 1Y + 0X >= 1 + 0Z + 1Y + 0X active# fst(0(), Z) -> mark# nil() 1 + 1Z >= 1 mark# len X -> active# len mark X 1 + 1X >= 1 + 1X mark# len X -> mark# X 1 + 1X >= 0 + 1X mark# add(X1, X2) -> active# add(mark X1, mark X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 mark# add(X1, X2) -> mark# X2 0 + 1X1 + 1X2 >= 0 + 1X2 mark# add(X1, X2) -> mark# X1 0 + 1X1 + 1X2 >= 0 + 1X1 mark# from X -> active# from mark X 1 + 1X >= 1 + 1X mark# from X -> mark# X 1 + 1X >= 0 + 1X mark# s X -> active# s X 0 + 0X >= 0 + 0X mark# cons(X1, X2) -> active# cons(mark X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 mark# cons(X1, X2) -> mark# X1 1 + 1X1 + 0X2 >= 0 + 1X1 mark# 0() -> active# 0() 0 >= 0 mark# fst(X1, X2) -> active# fst(mark X1, mark X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 mark# fst(X1, X2) -> mark# X2 1 + 1X1 + 1X2 >= 0 + 1X2 mark# fst(X1, X2) -> mark# X1 1 + 1X1 + 1X2 >= 0 + 1X1 mark# nil() -> active# nil() 1 >= 1 Weak: len active X -> len X 1 + 1X >= 1 + 1X len mark X -> len 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 from active X -> from X 1 + 1X >= 1 + 1X from mark X -> from X 1 + 1X >= 1 + 1X s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X cons(active X1, X2) -> cons(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 cons(mark X1, X2) -> cons(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 cons(X1, active X2) -> cons(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 cons(X1, mark X2) -> cons(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 fst(active X1, X2) -> fst(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 fst(mark X1, X2) -> fst(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 fst(X1, active X2) -> fst(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 fst(X1, mark X2) -> fst(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 active len cons(X, Z) -> mark s len Z 2 + 0Z + 1X >= 0 + 0Z active len nil() -> mark 0() 2 >= 0 active add(s X, Y) -> mark s add(X, Y) 0 + 1Y + 0X >= 0 + 0Y + 0X active add(0(), X) -> mark X 0 + 1X >= 0 + 1X active from X -> mark cons(X, from s X) 1 + 1X >= 1 + 1X active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)) 2 + 0Z + 1Y + 0X >= 1 + 0Z + 1Y + 0X active fst(0(), Z) -> mark nil() 1 + 1Z >= 1 mark len X -> active len mark X 1 + 1X >= 1 + 1X mark add(X1, X2) -> active add(mark X1, mark X2) 0 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 mark from X -> active from mark X 1 + 1X >= 1 + 1X mark s X -> active s X 0 + 0X >= 0 + 0X mark cons(X1, X2) -> active cons(mark X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 mark 0() -> active 0() 0 >= 0 mark fst(X1, X2) -> active fst(mark X1, mark X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 mark nil() -> active nil() 1 >= 1 SCCS (1): Scc: { mark# nil() -> active# nil(), mark# fst(X1, X2) -> active# fst(mark X1, mark X2), mark# 0() -> active# 0(), mark# cons(X1, X2) -> active# cons(mark X1, X2), mark# s X -> active# s X, mark# from X -> active# from mark X, mark# add(X1, X2) -> mark# X1, mark# add(X1, X2) -> mark# X2, mark# add(X1, X2) -> active# add(mark X1, mark X2), mark# len X -> active# len mark X, active# fst(0(), Z) -> mark# nil(), active# from X -> mark# cons(X, from s X), active# add(0(), X) -> mark# X, active# add(s X, Y) -> mark# s add(X, Y)} SCC (14): Strict: { mark# nil() -> active# nil(), mark# fst(X1, X2) -> active# fst(mark X1, mark X2), mark# 0() -> active# 0(), mark# cons(X1, X2) -> active# cons(mark X1, X2), mark# s X -> active# s X, mark# from X -> active# from mark X, mark# add(X1, X2) -> mark# X1, mark# add(X1, X2) -> mark# X2, mark# add(X1, X2) -> active# add(mark X1, mark X2), mark# len X -> active# len mark X, active# fst(0(), Z) -> mark# nil(), active# from X -> mark# cons(X, from s X), active# add(0(), X) -> mark# X, active# add(s X, Y) -> mark# s add(X, Y)} Weak: { mark nil() -> active nil(), mark fst(X1, X2) -> active fst(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s X, mark from X -> active from mark X, mark add(X1, X2) -> active add(mark X1, mark X2), mark len X -> active len mark X, active fst(0(), Z) -> mark nil(), active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)), active from X -> mark cons(X, from s X), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active len nil() -> mark 0(), active len cons(X, Z) -> mark s len Z, fst(X1, mark X2) -> fst(X1, X2), fst(X1, active X2) -> fst(X1, X2), fst(mark X1, X2) -> fst(X1, X2), fst(active X1, X2) -> fst(X1, X2), cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X, 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), len mark X -> len X, len active X -> len X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [fst](x0, x1) = 0, [cons](x0, x1) = 0, [add](x0, x1) = x0 + x1 + 1, [mark](x0) = x0, [active](x0) = x0, [s](x0) = 0, [from](x0) = 0, [len](x0) = 0, [nil] = 0, [0] = 0, [mark#](x0) = x0, [active#](x0) = x0 Strict: active# add(s X, Y) -> mark# s add(X, Y) 1 + 1Y + 0X >= 0 + 0Y + 0X active# add(0(), X) -> mark# X 1 + 1X >= 0 + 1X active# from X -> mark# cons(X, from s X) 0 + 0X >= 0 + 0X active# fst(0(), Z) -> mark# nil() 0 + 0Z >= 0 mark# len X -> active# len mark X 0 + 0X >= 0 + 0X mark# add(X1, X2) -> active# add(mark X1, mark X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 mark# add(X1, X2) -> mark# X2 1 + 1X1 + 1X2 >= 0 + 1X2 mark# add(X1, X2) -> mark# X1 1 + 1X1 + 1X2 >= 0 + 1X1 mark# from X -> active# from mark X 0 + 0X >= 0 + 0X mark# s X -> active# s X 0 + 0X >= 0 + 0X mark# cons(X1, X2) -> active# cons(mark X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark# 0() -> active# 0() 0 >= 0 mark# fst(X1, X2) -> active# fst(mark X1, mark X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark# nil() -> active# nil() 0 >= 0 Weak: len active X -> len X 0 + 0X >= 0 + 0X len mark X -> len X 0 + 0X >= 0 + 0X add(active X1, X2) -> add(X1, X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 add(mark X1, X2) -> add(X1, X2) 1 + 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) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 from active X -> from X 0 + 0X >= 0 + 0X from mark X -> from X 0 + 0X >= 0 + 0X s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X cons(active X1, X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(mark X1, X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(X1, active X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(X1, mark X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 fst(active X1, X2) -> fst(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 fst(mark X1, X2) -> fst(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 fst(X1, active X2) -> fst(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 fst(X1, mark X2) -> fst(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active len cons(X, Z) -> mark s len Z 0 + 0Z + 0X >= 0 + 0Z active len nil() -> mark 0() 0 >= 0 active add(s X, Y) -> mark s add(X, Y) 1 + 1Y + 0X >= 0 + 0Y + 0X active add(0(), X) -> mark X 1 + 1X >= 0 + 1X active from X -> mark cons(X, from s X) 0 + 0X >= 0 + 0X active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)) 0 + 0Z + 0Y + 0X >= 0 + 0Z + 0Y + 0X active fst(0(), Z) -> mark nil() 0 + 0Z >= 0 mark len X -> active len mark X 0 + 0X >= 0 + 0X mark add(X1, X2) -> active add(mark X1, mark X2) 1 + 1X1 + 1X2 >= 1 + 1X1 + 1X2 mark from X -> active from mark X 0 + 0X >= 0 + 0X mark s X -> active s X 0 + 0X >= 0 + 0X mark cons(X1, X2) -> active cons(mark X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark 0() -> active 0() 0 >= 0 mark fst(X1, X2) -> active fst(mark X1, mark X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark nil() -> active nil() 0 >= 0 SCCS (1): Scc: { mark# nil() -> active# nil(), mark# fst(X1, X2) -> active# fst(mark X1, mark X2), mark# 0() -> active# 0(), mark# cons(X1, X2) -> active# cons(mark X1, X2), mark# s X -> active# s X, mark# from X -> active# from mark X, mark# add(X1, X2) -> active# add(mark X1, mark X2), mark# len X -> active# len mark X, active# fst(0(), Z) -> mark# nil(), active# from X -> mark# cons(X, from s X)} SCC (10): Strict: { mark# nil() -> active# nil(), mark# fst(X1, X2) -> active# fst(mark X1, mark X2), mark# 0() -> active# 0(), mark# cons(X1, X2) -> active# cons(mark X1, X2), mark# s X -> active# s X, mark# from X -> active# from mark X, mark# add(X1, X2) -> active# add(mark X1, mark X2), mark# len X -> active# len mark X, active# fst(0(), Z) -> mark# nil(), active# from X -> mark# cons(X, from s X)} Weak: { mark nil() -> active nil(), mark fst(X1, X2) -> active fst(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s X, mark from X -> active from mark X, mark add(X1, X2) -> active add(mark X1, mark X2), mark len X -> active len mark X, active fst(0(), Z) -> mark nil(), active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)), active from X -> mark cons(X, from s X), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active len nil() -> mark 0(), active len cons(X, Z) -> mark s len Z, fst(X1, mark X2) -> fst(X1, X2), fst(X1, active X2) -> fst(X1, X2), fst(mark X1, X2) -> fst(X1, X2), fst(active X1, X2) -> fst(X1, X2), cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X, 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), len mark X -> len X, len active X -> len X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [fst](x0, x1) = 0, [cons](x0, x1) = 0, [add](x0, x1) = 0, [mark](x0) = 0, [active](x0) = 0, [s](x0) = 0, [from](x0) = 0, [len](x0) = 1, [nil] = 0, [0] = 0, [mark#](x0) = x0 + 1, [active#](x0) = 1 Strict: active# from X -> mark# cons(X, from s X) 1 + 0X >= 1 + 0X active# fst(0(), Z) -> mark# nil() 1 + 0Z >= 1 mark# len X -> active# len mark X 2 + 0X >= 1 + 0X mark# add(X1, X2) -> active# add(mark X1, mark X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark# from X -> active# from mark X 1 + 0X >= 1 + 0X mark# s X -> active# s X 1 + 0X >= 1 + 0X mark# cons(X1, X2) -> active# cons(mark X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark# 0() -> active# 0() 1 >= 1 mark# fst(X1, X2) -> active# fst(mark X1, mark X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark# nil() -> active# nil() 1 >= 1 Weak: len active X -> len X 1 + 0X >= 1 + 0X len mark X -> len X 1 + 0X >= 1 + 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 from active X -> from X 0 + 0X >= 0 + 0X from mark X -> from X 0 + 0X >= 0 + 0X s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X cons(active X1, X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(mark X1, X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(X1, active X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(X1, mark X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 fst(active X1, X2) -> fst(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 fst(mark X1, X2) -> fst(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 fst(X1, active X2) -> fst(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 fst(X1, mark X2) -> fst(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active len cons(X, Z) -> mark s len Z 0 + 0Z + 0X >= 0 + 0Z active len nil() -> mark 0() 0 >= 0 active add(s X, Y) -> mark s add(X, Y) 0 + 0Y + 0X >= 0 + 0Y + 0X active add(0(), X) -> mark X 0 + 0X >= 0 + 0X active from X -> mark cons(X, from s X) 0 + 0X >= 0 + 0X active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)) 0 + 0Z + 0Y + 0X >= 0 + 0Z + 0Y + 0X active fst(0(), Z) -> mark nil() 0 + 0Z >= 0 mark len X -> active len mark X 0 + 0X >= 0 + 0X mark add(X1, X2) -> active add(mark X1, mark X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark from X -> active from mark X 0 + 0X >= 0 + 0X mark s X -> active s X 0 + 0X >= 0 + 0X mark cons(X1, X2) -> active cons(mark X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark 0() -> active 0() 0 >= 0 mark fst(X1, X2) -> active fst(mark X1, mark X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark nil() -> active nil() 0 >= 0 SCCS (1): Scc: { mark# nil() -> active# nil(), mark# fst(X1, X2) -> active# fst(mark X1, mark X2), mark# 0() -> active# 0(), mark# cons(X1, X2) -> active# cons(mark X1, X2), mark# s X -> active# s X, mark# from X -> active# from mark X, mark# add(X1, X2) -> active# add(mark X1, mark X2), active# fst(0(), Z) -> mark# nil(), active# from X -> mark# cons(X, from s X)} SCC (9): Strict: { mark# nil() -> active# nil(), mark# fst(X1, X2) -> active# fst(mark X1, mark X2), mark# 0() -> active# 0(), mark# cons(X1, X2) -> active# cons(mark X1, X2), mark# s X -> active# s X, mark# from X -> active# from mark X, mark# add(X1, X2) -> active# add(mark X1, mark X2), active# fst(0(), Z) -> mark# nil(), active# from X -> mark# cons(X, from s X)} Weak: { mark nil() -> active nil(), mark fst(X1, X2) -> active fst(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s X, mark from X -> active from mark X, mark add(X1, X2) -> active add(mark X1, mark X2), mark len X -> active len mark X, active fst(0(), Z) -> mark nil(), active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)), active from X -> mark cons(X, from s X), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active len nil() -> mark 0(), active len cons(X, Z) -> mark s len Z, fst(X1, mark X2) -> fst(X1, X2), fst(X1, active X2) -> fst(X1, X2), fst(mark X1, X2) -> fst(X1, X2), fst(active X1, X2) -> fst(X1, X2), cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X, 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), len mark X -> len X, len active X -> len X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [fst](x0, x1) = 0, [cons](x0, x1) = 0, [add](x0, x1) = 0, [mark](x0) = 0, [active](x0) = 0, [s](x0) = 0, [from](x0) = 0, [len](x0) = 0, [nil] = 0, [0] = 1, [mark#](x0) = x0 + 1, [active#](x0) = 1 Strict: active# from X -> mark# cons(X, from s X) 1 + 0X >= 1 + 0X active# fst(0(), Z) -> mark# nil() 1 + 0Z >= 1 mark# add(X1, X2) -> active# add(mark X1, mark X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark# from X -> active# from mark X 1 + 0X >= 1 + 0X mark# s X -> active# s X 1 + 0X >= 1 + 0X mark# cons(X1, X2) -> active# cons(mark X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark# 0() -> active# 0() 2 >= 1 mark# fst(X1, X2) -> active# fst(mark X1, mark X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark# nil() -> active# nil() 1 >= 1 Weak: len active X -> len X 0 + 0X >= 0 + 0X len mark X -> len 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 from active X -> from X 0 + 0X >= 0 + 0X from mark X -> from X 0 + 0X >= 0 + 0X s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X cons(active X1, X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(mark X1, X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(X1, active X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(X1, mark X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 fst(active X1, X2) -> fst(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 fst(mark X1, X2) -> fst(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 fst(X1, active X2) -> fst(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 fst(X1, mark X2) -> fst(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active len cons(X, Z) -> mark s len Z 0 + 0Z + 0X >= 0 + 0Z active len nil() -> mark 0() 0 >= 0 active add(s X, Y) -> mark s add(X, Y) 0 + 0Y + 0X >= 0 + 0Y + 0X active add(0(), X) -> mark X 0 + 0X >= 0 + 0X active from X -> mark cons(X, from s X) 0 + 0X >= 0 + 0X active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)) 0 + 0Z + 0Y + 0X >= 0 + 0Z + 0Y + 0X active fst(0(), Z) -> mark nil() 0 + 0Z >= 0 mark len X -> active len mark X 0 + 0X >= 0 + 0X mark add(X1, X2) -> active add(mark X1, mark X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark from X -> active from mark X 0 + 0X >= 0 + 0X mark s X -> active s X 0 + 0X >= 0 + 0X mark cons(X1, X2) -> active cons(mark X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark 0() -> active 0() 0 >= 0 mark fst(X1, X2) -> active fst(mark X1, mark X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark nil() -> active nil() 0 >= 0 SCCS (1): Scc: { mark# nil() -> active# nil(), mark# fst(X1, X2) -> active# fst(mark X1, mark X2), mark# cons(X1, X2) -> active# cons(mark X1, X2), mark# s X -> active# s X, mark# from X -> active# from mark X, mark# add(X1, X2) -> active# add(mark X1, mark X2), active# fst(0(), Z) -> mark# nil(), active# from X -> mark# cons(X, from s X)} SCC (8): Strict: { mark# nil() -> active# nil(), mark# fst(X1, X2) -> active# fst(mark X1, mark X2), mark# cons(X1, X2) -> active# cons(mark X1, X2), mark# s X -> active# s X, mark# from X -> active# from mark X, mark# add(X1, X2) -> active# add(mark X1, mark X2), active# fst(0(), Z) -> mark# nil(), active# from X -> mark# cons(X, from s X)} Weak: { mark nil() -> active nil(), mark fst(X1, X2) -> active fst(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s X, mark from X -> active from mark X, mark add(X1, X2) -> active add(mark X1, mark X2), mark len X -> active len mark X, active fst(0(), Z) -> mark nil(), active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)), active from X -> mark cons(X, from s X), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active len nil() -> mark 0(), active len cons(X, Z) -> mark s len Z, fst(X1, mark X2) -> fst(X1, X2), fst(X1, active X2) -> fst(X1, X2), fst(mark X1, X2) -> fst(X1, X2), fst(active X1, X2) -> fst(X1, X2), cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X, 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), len mark X -> len X, len active X -> len X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [fst](x0, x1) = 0, [cons](x0, x1) = 0, [add](x0, x1) = x0, [mark](x0) = 1, [active](x0) = 0, [s](x0) = x0 + 1, [from](x0) = 0, [len](x0) = x0 + 1, [nil] = 0, [0] = 0, [mark#](x0) = x0 + 1, [active#](x0) = 1 Strict: active# from X -> mark# cons(X, from s X) 1 + 0X >= 1 + 0X active# fst(0(), Z) -> mark# nil() 1 + 0Z >= 1 mark# add(X1, X2) -> active# add(mark X1, mark X2) 1 + 1X1 + 0X2 >= 1 + 0X1 + 0X2 mark# from X -> active# from mark X 1 + 0X >= 1 + 0X mark# s X -> active# s X 2 + 1X >= 1 + 0X mark# cons(X1, X2) -> active# cons(mark X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark# fst(X1, X2) -> active# fst(mark X1, mark X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark# nil() -> active# nil() 1 >= 1 Weak: len active X -> len X 1 + 0X >= 1 + 1X len mark X -> len X 2 + 0X >= 1 + 1X add(active X1, X2) -> add(X1, X2) 0 + 0X1 + 0X2 >= 0 + 1X1 + 0X2 add(mark X1, X2) -> add(X1, X2) 1 + 0X1 + 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 from active X -> from X 0 + 0X >= 0 + 0X from mark X -> from X 0 + 0X >= 0 + 0X s active X -> s X 1 + 0X >= 1 + 1X s mark X -> s X 2 + 0X >= 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 fst(active X1, X2) -> fst(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 fst(mark X1, X2) -> fst(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 fst(X1, active X2) -> fst(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 fst(X1, mark X2) -> fst(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active len cons(X, Z) -> mark s len Z 0 + 0Z + 0X >= 1 + 0Z active len nil() -> mark 0() 0 >= 1 active add(s X, Y) -> mark s add(X, Y) 0 + 0Y + 0X >= 1 + 0Y + 0X active add(0(), X) -> mark X 0 + 0X >= 1 + 0X active from X -> mark cons(X, from s X) 0 + 0X >= 1 + 0X active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)) 0 + 0Z + 0Y + 0X >= 1 + 0Z + 0Y + 0X active fst(0(), Z) -> mark nil() 0 + 0Z >= 1 mark len X -> active len mark X 1 + 0X >= 0 + 0X mark add(X1, X2) -> active add(mark X1, mark X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark from X -> active from mark X 1 + 0X >= 0 + 0X mark s X -> active s X 1 + 0X >= 0 + 0X mark cons(X1, X2) -> active cons(mark X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark 0() -> active 0() 1 >= 0 mark fst(X1, X2) -> active fst(mark X1, mark X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 0 SCCS (1): Scc: { mark# nil() -> active# nil(), mark# fst(X1, X2) -> active# fst(mark X1, mark X2), mark# cons(X1, X2) -> active# cons(mark X1, X2), mark# from X -> active# from mark X, mark# add(X1, X2) -> active# add(mark X1, mark X2), active# fst(0(), Z) -> mark# nil(), active# from X -> mark# cons(X, from s X)} SCC (7): Strict: { mark# nil() -> active# nil(), mark# fst(X1, X2) -> active# fst(mark X1, mark X2), mark# cons(X1, X2) -> active# cons(mark X1, X2), mark# from X -> active# from mark X, mark# add(X1, X2) -> active# add(mark X1, mark X2), active# fst(0(), Z) -> mark# nil(), active# from X -> mark# cons(X, from s X)} Weak: { mark nil() -> active nil(), mark fst(X1, X2) -> active fst(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s X, mark from X -> active from mark X, mark add(X1, X2) -> active add(mark X1, mark X2), mark len X -> active len mark X, active fst(0(), Z) -> mark nil(), active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)), active from X -> mark cons(X, from s X), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active len nil() -> mark 0(), active len cons(X, Z) -> mark s len Z, fst(X1, mark X2) -> fst(X1, X2), fst(X1, active X2) -> fst(X1, X2), fst(mark X1, X2) -> fst(X1, X2), fst(active X1, X2) -> fst(X1, X2), cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X, 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), len mark X -> len X, len active X -> len X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [fst](x0, x1) = 0, [cons](x0, x1) = 0, [add](x0, x1) = x0 + x1, [mark](x0) = x0 + 1, [active](x0) = 0, [s](x0) = x0 + 1, [from](x0) = x0 + 1, [len](x0) = x0 + 1, [nil] = 0, [0] = 0, [mark#](x0) = x0, [active#](x0) = 0 Strict: active# from X -> mark# cons(X, from s X) 0 + 0X >= 0 + 0X active# fst(0(), Z) -> mark# nil() 0 + 0Z >= 0 mark# add(X1, X2) -> active# add(mark X1, mark X2) 0 + 1X1 + 1X2 >= 0 + 0X1 + 0X2 mark# from X -> active# from mark X 1 + 1X >= 0 + 0X mark# cons(X1, X2) -> active# cons(mark X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark# fst(X1, X2) -> active# fst(mark X1, mark X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark# nil() -> active# nil() 0 >= 0 Weak: len active X -> len X 1 + 0X >= 1 + 1X len mark X -> len X 2 + 1X >= 1 + 1X add(active X1, X2) -> add(X1, X2) 0 + 0X1 + 1X2 >= 0 + 1X1 + 1X2 add(mark X1, X2) -> add(X1, X2) 1 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 add(X1, active X2) -> add(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 1X2 add(X1, mark X2) -> add(X1, X2) 1 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 from active X -> from X 1 + 0X >= 1 + 1X from mark X -> from X 2 + 1X >= 1 + 1X s active X -> s X 1 + 0X >= 1 + 1X s mark X -> s X 2 + 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 fst(active X1, X2) -> fst(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 fst(mark X1, X2) -> fst(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 fst(X1, active X2) -> fst(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 fst(X1, mark X2) -> fst(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active len cons(X, Z) -> mark s len Z 0 + 0Z + 0X >= 3 + 1Z active len nil() -> mark 0() 0 >= 1 active add(s X, Y) -> mark s add(X, Y) 0 + 0Y + 0X >= 2 + 1Y + 1X active add(0(), X) -> mark X 0 + 0X >= 1 + 1X active from X -> mark cons(X, from s X) 0 + 0X >= 1 + 0X active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)) 0 + 0Z + 0Y + 0X >= 1 + 0Z + 0Y + 0X active fst(0(), Z) -> mark nil() 0 + 0Z >= 1 mark len X -> active len mark X 2 + 1X >= 0 + 0X mark add(X1, X2) -> active add(mark X1, mark X2) 1 + 1X1 + 1X2 >= 0 + 0X1 + 0X2 mark from X -> active from mark X 2 + 1X >= 0 + 0X mark s X -> active s X 2 + 1X >= 0 + 0X mark cons(X1, X2) -> active cons(mark X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark 0() -> active 0() 1 >= 0 mark fst(X1, X2) -> active fst(mark X1, mark X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 0 SCCS (1): Scc: { mark# nil() -> active# nil(), mark# fst(X1, X2) -> active# fst(mark X1, mark X2), mark# cons(X1, X2) -> active# cons(mark X1, X2), mark# add(X1, X2) -> active# add(mark X1, mark X2), active# fst(0(), Z) -> mark# nil(), active# from X -> mark# cons(X, from s X)} SCC (6): Strict: { mark# nil() -> active# nil(), mark# fst(X1, X2) -> active# fst(mark X1, mark X2), mark# cons(X1, X2) -> active# cons(mark X1, X2), mark# add(X1, X2) -> active# add(mark X1, mark X2), active# fst(0(), Z) -> mark# nil(), active# from X -> mark# cons(X, from s X)} Weak: { mark nil() -> active nil(), mark fst(X1, X2) -> active fst(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s X, mark from X -> active from mark X, mark add(X1, X2) -> active add(mark X1, mark X2), mark len X -> active len mark X, active fst(0(), Z) -> mark nil(), active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)), active from X -> mark cons(X, from s X), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active len nil() -> mark 0(), active len cons(X, Z) -> mark s len Z, fst(X1, mark X2) -> fst(X1, X2), fst(X1, active X2) -> fst(X1, X2), fst(mark X1, X2) -> fst(X1, X2), fst(active X1, X2) -> fst(X1, X2), cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X, 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), len mark X -> len X, len active X -> len X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [fst](x0, x1) = 1, [cons](x0, x1) = 0, [add](x0, x1) = x0 + x1, [mark](x0) = x0 + 1, [active](x0) = 0, [s](x0) = 1, [from](x0) = x0 + 1, [len](x0) = x0 + 1, [nil] = 0, [0] = 0, [mark#](x0) = x0, [active#](x0) = 0 Strict: active# from X -> mark# cons(X, from s X) 0 + 0X >= 0 + 0X active# fst(0(), Z) -> mark# nil() 0 + 0Z >= 0 mark# add(X1, X2) -> active# add(mark X1, mark X2) 0 + 1X1 + 1X2 >= 0 + 0X1 + 0X2 mark# cons(X1, X2) -> active# cons(mark X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark# fst(X1, X2) -> active# fst(mark X1, mark X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark# nil() -> active# nil() 0 >= 0 Weak: len active X -> len X 1 + 0X >= 1 + 1X len mark X -> len X 2 + 1X >= 1 + 1X add(active X1, X2) -> add(X1, X2) 0 + 0X1 + 1X2 >= 0 + 1X1 + 1X2 add(mark X1, X2) -> add(X1, X2) 1 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 add(X1, active X2) -> add(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 1X2 add(X1, mark X2) -> add(X1, X2) 1 + 1X1 + 1X2 >= 0 + 1X1 + 1X2 from active X -> from X 1 + 0X >= 1 + 1X from mark X -> from X 2 + 1X >= 1 + 1X s active X -> s X 1 + 0X >= 1 + 0X s mark X -> s 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 fst(active X1, X2) -> fst(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 fst(mark X1, X2) -> fst(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 fst(X1, active X2) -> fst(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 fst(X1, mark X2) -> fst(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active len cons(X, Z) -> mark s len Z 0 + 0Z + 0X >= 2 + 0Z active len nil() -> mark 0() 0 >= 1 active add(s X, Y) -> mark s add(X, Y) 0 + 0Y + 0X >= 2 + 0Y + 0X active add(0(), X) -> mark X 0 + 0X >= 1 + 1X active from X -> mark cons(X, from s X) 0 + 0X >= 1 + 0X active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)) 0 + 0Z + 0Y + 0X >= 1 + 0Z + 0Y + 0X active fst(0(), Z) -> mark nil() 0 + 0Z >= 1 mark len X -> active len mark X 2 + 1X >= 0 + 0X mark add(X1, X2) -> active add(mark X1, mark X2) 1 + 1X1 + 1X2 >= 0 + 0X1 + 0X2 mark from X -> active from mark X 2 + 1X >= 0 + 0X mark s X -> active s X 2 + 0X >= 0 + 0X mark cons(X1, X2) -> active cons(mark X1, X2) 1 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark 0() -> active 0() 1 >= 0 mark fst(X1, X2) -> active fst(mark X1, mark X2) 2 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 0 SCCS (1): Scc: { mark# nil() -> active# nil(), mark# cons(X1, X2) -> active# cons(mark X1, X2), mark# add(X1, X2) -> active# add(mark X1, mark X2), active# fst(0(), Z) -> mark# nil(), active# from X -> mark# cons(X, from s X)} SCC (5): Strict: { mark# nil() -> active# nil(), mark# cons(X1, X2) -> active# cons(mark X1, X2), mark# add(X1, X2) -> active# add(mark X1, mark X2), active# fst(0(), Z) -> mark# nil(), active# from X -> mark# cons(X, from s X)} Weak: { mark nil() -> active nil(), mark fst(X1, X2) -> active fst(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s X, mark from X -> active from mark X, mark add(X1, X2) -> active add(mark X1, mark X2), mark len X -> active len mark X, active fst(0(), Z) -> mark nil(), active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)), active from X -> mark cons(X, from s X), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active len nil() -> mark 0(), active len cons(X, Z) -> mark s len Z, fst(X1, mark X2) -> fst(X1, X2), fst(X1, active X2) -> fst(X1, X2), fst(mark X1, X2) -> fst(X1, X2), fst(active X1, X2) -> fst(X1, X2), cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X, 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), len mark X -> len X, len active X -> len X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [fst](x0, x1) = x0 + 1, [cons](x0, x1) = 0, [add](x0, x1) = 0, [mark](x0) = x0 + 1, [active](x0) = 1, [s](x0) = 1, [from](x0) = 0, [len](x0) = 0, [nil] = 0, [0] = 1, [mark#](x0) = 0, [active#](x0) = x0 Strict: active# from X -> mark# cons(X, from s X) 0 + 0X >= 0 + 0X active# fst(0(), Z) -> mark# nil() 2 + 0Z >= 0 mark# add(X1, X2) -> active# add(mark X1, mark X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark# cons(X1, X2) -> active# cons(mark X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark# nil() -> active# nil() 0 >= 0 Weak: len active X -> len X 0 + 0X >= 0 + 0X len mark X -> len 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 from active X -> from X 0 + 0X >= 0 + 0X from mark X -> from X 0 + 0X >= 0 + 0X s active X -> s X 1 + 0X >= 1 + 0X s mark X -> s 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 fst(active X1, X2) -> fst(X1, X2) 2 + 0X1 + 0X2 >= 1 + 1X1 + 0X2 fst(mark X1, X2) -> fst(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 fst(X1, active X2) -> fst(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 fst(X1, mark X2) -> fst(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 active len cons(X, Z) -> mark s len Z 1 + 0Z + 0X >= 2 + 0Z active len nil() -> mark 0() 1 >= 2 active add(s X, Y) -> mark s add(X, Y) 1 + 0Y + 0X >= 2 + 0Y + 0X active add(0(), X) -> mark X 1 + 0X >= 1 + 1X active from X -> mark cons(X, from s X) 1 + 0X >= 1 + 0X active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)) 1 + 0Z + 0Y + 0X >= 1 + 0Z + 0Y + 0X active fst(0(), Z) -> mark nil() 1 + 0Z >= 1 mark len X -> active len mark X 1 + 0X >= 1 + 0X mark add(X1, X2) -> active add(mark X1, mark X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark from X -> active from mark X 1 + 0X >= 1 + 0X mark s X -> active s X 2 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(mark X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark 0() -> active 0() 2 >= 1 mark fst(X1, X2) -> active fst(mark X1, mark X2) 2 + 1X1 + 0X2 >= 1 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 1 SCCS (1): Scc: { mark# nil() -> active# nil(), mark# cons(X1, X2) -> active# cons(mark X1, X2), mark# add(X1, X2) -> active# add(mark X1, mark X2), active# from X -> mark# cons(X, from s X)} SCC (4): Strict: { mark# nil() -> active# nil(), mark# cons(X1, X2) -> active# cons(mark X1, X2), mark# add(X1, X2) -> active# add(mark X1, mark X2), active# from X -> mark# cons(X, from s X)} Weak: { mark nil() -> active nil(), mark fst(X1, X2) -> active fst(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s X, mark from X -> active from mark X, mark add(X1, X2) -> active add(mark X1, mark X2), mark len X -> active len mark X, active fst(0(), Z) -> mark nil(), active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)), active from X -> mark cons(X, from s X), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active len nil() -> mark 0(), active len cons(X, Z) -> mark s len Z, fst(X1, mark X2) -> fst(X1, X2), fst(X1, active X2) -> fst(X1, X2), fst(mark X1, X2) -> fst(X1, X2), fst(active X1, X2) -> fst(X1, X2), cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X, 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), len mark X -> len X, len active X -> len X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [fst](x0, x1) = x0 + 1, [cons](x0, x1) = 0, [add](x0, x1) = x0 + 1, [mark](x0) = 1, [active](x0) = x0 + 1, [s](x0) = 1, [from](x0) = x0 + 1, [len](x0) = x0 + 1, [nil] = 0, [0] = 1, [mark#](x0) = x0, [active#](x0) = 0 Strict: active# from X -> mark# cons(X, from s X) 0 + 0X >= 0 + 0X mark# add(X1, X2) -> active# add(mark X1, mark X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 0X2 mark# cons(X1, X2) -> active# cons(mark X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark# nil() -> active# nil() 0 >= 0 Weak: len active X -> len X 2 + 1X >= 1 + 1X len mark X -> len X 2 + 0X >= 1 + 1X add(active X1, X2) -> add(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 add(mark X1, X2) -> add(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 add(X1, active X2) -> add(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 add(X1, mark X2) -> add(X1, X2) 2 + 0X1 + 0X2 >= 1 + 0X1 + 1X2 from active X -> from X 2 + 1X >= 1 + 1X from mark X -> from X 2 + 0X >= 1 + 1X s active X -> s X 1 + 0X >= 1 + 0X s mark X -> s 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 fst(active X1, X2) -> fst(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 fst(mark X1, X2) -> fst(X1, X2) 2 + 0X1 + 0X2 >= 1 + 1X1 + 0X2 fst(X1, active X2) -> fst(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 fst(X1, mark X2) -> fst(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 active len cons(X, Z) -> mark s len Z 2 + 0Z + 0X >= 1 + 0Z active len nil() -> mark 0() 2 >= 1 active add(s X, Y) -> mark s add(X, Y) 2 + 1Y + 0X >= 1 + 0Y + 0X active add(0(), X) -> mark X 2 + 1X >= 1 + 0X active from X -> mark cons(X, from s X) 2 + 1X >= 1 + 0X active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)) 3 + 0Z + 0Y + 0X >= 1 + 0Z + 0Y + 0X active fst(0(), Z) -> mark nil() 3 + 0Z >= 1 mark len X -> active len mark X 1 + 0X >= 3 + 0X mark add(X1, X2) -> active add(mark X1, mark X2) 1 + 0X1 + 0X2 >= 3 + 0X1 + 0X2 mark from X -> active from mark X 1 + 0X >= 3 + 0X mark s X -> active s X 1 + 0X >= 2 + 0X mark cons(X1, X2) -> active cons(mark X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark 0() -> active 0() 1 >= 2 mark fst(X1, X2) -> active fst(mark X1, mark X2) 1 + 0X1 + 0X2 >= 3 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 1 SCCS (1): Scc: { mark# nil() -> active# nil(), mark# cons(X1, X2) -> active# cons(mark X1, X2), active# from X -> mark# cons(X, from s X)} SCC (3): Strict: { mark# nil() -> active# nil(), mark# cons(X1, X2) -> active# cons(mark X1, X2), active# from X -> mark# cons(X, from s X)} Weak: { mark nil() -> active nil(), mark fst(X1, X2) -> active fst(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s X, mark from X -> active from mark X, mark add(X1, X2) -> active add(mark X1, mark X2), mark len X -> active len mark X, active fst(0(), Z) -> mark nil(), active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)), active from X -> mark cons(X, from s X), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active len nil() -> mark 0(), active len cons(X, Z) -> mark s len Z, fst(X1, mark X2) -> fst(X1, X2), fst(X1, active X2) -> fst(X1, X2), fst(mark X1, X2) -> fst(X1, X2), fst(active X1, X2) -> fst(X1, X2), cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X, 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), len mark X -> len X, len active X -> len X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [fst](x0, x1) = 0, [cons](x0, x1) = 0, [add](x0, x1) = x0, [mark](x0) = 0, [active](x0) = x0 + 1, [s](x0) = x0 + 1, [from](x0) = 0, [len](x0) = x0, [nil] = 1, [0] = 1, [mark#](x0) = x0, [active#](x0) = 0 Strict: active# from X -> mark# cons(X, from s X) 0 + 0X >= 0 + 0X mark# cons(X1, X2) -> active# cons(mark X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 mark# nil() -> active# nil() 1 >= 0 Weak: len active X -> len X 1 + 1X >= 0 + 1X len mark X -> len X 0 + 0X >= 0 + 1X add(active X1, X2) -> add(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 add(mark X1, X2) -> add(X1, X2) 0 + 0X1 + 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 from active X -> from X 0 + 0X >= 0 + 0X from mark X -> from X 0 + 0X >= 0 + 0X s active X -> s X 2 + 1X >= 1 + 1X s mark X -> s X 1 + 0X >= 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 fst(active X1, X2) -> fst(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 fst(mark X1, X2) -> fst(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 fst(X1, active X2) -> fst(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 fst(X1, mark X2) -> fst(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active len cons(X, Z) -> mark s len Z 1 + 0Z + 0X >= 0 + 0Z active len nil() -> mark 0() 2 >= 0 active add(s X, Y) -> mark s add(X, Y) 2 + 0Y + 1X >= 0 + 0Y + 0X active add(0(), X) -> mark X 2 + 0X >= 0 + 0X active from X -> mark cons(X, from s X) 1 + 0X >= 0 + 0X active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)) 1 + 0Z + 0Y + 0X >= 0 + 0Z + 0Y + 0X active fst(0(), Z) -> mark nil() 1 + 0Z >= 0 mark len X -> active len mark X 0 + 0X >= 1 + 0X mark add(X1, X2) -> active add(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark from X -> active from mark X 0 + 0X >= 1 + 0X mark s X -> active s X 0 + 0X >= 2 + 1X mark cons(X1, X2) -> active cons(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark 0() -> active 0() 0 >= 2 mark fst(X1, X2) -> active fst(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark nil() -> active nil() 0 >= 2 SCCS (1): Scc: {mark# cons(X1, X2) -> active# cons(mark X1, X2), active# from X -> mark# cons(X, from s X)} SCC (2): Strict: {mark# cons(X1, X2) -> active# cons(mark X1, X2), active# from X -> mark# cons(X, from s X)} Weak: { mark nil() -> active nil(), mark fst(X1, X2) -> active fst(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s X, mark from X -> active from mark X, mark add(X1, X2) -> active add(mark X1, mark X2), mark len X -> active len mark X, active fst(0(), Z) -> mark nil(), active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)), active from X -> mark cons(X, from s X), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active len nil() -> mark 0(), active len cons(X, Z) -> mark s len Z, fst(X1, mark X2) -> fst(X1, X2), fst(X1, active X2) -> fst(X1, X2), fst(mark X1, X2) -> fst(X1, X2), fst(active X1, X2) -> fst(X1, X2), cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X, 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), len mark X -> len X, len active X -> len X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [fst](x0, x1) = 1, [cons](x0, x1) = 0, [add](x0, x1) = 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [s](x0) = x0 + 1, [from](x0) = x0 + 1, [len](x0) = x0 + 1, [nil] = 1, [0] = 1, [mark#](x0) = 0, [active#](x0) = x0 Strict: active# from X -> mark# cons(X, from s X) 1 + 1X >= 0 + 0X mark# cons(X1, X2) -> active# cons(mark X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 Weak: len active X -> len X 2 + 1X >= 1 + 1X len mark X -> len 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 from active X -> from X 2 + 1X >= 1 + 1X from mark X -> from X 2 + 1X >= 1 + 1X s active X -> s X 2 + 1X >= 1 + 1X s mark X -> s X 2 + 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 fst(active X1, X2) -> fst(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 fst(mark X1, X2) -> fst(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 fst(X1, active X2) -> fst(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 fst(X1, mark X2) -> fst(X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 active len cons(X, Z) -> mark s len Z 2 + 0Z + 0X >= 3 + 1Z active len nil() -> mark 0() 3 >= 2 active add(s X, Y) -> mark s add(X, Y) 2 + 0Y + 0X >= 3 + 0Y + 0X active add(0(), X) -> mark X 2 + 0X >= 1 + 1X active from X -> mark cons(X, from s X) 2 + 1X >= 1 + 0X active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)) 2 + 0Z + 0Y + 0X >= 1 + 0Z + 0Y + 0X active fst(0(), Z) -> mark nil() 2 + 0Z >= 2 mark len X -> active len mark X 2 + 1X >= 3 + 1X mark add(X1, X2) -> active add(mark X1, mark X2) 2 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 mark from X -> active from mark X 2 + 1X >= 3 + 1X mark s X -> active s X 2 + 1X >= 2 + 1X mark cons(X1, X2) -> active cons(mark X1, X2) 1 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark 0() -> active 0() 2 >= 2 mark fst(X1, X2) -> active fst(mark X1, mark X2) 2 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 mark nil() -> active nil() 2 >= 2 SCCS (0): SCC (2): Strict: { len# mark X -> len# X, len# active X -> len# X} Weak: { mark nil() -> active nil(), mark fst(X1, X2) -> active fst(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s X, mark from X -> active from mark X, mark add(X1, X2) -> active add(mark X1, mark X2), mark len X -> active len mark X, active fst(0(), Z) -> mark nil(), active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)), active from X -> mark cons(X, from s X), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active len nil() -> mark 0(), active len cons(X, Z) -> mark s len Z, fst(X1, mark X2) -> fst(X1, X2), fst(X1, active X2) -> fst(X1, X2), fst(mark X1, X2) -> fst(X1, X2), fst(active X1, X2) -> fst(X1, X2), cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X, 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), len mark X -> len X, len active X -> len X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [fst](x0, x1) = x0 + 1, [cons](x0, x1) = x0, [add](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [from](x0) = 0, [len](x0) = 0, [nil] = 1, [0] = 1, [len#](x0) = x0 Strict: len# active X -> len# X 1 + 1X >= 0 + 1X len# mark X -> len# X 0 + 1X >= 0 + 1X Weak: len active X -> len X 0 + 0X >= 0 + 0X len mark X -> len 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 from active X -> from X 0 + 0X >= 0 + 0X from mark X -> from X 0 + 0X >= 0 + 0X s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X cons(active X1, X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(mark X1, X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(X1, active X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(X1, mark X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 fst(active X1, X2) -> fst(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 fst(mark X1, X2) -> fst(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 fst(X1, active X2) -> fst(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 fst(X1, mark X2) -> fst(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active len cons(X, Z) -> mark s len Z 1 + 0Z + 0X >= 0 + 0Z active len nil() -> mark 0() 1 >= 1 active add(s X, Y) -> mark s add(X, Y) 1 + 0Y + 0X >= 0 + 0Y + 0X active add(0(), X) -> mark X 1 + 0X >= 0 + 1X active from X -> mark cons(X, from s X) 1 + 0X >= 0 + 0X active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)) 2 + 1Z + 0Y + 0X >= 1 + 1Z + 0Y + 0X active fst(0(), Z) -> mark nil() 2 + 1Z >= 1 mark len X -> active len mark X 0 + 0X >= 1 + 0X mark add(X1, X2) -> active add(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark from X -> active from mark X 0 + 0X >= 1 + 0X mark s X -> active s X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(mark X1, X2) 0 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 mark 0() -> active 0() 1 >= 2 mark fst(X1, X2) -> active fst(mark X1, mark X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 mark nil() -> active nil() 1 >= 2 SCCS (1): Scc: {len# mark X -> len# X} SCC (1): Strict: {len# mark X -> len# X} Weak: { mark nil() -> active nil(), mark fst(X1, X2) -> active fst(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s X, mark from X -> active from mark X, mark add(X1, X2) -> active add(mark X1, mark X2), mark len X -> active len mark X, active fst(0(), Z) -> mark nil(), active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)), active from X -> mark cons(X, from s X), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active len nil() -> mark 0(), active len cons(X, Z) -> mark s len Z, fst(X1, mark X2) -> fst(X1, X2), fst(X1, active X2) -> fst(X1, X2), fst(mark X1, X2) -> fst(X1, X2), fst(active X1, X2) -> fst(X1, X2), cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X, 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), len mark X -> len X, len active X -> len X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [fst](x0, x1) = x0, [cons](x0, x1) = x0 + 1, [add](x0, x1) = 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [s](x0) = 1, [from](x0) = x0 + 1, [len](x0) = x0 + 1, [nil] = 1, [0] = 1, [len#](x0) = x0 Strict: len# mark X -> len# X 1 + 1X >= 0 + 1X Weak: len active X -> len X 2 + 1X >= 1 + 1X len mark X -> len 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 from active X -> from X 2 + 1X >= 1 + 1X from mark X -> from X 2 + 1X >= 1 + 1X s active X -> s X 1 + 0X >= 1 + 0X s mark X -> s X 1 + 0X >= 1 + 0X cons(active X1, X2) -> cons(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 cons(mark X1, X2) -> cons(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 cons(X1, active X2) -> cons(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 cons(X1, mark X2) -> cons(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 fst(active X1, X2) -> fst(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 fst(mark X1, X2) -> fst(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 fst(X1, active X2) -> fst(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 fst(X1, mark X2) -> fst(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 active len cons(X, Z) -> mark s len Z 3 + 0Z + 1X >= 2 + 0Z active len nil() -> mark 0() 3 >= 2 active add(s X, Y) -> mark s add(X, Y) 2 + 0Y + 0X >= 2 + 0Y + 0X active add(0(), X) -> mark X 2 + 0X >= 1 + 1X active from X -> mark cons(X, from s X) 2 + 1X >= 2 + 1X active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)) 2 + 0Z + 0Y + 0X >= 2 + 0Z + 1Y + 0X active fst(0(), Z) -> mark nil() 2 + 0Z >= 2 mark len X -> active len mark X 2 + 1X >= 3 + 1X mark add(X1, X2) -> active add(mark X1, mark X2) 2 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 mark from X -> active from mark X 2 + 1X >= 3 + 1X mark s X -> active s X 2 + 0X >= 2 + 0X mark cons(X1, X2) -> active cons(mark X1, X2) 2 + 1X1 + 0X2 >= 3 + 1X1 + 0X2 mark 0() -> active 0() 2 >= 2 mark fst(X1, X2) -> active fst(mark X1, mark X2) 1 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark nil() -> active nil() 2 >= 2 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 nil() -> active nil(), mark fst(X1, X2) -> active fst(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s X, mark from X -> active from mark X, mark add(X1, X2) -> active add(mark X1, mark X2), mark len X -> active len mark X, active fst(0(), Z) -> mark nil(), active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)), active from X -> mark cons(X, from s X), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active len nil() -> mark 0(), active len cons(X, Z) -> mark s len Z, fst(X1, mark X2) -> fst(X1, X2), fst(X1, active X2) -> fst(X1, X2), fst(mark X1, X2) -> fst(X1, X2), fst(active X1, X2) -> fst(X1, X2), cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X, 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), len mark X -> len X, len active X -> len X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [fst](x0, x1) = 0, [cons](x0, x1) = 0, [add](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [from](x0) = 0, [len](x0) = 0, [nil] = 1, [0] = 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: len active X -> len X 0 + 0X >= 0 + 0X len mark X -> len 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 from active X -> from X 0 + 0X >= 0 + 0X from mark X -> from X 0 + 0X >= 0 + 0X s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X cons(active X1, X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(mark X1, X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(X1, active X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(X1, mark X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 fst(active X1, X2) -> fst(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 fst(mark X1, X2) -> fst(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 fst(X1, active X2) -> fst(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 fst(X1, mark X2) -> fst(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active len cons(X, Z) -> mark s len Z 1 + 0Z + 0X >= 0 + 0Z active len nil() -> mark 0() 1 >= 1 active add(s X, Y) -> mark s add(X, Y) 1 + 0Y + 0X >= 0 + 0Y + 0X active add(0(), X) -> mark X 1 + 0X >= 0 + 1X active from X -> mark cons(X, from s X) 1 + 0X >= 0 + 0X active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)) 1 + 0Z + 0Y + 0X >= 0 + 0Z + 0Y + 0X active fst(0(), Z) -> mark nil() 1 + 0Z >= 1 mark len X -> active len mark X 0 + 0X >= 1 + 0X mark add(X1, X2) -> active add(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark from X -> active from mark X 0 + 0X >= 1 + 0X mark s X -> active s X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark 0() -> active 0() 1 >= 2 mark fst(X1, X2) -> active fst(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 2 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 nil() -> active nil(), mark fst(X1, X2) -> active fst(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s X, mark from X -> active from mark X, mark add(X1, X2) -> active add(mark X1, mark X2), mark len X -> active len mark X, active fst(0(), Z) -> mark nil(), active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)), active from X -> mark cons(X, from s X), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active len nil() -> mark 0(), active len cons(X, Z) -> mark s len Z, fst(X1, mark X2) -> fst(X1, X2), fst(X1, active X2) -> fst(X1, X2), fst(mark X1, X2) -> fst(X1, X2), fst(active X1, X2) -> fst(X1, X2), cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X, 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), len mark X -> len X, len active X -> len X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [fst](x0, x1) = x0, [cons](x0, x1) = x0 + 1, [add](x0, x1) = 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [s](x0) = 1, [from](x0) = x0 + 1, [len](x0) = 0, [nil] = 1, [0] = 1, [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: len active X -> len X 0 + 0X >= 0 + 0X len mark X -> len 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 from active X -> from X 2 + 1X >= 1 + 1X from mark X -> from X 2 + 1X >= 1 + 1X s active X -> s X 1 + 0X >= 1 + 0X s mark X -> s X 1 + 0X >= 1 + 0X cons(active X1, X2) -> cons(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 cons(mark X1, X2) -> cons(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 cons(X1, active X2) -> cons(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 cons(X1, mark X2) -> cons(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 fst(active X1, X2) -> fst(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 fst(mark X1, X2) -> fst(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 fst(X1, active X2) -> fst(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 fst(X1, mark X2) -> fst(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 active len cons(X, Z) -> mark s len Z 1 + 0Z + 0X >= 2 + 0Z active len nil() -> mark 0() 1 >= 2 active add(s X, Y) -> mark s add(X, Y) 2 + 0Y + 0X >= 2 + 0Y + 0X active add(0(), X) -> mark X 2 + 0X >= 1 + 1X active from X -> mark cons(X, from s X) 2 + 1X >= 2 + 1X active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)) 2 + 0Z + 1Y + 0X >= 2 + 0Z + 1Y + 0X active fst(0(), Z) -> mark nil() 1 + 1Z >= 2 mark len X -> active len mark X 1 + 0X >= 1 + 0X mark add(X1, X2) -> active add(mark X1, mark X2) 2 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 mark from X -> active from mark X 2 + 1X >= 3 + 1X mark s X -> active s X 2 + 0X >= 2 + 0X mark cons(X1, X2) -> active cons(mark X1, X2) 2 + 1X1 + 0X2 >= 3 + 1X1 + 0X2 mark 0() -> active 0() 2 >= 2 mark fst(X1, X2) -> active fst(mark X1, mark X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 mark nil() -> active nil() 2 >= 2 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 nil() -> active nil(), mark fst(X1, X2) -> active fst(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s X, mark from X -> active from mark X, mark add(X1, X2) -> active add(mark X1, mark X2), mark len X -> active len mark X, active fst(0(), Z) -> mark nil(), active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)), active from X -> mark cons(X, from s X), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active len nil() -> mark 0(), active len cons(X, Z) -> mark s len Z, fst(X1, mark X2) -> fst(X1, X2), fst(X1, active X2) -> fst(X1, X2), fst(mark X1, X2) -> fst(X1, X2), fst(active X1, X2) -> fst(X1, X2), cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X, 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), len mark X -> len X, len active X -> len X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [fst](x0, x1) = x0 + 1, [cons](x0, x1) = x0, [add](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [from](x0) = 0, [len](x0) = 0, [nil] = 1, [0] = 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: len active X -> len X 0 + 0X >= 0 + 0X len mark X -> len 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 from active X -> from X 0 + 0X >= 0 + 0X from mark X -> from X 0 + 0X >= 0 + 0X s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X cons(active X1, X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(mark X1, X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(X1, active X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(X1, mark X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 fst(active X1, X2) -> fst(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 fst(mark X1, X2) -> fst(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 fst(X1, active X2) -> fst(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 fst(X1, mark X2) -> fst(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active len cons(X, Z) -> mark s len Z 1 + 0Z + 0X >= 0 + 0Z active len nil() -> mark 0() 1 >= 1 active add(s X, Y) -> mark s add(X, Y) 1 + 0Y + 0X >= 0 + 0Y + 0X active add(0(), X) -> mark X 1 + 0X >= 0 + 1X active from X -> mark cons(X, from s X) 1 + 0X >= 0 + 0X active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)) 2 + 1Z + 0Y + 0X >= 1 + 1Z + 0Y + 0X active fst(0(), Z) -> mark nil() 2 + 1Z >= 1 mark len X -> active len mark X 0 + 0X >= 1 + 0X mark add(X1, X2) -> active add(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark from X -> active from mark X 0 + 0X >= 1 + 0X mark s X -> active s X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(mark X1, X2) 0 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 mark 0() -> active 0() 1 >= 2 mark fst(X1, X2) -> active fst(mark X1, mark X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 mark nil() -> active nil() 1 >= 2 SCCS (1): Scc: {add#(X1, mark X2) -> add#(X1, X2)} SCC (1): Strict: {add#(X1, mark X2) -> add#(X1, X2)} Weak: { mark nil() -> active nil(), mark fst(X1, X2) -> active fst(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s X, mark from X -> active from mark X, mark add(X1, X2) -> active add(mark X1, mark X2), mark len X -> active len mark X, active fst(0(), Z) -> mark nil(), active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)), active from X -> mark cons(X, from s X), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active len nil() -> mark 0(), active len cons(X, Z) -> mark s len Z, fst(X1, mark X2) -> fst(X1, X2), fst(X1, active X2) -> fst(X1, X2), fst(mark X1, X2) -> fst(X1, X2), fst(active X1, X2) -> fst(X1, X2), cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X, 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), len mark X -> len X, len active X -> len X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [fst](x0, x1) = x0, [cons](x0, x1) = x0 + 1, [add](x0, x1) = 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [s](x0) = 1, [from](x0) = x0 + 1, [len](x0) = x0 + 1, [nil] = 1, [0] = 1, [add#](x0, x1) = x0 Strict: add#(X1, mark X2) -> add#(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 Weak: len active X -> len X 2 + 1X >= 1 + 1X len mark X -> len 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 from active X -> from X 2 + 1X >= 1 + 1X from mark X -> from X 2 + 1X >= 1 + 1X s active X -> s X 1 + 0X >= 1 + 0X s mark X -> s X 1 + 0X >= 1 + 0X cons(active X1, X2) -> cons(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 cons(mark X1, X2) -> cons(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 cons(X1, active X2) -> cons(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 cons(X1, mark X2) -> cons(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 fst(active X1, X2) -> fst(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 fst(mark X1, X2) -> fst(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 fst(X1, active X2) -> fst(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 fst(X1, mark X2) -> fst(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 active len cons(X, Z) -> mark s len Z 3 + 0Z + 1X >= 2 + 0Z active len nil() -> mark 0() 3 >= 2 active add(s X, Y) -> mark s add(X, Y) 2 + 0Y + 0X >= 2 + 0Y + 0X active add(0(), X) -> mark X 2 + 0X >= 1 + 1X active from X -> mark cons(X, from s X) 2 + 1X >= 2 + 1X active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)) 2 + 0Z + 0Y + 0X >= 2 + 0Z + 1Y + 0X active fst(0(), Z) -> mark nil() 2 + 0Z >= 2 mark len X -> active len mark X 2 + 1X >= 3 + 1X mark add(X1, X2) -> active add(mark X1, mark X2) 2 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 mark from X -> active from mark X 2 + 1X >= 3 + 1X mark s X -> active s X 2 + 0X >= 2 + 0X mark cons(X1, X2) -> active cons(mark X1, X2) 2 + 1X1 + 0X2 >= 3 + 1X1 + 0X2 mark 0() -> active 0() 2 >= 2 mark fst(X1, X2) -> active fst(mark X1, mark X2) 1 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark nil() -> active nil() 2 >= 2 Qed SCC (2): Strict: { from# mark X -> from# X, from# active X -> from# X} Weak: { mark nil() -> active nil(), mark fst(X1, X2) -> active fst(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s X, mark from X -> active from mark X, mark add(X1, X2) -> active add(mark X1, mark X2), mark len X -> active len mark X, active fst(0(), Z) -> mark nil(), active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)), active from X -> mark cons(X, from s X), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active len nil() -> mark 0(), active len cons(X, Z) -> mark s len Z, fst(X1, mark X2) -> fst(X1, X2), fst(X1, active X2) -> fst(X1, X2), fst(mark X1, X2) -> fst(X1, X2), fst(active X1, X2) -> fst(X1, X2), cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X, 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), len mark X -> len X, len active X -> len X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [fst](x0, x1) = x0 + 1, [cons](x0, x1) = x0, [add](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [from](x0) = 0, [len](x0) = 0, [nil] = 1, [0] = 1, [from#](x0) = x0 Strict: from# active X -> from# X 1 + 1X >= 0 + 1X from# mark X -> from# X 0 + 1X >= 0 + 1X Weak: len active X -> len X 0 + 0X >= 0 + 0X len mark X -> len 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 from active X -> from X 0 + 0X >= 0 + 0X from mark X -> from X 0 + 0X >= 0 + 0X s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X cons(active X1, X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(mark X1, X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(X1, active X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(X1, mark X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 fst(active X1, X2) -> fst(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 fst(mark X1, X2) -> fst(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 fst(X1, active X2) -> fst(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 fst(X1, mark X2) -> fst(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active len cons(X, Z) -> mark s len Z 1 + 0Z + 0X >= 0 + 0Z active len nil() -> mark 0() 1 >= 1 active add(s X, Y) -> mark s add(X, Y) 1 + 0Y + 0X >= 0 + 0Y + 0X active add(0(), X) -> mark X 1 + 0X >= 0 + 1X active from X -> mark cons(X, from s X) 1 + 0X >= 0 + 0X active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)) 2 + 1Z + 0Y + 0X >= 1 + 1Z + 0Y + 0X active fst(0(), Z) -> mark nil() 2 + 1Z >= 1 mark len X -> active len mark X 0 + 0X >= 1 + 0X mark add(X1, X2) -> active add(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark from X -> active from mark X 0 + 0X >= 1 + 0X mark s X -> active s X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(mark X1, X2) 0 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 mark 0() -> active 0() 1 >= 2 mark fst(X1, X2) -> active fst(mark X1, mark X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 mark nil() -> active nil() 1 >= 2 SCCS (1): Scc: {from# mark X -> from# X} SCC (1): Strict: {from# mark X -> from# X} Weak: { mark nil() -> active nil(), mark fst(X1, X2) -> active fst(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s X, mark from X -> active from mark X, mark add(X1, X2) -> active add(mark X1, mark X2), mark len X -> active len mark X, active fst(0(), Z) -> mark nil(), active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)), active from X -> mark cons(X, from s X), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active len nil() -> mark 0(), active len cons(X, Z) -> mark s len Z, fst(X1, mark X2) -> fst(X1, X2), fst(X1, active X2) -> fst(X1, X2), fst(mark X1, X2) -> fst(X1, X2), fst(active X1, X2) -> fst(X1, X2), cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X, 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), len mark X -> len X, len active X -> len X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [fst](x0, x1) = x0, [cons](x0, x1) = x0 + 1, [add](x0, x1) = 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [s](x0) = 1, [from](x0) = x0 + 1, [len](x0) = x0 + 1, [nil] = 1, [0] = 1, [from#](x0) = x0 Strict: from# mark X -> from# X 1 + 1X >= 0 + 1X Weak: len active X -> len X 2 + 1X >= 1 + 1X len mark X -> len 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 from active X -> from X 2 + 1X >= 1 + 1X from mark X -> from X 2 + 1X >= 1 + 1X s active X -> s X 1 + 0X >= 1 + 0X s mark X -> s X 1 + 0X >= 1 + 0X cons(active X1, X2) -> cons(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 cons(mark X1, X2) -> cons(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 cons(X1, active X2) -> cons(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 cons(X1, mark X2) -> cons(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 fst(active X1, X2) -> fst(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 fst(mark X1, X2) -> fst(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 fst(X1, active X2) -> fst(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 fst(X1, mark X2) -> fst(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 active len cons(X, Z) -> mark s len Z 3 + 0Z + 1X >= 2 + 0Z active len nil() -> mark 0() 3 >= 2 active add(s X, Y) -> mark s add(X, Y) 2 + 0Y + 0X >= 2 + 0Y + 0X active add(0(), X) -> mark X 2 + 0X >= 1 + 1X active from X -> mark cons(X, from s X) 2 + 1X >= 2 + 1X active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)) 2 + 0Z + 0Y + 0X >= 2 + 0Z + 1Y + 0X active fst(0(), Z) -> mark nil() 2 + 0Z >= 2 mark len X -> active len mark X 2 + 1X >= 3 + 1X mark add(X1, X2) -> active add(mark X1, mark X2) 2 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 mark from X -> active from mark X 2 + 1X >= 3 + 1X mark s X -> active s X 2 + 0X >= 2 + 0X mark cons(X1, X2) -> active cons(mark X1, X2) 2 + 1X1 + 0X2 >= 3 + 1X1 + 0X2 mark 0() -> active 0() 2 >= 2 mark fst(X1, X2) -> active fst(mark X1, mark X2) 1 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark nil() -> active nil() 2 >= 2 Qed SCC (2): Strict: { s# mark X -> s# X, s# active X -> s# X} Weak: { mark nil() -> active nil(), mark fst(X1, X2) -> active fst(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s X, mark from X -> active from mark X, mark add(X1, X2) -> active add(mark X1, mark X2), mark len X -> active len mark X, active fst(0(), Z) -> mark nil(), active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)), active from X -> mark cons(X, from s X), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active len nil() -> mark 0(), active len cons(X, Z) -> mark s len Z, fst(X1, mark X2) -> fst(X1, X2), fst(X1, active X2) -> fst(X1, X2), fst(mark X1, X2) -> fst(X1, X2), fst(active X1, X2) -> fst(X1, X2), cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X, 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), len mark X -> len X, len active X -> len X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [fst](x0, x1) = x0 + 1, [cons](x0, x1) = x0, [add](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [from](x0) = 0, [len](x0) = 0, [nil] = 1, [0] = 1, [s#](x0) = x0 Strict: s# active X -> s# X 1 + 1X >= 0 + 1X s# mark X -> s# X 0 + 1X >= 0 + 1X Weak: len active X -> len X 0 + 0X >= 0 + 0X len mark X -> len 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 from active X -> from X 0 + 0X >= 0 + 0X from mark X -> from X 0 + 0X >= 0 + 0X s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X cons(active X1, X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(mark X1, X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(X1, active X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(X1, mark X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 fst(active X1, X2) -> fst(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 fst(mark X1, X2) -> fst(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 fst(X1, active X2) -> fst(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 fst(X1, mark X2) -> fst(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active len cons(X, Z) -> mark s len Z 1 + 0Z + 0X >= 0 + 0Z active len nil() -> mark 0() 1 >= 1 active add(s X, Y) -> mark s add(X, Y) 1 + 0Y + 0X >= 0 + 0Y + 0X active add(0(), X) -> mark X 1 + 0X >= 0 + 1X active from X -> mark cons(X, from s X) 1 + 0X >= 0 + 0X active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)) 2 + 1Z + 0Y + 0X >= 1 + 1Z + 0Y + 0X active fst(0(), Z) -> mark nil() 2 + 1Z >= 1 mark len X -> active len mark X 0 + 0X >= 1 + 0X mark add(X1, X2) -> active add(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark from X -> active from mark X 0 + 0X >= 1 + 0X mark s X -> active s X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(mark X1, X2) 0 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 mark 0() -> active 0() 1 >= 2 mark fst(X1, X2) -> active fst(mark X1, mark X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 mark nil() -> active nil() 1 >= 2 SCCS (1): Scc: {s# mark X -> s# X} SCC (1): Strict: {s# mark X -> s# X} Weak: { mark nil() -> active nil(), mark fst(X1, X2) -> active fst(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s X, mark from X -> active from mark X, mark add(X1, X2) -> active add(mark X1, mark X2), mark len X -> active len mark X, active fst(0(), Z) -> mark nil(), active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)), active from X -> mark cons(X, from s X), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active len nil() -> mark 0(), active len cons(X, Z) -> mark s len Z, fst(X1, mark X2) -> fst(X1, X2), fst(X1, active X2) -> fst(X1, X2), fst(mark X1, X2) -> fst(X1, X2), fst(active X1, X2) -> fst(X1, X2), cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X, 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), len mark X -> len X, len active X -> len X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [fst](x0, x1) = x0, [cons](x0, x1) = x0 + 1, [add](x0, x1) = 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [s](x0) = 1, [from](x0) = x0 + 1, [len](x0) = x0 + 1, [nil] = 1, [0] = 1, [s#](x0) = x0 Strict: s# mark X -> s# X 1 + 1X >= 0 + 1X Weak: len active X -> len X 2 + 1X >= 1 + 1X len mark X -> len 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 from active X -> from X 2 + 1X >= 1 + 1X from mark X -> from X 2 + 1X >= 1 + 1X s active X -> s X 1 + 0X >= 1 + 0X s mark X -> s X 1 + 0X >= 1 + 0X cons(active X1, X2) -> cons(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 cons(mark X1, X2) -> cons(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 cons(X1, active X2) -> cons(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 cons(X1, mark X2) -> cons(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 fst(active X1, X2) -> fst(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 fst(mark X1, X2) -> fst(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 fst(X1, active X2) -> fst(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 fst(X1, mark X2) -> fst(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 active len cons(X, Z) -> mark s len Z 3 + 0Z + 1X >= 2 + 0Z active len nil() -> mark 0() 3 >= 2 active add(s X, Y) -> mark s add(X, Y) 2 + 0Y + 0X >= 2 + 0Y + 0X active add(0(), X) -> mark X 2 + 0X >= 1 + 1X active from X -> mark cons(X, from s X) 2 + 1X >= 2 + 1X active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)) 2 + 0Z + 0Y + 0X >= 2 + 0Z + 1Y + 0X active fst(0(), Z) -> mark nil() 2 + 0Z >= 2 mark len X -> active len mark X 2 + 1X >= 3 + 1X mark add(X1, X2) -> active add(mark X1, mark X2) 2 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 mark from X -> active from mark X 2 + 1X >= 3 + 1X mark s X -> active s X 2 + 0X >= 2 + 0X mark cons(X1, X2) -> active cons(mark X1, X2) 2 + 1X1 + 0X2 >= 3 + 1X1 + 0X2 mark 0() -> active 0() 2 >= 2 mark fst(X1, X2) -> active fst(mark X1, mark X2) 1 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark nil() -> active nil() 2 >= 2 Qed SCC (4): Strict: { fst#(X1, mark X2) -> fst#(X1, X2), fst#(X1, active X2) -> fst#(X1, X2), fst#(mark X1, X2) -> fst#(X1, X2), fst#(active X1, X2) -> fst#(X1, X2)} Weak: { mark nil() -> active nil(), mark fst(X1, X2) -> active fst(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s X, mark from X -> active from mark X, mark add(X1, X2) -> active add(mark X1, mark X2), mark len X -> active len mark X, active fst(0(), Z) -> mark nil(), active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)), active from X -> mark cons(X, from s X), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active len nil() -> mark 0(), active len cons(X, Z) -> mark s len Z, fst(X1, mark X2) -> fst(X1, X2), fst(X1, active X2) -> fst(X1, X2), fst(mark X1, X2) -> fst(X1, X2), fst(active X1, X2) -> fst(X1, X2), cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X, 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), len mark X -> len X, len active X -> len X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [fst](x0, x1) = 0, [cons](x0, x1) = 0, [add](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [from](x0) = 0, [len](x0) = 0, [nil] = 1, [0] = 1, [fst#](x0, x1) = x0 Strict: fst#(active X1, X2) -> fst#(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 fst#(mark X1, X2) -> fst#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 fst#(X1, active X2) -> fst#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 fst#(X1, mark X2) -> fst#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 Weak: len active X -> len X 0 + 0X >= 0 + 0X len mark X -> len 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 from active X -> from X 0 + 0X >= 0 + 0X from mark X -> from X 0 + 0X >= 0 + 0X s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X cons(active X1, X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(mark X1, X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(X1, active X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(X1, mark X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 fst(active X1, X2) -> fst(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 fst(mark X1, X2) -> fst(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 fst(X1, active X2) -> fst(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 fst(X1, mark X2) -> fst(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active len cons(X, Z) -> mark s len Z 1 + 0Z + 0X >= 0 + 0Z active len nil() -> mark 0() 1 >= 1 active add(s X, Y) -> mark s add(X, Y) 1 + 0Y + 0X >= 0 + 0Y + 0X active add(0(), X) -> mark X 1 + 0X >= 0 + 1X active from X -> mark cons(X, from s X) 1 + 0X >= 0 + 0X active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)) 1 + 0Z + 0Y + 0X >= 0 + 0Z + 0Y + 0X active fst(0(), Z) -> mark nil() 1 + 0Z >= 1 mark len X -> active len mark X 0 + 0X >= 1 + 0X mark add(X1, X2) -> active add(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark from X -> active from mark X 0 + 0X >= 1 + 0X mark s X -> active s X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark 0() -> active 0() 1 >= 2 mark fst(X1, X2) -> active fst(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 2 SCCS (1): Scc: { fst#(X1, mark X2) -> fst#(X1, X2), fst#(X1, active X2) -> fst#(X1, X2), fst#(mark X1, X2) -> fst#(X1, X2)} SCC (3): Strict: { fst#(X1, mark X2) -> fst#(X1, X2), fst#(X1, active X2) -> fst#(X1, X2), fst#(mark X1, X2) -> fst#(X1, X2)} Weak: { mark nil() -> active nil(), mark fst(X1, X2) -> active fst(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s X, mark from X -> active from mark X, mark add(X1, X2) -> active add(mark X1, mark X2), mark len X -> active len mark X, active fst(0(), Z) -> mark nil(), active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)), active from X -> mark cons(X, from s X), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active len nil() -> mark 0(), active len cons(X, Z) -> mark s len Z, fst(X1, mark X2) -> fst(X1, X2), fst(X1, active X2) -> fst(X1, X2), fst(mark X1, X2) -> fst(X1, X2), fst(active X1, X2) -> fst(X1, X2), cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X, 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), len mark X -> len X, len active X -> len X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [fst](x0, x1) = x0, [cons](x0, x1) = x0 + 1, [add](x0, x1) = 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [s](x0) = 1, [from](x0) = x0 + 1, [len](x0) = 0, [nil] = 1, [0] = 1, [fst#](x0, x1) = x0 Strict: fst#(mark X1, X2) -> fst#(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 fst#(X1, active X2) -> fst#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 fst#(X1, mark X2) -> fst#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 Weak: len active X -> len X 0 + 0X >= 0 + 0X len mark X -> len 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 from active X -> from X 2 + 1X >= 1 + 1X from mark X -> from X 2 + 1X >= 1 + 1X s active X -> s X 1 + 0X >= 1 + 0X s mark X -> s X 1 + 0X >= 1 + 0X cons(active X1, X2) -> cons(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 cons(mark X1, X2) -> cons(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 cons(X1, active X2) -> cons(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 cons(X1, mark X2) -> cons(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 fst(active X1, X2) -> fst(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 fst(mark X1, X2) -> fst(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 fst(X1, active X2) -> fst(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 fst(X1, mark X2) -> fst(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 active len cons(X, Z) -> mark s len Z 1 + 0Z + 0X >= 2 + 0Z active len nil() -> mark 0() 1 >= 2 active add(s X, Y) -> mark s add(X, Y) 2 + 0Y + 0X >= 2 + 0Y + 0X active add(0(), X) -> mark X 2 + 0X >= 1 + 1X active from X -> mark cons(X, from s X) 2 + 1X >= 2 + 1X active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)) 2 + 0Z + 1Y + 0X >= 2 + 0Z + 1Y + 0X active fst(0(), Z) -> mark nil() 1 + 1Z >= 2 mark len X -> active len mark X 1 + 0X >= 1 + 0X mark add(X1, X2) -> active add(mark X1, mark X2) 2 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 mark from X -> active from mark X 2 + 1X >= 3 + 1X mark s X -> active s X 2 + 0X >= 2 + 0X mark cons(X1, X2) -> active cons(mark X1, X2) 2 + 1X1 + 0X2 >= 3 + 1X1 + 0X2 mark 0() -> active 0() 2 >= 2 mark fst(X1, X2) -> active fst(mark X1, mark X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 mark nil() -> active nil() 2 >= 2 SCCS (1): Scc: { fst#(X1, mark X2) -> fst#(X1, X2), fst#(X1, active X2) -> fst#(X1, X2)} SCC (2): Strict: { fst#(X1, mark X2) -> fst#(X1, X2), fst#(X1, active X2) -> fst#(X1, X2)} Weak: { mark nil() -> active nil(), mark fst(X1, X2) -> active fst(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s X, mark from X -> active from mark X, mark add(X1, X2) -> active add(mark X1, mark X2), mark len X -> active len mark X, active fst(0(), Z) -> mark nil(), active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)), active from X -> mark cons(X, from s X), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active len nil() -> mark 0(), active len cons(X, Z) -> mark s len Z, fst(X1, mark X2) -> fst(X1, X2), fst(X1, active X2) -> fst(X1, X2), fst(mark X1, X2) -> fst(X1, X2), fst(active X1, X2) -> fst(X1, X2), cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X, 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), len mark X -> len X, len active X -> len X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [fst](x0, x1) = x0 + 1, [cons](x0, x1) = x0, [add](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [from](x0) = 0, [len](x0) = 0, [nil] = 1, [0] = 1, [fst#](x0, x1) = x0 Strict: fst#(X1, active X2) -> fst#(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 fst#(X1, mark X2) -> fst#(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 Weak: len active X -> len X 0 + 0X >= 0 + 0X len mark X -> len 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 from active X -> from X 0 + 0X >= 0 + 0X from mark X -> from X 0 + 0X >= 0 + 0X s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X cons(active X1, X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(mark X1, X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(X1, active X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(X1, mark X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 fst(active X1, X2) -> fst(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 fst(mark X1, X2) -> fst(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 fst(X1, active X2) -> fst(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 fst(X1, mark X2) -> fst(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active len cons(X, Z) -> mark s len Z 1 + 0Z + 0X >= 0 + 0Z active len nil() -> mark 0() 1 >= 1 active add(s X, Y) -> mark s add(X, Y) 1 + 0Y + 0X >= 0 + 0Y + 0X active add(0(), X) -> mark X 1 + 0X >= 0 + 1X active from X -> mark cons(X, from s X) 1 + 0X >= 0 + 0X active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)) 2 + 1Z + 0Y + 0X >= 1 + 1Z + 0Y + 0X active fst(0(), Z) -> mark nil() 2 + 1Z >= 1 mark len X -> active len mark X 0 + 0X >= 1 + 0X mark add(X1, X2) -> active add(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark from X -> active from mark X 0 + 0X >= 1 + 0X mark s X -> active s X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(mark X1, X2) 0 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 mark 0() -> active 0() 1 >= 2 mark fst(X1, X2) -> active fst(mark X1, mark X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 mark nil() -> active nil() 1 >= 2 SCCS (1): Scc: {fst#(X1, mark X2) -> fst#(X1, X2)} SCC (1): Strict: {fst#(X1, mark X2) -> fst#(X1, X2)} Weak: { mark nil() -> active nil(), mark fst(X1, X2) -> active fst(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s X, mark from X -> active from mark X, mark add(X1, X2) -> active add(mark X1, mark X2), mark len X -> active len mark X, active fst(0(), Z) -> mark nil(), active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)), active from X -> mark cons(X, from s X), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active len nil() -> mark 0(), active len cons(X, Z) -> mark s len Z, fst(X1, mark X2) -> fst(X1, X2), fst(X1, active X2) -> fst(X1, X2), fst(mark X1, X2) -> fst(X1, X2), fst(active X1, X2) -> fst(X1, X2), cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X, 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), len mark X -> len X, len active X -> len X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [fst](x0, x1) = x0, [cons](x0, x1) = x0 + 1, [add](x0, x1) = 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [s](x0) = 1, [from](x0) = x0 + 1, [len](x0) = x0 + 1, [nil] = 1, [0] = 1, [fst#](x0, x1) = x0 Strict: fst#(X1, mark X2) -> fst#(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 Weak: len active X -> len X 2 + 1X >= 1 + 1X len mark X -> len 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 from active X -> from X 2 + 1X >= 1 + 1X from mark X -> from X 2 + 1X >= 1 + 1X s active X -> s X 1 + 0X >= 1 + 0X s mark X -> s X 1 + 0X >= 1 + 0X cons(active X1, X2) -> cons(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 cons(mark X1, X2) -> cons(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 cons(X1, active X2) -> cons(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 cons(X1, mark X2) -> cons(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 fst(active X1, X2) -> fst(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 fst(mark X1, X2) -> fst(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 fst(X1, active X2) -> fst(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 fst(X1, mark X2) -> fst(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 active len cons(X, Z) -> mark s len Z 3 + 0Z + 1X >= 2 + 0Z active len nil() -> mark 0() 3 >= 2 active add(s X, Y) -> mark s add(X, Y) 2 + 0Y + 0X >= 2 + 0Y + 0X active add(0(), X) -> mark X 2 + 0X >= 1 + 1X active from X -> mark cons(X, from s X) 2 + 1X >= 2 + 1X active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)) 2 + 0Z + 0Y + 0X >= 2 + 0Z + 1Y + 0X active fst(0(), Z) -> mark nil() 2 + 0Z >= 2 mark len X -> active len mark X 2 + 1X >= 3 + 1X mark add(X1, X2) -> active add(mark X1, mark X2) 2 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 mark from X -> active from mark X 2 + 1X >= 3 + 1X mark s X -> active s X 2 + 0X >= 2 + 0X mark cons(X1, X2) -> active cons(mark X1, X2) 2 + 1X1 + 0X2 >= 3 + 1X1 + 0X2 mark 0() -> active 0() 2 >= 2 mark fst(X1, X2) -> active fst(mark X1, mark X2) 1 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark nil() -> active nil() 2 >= 2 Qed SCC (4): Strict: { cons#(X1, mark X2) -> cons#(X1, X2), cons#(X1, active X2) -> cons#(X1, X2), cons#(mark X1, X2) -> cons#(X1, X2), cons#(active X1, X2) -> cons#(X1, X2)} Weak: { mark nil() -> active nil(), mark fst(X1, X2) -> active fst(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s X, mark from X -> active from mark X, mark add(X1, X2) -> active add(mark X1, mark X2), mark len X -> active len mark X, active fst(0(), Z) -> mark nil(), active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)), active from X -> mark cons(X, from s X), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active len nil() -> mark 0(), active len cons(X, Z) -> mark s len Z, fst(X1, mark X2) -> fst(X1, X2), fst(X1, active X2) -> fst(X1, X2), fst(mark X1, X2) -> fst(X1, X2), fst(active X1, X2) -> fst(X1, X2), cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X, 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), len mark X -> len X, len active X -> len X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [fst](x0, x1) = 0, [cons](x0, x1) = 0, [add](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [from](x0) = 0, [len](x0) = 0, [nil] = 1, [0] = 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: len active X -> len X 0 + 0X >= 0 + 0X len mark X -> len 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 from active X -> from X 0 + 0X >= 0 + 0X from mark X -> from X 0 + 0X >= 0 + 0X s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X cons(active X1, X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(mark X1, X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(X1, active X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 cons(X1, mark X2) -> cons(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 fst(active X1, X2) -> fst(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 fst(mark X1, X2) -> fst(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 fst(X1, active X2) -> fst(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 fst(X1, mark X2) -> fst(X1, X2) 0 + 0X1 + 0X2 >= 0 + 0X1 + 0X2 active len cons(X, Z) -> mark s len Z 1 + 0Z + 0X >= 0 + 0Z active len nil() -> mark 0() 1 >= 1 active add(s X, Y) -> mark s add(X, Y) 1 + 0Y + 0X >= 0 + 0Y + 0X active add(0(), X) -> mark X 1 + 0X >= 0 + 1X active from X -> mark cons(X, from s X) 1 + 0X >= 0 + 0X active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)) 1 + 0Z + 0Y + 0X >= 0 + 0Z + 0Y + 0X active fst(0(), Z) -> mark nil() 1 + 0Z >= 1 mark len X -> active len mark X 0 + 0X >= 1 + 0X mark add(X1, X2) -> active add(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark from X -> active from mark X 0 + 0X >= 1 + 0X mark s X -> active s X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(mark X1, X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark 0() -> active 0() 1 >= 2 mark fst(X1, X2) -> active fst(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark nil() -> active nil() 1 >= 2 SCCS (1): Scc: { cons#(X1, mark X2) -> cons#(X1, X2), cons#(X1, active X2) -> cons#(X1, X2), cons#(mark X1, X2) -> cons#(X1, X2)} SCC (3): Strict: { cons#(X1, mark X2) -> cons#(X1, X2), cons#(X1, active X2) -> cons#(X1, X2), cons#(mark X1, X2) -> cons#(X1, X2)} Weak: { mark nil() -> active nil(), mark fst(X1, X2) -> active fst(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s X, mark from X -> active from mark X, mark add(X1, X2) -> active add(mark X1, mark X2), mark len X -> active len mark X, active fst(0(), Z) -> mark nil(), active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)), active from X -> mark cons(X, from s X), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active len nil() -> mark 0(), active len cons(X, Z) -> mark s len Z, fst(X1, mark X2) -> fst(X1, X2), fst(X1, active X2) -> fst(X1, X2), fst(mark X1, X2) -> fst(X1, X2), fst(active X1, X2) -> fst(X1, X2), cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X, 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), len mark X -> len X, len active X -> len X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [fst](x0, x1) = x0, [cons](x0, x1) = x0 + 1, [add](x0, x1) = 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [s](x0) = 1, [from](x0) = x0 + 1, [len](x0) = 0, [nil] = 1, [0] = 1, [cons#](x0, x1) = x0 Strict: cons#(mark X1, X2) -> cons#(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 cons#(X1, active X2) -> cons#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 cons#(X1, mark X2) -> cons#(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 Weak: len active X -> len X 0 + 0X >= 0 + 0X len mark X -> len 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 from active X -> from X 2 + 1X >= 1 + 1X from mark X -> from X 2 + 1X >= 1 + 1X s active X -> s X 1 + 0X >= 1 + 0X s mark X -> s X 1 + 0X >= 1 + 0X cons(active X1, X2) -> cons(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 cons(mark X1, X2) -> cons(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 cons(X1, active X2) -> cons(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 cons(X1, mark X2) -> cons(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 fst(active X1, X2) -> fst(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 fst(mark X1, X2) -> fst(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 fst(X1, active X2) -> fst(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 fst(X1, mark X2) -> fst(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 active len cons(X, Z) -> mark s len Z 1 + 0Z + 0X >= 2 + 0Z active len nil() -> mark 0() 1 >= 2 active add(s X, Y) -> mark s add(X, Y) 2 + 0Y + 0X >= 2 + 0Y + 0X active add(0(), X) -> mark X 2 + 0X >= 1 + 1X active from X -> mark cons(X, from s X) 2 + 1X >= 2 + 1X active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)) 2 + 0Z + 1Y + 0X >= 2 + 0Z + 1Y + 0X active fst(0(), Z) -> mark nil() 1 + 1Z >= 2 mark len X -> active len mark X 1 + 0X >= 1 + 0X mark add(X1, X2) -> active add(mark X1, mark X2) 2 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 mark from X -> active from mark X 2 + 1X >= 3 + 1X mark s X -> active s X 2 + 0X >= 2 + 0X mark cons(X1, X2) -> active cons(mark X1, X2) 2 + 1X1 + 0X2 >= 3 + 1X1 + 0X2 mark 0() -> active 0() 2 >= 2 mark fst(X1, X2) -> active fst(mark X1, mark X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 mark nil() -> active nil() 2 >= 2 SCCS (1): Scc: { cons#(X1, mark X2) -> cons#(X1, X2), cons#(X1, active X2) -> cons#(X1, X2)} SCC (2): Strict: { cons#(X1, mark X2) -> cons#(X1, X2), cons#(X1, active X2) -> cons#(X1, X2)} Weak: { mark nil() -> active nil(), mark fst(X1, X2) -> active fst(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s X, mark from X -> active from mark X, mark add(X1, X2) -> active add(mark X1, mark X2), mark len X -> active len mark X, active fst(0(), Z) -> mark nil(), active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)), active from X -> mark cons(X, from s X), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active len nil() -> mark 0(), active len cons(X, Z) -> mark s len Z, fst(X1, mark X2) -> fst(X1, X2), fst(X1, active X2) -> fst(X1, X2), fst(mark X1, X2) -> fst(X1, X2), fst(active X1, X2) -> fst(X1, X2), cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X, 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), len mark X -> len X, len active X -> len X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [fst](x0, x1) = x0 + 1, [cons](x0, x1) = x0, [add](x0, x1) = 0, [mark](x0) = x0, [active](x0) = x0 + 1, [s](x0) = 0, [from](x0) = 0, [len](x0) = 0, [nil] = 1, [0] = 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: len active X -> len X 0 + 0X >= 0 + 0X len mark X -> len 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 from active X -> from X 0 + 0X >= 0 + 0X from mark X -> from X 0 + 0X >= 0 + 0X s active X -> s X 0 + 0X >= 0 + 0X s mark X -> s X 0 + 0X >= 0 + 0X cons(active X1, X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(mark X1, X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(X1, active X2) -> cons(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 cons(X1, mark X2) -> cons(X1, X2) 0 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 fst(active X1, X2) -> fst(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 fst(mark X1, X2) -> fst(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 fst(X1, active X2) -> fst(X1, X2) 2 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 fst(X1, mark X2) -> fst(X1, X2) 1 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 active len cons(X, Z) -> mark s len Z 1 + 0Z + 0X >= 0 + 0Z active len nil() -> mark 0() 1 >= 1 active add(s X, Y) -> mark s add(X, Y) 1 + 0Y + 0X >= 0 + 0Y + 0X active add(0(), X) -> mark X 1 + 0X >= 0 + 1X active from X -> mark cons(X, from s X) 1 + 0X >= 0 + 0X active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)) 2 + 1Z + 0Y + 0X >= 1 + 1Z + 0Y + 0X active fst(0(), Z) -> mark nil() 2 + 1Z >= 1 mark len X -> active len mark X 0 + 0X >= 1 + 0X mark add(X1, X2) -> active add(mark X1, mark X2) 0 + 0X1 + 0X2 >= 1 + 0X1 + 0X2 mark from X -> active from mark X 0 + 0X >= 1 + 0X mark s X -> active s X 0 + 0X >= 1 + 0X mark cons(X1, X2) -> active cons(mark X1, X2) 0 + 0X1 + 1X2 >= 1 + 0X1 + 1X2 mark 0() -> active 0() 1 >= 2 mark fst(X1, X2) -> active fst(mark X1, mark X2) 1 + 0X1 + 1X2 >= 2 + 0X1 + 1X2 mark nil() -> active nil() 1 >= 2 SCCS (1): Scc: {cons#(X1, mark X2) -> cons#(X1, X2)} SCC (1): Strict: {cons#(X1, mark X2) -> cons#(X1, X2)} Weak: { mark nil() -> active nil(), mark fst(X1, X2) -> active fst(mark X1, mark X2), mark 0() -> active 0(), mark cons(X1, X2) -> active cons(mark X1, X2), mark s X -> active s X, mark from X -> active from mark X, mark add(X1, X2) -> active add(mark X1, mark X2), mark len X -> active len mark X, active fst(0(), Z) -> mark nil(), active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)), active from X -> mark cons(X, from s X), active add(0(), X) -> mark X, active add(s X, Y) -> mark s add(X, Y), active len nil() -> mark 0(), active len cons(X, Z) -> mark s len Z, fst(X1, mark X2) -> fst(X1, X2), fst(X1, active X2) -> fst(X1, X2), fst(mark X1, X2) -> fst(X1, X2), fst(active X1, X2) -> fst(X1, X2), cons(X1, mark X2) -> cons(X1, X2), cons(X1, active X2) -> cons(X1, X2), cons(mark X1, X2) -> cons(X1, X2), cons(active X1, X2) -> cons(X1, X2), s mark X -> s X, s active X -> s X, from mark X -> from X, from active X -> from X, 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), len mark X -> len X, len active X -> len X} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [fst](x0, x1) = x0, [cons](x0, x1) = x0 + 1, [add](x0, x1) = 1, [mark](x0) = x0 + 1, [active](x0) = x0 + 1, [s](x0) = 1, [from](x0) = x0 + 1, [len](x0) = x0 + 1, [nil] = 1, [0] = 1, [cons#](x0, x1) = x0 Strict: cons#(X1, mark X2) -> cons#(X1, X2) 1 + 0X1 + 1X2 >= 0 + 0X1 + 1X2 Weak: len active X -> len X 2 + 1X >= 1 + 1X len mark X -> len 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 from active X -> from X 2 + 1X >= 1 + 1X from mark X -> from X 2 + 1X >= 1 + 1X s active X -> s X 1 + 0X >= 1 + 0X s mark X -> s X 1 + 0X >= 1 + 0X cons(active X1, X2) -> cons(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 cons(mark X1, X2) -> cons(X1, X2) 2 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 cons(X1, active X2) -> cons(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 cons(X1, mark X2) -> cons(X1, X2) 1 + 1X1 + 0X2 >= 1 + 1X1 + 0X2 fst(active X1, X2) -> fst(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 fst(mark X1, X2) -> fst(X1, X2) 1 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 fst(X1, active X2) -> fst(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 fst(X1, mark X2) -> fst(X1, X2) 0 + 1X1 + 0X2 >= 0 + 1X1 + 0X2 active len cons(X, Z) -> mark s len Z 3 + 0Z + 1X >= 2 + 0Z active len nil() -> mark 0() 3 >= 2 active add(s X, Y) -> mark s add(X, Y) 2 + 0Y + 0X >= 2 + 0Y + 0X active add(0(), X) -> mark X 2 + 0X >= 1 + 1X active from X -> mark cons(X, from s X) 2 + 1X >= 2 + 1X active fst(s X, cons(Y, Z)) -> mark cons(Y, fst(X, Z)) 2 + 0Z + 0Y + 0X >= 2 + 0Z + 1Y + 0X active fst(0(), Z) -> mark nil() 2 + 0Z >= 2 mark len X -> active len mark X 2 + 1X >= 3 + 1X mark add(X1, X2) -> active add(mark X1, mark X2) 2 + 0X1 + 0X2 >= 2 + 0X1 + 0X2 mark from X -> active from mark X 2 + 1X >= 3 + 1X mark s X -> active s X 2 + 0X >= 2 + 0X mark cons(X1, X2) -> active cons(mark X1, X2) 2 + 1X1 + 0X2 >= 3 + 1X1 + 0X2 mark 0() -> active 0() 2 >= 2 mark fst(X1, X2) -> active fst(mark X1, mark X2) 1 + 1X1 + 0X2 >= 2 + 1X1 + 0X2 mark nil() -> active nil() 2 >= 2 Qed