*** 1 Progress [(O(1),O(n^1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: check(no(x)) -> no(x) check(no(x)) -> no(check(x)) check(rec(x)) -> rec(check(x)) check(sent(x)) -> sent(check(x)) check(up(x)) -> up(check(x)) no(up(x)) -> up(no(x)) rec(bot()) -> up(sent(bot())) rec(no(x)) -> sent(rec(x)) rec(rec(x)) -> sent(rec(x)) rec(sent(x)) -> sent(rec(x)) rec(up(x)) -> up(rec(x)) sent(up(x)) -> up(sent(x)) top(no(up(x))) -> top(check(rec(x))) top(rec(up(x))) -> top(check(rec(x))) top(sent(up(x))) -> top(check(rec(x))) Weak DP Rules: Weak TRS Rules: Signature: {check/1,no/1,rec/1,sent/1,top/1} / {bot/0,up/1} Obligation: Full basic terms: {check,no,rec,sent,top}/{bot,up} Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} Proof: The problem is match-bounded by 1. The enriched problem is compatible with follwoing automaton. bot_0() -> 2 bot_1() -> 4 check_0(2) -> 1 check_1(2) -> 3 no_0(2) -> 1 no_1(2) -> 3 rec_0(2) -> 1 rec_1(2) -> 3 sent_0(2) -> 1 sent_1(2) -> 3 sent_1(4) -> 3 top_0(2) -> 1 up_0(2) -> 2 up_1(3) -> 1 up_1(3) -> 3 *** 1.1 Progress [(O(1),O(1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: Weak DP Rules: Weak TRS Rules: check(no(x)) -> no(x) check(no(x)) -> no(check(x)) check(rec(x)) -> rec(check(x)) check(sent(x)) -> sent(check(x)) check(up(x)) -> up(check(x)) no(up(x)) -> up(no(x)) rec(bot()) -> up(sent(bot())) rec(no(x)) -> sent(rec(x)) rec(rec(x)) -> sent(rec(x)) rec(sent(x)) -> sent(rec(x)) rec(up(x)) -> up(rec(x)) sent(up(x)) -> up(sent(x)) top(no(up(x))) -> top(check(rec(x))) top(rec(up(x))) -> top(check(rec(x))) top(sent(up(x))) -> top(check(rec(x))) Signature: {check/1,no/1,rec/1,sent/1,top/1} / {bot/0,up/1} Obligation: Full basic terms: {check,no,rec,sent,top}/{bot,up} Applied Processor: EmptyProcessor Proof: The problem is already closed. The intended complexity is O(1).