details

property	value
status	complete
benchmark	272.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n092.star.cs.uiowa.edu
space	COPS

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.4947988987 seconds
cpu usage	6.119252175
max memory	4.78674944E8

stage attributes

key	value
output-size	3911
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Quasi decreasingness of the given CTRS could be proven: (0) CTRS (1) CTRSToQTRSProof [SOUND, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 155 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 0 ms] (6) QTRS (7) RisEmptyProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Conditional term rewrite system: The TRS R consists of the following rules: lte(0, n) -> true lte(s(m), 0) -> false lte(s(m), s(n)) -> lte(m, n) insert(nil, m) -> cons(m, nil) ordered(nil) -> true ordered(cons(m, nil)) -> true The conditional TRS C consists of the following conditional rules: insert(cons(n, l), m) -> cons(m, cons(n, l)) <= lte(m, n) -> true insert(cons(n, l), m) -> cons(n, insert(l, m)) <= lte(m, n) -> false ordered(cons(m, cons(n, l))) -> ordered(cons(n, l)) <= lte(m, n) -> true ordered(cons(m, cons(n, l))) -> false <= lte(m, n) -> false ---------------------------------------- (1) CTRSToQTRSProof (SOUND) The conditional rules have been transormed into unconditional rules according to [CTRS,AAECCNOC]. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: insert(cons(n, l), m) -> U1(lte(m, n), n, l, m) U1(false, n, l, m) -> cons(n, insert(l, m)) U1(true, n, l, m) -> cons(m, cons(n, l)) ordered(cons(m, cons(n, l))) -> U2(lte(m, n), n, l) U2(true, n, l) -> ordered(cons(n, l)) U2(false, n, l) -> false lte(0, n) -> true lte(s(m), 0) -> false lte(s(m), s(n)) -> lte(m, n) insert(nil, m) -> cons(m, nil) ordered(nil) -> true ordered(cons(m, nil)) -> true Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: insert/2(YES,YES) cons/2(YES,YES) U1/4(YES,YES,YES,YES) lte/2(YES,YES) false/0) true/0) ordered/1)YES( U2/3(YES,YES,YES) 0/0) s/1)YES( nil/0) Quasi precedence: [insert_2, U1_4, nil] > [true, 0] > [cons_2, lte_2, U2_3] > false Status: insert_2: [1,2] cons_2: [2,1] U1_4: [3,4,1,2] lte_2: [2,1] false: multiset status true: multiset status U2_3: [3,2,1] popout

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job log

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actions

all output return to TRS Conditional