details

property	value
status	complete
benchmark	4.03.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n183.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.86917 seconds
cpu usage	4.00335
user time	3.80592
system time	0.197427
max virtual memory	1.8408912E7
max residence set size	245908.0

stage attributes

key	value
starexec-result	YES

output

YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 44 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 13 ms] (4) QTRS (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: +(x, 0) -> x +(minus(x), x) -> 0 minus(0) -> 0 minus(minus(x)) -> x minus(+(x, y)) -> +(minus(y), minus(x)) *(x, 1) -> x *(x, 0) -> 0 *(x, +(y, z)) -> +(*(x, y), *(x, z)) *(x, minus(y)) -> minus(*(x, y)) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: +/2(YES,YES) 0/0) minus/1)YES( */2(YES,YES) 1/0) Quasi precedence: *_2 > +_2 > 0 Status: +_2: multiset status 0: multiset status *_2: [1,2] 1: multiset status With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: +(x, 0) -> x +(minus(x), x) -> 0 *(x, 1) -> x *(x, 0) -> 0 *(x, +(y, z)) -> +(*(x, y), *(x, z)) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: minus(0) -> 0 minus(minus(x)) -> x minus(+(x, y)) -> +(minus(y), minus(x)) *(x, minus(y)) -> minus(*(x, y)) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Quasi precedence: *_2 > minus_1 > 0 *_2 > minus_1 > +_2 Status: minus_1: multiset status 0: multiset status +_2: multiset status *_2: [1,2] With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: minus(0) -> 0 minus(minus(x)) -> x minus(+(x, y)) -> +(minus(y), minus(x)) popout

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