details

property	value
status	complete
benchmark	4.14.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n060.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.24353313446 seconds
cpu usage	5.815202661
max memory	4.79076352E8

stage attributes

key	value
output-size	2608
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 112 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4) QTRS (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: p(s(x)) -> x s(p(x)) -> x +(0, y) -> y +(s(x), y) -> s(+(x, y)) +(p(x), y) -> p(+(x, y)) minus(0) -> 0 minus(s(x)) -> p(minus(x)) minus(p(x)) -> s(minus(x)) *(0, y) -> 0 *(s(x), y) -> +(*(x, y), y) *(p(x), y) -> +(*(x, y), minus(y)) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: p/1(YES) s/1(YES) +/2(YES,YES) 0/0) minus/1)YES( */2(YES,YES) Quasi precedence: *_2 > +_2 > [p_1, s_1] > 0 Status: p_1: multiset status s_1: multiset status +_2: multiset status 0: multiset status *_2: multiset status With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: p(s(x)) -> x s(p(x)) -> x +(0, y) -> y +(s(x), y) -> s(+(x, y)) +(p(x), y) -> p(+(x, y)) *(0, y) -> 0 *(s(x), y) -> +(*(x, y), y) *(p(x), y) -> +(*(x, y), minus(y)) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: minus(0) -> 0 minus(s(x)) -> p(minus(x)) minus(p(x)) -> s(minus(x)) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Knuth-Bendix order [KBO] with precedence:minus_1 > p_1 > 0 > s_1 and weight map: popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to TRS Standard