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TRS Standard pair #516965045
details
property
value
status
complete
benchmark
016.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n083.star.cs.uiowa.edu
space
AotoYamada_05
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.44936704636 seconds
cpu usage
6.469027863
max memory
4.8218112E8
stage attributes
key
value
output-size
15979
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 36 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) QDP (8) UsableRulesProof [EQUIVALENT, 0 ms] (9) QDP (10) QReductionProof [EQUIVALENT, 0 ms] (11) QDP (12) ATransformationProof [EQUIVALENT, 0 ms] (13) QDP (14) QReductionProof [EQUIVALENT, 0 ms] (15) QDP (16) QDPSizeChangeProof [EQUIVALENT, 0 ms] (17) YES (18) QDP (19) UsableRulesProof [EQUIVALENT, 0 ms] (20) QDP (21) QReductionProof [EQUIVALENT, 0 ms] (22) QDP (23) QDPSizeChangeProof [EQUIVALENT, 0 ms] (24) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: app(app(neq, 0), 0) -> false app(app(neq, 0), app(s, y)) -> true app(app(neq, app(s, x)), 0) -> true app(app(neq, app(s, x)), app(s, y)) -> app(app(neq, x), y) app(app(filter, f), nil) -> nil app(app(filter, f), app(app(cons, y), ys)) -> app(app(app(filtersub, app(f, y)), f), app(app(cons, y), ys)) app(app(app(filtersub, true), f), app(app(cons, y), ys)) -> app(app(cons, y), app(app(filter, f), ys)) app(app(app(filtersub, false), f), app(app(cons, y), ys)) -> app(app(filter, f), ys) nonzero -> app(filter, app(neq, 0)) Q is empty. ---------------------------------------- (1) Overlay + Local Confluence (EQUIVALENT) The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: app(app(neq, 0), 0) -> false app(app(neq, 0), app(s, y)) -> true app(app(neq, app(s, x)), 0) -> true app(app(neq, app(s, x)), app(s, y)) -> app(app(neq, x), y) app(app(filter, f), nil) -> nil app(app(filter, f), app(app(cons, y), ys)) -> app(app(app(filtersub, app(f, y)), f), app(app(cons, y), ys)) app(app(app(filtersub, true), f), app(app(cons, y), ys)) -> app(app(cons, y), app(app(filter, f), ys)) app(app(app(filtersub, false), f), app(app(cons, y), ys)) -> app(app(filter, f), ys) nonzero -> app(filter, app(neq, 0)) The set Q consists of the following terms: app(app(neq, 0), 0) app(app(neq, 0), app(s, x0)) app(app(neq, app(s, x0)), 0) app(app(neq, app(s, x0)), app(s, x1)) app(app(filter, x0), nil) app(app(filter, x0), app(app(cons, x1), x2)) app(app(app(filtersub, true), x0), app(app(cons, x1), x2)) app(app(app(filtersub, false), x0), app(app(cons, x1), x2)) nonzero ---------------------------------------- (3) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (4)
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