details

property	value
status	complete
benchmark	Ex8Polymorphic.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n034.star.cs.uiowa.edu
space	Applicative_05

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.3019490242 seconds
cpu usage	5.935239531
max memory	4.74361856E8

stage attributes

key	value
output-size	5608
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof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, 37 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) QDP (7) QDPSizeChangeProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: app(app(twice, f), x) -> app(f, app(f, x)) app(app(map, f), nil) -> nil app(app(map, f), app(app(cons, h), t)) -> app(app(cons, app(f, h)), app(app(map, f), t)) app(app(fmap, nil), x) -> nil app(app(fmap, app(app(cons, f), t_f)), x) -> app(app(cons, app(f, x)), app(app(fmap, t_f), x)) 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(twice, f), x) -> app(f, app(f, x)) app(app(map, f), nil) -> nil app(app(map, f), app(app(cons, h), t)) -> app(app(cons, app(f, h)), app(app(map, f), t)) app(app(fmap, nil), x) -> nil app(app(fmap, app(app(cons, f), t_f)), x) -> app(app(cons, app(f, x)), app(app(fmap, t_f), x)) The set Q consists of the following terms: app(app(twice, x0), x1) app(app(map, x0), nil) app(app(map, x0), app(app(cons, x1), x2)) app(app(fmap, nil), x0) app(app(fmap, app(app(cons, x0), t_f)), x1) ---------------------------------------- (3) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: APP(app(twice, f), x) -> APP(f, app(f, x)) APP(app(twice, f), x) -> APP(f, x) APP(app(map, f), app(app(cons, h), t)) -> APP(app(cons, app(f, h)), app(app(map, f), t)) APP(app(map, f), app(app(cons, h), t)) -> APP(cons, app(f, h)) APP(app(map, f), app(app(cons, h), t)) -> APP(f, h) APP(app(map, f), app(app(cons, h), t)) -> APP(app(map, f), t) APP(app(fmap, app(app(cons, f), t_f)), x) -> APP(app(cons, app(f, x)), app(app(fmap, t_f), x)) APP(app(fmap, app(app(cons, f), t_f)), x) -> APP(cons, app(f, x)) APP(app(fmap, app(app(cons, f), t_f)), x) -> APP(f, x) APP(app(fmap, app(app(cons, f), t_f)), x) -> APP(app(fmap, t_f), x) APP(app(fmap, app(app(cons, f), t_f)), x) -> APP(fmap, t_f) The TRS R consists of the following rules: app(app(twice, f), x) -> app(f, app(f, x)) app(app(map, f), nil) -> nil app(app(map, f), app(app(cons, h), t)) -> app(app(cons, app(f, h)), app(app(map, f), t)) app(app(fmap, nil), x) -> nil app(app(fmap, app(app(cons, f), t_f)), x) -> app(app(cons, app(f, x)), app(app(fmap, t_f), x)) The set Q consists of the following terms: app(app(twice, x0), x1) app(app(map, x0), nil) popout

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

job log

popout

actions

all output return to TRS Standard