details

property	value
status	complete
benchmark	019.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n141.star.cs.uiowa.edu
space	AotoYamada_05

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.13316702843 seconds
cpu usage	5.516565219
max memory	4.71855104E8

stage attributes

key	value
output-size	3391
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 0 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(app(comp, f), g), x) -> app(f, app(g, x)) app(twice, f) -> app(app(comp, f), f) 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(app(comp, f), g), x) -> app(f, app(g, x)) app(twice, f) -> app(app(comp, f), f) The set Q consists of the following terms: app(app(app(comp, x0), x1), x2) app(twice, x0) ---------------------------------------- (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(app(comp, f), g), x) -> APP(f, app(g, x)) APP(app(app(comp, f), g), x) -> APP(g, x) APP(twice, f) -> APP(app(comp, f), f) APP(twice, f) -> APP(comp, f) The TRS R consists of the following rules: app(app(app(comp, f), g), x) -> app(f, app(g, x)) app(twice, f) -> app(app(comp, f), f) The set Q consists of the following terms: app(app(app(comp, x0), x1), x2) app(twice, x0) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (5) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (6) Obligation: Q DP problem: The TRS P consists of the following rules: APP(app(app(comp, f), g), x) -> APP(g, x) APP(app(app(comp, f), g), x) -> APP(f, app(g, x)) The TRS R consists of the following rules: app(app(app(comp, f), g), x) -> app(f, app(g, x)) popout

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

job log

popout

actions

all output return to TRS Standard