details

property	value
status	complete
benchmark	Ex2_8_1ConstSubstFix.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n191.star.cs.uiowa.edu
space	Applicative_05

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	6.51378 seconds
cpu usage	11.7562
user time	11.2906
system time	0.4656
max virtual memory	1.8646456E7
max residence set size	707968.0

stage attributes

key	value
starexec-result	NO

output

NO 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be disproven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 0 ms] (4) QDP (5) TransformationProof [EQUIVALENT, 0 ms] (6) QDP (7) TransformationProof [EQUIVALENT, 0 ms] (8) QDP (9) TransformationProof [EQUIVALENT, 0 ms] (10) QDP (11) MNOCProof [EQUIVALENT, 0 ms] (12) QDP (13) NonTerminationLoopProof [COMPLETE, 0 ms] (14) NO ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: app(app(const, x), y) -> x app(app(app(subst, f), g), x) -> app(app(f, x), app(g, x)) app(app(fix, f), x) -> app(app(f, app(fix, 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(const, x), y) -> x app(app(app(subst, f), g), x) -> app(app(f, x), app(g, x)) app(app(fix, f), x) -> app(app(f, app(fix, f)), x) The set Q consists of the following terms: app(app(const, x0), x1) app(app(app(subst, x0), x1), x2) app(app(fix, x0), 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(app(subst, f), g), x) -> APP(app(f, x), app(g, x)) APP(app(app(subst, f), g), x) -> APP(f, x) APP(app(app(subst, f), g), x) -> APP(g, x) APP(app(fix, f), x) -> APP(app(f, app(fix, f)), x) APP(app(fix, f), x) -> APP(f, app(fix, f)) The TRS R consists of the following rules: app(app(const, x), y) -> x app(app(app(subst, f), g), x) -> app(app(f, x), app(g, x)) app(app(fix, f), x) -> app(app(f, app(fix, f)), x) The set Q consists of the following terms: app(app(const, x0), x1) app(app(app(subst, x0), x1), x2) app(app(fix, x0), x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (5) TransformationProof (EQUIVALENT) By forward instantiating [JAR06] the rule APP(app(app(subst, f), g), x) -> APP(f, x) we obtained the following new rules [LPAR04]: (APP(app(app(subst, app(app(subst, y_0), y_1)), x1), x2) -> APP(app(app(subst, y_0), y_1), x2),APP(app(app(subst, app(app(subst, y_0), y_1)), x1), x2) -> APP(app(app(subst, y_0), y_1), x2)) (APP(app(app(subst, app(fix, y_0)), x1), x2) -> APP(app(fix, y_0), x2),APP(app(app(subst, app(fix, y_0)), x1), x2) -> APP(app(fix, y_0), x2)) ---------------------------------------- popout

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job log

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actions

all output return to TRS Standard