details

property	value
status	complete
benchmark	minus1.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n084.star.cs.uiowa.edu
space	Mixed_CTRS_2014

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.06337594986 seconds
cpu usage	5.360995126
max memory	4.7925248E8

stage attributes

key	value
output-size	1998
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Quasi decreasingness of the given CTRS could be proven: (0) CTRS (1) CTRSToQTRSProof [SOUND, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 35 ms] (4) QTRS (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Conditional term rewrite system: The TRS R consists of the following rules: minus(x, 0) -> x The conditional TRS C consists of the following conditional rules: minus(x, s(y)) -> z <= minus(x, y) -> s(z) ---------------------------------------- (1) CTRSToQTRSProof (SOUND) The conditional rules have been transormed into unconditional rules according to [CTRS,AAECCNOC]. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: minus(x, s(y)) -> U1(minus(x, y)) U1(s(z)) -> z minus(x, 0) -> x Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Knuth-Bendix order [KBO] with precedence:minus_2 > U1_1 > s_1 > 0 and weight map: 0=1 s_1=2 U1_1=1 minus_2=0 The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: minus(x, s(y)) -> U1(minus(x, y)) U1(s(z)) -> z minus(x, 0) -> x ---------------------------------------- (4) Obligation: Q restricted rewrite system: R is empty. Q is empty. ---------------------------------------- (5) RisEmptyProof (EQUIVALENT) The TRS R is empty. Hence, termination is trivially proven. ---------------------------------------- (6) YES popout

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job log

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actions

all output return to TRS Conditional