details

property	value
status	complete
benchmark	2.07.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n055.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.2349729538 seconds
cpu usage	5.400035133
max memory	4.728832E8

stage attributes

key	value
output-size	1752
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 97 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(0, y) -> y f(x, 0) -> x f(i(x), y) -> i(x) f(f(x, y), z) -> f(x, f(y, z)) f(g(x, y), z) -> g(f(x, z), f(y, z)) f(1, g(x, y)) -> x f(2, g(x, y)) -> y Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: f/2(YES,YES) 0/0) i/1)YES( g/2(YES,YES) 1/0) 2/0) Quasi precedence: f_2 > g_2 0 > g_2 1 > g_2 2 > g_2 Status: f_2: [1,2] 0: multiset status g_2: [1,2] 1: multiset status 2: multiset status With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: f(0, y) -> y f(x, 0) -> x f(i(x), y) -> i(x) f(f(x, y), z) -> f(x, f(y, z)) f(g(x, y), z) -> g(f(x, z), f(y, z)) f(1, g(x, y)) -> x f(2, g(x, y)) -> y ---------------------------------------- (2) Obligation: Q restricted rewrite system: R is empty. Q is empty. ---------------------------------------- (3) RisEmptyProof (EQUIVALENT) The TRS R is empty. Hence, termination is trivially proven. ---------------------------------------- (4) YES popout

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job log

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actions

all output return to TRS Standard