details

property	value
status	complete
benchmark	4.20.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n005.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	AProVE23
configuration	standard
runtime (wallclock)	1.71056890488 seconds
cpu usage	4.245126911
max memory	2.62098944E8

stage attributes

key	value
output-size	2073
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# AProVE Commit ID: 363435ff5b19173ec8a83b45cfdec073678dabcc jan-christoph 20230815 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 96 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: not(x) -> xor(x, true) or(x, y) -> xor(and(x, y), xor(x, y)) implies(x, y) -> xor(and(x, y), xor(x, true)) and(x, true) -> x and(x, false) -> false and(x, x) -> x xor(x, false) -> x xor(x, x) -> false and(xor(x, y), z) -> xor(and(x, z), and(y, z)) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Quasi precedence: or_2 > and_2 > [xor_2, false] implies_2 > [not_1, true] > [xor_2, false] implies_2 > and_2 > [xor_2, false] Status: not_1: multiset status xor_2: multiset status true: multiset status or_2: multiset status and_2: multiset status implies_2: multiset status false: multiset status With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: not(x) -> xor(x, true) or(x, y) -> xor(and(x, y), xor(x, y)) implies(x, y) -> xor(and(x, y), xor(x, true)) and(x, true) -> x and(x, false) -> false and(x, x) -> x xor(x, false) -> x xor(x, x) -> false and(xor(x, y), z) -> xor(and(x, z), and(y, z)) ---------------------------------------- (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

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

job log

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actions

all output return to TRS Standard