details

property	value
status	complete
benchmark	4.02.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n062.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	AProVE23
configuration	standard
runtime (wallclock)	1.74256682396 seconds
cpu usage	4.514811549
max memory	2.59956736E8

stage attributes

key	value
output-size	2077
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# AProVE Commit ID: 363435ff5b19173ec8a83b45cfdec073678dabcc jan-christoph 20230815 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 86 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: *(x, 1) -> x *(1, y) -> y *(i(x), x) -> 1 *(x, i(x)) -> 1 *(x, *(y, z)) -> *(*(x, y), z) i(1) -> 1 *(*(x, y), i(y)) -> x *(*(x, i(y)), y) -> x i(i(x)) -> x i(*(x, y)) -> *(i(y), i(x)) k(x, 1) -> 1 k(x, x) -> 1 *(k(x, y), k(y, x)) -> 1 *(*(i(x), k(y, z)), x) -> k(*(*(i(x), y), x), *(*(i(x), z), x)) k(*(x, i(y)), *(y, i(x))) -> 1 Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Quasi precedence: i_1 > *_2 > [1, k_2] Status: *_2: [2,1] 1: multiset status i_1: [1] k_2: [1,2] With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: *(x, 1) -> x *(1, y) -> y *(i(x), x) -> 1 *(x, i(x)) -> 1 *(x, *(y, z)) -> *(*(x, y), z) i(1) -> 1 *(*(x, y), i(y)) -> x *(*(x, i(y)), y) -> x i(i(x)) -> x i(*(x, y)) -> *(i(y), i(x)) k(x, 1) -> 1 k(x, x) -> 1 *(k(x, y), k(y, x)) -> 1 *(*(i(x), k(y, z)), x) -> k(*(*(i(x), y), x), *(*(i(x), z), x)) k(*(x, i(y)), *(y, i(x))) -> 1 ---------------------------------------- (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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all output return to TRS Standard