details

property	value
status	complete
benchmark	list-sum-prod-assoc.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n156.star.cs.uiowa.edu
space	CiME_04

run statistics

property	value
solver	AProVE23
configuration	standard
runtime (wallclock)	1.75251889229 seconds
cpu usage	4.476431632
max memory	2.73784832E8

stage attributes

key	value
output-size	2706
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# AProVE Commit ID: 363435ff5b19173ec8a83b45cfdec073678dabcc jan-christoph 20230815 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 133 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4) QTRS (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: +(x, 0) -> x +(0, x) -> x +(s(x), s(y)) -> s(s(+(x, y))) +(+(x, y), z) -> +(x, +(y, z)) *(x, 0) -> 0 *(0, x) -> 0 *(s(x), s(y)) -> s(+(*(x, y), +(x, y))) *(*(x, y), z) -> *(x, *(y, z)) sum(nil) -> 0 sum(cons(x, l)) -> +(x, sum(l)) prod(nil) -> s(0) prod(cons(x, l)) -> *(x, prod(l)) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Quasi precedence: sum_1 > +_2 > [s_1, prod_1] > [0, nil] cons_2 > *_2 > +_2 > [s_1, prod_1] > [0, nil] Status: +_2: [1,2] 0: multiset status s_1: multiset status *_2: [1,2] sum_1: multiset status nil: multiset status cons_2: multiset status prod_1: multiset status With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: +(x, 0) -> x +(0, x) -> x +(s(x), s(y)) -> s(s(+(x, y))) +(+(x, y), z) -> +(x, +(y, z)) *(x, 0) -> 0 *(0, x) -> 0 *(s(x), s(y)) -> s(+(*(x, y), +(x, y))) *(*(x, y), z) -> *(x, *(y, z)) sum(nil) -> 0 sum(cons(x, l)) -> +(x, sum(l)) prod(cons(x, l)) -> *(x, prod(l)) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: prod(nil) -> s(0) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Knuth-Bendix order [KBO] with precedence:0 > prod_1 > s_1 > nil and weight map: nil=1 popout

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actions

all output return to TRS Standard