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	n181.star.cs.uiowa.edu
space	CiME_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.72464 seconds
cpu usage	3.9426
user time	3.76592
system time	0.176685
max virtual memory	1.840914E7
max residence set size	250888.0

stage attributes

key	value
starexec-result	YES

output

YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 116 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4)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: prod/1(YES) nil/0) s/1)YES( 0/0) Quasi precedence: prod_1 > 0 nil > 0 Status: popout

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

job log

popout

actions

all output return to TRS Standard