details

property	value
status	complete
benchmark	322.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n028.star.cs.uiowa.edu
space	COPS

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.27748894691 seconds
cpu usage	5.869321264
max memory	4.72588288E8

stage attributes

key	value
output-size	2991
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Quasi decreasingness of the given CTRS could be proven: (0) CTRS (1) CTRSToQTRSProof [SOUND, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 144 ms] (4) QTRS (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Conditional term rewrite system: The TRS R consists of the following rules: split(x, nil) -> tp2(nil, nil) le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) The conditional TRS C consists of the following conditional rules: split(x, cons(y, ys)) -> tp2(zs1, cons(y, zs2)) <= split(x, ys) -> tp2(zs1, zs2), le(x, y) -> true split(x, cons(y, ys)) -> tp2(cons(y, zs1), zs2) <= split(x, ys) -> tp2(zs1, zs2), le(x, y) -> false ---------------------------------------- (1) CTRSToQTRSProof (SOUND) The conditional rules have been transormed into unconditional rules according to [CTRS,AAECCNOC]. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: split(x, cons(y, ys)) -> U1(split(x, ys), x, y) U1(tp2(zs1, zs2), x, y) -> U2(le(x, y), y, zs1, zs2) U2(false, y, zs1, zs2) -> tp2(cons(y, zs1), zs2) U2(true, y, zs1, zs2) -> tp2(zs1, cons(y, zs2)) split(x, nil) -> tp2(nil, nil) le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Quasi precedence: split_2 > U1_3 > U2_4 > [cons_2, tp2_2, le_2] split_2 > nil > [cons_2, tp2_2, le_2] 0 > [false, s_1] > [cons_2, tp2_2, le_2] 0 > true > [cons_2, tp2_2, le_2] Status: split_2: multiset status cons_2: [1,2] U1_3: multiset status tp2_2: multiset status U2_4: multiset status le_2: multiset status false: multiset status true: multiset status nil: multiset status 0: multiset status s_1: [1] With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: split(x, cons(y, ys)) -> U1(split(x, ys), x, y) U1(tp2(zs1, zs2), x, y) -> U2(le(x, y), y, zs1, zs2) U2(false, y, zs1, zs2) -> tp2(cons(y, zs1), zs2) U2(true, y, zs1, zs2) -> tp2(zs1, cons(y, zs2)) split(x, nil) -> tp2(nil, nil) le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) popout

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actions

all output return to TRS Conditional