details

property	value
status	complete
benchmark	353.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n056.star.cs.uiowa.edu
space	COPS

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.83001613617 seconds
cpu usage	8.171653115
max memory	5.68700928E8

stage attributes

key	value
output-size	15627
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Quasi decreasingness of the given CTRS could be proven: (0) CTRS (1) CTRSToQTRSProof [SOUND, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 120 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 28 ms] (6) QTRS (7) QTRSRRRProof [EQUIVALENT, 30 ms] (8) QTRS (9) QTRSRRRProof [EQUIVALENT, 0 ms] (10) QTRS (11) DependencyPairsProof [EQUIVALENT, 0 ms] (12) QDP (13) DependencyGraphProof [EQUIVALENT, 0 ms] (14) AND (15) QDP (16) UsableRulesProof [EQUIVALENT, 0 ms] (17) QDP (18) QDPSizeChangeProof [EQUIVALENT, 0 ms] (19) YES (20) QDP (21) UsableRulesReductionPairsProof [EQUIVALENT, 10 ms] (22) QDP (23) MRRProof [EQUIVALENT, 0 ms] (24) QDP (25) DependencyGraphProof [EQUIVALENT, 0 ms] (26) TRUE ---------------------------------------- (0) Obligation: Conditional term rewrite system: The TRS R consists of the following rules: ssp'(xs, 0) -> nil sub(z, 0) -> z get(cons(y, ys)) -> tp2(y, ys) The conditional TRS C consists of the following conditional rules: ssp'(cons(y', ws), v) -> cons(y', ys') <= sub(v, y') -> w, ssp'(ws, w) -> ys' ssp'(cons(x', xs'), v) -> cons(y', ys') <= get(xs') -> tp2(y', zs), sub(v, y') -> w, ssp'(cons(x', zs), w) -> ys' sub(s(v), s(w)) -> z <= sub(v, w) -> z get(cons(x', xs')) -> tp2(y, cons(x', zs)) <= get(xs') -> tp2(y, zs) ---------------------------------------- (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: ssp'(cons(y', ws), v) -> U1(sub(v, y'), y', ws) U1(w, y', ws) -> U2(ssp'(ws, w), y') U2(ys', y') -> cons(y', ys') ssp'(cons(x', xs'), v) -> U3(get(xs'), x', v) U3(tp2(y', zs), x', v) -> U4(sub(v, y'), x', y', zs) U4(w, x', y', zs) -> U5(ssp'(cons(x', zs), w), y') U5(ys', y') -> cons(y', ys') sub(s(v), s(w)) -> U6(sub(v, w)) U6(z) -> z get(cons(x', xs')) -> U7(get(xs'), x') U7(tp2(y, zs), x') -> tp2(y, cons(x', zs)) ssp'(xs, 0) -> nil sub(z, 0) -> z get(cons(y, ys)) -> tp2(y, ys) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(U1(x_1, x_2, x_3)) = x_1 + x_2 + 2*x_3 POL(U2(x_1, x_2)) = x_1 + x_2 POL(U3(x_1, x_2, x_3)) = 2*x_1 + 2*x_2 + x_3 POL(U4(x_1, x_2, x_3, x_4)) = x_1 + 2*x_2 + x_3 + 2*x_4 popout

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all output return to TRS Conditional