details

property	value
status	complete
benchmark	Ex16_Luc06_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n069.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.20624303818 seconds
cpu usage	5.940514357
max memory	4.74914816E8

stage attributes

key	value
output-size	4828
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 89 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 0 ms] (6) QTRS (7) QTRSRRRProof [EQUIVALENT, 3 ms] (8) QTRS (9) AAECC Innermost [EQUIVALENT, 0 ms] (10) QTRS (11) DependencyPairsProof [EQUIVALENT, 0 ms] (12) QDP (13) DependencyGraphProof [EQUIVALENT, 0 ms] (14) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a__f(X, X) -> a__f(a, b) a__b -> a mark(f(X1, X2)) -> a__f(mark(X1), X2) mark(b) -> a__b mark(a) -> a a__f(X1, X2) -> f(X1, X2) a__b -> b Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(a) = 0 POL(a__b) = 0 POL(a__f(x_1, x_2)) = 2 + 2*x_1 + 2*x_2 POL(b) = 0 POL(f(x_1, x_2)) = 1 + 2*x_1 + x_2 POL(mark(x_1)) = 2*x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: a__f(X1, X2) -> f(X1, X2) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a__f(X, X) -> a__f(a, b) a__b -> a mark(f(X1, X2)) -> a__f(mark(X1), X2) mark(b) -> a__b mark(a) -> a a__b -> b Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(a) = 0 POL(a__b) = 0 POL(a__f(x_1, x_2)) = x_1 + 2*x_2 POL(b) = 0 POL(f(x_1, x_2)) = 1 + 2*x_1 + x_2 POL(mark(x_1)) = 2*x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: mark(f(X1, X2)) -> a__f(mark(X1), X2) popout

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all output return to TRS Standard