details

property	value
status	complete
benchmark	sche128.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n080.star.cs.uiowa.edu
space	Mixed_CTRS_2014

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.62625598907 seconds
cpu usage	3.626122276
max memory	2.2818816E8

stage attributes

key	value
output-size	3279
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Quasi decreasingness of the given CTRS could be proven: (0) CTRS (1) CTRSToQTRSProof [SOUND, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 53 ms] (4) QTRS (5) AAECC Innermost [EQUIVALENT, 0 ms] (6) QTRS (7) DependencyPairsProof [EQUIVALENT, 0 ms] (8) QDP (9) DependencyGraphProof [EQUIVALENT, 0 ms] (10) TRUE ---------------------------------------- (0) Obligation: Conditional term rewrite system: The TRS R consists of the following rules: f(g(a)) -> g(b) g(a) -> b The conditional TRS C consists of the following conditional rules: h(x) -> h(g(x)) <= f(x) -> g(x) ---------------------------------------- (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: h(x) -> U1(f(x), x) U1(g(x), x) -> h(g(x)) f(g(a)) -> g(b) g(a) -> b Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(U1(x_1, x_2)) = x_1 + x_2 POL(a) = 1 POL(b) = 0 POL(f(x_1)) = x_1 POL(g(x_1)) = x_1 POL(h(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: f(g(a)) -> g(b) g(a) -> b ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: h(x) -> U1(f(x), x) U1(g(x), x) -> h(g(x)) Q is empty. ---------------------------------------- (5) AAECC Innermost (EQUIVALENT) We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is none The TRS R 2 is h(x) -> U1(f(x), x) U1(g(x), x) -> h(g(x)) popout

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all output return to TRS Condi 20667