details

property	value
status	complete
benchmark	364.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n106.star.cs.uiowa.edu
space	COPS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.62731981277 seconds
cpu usage	3.446108531
max memory	1.87031552E8

stage attributes

key	value
output-size	2166
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Quasi decreasingness of the given CTRS could be proven: (0) CTRS (1) CTRSToQTRSProof [SOUND, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4) QTRS (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Conditional term rewrite system: The TRS R consists of the following rules: even(0) -> true The conditional TRS C consists of the following conditional rules: even(s(x)) -> true <= odd(x) -> true odd(s(x)) -> true <= even(x) -> true ---------------------------------------- (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: even(s(x)) -> U1(odd(x)) U1(true) -> true odd(s(x)) -> U2(even(x)) U2(true) -> true even(0) -> true Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Knuth-Bendix order [KBO] with precedence:U2_1 > 0 > even_1 > true > odd_1 > U1_1 > s_1 and weight map: true=3 0=1 even_1=2 s_1=1 U1_1=1 odd_1=2 U2_1=0 The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: even(s(x)) -> U1(odd(x)) U1(true) -> true odd(s(x)) -> U2(even(x)) U2(true) -> true even(0) -> true ---------------------------------------- (4) Obligation: Q restricted rewrite system: R is empty. Q is empty. ---------------------------------------- (5) RisEmptyProof (EQUIVALENT) The TRS R is empty. Hence, termination is trivially proven. ---------------------------------------- (6) YES popout

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all output return to TRS Condi 20667