details

property	value
status	complete
benchmark	ohl206.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n095.star.cs.uiowa.edu
space	Mixed_CTRS_2014

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.78306698799 seconds
cpu usage	3.727370011
max memory	2.3089152E8

stage attributes

key	value
output-size	2805
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Quasi decreasingness of the given CTRS could be proven: (0) CTRS (1) CTRSToQTRSProof [SOUND, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 53 ms] (4) QTRS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) QTRSRRRProof [EQUIVALENT, 0 ms] (6) QTRS (7) RisEmptyProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Conditional term rewrite system: The TRS R consists of the following rules: plus(0, y) -> y plus(s(x), y) -> plus(x, s(y)) The conditional TRS C consists of the following conditional rules: f(x, y) -> plus(y, z) <= plus(x, y) -> plus(z, z) ---------------------------------------- (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: f(x, y) -> U1(plus(x, y), y) U1(plus(z, z), y) -> plus(y, z) plus(0, y) -> y plus(s(x), y) -> plus(x, s(y)) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 2 POL(U1(x_1, x_2)) = x_1 + x_2 POL(f(x_1, x_2)) = 2 + x_1 + 2*x_2 POL(plus(x_1, x_2)) = x_1 + x_2 POL(s(x_1)) = 2 + x_1 POL(z) = 0 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: f(x, y) -> U1(plus(x, y), y) plus(0, y) -> y ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: U1(plus(z, z), y) -> plus(y, z) plus(s(x), y) -> plus(x, s(y)) Q is empty. ---------------------------------------- (5) QTRSRRRProof (EQUIVALENT) Used ordering: Knuth-Bendix order [KBO] with precedence:s_1 > z > plus_2 > U1_2 and weight map: z=2 s_1=1 U1_2=0 popout

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all output return to TRS Conditional