details

property	value
status	complete
benchmark	292.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n140.star.cs.uiowa.edu
space	COPS

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.22081899643 seconds
cpu usage	5.838870834
max memory	4.7581184E8

stage attributes

key	value
output-size	3463
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Quasi decreasingness of the given CTRS could be proven: (0) CTRS (1) CTRSToQTRSProof [SOUND, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 81 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 12 ms] (6) QTRS (7) RisEmptyProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Conditional term rewrite system: The TRS R consists of the following rules: le(0, s(x)) -> true le(x, 0) -> false le(s(x), s(y)) -> le(x, y) min(cons(x, nil)) -> x The conditional TRS C consists of the following conditional rules: min(cons(x, l)) -> x <= le(x, min(l)) -> true min(cons(x, l)) -> min(l) <= le(x, min(l)) -> false min(cons(x, l)) -> min(l) <= min(l) -> 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: min(cons(x, l)) -> U1(le(x, min(l)), x, l) U1(true, x, l) -> x U1(false, x, l) -> min(l) min(cons(x, l)) -> U2(min(l), l) U2(x, l) -> min(l) le(0, s(x)) -> true le(x, 0) -> false le(s(x), s(y)) -> le(x, y) min(cons(x, nil)) -> x Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(U1(x_1, x_2, x_3)) = 2 + x_1 + x_2 + 2*x_3 POL(U2(x_1, x_2)) = x_1 + 2*x_2 POL(cons(x_1, x_2)) = 2 + x_1 + 2*x_2 POL(false) = 1 POL(le(x_1, x_2)) = 2 + x_1 + x_2 POL(min(x_1)) = 2*x_1 POL(nil) = 0 POL(s(x_1)) = 2*x_1 POL(true) = 0 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: U1(true, x, l) -> x U1(false, x, l) -> min(l) min(cons(x, l)) -> U2(min(l), l) le(0, s(x)) -> true le(x, 0) -> false min(cons(x, nil)) -> x ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to TRS Conditional