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	n139.star.cs.uiowa.edu
space	COPS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.8359708786 seconds
cpu usage	3.948749572
max memory	2.39149056E8

stage attributes

key	value
output-size	3470
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Quasi decreasingness of the given CTRS could be proven: (0) CTRS (1) CTRSToQTRSProof [SOUND, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 62 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 11 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