details

property	value
status	complete
benchmark	Liveness6.2.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n085.star.cs.uiowa.edu
space	AProVE_04

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.31612205505 seconds
cpu usage	6.006612348
max memory	4.7527936E8

stage attributes

key	value
output-size	7016
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 86 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 0 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) QDP (8) UsableRulesProof [EQUIVALENT, 0 ms] (9) QDP (10) QDPSizeChangeProof [EQUIVALENT, 0 ms] (11) YES (12) QDP (13) UsableRulesProof [EQUIVALENT, 0 ms] (14) QDP (15) RFCMatchBoundsDPProof [EQUIVALENT, 0 ms] (16) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: top(sent(x)) -> top(check(rest(x))) rest(nil) -> sent(nil) rest(cons(x, y)) -> sent(y) check(sent(x)) -> sent(check(x)) check(rest(x)) -> rest(check(x)) check(cons(x, y)) -> cons(check(x), y) check(cons(x, y)) -> cons(x, check(y)) check(cons(x, y)) -> cons(x, y) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(check(x_1)) = 2*x_1 POL(cons(x_1, x_2)) = 1 + 2*x_1 + 2*x_2 POL(nil) = 0 POL(rest(x_1)) = x_1 POL(sent(x_1)) = 2*x_1 POL(top(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: rest(cons(x, y)) -> sent(y) check(cons(x, y)) -> cons(check(x), y) check(cons(x, y)) -> cons(x, check(y)) check(cons(x, y)) -> cons(x, y) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: top(sent(x)) -> top(check(rest(x))) rest(nil) -> sent(nil) check(sent(x)) -> sent(check(x)) check(rest(x)) -> rest(check(x)) Q is empty. ---------------------------------------- (3) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: TOP(sent(x)) -> TOP(check(rest(x))) TOP(sent(x)) -> CHECK(rest(x)) TOP(sent(x)) -> REST(x) popout

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job log

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actions

all output return to TRS Standard