details

property	value
status	complete
benchmark	#4.31.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n007.star.cs.uiowa.edu
space	AG01_innermost

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	6.84127902985 seconds
cpu usage	14.155555493
max memory	1.213251584E9

stage attributes

key	value
output-size	7472
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 18 ms] (2) QDP (3) QDPOrderProof [EQUIVALENT, 619 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) QDP (8) UsableRulesProof [EQUIVALENT, 0 ms] (9) QDP (10) QReductionProof [EQUIVALENT, 0 ms] (11) QDP (12) QDPSizeChangeProof [EQUIVALENT, 0 ms] (13) YES (14) QDP (15) UsableRulesProof [EQUIVALENT, 0 ms] (16) QDP (17) QReductionProof [EQUIVALENT, 0 ms] (18) QDP (19) QDPSizeChangeProof [EQUIVALENT, 0 ms] (20) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(d(x)) -> d(c(b(a(x)))) b(c(x)) -> c(d(a(b(x)))) a(c(x)) -> x b(d(x)) -> x The set Q consists of the following terms: a(d(x0)) b(c(x0)) a(c(x0)) b(d(x0)) ---------------------------------------- (1) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (2) Obligation: Q DP problem: The TRS P consists of the following rules: A(d(x)) -> B(a(x)) A(d(x)) -> A(x) B(c(x)) -> A(b(x)) B(c(x)) -> B(x) The TRS R consists of the following rules: a(d(x)) -> d(c(b(a(x)))) b(c(x)) -> c(d(a(b(x)))) a(c(x)) -> x b(d(x)) -> x The set Q consists of the following terms: a(d(x0)) b(c(x0)) a(c(x0)) b(d(x0)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (3) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. A(d(x)) -> B(a(x)) The remaining pairs can at least be oriented weakly. Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]: <<< popout

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

job log

popout

actions

all output return to TRS Innermost