details

property	value
status	complete
benchmark	random-530.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n116.star.cs.uiowa.edu
space	Waldmann_19

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	6.68491101265 seconds
cpu usage	22.853910639
max memory	1.36923136E9

stage attributes

key	value
output-size	5607
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 25 ms] (2) QDP (3) MRRProof [EQUIVALENT, 25 ms] (4) QDP (5) QDPOrderProof [EQUIVALENT, 150 ms] (6) QDP (7) QDPOrderProof [EQUIVALENT, 171 ms] (8) QDP (9) DependencyGraphProof [EQUIVALENT, 0 ms] (10) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: b(b(a(a(x1)))) -> a(b(a(a(x1)))) a(a(b(a(x1)))) -> b(b(a(a(x1)))) a(a(b(a(x1)))) -> b(b(b(b(x1)))) Q is empty. ---------------------------------------- (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: B(b(a(a(x1)))) -> A(b(a(a(x1)))) A(a(b(a(x1)))) -> B(b(a(a(x1)))) A(a(b(a(x1)))) -> B(a(a(x1))) A(a(b(a(x1)))) -> A(a(x1)) A(a(b(a(x1)))) -> B(b(b(b(x1)))) A(a(b(a(x1)))) -> B(b(b(x1))) A(a(b(a(x1)))) -> B(b(x1)) A(a(b(a(x1)))) -> B(x1) The TRS R consists of the following rules: b(b(a(a(x1)))) -> a(b(a(a(x1)))) a(a(b(a(x1)))) -> b(b(a(a(x1)))) a(a(b(a(x1)))) -> b(b(b(b(x1)))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (3) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented dependency pairs: A(a(b(a(x1)))) -> B(a(a(x1))) A(a(b(a(x1)))) -> A(a(x1)) A(a(b(a(x1)))) -> B(b(b(x1))) A(a(b(a(x1)))) -> B(b(x1)) A(a(b(a(x1)))) -> B(x1) Used ordering: Polynomial interpretation [POLO]: POL(A(x_1)) = 2*x_1 POL(B(x_1)) = 2*x_1 POL(a(x_1)) = 2 + x_1 POL(b(x_1)) = 2 + x_1 ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: B(b(a(a(x1)))) -> A(b(a(a(x1)))) A(a(b(a(x1)))) -> B(b(a(a(x1)))) A(a(b(a(x1)))) -> B(b(b(b(x1)))) popout

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