details

property	value
status	complete
benchmark	05.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n028.star.cs.uiowa.edu
space	Mixed_SRS

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	6.70054197311 seconds
cpu usage	23.121229641
max memory	1.448804352E9

stage attributes

key	value
output-size	5900
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 23 ms] (2) QDP (3) QDPOrderProof [EQUIVALENT, 255 ms] (4) QDP (5) QDPOrderProof [EQUIVALENT, 71 ms] (6) QDP (7) DependencyGraphProof [EQUIVALENT, 0 ms] (8) QDP (9) QDPOrderProof [EQUIVALENT, 12 ms] (10) QDP (11) PisEmptyProof [EQUIVALENT, 0 ms] (12) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(a(b(a(x1)))) -> a(b(b(b(x1)))) b(b(b(x1))) -> b(a(a(a(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: A(a(b(a(x1)))) -> A(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) B(b(b(x1))) -> B(a(a(a(x1)))) B(b(b(x1))) -> A(a(a(x1))) B(b(b(x1))) -> A(a(x1)) B(b(b(x1))) -> A(x1) The TRS R consists of the following rules: a(a(b(a(x1)))) -> a(b(b(b(x1)))) b(b(b(x1))) -> b(a(a(a(x1)))) Q is empty. 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(a(b(a(x1)))) -> A(b(b(b(x1)))) The remaining pairs can at least be oriented weakly. Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]: <<< POL(A(x_1)) = [[0A]] + [[-I, -I, 0A]] * x_1 >>> <<< POL(a(x_1)) = [[-I], [-I], [0A]] + [[0A, 0A, 0A], [0A, -I, -I], [0A, 0A, 0A]] * x_1 >>> <<< POL(b(x_1)) = [[-I], [1A], [0A]] + [[0A, 0A, -I], [0A, 0A, 0A], [-I, -I, -I]] * x_1 >>> <<< POL(B(x_1)) = [[0A]] + [[0A, 0A, 0A]] * x_1 >>> The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: b(b(b(x1))) -> b(a(a(a(x1)))) a(a(b(a(x1)))) -> a(b(b(b(x1)))) popout

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