details

property	value
status	complete
benchmark	x10.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n002.star.cs.uiowa.edu
space	Secret_07_SRS

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	12.6449179649 seconds
cpu usage	47.233476274
max memory	2.0389888E9

stage attributes

key	value
output-size	7638
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 24 ms] (2) QDP (3) QDPOrderProof [EQUIVALENT, 236 ms] (4) QDP (5) QDPOrderProof [EQUIVALENT, 90 ms] (6) QDP (7) QDPOrderProof [EQUIVALENT, 77 ms] (8) QDP (9) QDPOrderProof [EQUIVALENT, 42 ms] (10) QDP (11) DependencyGraphProof [EQUIVALENT, 0 ms] (12) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(a(b(c(x1)))) -> b(b(a(a(x1)))) b(x1) -> c(c(a(a(x1)))) b(c(x1)) -> a(x1) a(a(c(x1))) -> 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(c(x1)))) -> B(b(a(a(x1)))) A(a(b(c(x1)))) -> B(a(a(x1))) A(a(b(c(x1)))) -> A(a(x1)) A(a(b(c(x1)))) -> A(x1) B(x1) -> A(a(x1)) B(x1) -> A(x1) B(c(x1)) -> A(x1) The TRS R consists of the following rules: a(a(b(c(x1)))) -> b(b(a(a(x1)))) b(x1) -> c(c(a(a(x1)))) b(c(x1)) -> a(x1) a(a(c(x1))) -> 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(c(x1)))) -> B(a(a(x1))) A(a(b(c(x1)))) -> A(a(x1)) A(a(b(c(x1)))) -> A(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], [-I]] + [[0A, 0A, 0A], [0A, 0A, 0A], [-I, -I, 0A]] * x_1 >>> <<< POL(b(x_1)) = [[0A], [1A], [0A]] + [[0A, 0A, 0A], [0A, 0A, 0A], [1A, 0A, 0A]] * x_1 >>> <<< POL(c(x_1)) = [[0A], [0A], [-I]] + [[0A, 0A, 0A], [0A, 0A, 0A], [0A, 0A, 0A]] * x_1 >>> popout

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

job log

popout

actions

all output return to SRS Standard