details

property	value
status	complete
benchmark	cade09.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n071.star.cs.uiowa.edu
space	GTSSK07

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.404085874557 seconds
cpu usage	0.389064425
max memory	9965568.0

stage attributes

key	value
output-size	1538
starexec-result	MAYBE

output

/export/starexec/sandbox/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- MAYBE We consider the system theBenchmark. We are asked to determine termination of the following first-order TRS. 0 : [] --> o f : [o * o * o] --> o false : [] --> o gt : [o * o] --> o round : [o] --> o s : [o] --> o true : [] --> o f(true, X, Y) => f(gt(X, Y), X, round(s(Y))) round(0) => 0 round(s(0)) => s(s(0)) round(s(s(X))) => s(s(round(X))) gt(0, X) => false gt(s(X), 0) => true gt(s(X), s(Y)) => gt(X, Y) As the system is orthogonal, it is terminating if it is innermost terminating by [Gra95]. Then, by [FuhGieParSchSwi11], it suffices to prove (innermost) termination of the typed system, with sort annotations chosen to respect the rules, as follows: 0 : [] --> nb f : [rb * nb * nb] --> z false : [] --> rb gt : [nb * nb] --> rb round : [nb] --> nb s : [nb] --> nb true : [] --> rb +++ Citations +++ [FuhGieParSchSwi11] C. Fuhs, J. Giesl, M. Parting, P. Schneider-Kamp, and S. Swiderski. Proving Termination by Dependency Pairs and Inductive Theorem Proving. In volume 47(2) of Journal of Automated Reasoning. 133--160, 2011. [Gra95] B. Gramlich. Abstract Relations Between Restricted Termination and Confluence Properties of Rewrite Systems. In volume 24(1-2) of Fundamentae Informaticae. 3--23, 1995. popout

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job log

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actions

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