details

property	value
status	complete
benchmark	13.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n110.star.cs.uiowa.edu
space	Beerendonk_07

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.380785942078 seconds
cpu usage	0.353544221
max memory	1.2087296E7

stage attributes

key	value
output-size	1648
starexec-result	MAYBE

output

/export/starexec/sandbox2/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- MAYBE We consider the system theBenchmark. We are asked to determine termination of the following first-order TRS. 0 : [] --> o cond1 : [o * o * o] --> o cond2 : [o * o * o] --> o false : [] --> o gr : [o * o] --> o p : [o] --> o s : [o] --> o true : [] --> o cond1(true, X, Y) => cond2(gr(X, Y), X, Y) cond2(true, X, Y) => cond1(gr(X, 0), Y, Y) cond2(false, X, Y) => cond1(gr(X, 0), p(X), Y) gr(0, X) => false gr(s(X), 0) => true gr(s(X), s(Y)) => gr(X, Y) p(0) => 0 p(s(X)) => X 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 : [] --> ac cond1 : [sb * ac * ac] --> xa cond2 : [sb * ac * ac] --> xa false : [] --> sb gr : [ac * ac] --> sb p : [ac] --> ac s : [ac] --> ac true : [] --> sb +++ 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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