details

property	value
status	complete
benchmark	16.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n069.star.cs.uiowa.edu
space	Beerendonk_07

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.961077928543 seconds
cpu usage	0.940144482
max memory	3.0203904E7

stage attributes

key	value
output-size	1983
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 add : [o * o] --> o cond1 : [o * o * o * o] --> o cond2 : [o * o * o * o] --> o cond3 : [o * o * o * o] --> o false : [] --> o gr : [o * o] --> o p : [o] --> o s : [o] --> o true : [] --> o cond1(true, X, Y, Z) => cond2(gr(X, 0), X, Y, Z) cond2(true, X, Y, Z) => cond1(gr(add(X, Y), Z), p(X), Y, Z) cond2(false, X, Y, Z) => cond3(gr(Y, 0), X, Y, Z) cond3(true, X, Y, Z) => cond1(gr(add(X, Y), Z), X, p(Y), Z) cond3(false, X, Y, Z) => cond1(gr(add(X, Y), Z), X, Y, Z) gr(0, X) => false gr(s(X), 0) => true gr(s(X), s(Y)) => gr(X, Y) add(0, X) => X add(s(X), Y) => s(add(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 : [] --> ie add : [ie * ie] --> ie cond1 : [md * ie * ie * ie] --> rc cond2 : [md * ie * ie * ie] --> rc cond3 : [md * ie * ie * ie] --> rc false : [] --> md gr : [ie * ie] --> md p : [ie] --> ie s : [ie] --> ie true : [] --> md +++ 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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