details

property	value
status	complete
benchmark	emmes-nonloop-ex7_7.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n102.star.cs.uiowa.edu
space	EEG_IJCAR_12

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	2.67054891586 seconds
cpu usage	2.622015417
max memory	4.182016E7

stage attributes

key	value
output-size	1851
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 a : [] --> o append : [o * o] --> o b : [] --> o cons : [o * o] --> o eq : [o * o] --> o f : [o * o] --> o false : [] --> o length : [o] --> o nil : [] --> o s : [o] --> o true : [] --> o f(true, X) => f(eq(s(length(X)), length(cons(a, X))), append(cons(b, nil), X)) length(nil) => 0 length(cons(X, Y)) => s(length(Y)) eq(0, 0) => true eq(s(X), 0) => false eq(0, s(X)) => false eq(s(X), s(Y)) => eq(X, Y) append(nil, X) => X append(cons(X, Y), Z) => cons(X, append(Y, Z)) 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 : [] --> wb a : [] --> wb append : [rc * rc] --> rc b : [] --> wb cons : [wb * rc] --> rc eq : [wb * wb] --> ac f : [ac * rc] --> ka false : [] --> ac length : [rc] --> wb nil : [] --> rc s : [wb] --> wb true : [] --> ac +++ 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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