details

property	value
status	complete
benchmark	emmes-nonloop-ex7_9.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n072.star.cs.uiowa.edu
space	EEG_IJCAR_12

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	3.09509587288 seconds
cpu usage	2.970682168
max memory	4.6829568E7

stage attributes

key	value
output-size	2095
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 appendAkk : [o * o] --> o b : [] --> o cons : [o * o] --> o eq : [o * o] --> o f : [o * o] --> o false : [] --> o length : [o] --> o nil : [] --> o reverse : [o] --> 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(X, Y) => appendAkk(reverse(X), Y) appendAkk(nil, X) => X appendAkk(cons(X, Y), Z) => appendAkk(Y, cons(X, Z)) reverse(nil) => nil reverse(cons(X, Y)) => append(reverse(Y), cons(X, nil)) 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 : [] --> zb a : [] --> zb append : [td * td] --> td appendAkk : [td * td] --> td b : [] --> zb cons : [zb * td] --> td eq : [zb * zb] --> dc f : [dc * td] --> na false : [] --> dc length : [td] --> zb nil : [] --> td reverse : [td] --> td s : [zb] --> zb true : [] --> dc +++ 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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all output return to TRS Stand 20472