details

property	value
status	complete
benchmark	cade16.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n087.star.cs.uiowa.edu
space	GTSSK07

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.335703134537 seconds
cpu usage	0.270516244
max memory	1.1288576E7

stage attributes

key	value
output-size	1831
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 cond : [o * o * o] --> o cons : [o * o] --> o false : [] --> o ge : [o * o] --> o length : [o] --> o nil : [] --> o nthtail : [o * o] --> o s : [o] --> o tail : [o] --> o true : [] --> o nthtail(X, Y) => cond(ge(X, length(Y)), X, Y) cond(true, X, Y) => Y cond(false, X, Y) => tail(nthtail(s(X), Y)) tail(nil) => nil tail(cons(X, Y)) => Y length(nil) => 0 length(cons(X, Y)) => s(length(Y)) ge(X, 0) => true ge(0, s(X)) => false ge(s(X), s(Y)) => ge(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 : [] --> lc cond : [pc * lc * pb] --> pb cons : [cb * pb] --> pb false : [] --> pc ge : [lc * lc] --> pc length : [pb] --> lc nil : [] --> pb nthtail : [lc * pb] --> pb s : [lc] --> lc tail : [pb] --> pb true : [] --> pc +++ 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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