details

property	value
status	complete
benchmark	ExIntrod_GM01.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n005.star.cs.uiowa.edu
space	Strategy_removed_CSR_05

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.113081932068 seconds
cpu usage	0.109728619
max memory	4939776.0

stage attributes

key	value
output-size	1675
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 adx : [o] --> o cons : [o * o] --> o head : [o] --> o incr : [o] --> o nats : [] --> o nil : [] --> o s : [o] --> o tail : [o] --> o zeros : [] --> o incr(nil) => nil incr(cons(X, Y)) => cons(s(X), incr(Y)) adx(nil) => nil adx(cons(X, Y)) => incr(cons(X, adx(Y))) nats => adx(zeros) zeros => cons(0, zeros) head(cons(X, Y)) => X tail(cons(X, Y)) => 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 : [] --> za adx : [nb] --> nb cons : [za * nb] --> nb head : [nb] --> za incr : [nb] --> nb nats : [] --> nb nil : [] --> nb s : [za] --> za tail : [nb] --> nb zeros : [] --> nb +++ 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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actions

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