details

property	value
status	complete
benchmark	div.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n054.star.cs.uiowa.edu
space	AProVE_09_Inductive

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.341132879257 seconds
cpu usage	0.329879003
max memory	1.8296832E7

stage attributes

key	value
output-size	1988
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 div : [o * o] --> o false : [] --> o ge : [o * o] --> o gt : [o * o] --> o if : [o * o * o] --> o if1 : [o * o * o] --> o if2 : [o * o * o] --> o minus : [o * o] --> o s : [o] --> o true : [] --> o minus(s(X), Y) => if(gt(s(X), Y), X, Y) if(true, X, Y) => s(minus(X, Y)) if(false, X, Y) => 0 ge(X, 0) => true ge(0, s(X)) => false ge(s(X), s(Y)) => ge(X, Y) gt(0, X) => false gt(s(X), 0) => true gt(s(X), s(Y)) => gt(X, Y) div(X, Y) => if1(ge(X, Y), X, Y) if1(true, X, Y) => if2(gt(Y, 0), X, Y) if1(false, X, Y) => 0 if2(true, X, Y) => s(div(minus(X, Y), Y)) if2(false, X, Y) => 0 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 : [] --> fe div : [fe * fe] --> fe false : [] --> gd ge : [fe * fe] --> gd gt : [fe * fe] --> gd if : [gd * fe * fe] --> fe if1 : [gd * fe * fe] --> fe if2 : [gd * fe * fe] --> fe minus : [fe * fe] --> fe s : [fe] --> fe true : [] --> gd +++ 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

all output return to TRS Stand 20472