details

property	value
status	complete
benchmark	thiemann32.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n033.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.627616882324 seconds
cpu usage	0.616298005
max memory	2.6210304E7

stage attributes

key	value
output-size	2239
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 10 : [] --> o cons : [o * o] --> o entry : [o * o * o] --> o false : [] --> o gen : [o] --> o if1 : [o * o] --> o if2 : [o * o] --> o if3 : [o * o * o] --> o le : [o * o] --> o nil : [] --> o plus : [o * o] --> o s : [o] --> o table : [] --> o times : [o * o] --> o true : [] --> o table => gen(s(0)) gen(X) => if1(le(X, 10), X) if1(false, X) => nil if1(true, X) => if2(X, X) if2(X, Y) => if3(le(Y, 10), X, Y) if3(true, X, Y) => cons(entry(X, Y, times(X, Y)), if2(X, s(Y))) if3(false, X, Y) => gen(s(X)) le(0, X) => true le(s(X), 0) => false le(s(X), s(Y)) => le(X, Y) plus(0, X) => X plus(s(X), Y) => s(plus(X, Y)) times(0, X) => 0 times(s(X), Y) => plus(Y, times(X, Y)) 10 => s(s(s(s(s(s(s(s(s(s(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 : [] --> we 10 : [] --> we cons : [yb * lc] --> lc entry : [we * we * we] --> yb false : [] --> fd gen : [we] --> lc if1 : [fd * we] --> lc if2 : [we * we] --> lc if3 : [fd * we * we] --> lc le : [we * we] --> fd nil : [] --> lc plus : [we * we] --> we s : [we] --> we table : [] --> lc times : [we * we] --> we true : [] --> fd +++ 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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