details

property	value
status	complete
benchmark	thiemann22.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n086.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.592386960983 seconds
cpu usage	0.588556596
max memory	1.6908288E7

stage attributes

key	value
output-size	1810
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 double : [o] --> o false : [] --> o if : [o * o * o * o] --> o le : [o * o] --> o log : [o] --> o logError : [] --> o loop : [o * o * o] --> o s : [o] --> o true : [] --> o le(s(X), 0) => false le(0, X) => true le(s(X), s(Y)) => le(X, Y) double(0) => 0 double(s(X)) => s(s(double(X))) log(0) => logError log(s(X)) => loop(s(X), s(0), 0) loop(X, s(Y), Z) => if(le(X, s(Y)), X, s(Y), Z) if(true, X, Y, Z) => Z if(false, X, Y, Z) => loop(X, double(Y), s(Z)) 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 : [] --> xc double : [xc] --> xc false : [] --> zb if : [zb * xc * xc * xc] --> xc le : [xc * xc] --> zb log : [xc] --> xc logError : [] --> xc loop : [xc * xc * xc] --> xc s : [xc] --> xc true : [] --> zb +++ 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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