details

property	value
status	complete
benchmark	emmes-nonloop-ex2_5.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n069.star.cs.uiowa.edu
space	EEG_IJCAR_12

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.330877065659 seconds
cpu usage	0.322180716
max memory	1.3201408E7

stage attributes

key	value
output-size	1719
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 double : [o] --> o f : [o * o * o] --> o false : [] --> o gt : [o * o] --> o plus : [o * o] --> o s : [o] --> o times : [o * o] --> o true : [] --> o f(true, X, Y) => f(gt(X, Y), double(X), s(Y)) gt(s(X), 0) => true gt(0, X) => false gt(s(X), s(Y)) => gt(X, Y) double(X) => times(X, s(s(0))) times(0, X) => 0 times(s(X), Y) => plus(Y, times(X, Y)) plus(0, X) => X plus(s(X), Y) => s(plus(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 : [] --> kc double : [kc] --> kc f : [xa * kc * kc] --> ba false : [] --> xa gt : [kc * kc] --> xa plus : [kc * kc] --> kc s : [kc] --> kc times : [kc * kc] --> kc true : [] --> xa +++ 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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