details

property	value
status	complete
benchmark	otto12.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n081.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.378525018692 seconds
cpu usage	0.37478655
max memory	2.0303872E7

stage attributes

key	value
output-size	2047
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 exp : [o * o] --> o false : [] --> o ge : [o * o] --> o help : [o * o * o * o * o] --> o plus : [o * o] --> o s : [o] --> o times : [o * o] --> o tower : [o * o] --> o towerIter : [o * o * o * o] --> o true : [] --> o 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)) exp(X, 0) => s(0) exp(X, s(Y)) => times(X, exp(X, Y)) ge(X, 0) => true ge(0, s(X)) => false ge(s(X), s(Y)) => ge(X, Y) tower(X, Y) => towerIter(0, X, Y, s(0)) towerIter(X, Y, Z, U) => help(ge(X, Y), X, Y, Z, U) help(true, X, Y, Z, U) => U help(false, X, Y, Z, U) => towerIter(s(X), Y, Z, exp(Z, U)) 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 : [] --> ie exp : [ie * ie] --> ie false : [] --> gd ge : [ie * ie] --> gd help : [gd * ie * ie * ie * ie] --> ie plus : [ie * ie] --> ie s : [ie] --> ie times : [ie * ie] --> ie tower : [ie * ie] --> ie towerIter : [ie * ie * ie * ie] --> ie 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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all output return to TRS Stand 20472