details

property	value
status	complete
benchmark	tpa08.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n083.star.cs.uiowa.edu
space	Secret_06_TRS

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	74.630781889 seconds
cpu usage	74.589613867
max memory	1.252401152E9

stage attributes

key	value
output-size	1599
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. !minus : [o * o] --> o !plus : [o * o] --> o !times : [o * o] --> o 0 : [] --> o f : [o] --> o s : [o] --> o !minus(X, 0) => X !minus(s(X), s(Y)) => !minus(X, Y) !plus(0, X) => X !plus(s(X), Y) => s(!plus(X, Y)) !times(X, 0) => 0 !times(X, s(Y)) => !plus(X, !times(X, Y)) f(s(X)) => f(!minus(!plus(!times(s(X), s(X)), !times(s(X), s(s(s(0))))), !times(s(s(X)), s(s(X))))) 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: !minus : [dc * dc] --> dc !plus : [dc * dc] --> dc !times : [dc * dc] --> dc 0 : [] --> dc f : [dc] --> ec s : [dc] --> dc +++ 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

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