details

property	value
status	complete
benchmark	27.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	Various_04

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.021192073822 seconds
cpu usage	0.017774772
max memory	1400832.0

stage attributes

key	value
output-size	1956
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. We are asked to determine termination of the following first-order TRS. a : [] --> o b : [] --> o g : [o * o * o] --> o g(X, a, b) => g(b, b, a) 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: a : [] --> h b : [] --> h g : [h * h * h] --> m We use rule removal, following [Kop12, Theorem 2.23]. This gives the following requirements (possibly using Theorems 2.25 and 2.26 in [Kop12]): g(X, a, b) >? g(b, b, a) We orient these requirements with a polynomial interpretation in the natural numbers. The following interpretation satisfies the requirements: a = 2 b = 0 g = \y0y1y2.y0 + y2 + 2y1 Using this interpretation, the requirements translate to: [[g(_x0, a, b)]] = 4 + x0 > 2 = [[g(b, b, a)]] We can thus remove the following rules: g(X, a, b) => g(b, b, a) All rules were succesfully removed. Thus, termination of the original system has been reduced to termination of the beta-rule, which is well-known to hold. +++ 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. [Kop12] C. Kop. Higher Order Termination. PhD Thesis, 2012. popout

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