details

property	value
status	complete
benchmark	t007.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n099.star.cs.uiowa.edu
space	HirokawaMiddeldorp_04

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.0563189983368 seconds
cpu usage	0.033674311
max memory	1396736.0

stage attributes

key	value
output-size	2389
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/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 f : [o] --> o g : [o] --> o f(a) => f(b) g(b) => g(a) f(X) => g(X) We use rule removal, following [Kop12, Theorem 2.23]. This gives the following requirements (possibly using Theorems 2.25 and 2.26 in [Kop12]): f(a) >? f(b) g(b) >? g(a) f(X) >? g(X) We orient these requirements with a polynomial interpretation in the natural numbers. The following interpretation satisfies the requirements: a = 0 b = 0 f = \y0.3 + 2y0 g = \y0.2y0 Using this interpretation, the requirements translate to: [[f(a)]] = 3 >= 3 = [[f(b)]] [[g(b)]] = 0 >= 0 = [[g(a)]] [[f(_x0)]] = 3 + 2x0 > 2x0 = [[g(_x0)]] We can thus remove the following rules: f(X) => g(X) We use the dependency pair framework as described in [Kop12, Ch. 6/7], with static dependency pairs (see [KusIsoSakBla09] and the adaptation for AFSMs in [Kop12, Ch. 7.8]). We thus obtain the following dependency pair problem (P_0, R_0, minimal, formative): Dependency Pairs P_0: 0] f#(a) =#> f#(b) 1] g#(b) =#> g#(a) Rules R_0: f(a) => f(b) g(b) => g(a) Thus, the original system is terminating if (P_0, R_0, minimal, formative) is finite. We consider the dependency pair problem (P_0, R_0, minimal, formative). We place the elements of P in a dependency graph approximation G (see e.g. [Kop12, Thm. 7.27, 7.29], as follows: * 0 : * 1 : This graph has no strongly connected components. By [Kop12, Thm. 7.31], this implies finiteness of the dependency pair problem. As all dependency pair problems were succesfully simplified with sound (and complete) processors until nothing remained, we conclude termination. +++ Citations +++ [Kop12] C. Kop. Higher Order Termination. PhD Thesis, 2012. [KusIsoSakBla09] K. Kusakari, Y. Isogai, M. Sakai, and F. Blanqui. Static Dependency Pair Method Based On Strong Computability for Higher-Order Rewrite Systems. In volume 92(10) of IEICE Transactions on Information and Systems. 2007--2015, 2009. popout

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