details

property	value
status	complete
benchmark	ex5.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n084.star.cs.uiowa.edu
space	AProVE_10

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.0259160995483 seconds
cpu usage	0.022228335
max memory	1400832.0

stage attributes

key	value
output-size	1372
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. 0 : [] --> o f : [o] --> o g : [o] --> o s : [o] --> o g(0) => 0 g(s(X)) => f(g(X)) f(0) => 0 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(0) >? 0 g(s(X)) >? f(g(X)) f(0) >? 0 We orient these requirements with a polynomial interpretation in the natural numbers. The following interpretation satisfies the requirements: 0 = 2 f = \y0.2y0 g = \y0.3y0 s = \y0.3 + 3y0 Using this interpretation, the requirements translate to: [[g(0)]] = 6 > 2 = [[0]] [[g(s(_x0))]] = 9 + 9x0 > 6x0 = [[f(g(_x0))]] [[f(0)]] = 4 > 2 = [[0]] We can thus remove the following rules: g(0) => 0 g(s(X)) => f(g(X)) f(0) => 0 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 +++ [Kop12] C. Kop. Higher Order Termination. PhD Thesis, 2012. popout

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all output return to TRS Stand 20472