details

property	value
status	complete
benchmark	jw44.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n080.star.cs.uiowa.edu
space	Zantema_05

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.0225479602814 seconds
cpu usage	0.019856017
max memory	1396736.0

stage attributes

key	value
output-size	1284
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 f : [o * o] --> o f(a, f(f(a, X), a)) => f(f(a, f(a, X)), a) 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(f(a, X), a)) >? f(f(a, f(a, X)), a) We orient these requirements with a polynomial interpretation in the natural numbers. The following interpretation satisfies the requirements: a = 3 f = \y0y1.1 + y0 + 3y1 Using this interpretation, the requirements translate to: [[f(a, f(f(a, _x0), a))]] = 46 + 9x0 > 26 + 9x0 = [[f(f(a, f(a, _x0)), a)]] We can thus remove the following rules: f(a, f(f(a, X), a)) => f(f(a, f(a, X)), 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 +++ [Kop12] C. Kop. Higher Order Termination. PhD Thesis, 2012. popout

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all output return to TRS Stand 20472