details

property	value
status	complete
benchmark	curry.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n079.star.cs.uiowa.edu
space	Mixed_HO_10

run statistics

property	value
solver	Wanda
configuration	HigherOrder
runtime (wallclock)	0.0175108909607 seconds
cpu usage	0.013548836
max memory	1044480.0

stage attributes

key	value
output-size	1943
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_HigherOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. Alphabet: a : [] --> N f : [N] --> N Rules: g a => f(a) Using the transformations described in [Kop11], this system can be brought in a form without leading free variables in the left-hand side, and where the left-hand side of a variable is always a functional term or application headed by a functional term. We now transform the resulting AFS into an AFSM by replacing all free variables by meta-variables (with arity 0). This leads to the following AFSM: Alphabet: a : [] --> N f : [N] --> N ~AP1 : [N -> N * N] --> N Rules: ~AP1(F, a) => f(a) ~AP1(F, X) => F 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]): ~AP1(F, a) >? f(a) ~AP1(F, X) >? F X We orient these requirements with a polynomial interpretation in the natural numbers. The following interpretation satisfies the requirements: a = 0 f = \y0.y0 ~AP1 = \G0y1.3 + 3y1 + G0(y1) Using this interpretation, the requirements translate to: [[~AP1(_F0, a)]] = 3 + F0(0) > 0 = [[f(a)]] [[~AP1(_F0, _x1)]] = 3 + 3x1 + F0(x1) > x1 + F0(x1) = [[_F0 _x1]] We can thus remove the following rules: ~AP1(F, a) => f(a) ~AP1(F, X) => F X 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 +++ [Kop11] C. Kop. Simplifying Algebraic Functional Systems. In Proceedings of CAI 2011, volume 6742 of LNCS. 201--215, Springer, 2011. [Kop12] C. Kop. Higher Order Termination. PhD Thesis, 2012. popout

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job log

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actions

all output return to HRS union beta 16688