details

property	value
status	complete
benchmark	04arrow.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n072.star.cs.uiowa.edu
space	Blanqui_15

run statistics

property	value
solver	Wanda
configuration	HigherOrder
runtime (wallclock)	0.0176351070404 seconds
cpu usage	0.01385036
max memory	978944.0

stage attributes

key	value
output-size	1605
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_HigherOrder /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. Alphabet: and : [c * c] --> c arrow : [t * t] --> t lessthan : [t * t] --> c Rules: lessthan(arrow(x, y), arrow(z, u)) => and(lessthan(z, x), lessthan(y, u)) This AFS is converted to an AFSM simply by replacing all free variables by meta-variables (with arity 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]): lessthan(arrow(X, Y), arrow(Z, U)) >? and(lessthan(Z, X), lessthan(Y, U)) We orient these requirements with a polynomial interpretation in the natural numbers. The following interpretation satisfies the requirements: and = \y0y1.y0 + y1 arrow = \y0y1.3 + 3y0 + 3y1 lessthan = \y0y1.2y0 + 3y1 Using this interpretation, the requirements translate to: [[lessthan(arrow(_x0, _x1), arrow(_x2, _x3))]] = 15 + 6x0 + 6x1 + 9x2 + 9x3 > 2x1 + 2x2 + 3x0 + 3x3 = [[and(lessthan(_x2, _x0), lessthan(_x1, _x3))]] We can thus remove the following rules: lessthan(arrow(X, Y), arrow(Z, U)) => and(lessthan(Z, X), lessthan(Y, U)) 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 HRS union beta 16688