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HRS union beta 16688 pair #381734448
details
property
value
status
complete
benchmark
AotoYamada_05__017.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n088.star.cs.uiowa.edu
space
Uncurried_Applicative_11
run statistics
property
value
solver
Wanda
configuration
HigherOrder
runtime (wallclock)
0.0167989730835 seconds
cpu usage
0.013172848
max memory
1212416.0
stage attributes
key
value
output-size
1329
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: uncurry : [a -> b -> c * a * b] --> c Rules: uncurry(f, x, y) => f x y 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]): uncurry(F, X, Y) >? F X Y We orient these requirements with a polynomial interpretation in the natural numbers. The following interpretation satisfies the requirements: uncurry = \G0y1y2.1 + y1 + y2 + G0(y1,y2) Using this interpretation, the requirements translate to: [[uncurry(_F0, _x1, _x2)]] = 1 + x1 + x2 + F0(x1,x2) > x1 + x2 + F0(x1,x2) = [[_F0 _x1 _x2]] We can thus remove the following rules: uncurry(F, X, Y) => F X Y 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.
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