details

property	value
status	complete
benchmark	Applicative_05__Ex2_6_1Composition.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n012.star.cs.uiowa.edu
space	Uncurried_Applicative_11

run statistics

property	value
solver	Wanda
configuration	HigherOrder
runtime (wallclock)	0.021281003952 seconds
cpu usage	0.01862183
max memory	1691648.0

stage attributes

key	value
output-size	1744
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: compose : [b -> c * a -> b * a] --> c Rules: compose(f, g, x) => f (g x) 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]): compose(F, G, X) >? F (G X) about to try horpo We use a recursive path ordering as defined in [Kop12, Chapter 5]. We choose Lex = {} and Mul = {@_{o -> o}, compose}, and the following precedence: compose > @_{o -> o} With these choices, we have: 1] compose(F, G, X) > @_{o -> o}(F, @_{o -> o}(G, X)) because [2], by definition 2] compose*(F, G, X) >= @_{o -> o}(F, @_{o -> o}(G, X)) because compose > @_{o -> o}, [3] and [5], by (Copy) 3] compose*(F, G, X) >= F because [4], by (Select) 4] F >= F by (Meta) 5] compose*(F, G, X) >= @_{o -> o}(G, X) because compose > @_{o -> o}, [6] and [8], by (Copy) 6] compose*(F, G, X) >= G because [7], by (Select) 7] G >= G by (Meta) 8] compose*(F, G, X) >= X because [9], by (Select) 9] X >= X by (Meta) We can thus remove the following rules: compose(F, G, X) => F (G 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 +++ [Kop12] C. Kop. Higher Order Termination. PhD Thesis, 2012. popout

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all output return to HRS union beta 16688