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Higher Order Rewriting Union Beta pair #487094023
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
n148.star.cs.uiowa.edu
space
Uncurried_Applicative_11
run statistics
property
value
solver
Wanda 2.2a
configuration
default
runtime (wallclock)
0.0327209 seconds
cpu usage
0.032795
user time
0.020133
system time
0.012662
max virtual memory
113188.0
max residence set size
2544.0
stage attributes
key
value
starexec-result
YES
output
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) 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.
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