Higher_Order_Rewriting_Union_Beta 2019-03-28 22.10 pair #432270613

details

property	value
status	complete
benchmark	Applicative_05__TypeEx3.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n058.star.cs.uiowa.edu
space	Uncurried_Applicative_11

run statistics

property	value
solver	Wanda 2.1c
configuration	default
runtime (wallclock)	1.20005 seconds
cpu usage	1.19812
user time	1.06313
system time	0.134993
max virtual memory	167448.0
max residence set size	52188.0

stage attributes

key	value
starexec-result	MAYBE

output

1.17/1.19	MAYBE
1.17/1.19	We consider the system theBenchmark.
1.17/1.19	
1.17/1.19	  Alphabet:
1.17/1.19	
1.17/1.19	    0 : [] --> a -> b 
1.17/1.19	    cons : [] --> (a -> b) -> c -> c 
1.17/1.19	    hd : [] --> c -> a -> b 
1.17/1.19	    map : [] --> ((a -> b) -> a -> b) -> c -> c 
1.17/1.19	    nil : [] --> c 
1.17/1.19	
1.17/1.19	  Rules:
1.17/1.19	
1.17/1.19	    f 0 x => hd (map f (cons 0 nil)) x 
1.17/1.19	    map f nil => nil 
1.17/1.19	    map f (cons g x) => cons (f g) (map f x) 
1.17/1.19	
1.17/1.19	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.
1.17/1.19	
1.17/1.19	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:
1.17/1.19	
1.17/1.19	  Alphabet:
1.17/1.19	
1.17/1.19	    0 : [] --> a -> b 
1.17/1.19	    cons : [a -> b * c] --> c 
1.17/1.19	    hd : [c * a] --> b 
1.17/1.19	    map : [(a -> b) -> a -> b * c] --> c 
1.17/1.19	    nil : [] --> c 
1.17/1.19	    ~AP1 : [(a -> b) -> a -> b * a -> b] --> a -> b 
1.17/1.19	
1.17/1.19	  Rules:
1.17/1.19	
1.17/1.19	    ~AP1(F, 0) X => hd(map(F, cons(0, nil)), X) 
1.17/1.19	    map(F, nil) => nil 
1.17/1.19	    map(F, cons(G, X)) => cons(~AP1(F, G), map(F, X)) 
1.17/1.19	    ~AP1(F, G) => F G 
1.17/1.19	
1.17/1.19	
1.17/1.19	+++ Citations +++
1.17/1.19	
1.17/1.19	[Kop11]  C. Kop.  Simplifying Algebraic Functional Systems.  In Proceedings of CAI 2011, volume 6742 of LNCS.  201--215, Springer, 2011.
1.17/1.20	EOF

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