Higher_Order_Rewriting_Union_Beta 2019-03-28 22.10 pair #432270399

details

property	value
status	complete
benchmark	h18.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n051.star.cs.uiowa.edu
space	Hamana_Kikuchi_18

run statistics

property	value
solver	Wanda 2.1c
configuration	default
runtime (wallclock)	81.4096 seconds
cpu usage	81.3994
user time	79.8546
system time	1.54471
max virtual memory	1522600.0
max residence set size	1269744.0

stage attributes

key	value
starexec-result	MAYBE

output

81.24/81.30	MAYBE
81.24/81.31	We consider the system theBenchmark.
81.24/81.31	
81.24/81.31	  Alphabet:
81.24/81.31	
81.24/81.31	    cons : [] --> a -> alist -> alist 
81.24/81.31	    map : [] --> (a -> a) -> alist -> alist 
81.24/81.31	    nil : [] --> alist 
81.24/81.31	    o : [] --> (a -> a) -> (a -> a) -> a -> a 
81.24/81.31	    xap : [] --> (a -> a) -> a -> a 
81.24/81.31	
81.24/81.31	  Rules:
81.24/81.31	
81.24/81.31	    map (/\x.xap f x) nil => nil 
81.24/81.31	    map (/\x.xap f x) (cons y z) => cons (xap f y) (map (/\u.xap f u) z) 
81.24/81.31	    map (/\x.xap f x) (map (/\y.xap g y) z) => map (o (/\u.xap f u) (/\v.xap g v)) z 
81.24/81.31	    o (/\x.f x) (/\y.g y) z => f (g z) 
81.24/81.31	    xap f x => f x 
81.24/81.31	
81.24/81.31	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.
81.24/81.31	
81.24/81.31	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:
81.24/81.31	
81.24/81.31	  Alphabet:
81.24/81.31	
81.24/81.31	    cons : [a * alist] --> alist 
81.24/81.31	    map : [a -> a * alist] --> alist 
81.24/81.31	    nil : [] --> alist 
81.24/81.31	    o : [a -> a * a -> a] --> a -> a 
81.24/81.31	    xap : [a -> a * a] --> a 
81.24/81.31	    ~AP1 : [a -> a * a] --> a 
81.24/81.31	
81.24/81.31	  Rules:
81.24/81.31	
81.24/81.31	    map(/\x.xap(F, x), nil) => nil 
81.24/81.31	    map(/\x.xap(F, x), cons(X, Y)) => cons(xap(F, X), map(/\y.xap(F, y), Y)) 
81.24/81.31	    map(/\x.xap(F, x), map(/\y.xap(G, y), X)) => map(o(/\z.xap(F, z), /\u.xap(G, u)), X) 
81.24/81.31	    o(/\x.~AP1(F, x), /\y.~AP1(G, y)) X => ~AP1(F, ~AP1(G, X)) 
81.24/81.31	    xap(F, X) => ~AP1(F, X) 
81.24/81.31	    o(/\x.o(F, G) x, /\y.~AP1(H, y)) X => o(F, G) ~AP1(H, X) 
81.24/81.31	    o(/\x.xap(F, x), /\y.~AP1(G, y)) X => xap(F, ~AP1(G, X)) 
81.24/81.31	    o(/\x.~AP1(F, x), /\y.o(G, H) y) X => ~AP1(F, o(G, H) X) 
81.24/81.31	    o(/\x.~AP1(F, x), /\y.xap(G, y)) X => ~AP1(F, xap(G, X)) 
81.24/81.31	    o(/\x.o(F, G) x, /\y.o(H, I) y) X => o(F, G) (o(H, I) X) 
81.24/81.31	    o(/\x.o(F, G) x, /\y.xap(H, y)) X => o(F, G) xap(H, X) 
81.24/81.31	    o(/\x.xap(F, x), /\y.o(G, H) y) X => xap(F, o(G, H) X) 
81.24/81.31	    o(/\x.xap(F, x), /\y.xap(G, y)) X => xap(F, xap(G, X)) 
81.24/81.31	    ~AP1(F, X) => F X 
81.24/81.31	
81.24/81.31	
81.24/81.31	+++ Citations +++
81.24/81.31	
81.24/81.31	[Kop11]  C. Kop.  Simplifying Algebraic Functional Systems.  In Proceedings of CAI 2011, volume 6742 of LNCS.  201--215, Springer, 2011.
81.32/81.40	EOF

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