Higher_Order_Rewriting_Union_Beta 2019-03-28 22.10 pair #432270371

details

property	value
status	complete
benchmark	h04.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n059.star.cs.uiowa.edu
space	Hamana_Kikuchi_18

run statistics

property	value
solver	Wanda 2.1c
configuration	default
runtime (wallclock)	58.2846 seconds
cpu usage	59.0671
user time	52.2012
system time	6.8659
max virtual memory	7403580.0
max residence set size	4007720.0

stage attributes

key	value
starexec-result	MAYBE

output

58.74/57.97	MAYBE
58.74/57.98	We consider the system theBenchmark.
58.74/57.98	
58.74/57.98	  Alphabet:
58.74/57.98	
58.74/57.98	    0 : [] --> N 
58.74/57.98	    even : [] --> N -> N -> B 
58.74/57.98	    false : [] --> B 
58.74/57.98	    g : [] --> N -> B 
58.74/57.98	    h : [] --> N -> (N -> B) -> N -> B 
58.74/57.98	    not : [] --> B -> B 
58.74/57.98	    rec : [] --> (N -> (N -> B) -> N -> B) -> B -> N -> B 
58.74/57.98	    s : [] --> N -> N 
58.74/57.98	    true : [] --> B 
58.74/57.98	
58.74/57.98	  Rules:
58.74/57.98	
58.74/57.98	    rec f (i 0) => i 
58.74/57.98	    rec f (i (s x)) => f x (rec f (i x)) 
58.74/57.98	    g x => true 
58.74/57.98	    h x f y => not (f y) 
58.74/57.98	    not true => false 
58.74/57.98	    not false => true 
58.74/57.98	    even x y => rec h (g x) y 
58.74/57.98	
58.74/57.98	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.
58.74/57.98	
58.74/57.98	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:
58.74/57.98	
58.74/57.98	  Alphabet:
58.74/57.98	
58.74/57.98	    0 : [] --> N 
58.74/57.98	    even : [N] --> N -> B 
58.74/57.98	    false : [] --> B 
58.74/57.98	    g : [] --> N -> B 
58.74/57.98	    h : [] --> N -> (N -> B) -> N -> B 
58.74/57.98	    not : [B] --> B 
58.74/57.98	    rec : [N -> (N -> B) -> N -> B * B] --> N -> B 
58.74/57.98	    s : [N] --> N 
58.74/57.98	    true : [] --> B 
58.74/57.98	    ~AP1 : [N -> B * N] --> B 
58.74/57.98	
58.74/57.98	  Rules:
58.74/57.98	
58.74/57.98	    rec(F, ~AP1(G, 0)) => G 
58.74/57.98	    rec(F, ~AP1(G, s(X))) => F X rec(F, ~AP1(G, X)) 
58.74/57.98	    g X => true 
58.74/57.98	    h X F Y => not(~AP1(F, Y)) 
58.74/57.98	    not(true) => false 
58.74/57.98	    not(false) => true 
58.74/57.98	    even(X) Y => ~AP1(rec(h, g X), Y) 
58.74/57.98	    rec(F, even(X) 0) => even(X) 
58.74/57.98	    rec(F, g 0) => g 
58.74/57.98	    rec(F, h X G 0) => h X G 
58.74/57.98	    rec(F, even(X) s(Y)) => F Y rec(F, even(X) Y) 
58.74/57.98	    rec(F, g s(X)) => F X rec(F, g X) 
58.74/57.98	    rec(F, h X G s(Y)) => F Y rec(F, h X G Y) 
58.74/57.98	    ~AP1(F, X) => F X 
58.74/57.98	
58.74/57.98	
58.74/57.98	+++ Citations +++
58.74/57.98	
58.74/57.98	[Kop11]  C. Kop.  Simplifying Algebraic Functional Systems.  In Proceedings of CAI 2011, volume 6742 of LNCS.  201--215, Springer, 2011.
59.04/58.28	EOF

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