Higher_Order_Rewriting_Union_Beta 2019-03-28 22.10 pair #432270375

details

property	value
status	complete
benchmark	h06.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n007.star.cs.uiowa.edu
space	Hamana_Kikuchi_18

run statistics

property	value
solver	Wanda 2.1c
configuration	default
runtime (wallclock)	48.6681 seconds
cpu usage	49.4525
user time	44.0741
system time	5.37846
max virtual memory	6869080.0
max residence set size	3240672.0

stage attributes

key	value
starexec-result	MAYBE

output

49.18/48.43	MAYBE
49.18/48.44	We consider the system theBenchmark.
49.18/48.44	
49.18/48.44	  Alphabet:
49.18/48.44	
49.18/48.44	    0 : [] --> N 
49.18/48.44	    false : [] --> B 
49.18/48.44	    g : [] --> N -> B 
49.18/48.44	    h : [] --> N -> (N -> B) -> N -> B 
49.18/48.44	    iszero : [] --> N -> N -> B 
49.18/48.44	    rec : [] --> (N -> (N -> B) -> N -> B) -> B -> N -> B 
49.18/48.44	    s : [] --> N -> N 
49.18/48.44	    true : [] --> B 
49.18/48.44	
49.18/48.44	  Rules:
49.18/48.44	
49.18/48.44	    rec f (i 0) => i 
49.18/48.44	    rec f (i (s x)) => f x (rec f (i x)) 
49.18/48.44	    g x => true 
49.18/48.44	    h x f y => false 
49.18/48.44	    iszero x y => rec h (g x) y 
49.18/48.44	
49.18/48.44	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.
49.18/48.44	
49.18/48.44	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:
49.18/48.44	
49.18/48.44	  Alphabet:
49.18/48.44	
49.18/48.44	    0 : [] --> N 
49.18/48.44	    false : [] --> B 
49.18/48.44	    g : [] --> N -> B 
49.18/48.44	    h : [] --> N -> (N -> B) -> N -> B 
49.18/48.44	    iszero : [N] --> N -> B 
49.18/48.44	    rec : [N -> (N -> B) -> N -> B * B] --> N -> B 
49.18/48.44	    s : [N] --> N 
49.18/48.44	    true : [] --> B 
49.18/48.44	    ~AP1 : [N -> B * N] --> B 
49.18/48.44	
49.18/48.44	  Rules:
49.18/48.44	
49.18/48.44	    rec(F, ~AP1(G, 0)) => G 
49.18/48.44	    rec(F, ~AP1(G, s(X))) => F X rec(F, ~AP1(G, X)) 
49.18/48.44	    g X => true 
49.18/48.44	    h X F Y => false 
49.18/48.44	    iszero(X) Y => ~AP1(rec(h, g X), Y) 
49.18/48.44	    rec(F, g 0) => g 
49.18/48.44	    rec(F, h X G 0) => h X G 
49.18/48.44	    rec(F, iszero(X) 0) => iszero(X) 
49.18/48.44	    rec(F, g s(X)) => F X rec(F, g X) 
49.18/48.44	    rec(F, h X G s(Y)) => F Y rec(F, h X G Y) 
49.18/48.44	    rec(F, iszero(X) s(Y)) => F Y rec(F, iszero(X) Y) 
49.18/48.44	    ~AP1(F, X) => F X 
49.18/48.44	
49.18/48.44	
49.18/48.44	+++ Citations +++
49.18/48.44	
49.18/48.44	[Kop11]  C. Kop.  Simplifying Algebraic Functional Systems.  In Proceedings of CAI 2011, volume 6742 of LNCS.  201--215, Springer, 2011.
49.43/48.66	EOF

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