Higher_Order_Rewriting_Union_Beta 2019-03-28 22.10 pair #432270373

details

property	value
status	complete
benchmark	h05.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n156.star.cs.uiowa.edu
space	Hamana_Kikuchi_18

run statistics

property	value
solver	Wanda 2.1c
configuration	default
runtime (wallclock)	124.135 seconds
cpu usage	124.861
user time	110.356
system time	14.5051
max virtual memory	8817476.0
max residence set size	8558084.0

stage attributes

key	value
starexec-result	MAYBE

output

124.16/123.48	MAYBE
124.16/123.49	We consider the system theBenchmark.
124.16/123.49	
124.16/123.49	  Alphabet:
124.16/123.49	
124.16/123.49	    0 : [] --> N 
124.16/123.49	    false : [] --> B 
124.16/123.49	    g : [] --> N -> B 
124.16/123.49	    g2 : [] --> N -> B 
124.16/123.49	    geq : [] --> N -> N -> B 
124.16/123.49	    h : [] --> N -> (N -> B) -> N -> B 
124.16/123.49	    h2 : [] --> N -> (N -> B) -> N -> B 
124.16/123.49	    iszero : [] --> N -> N -> B 
124.16/123.49	    pred : [] --> N -> N 
124.16/123.49	    rec : [] --> (N -> (N -> B) -> N -> B) -> B -> N -> B 
124.16/123.49	    s : [] --> N -> N 
124.16/123.49	    true : [] --> B 
124.16/123.49	
124.16/123.49	  Rules:
124.16/123.49	
124.16/123.49	    rec f (i 0) => i 
124.16/123.49	    rec f (i (s x)) => f x (rec f (i x)) 
124.16/123.49	    g x => true 
124.16/123.49	    h x f y => false 
124.16/123.49	    iszero x y => rec h (g x) y 
124.16/123.49	    pred 0 => 0 
124.16/123.49	    pred (s x) => x 
124.16/123.49	    g2 x => iszero x 0 
124.16/123.49	    h2 x f y => f (pred y) 
124.16/123.49	    geq x y => rec h2 (g2 x) y 
124.16/123.49	
124.16/123.49	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.
124.16/123.49	
124.16/123.49	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:
124.16/123.49	
124.16/123.49	  Alphabet:
124.16/123.49	
124.16/123.49	    0 : [] --> N 
124.16/123.49	    false : [] --> B 
124.16/123.49	    g : [] --> N -> B 
124.16/123.49	    g2 : [] --> N -> B 
124.16/123.49	    geq : [N] --> N -> B 
124.16/123.49	    h : [] --> N -> (N -> B) -> N -> B 
124.16/123.49	    h2 : [] --> N -> (N -> B) -> N -> B 
124.16/123.49	    iszero : [N] --> N -> B 
124.16/123.49	    pred : [N] --> N 
124.16/123.49	    rec : [N -> (N -> B) -> N -> B * B] --> N -> B 
124.16/123.49	    s : [N] --> N 
124.16/123.49	    true : [] --> B 
124.16/123.49	    ~AP1 : [N -> B * N] --> B 
124.16/123.49	
124.16/123.49	  Rules:
124.16/123.49	
124.16/123.49	    rec(F, ~AP1(G, 0)) => G 
124.16/123.49	    rec(F, ~AP1(G, s(X))) => F X rec(F, ~AP1(G, X)) 
124.16/123.49	    g X => true 
124.16/123.49	    h X F Y => false 
124.16/123.49	    iszero(X) Y => ~AP1(rec(h, g X), Y) 
124.16/123.49	    pred(0) => 0 
124.16/123.49	    pred(s(X)) => X 
124.16/123.49	    g2 X => iszero(X) 0 
124.16/123.49	    h2 X F Y => ~AP1(F, pred(Y)) 
124.16/123.49	    geq(X) Y => ~AP1(rec(h2, g2 X), Y) 
124.16/123.49	    rec(F, g 0) => g 
124.16/123.49	    rec(F, g2 0) => g2 
124.16/123.49	    rec(F, geq(X) 0) => geq(X) 
124.16/123.49	    rec(F, h X G 0) => h X G 
124.16/123.49	    rec(F, h2 X G 0) => h2 X G 
124.16/123.49	    rec(F, iszero(X) 0) => iszero(X) 
124.16/123.49	    rec(F, g s(X)) => F X rec(F, g X) 
124.16/123.49	    rec(F, g2 s(X)) => F X rec(F, g2 X) 
124.16/123.49	    rec(F, geq(X) s(Y)) => F Y rec(F, geq(X) Y) 
124.16/123.49	    rec(F, h X G s(Y)) => F Y rec(F, h X G Y) 
124.16/123.49	    rec(F, h2 X G s(Y)) => F Y rec(F, h2 X G Y) 
124.16/123.49	    rec(F, iszero(X) s(Y)) => F Y rec(F, iszero(X) Y) 
124.16/123.49	    ~AP1(F, X) => F X 
124.16/123.49	
124.16/123.49	
124.16/123.49	+++ Citations +++
124.16/123.49	
124.16/123.49	[Kop11]  C. Kop.  Simplifying Algebraic Functional Systems.  In Proceedings of CAI 2011, volume 6742 of LNCS.  201--215, Springer, 2011.
124.81/124.13	EOF

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