Higher_Order_Rewriting_Union_Beta 2019-03-28 22.10 pair #432270571

details

property	value
status	complete
benchmark	Applicative_05__Ex4MapList.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n102.star.cs.uiowa.edu
space	Uncurried_Applicative_11

run statistics

property	value
solver	Wanda 2.1c
configuration	default
runtime (wallclock)	0.0895811 seconds
cpu usage	0.078308
user time	0.052654
system time	0.025654
max virtual memory	113176.0
max residence set size	3396.0

stage attributes

key	value
starexec-result	YES

output

0.00/0.08	YES
0.00/0.08	We consider the system theBenchmark.
0.00/0.08	
0.00/0.08	  Alphabet:
0.00/0.08	
0.00/0.08	    cons : [c * d] --> d 
0.00/0.08	    fcons : [b -> c * a] --> a 
0.00/0.08	    fmap : [a * b] --> d 
0.00/0.08	    fnil : [] --> a 
0.00/0.08	    nil : [] --> d 
0.00/0.08	
0.00/0.08	  Rules:
0.00/0.08	
0.00/0.08	    fmap(fnil, x) => nil 
0.00/0.08	    fmap(fcons(f, x), y) => cons(f y, fmap(x, y)) 
0.00/0.08	
0.00/0.08	This AFS is converted to an AFSM simply by replacing all free variables by meta-variables (with arity 0).
0.00/0.08	
0.00/0.08	We use the dependency pair framework as described in [Kop12, Ch. 6/7], with static dependency pairs (see [KusIsoSakBla09] and the adaptation for AFSMs and accessible arguments in [Kop13]).
0.00/0.08	
0.00/0.08	We thus obtain the following dependency pair problem (P_0, R_0, static, formative):
0.00/0.08	
0.00/0.08	  Dependency Pairs P_0:
0.00/0.08	
0.00/0.08	    0] fmap#(fcons(F, X), Y) =#> fmap#(X, Y)   
0.00/0.08	
0.00/0.08	  Rules R_0:
0.00/0.08	
0.00/0.08	    fmap(fnil, X) => nil 
0.00/0.08	    fmap(fcons(F, X), Y) => cons(F Y, fmap(X, Y)) 
0.00/0.08	
0.00/0.08	Thus, the original system is terminating if (P_0, R_0, static, formative) is finite.
0.00/0.08	
0.00/0.08	We consider the dependency pair problem (P_0, R_0, static, formative).
0.00/0.08	
0.00/0.08	We apply the subterm criterion with the following projection function:
0.00/0.08	
0.00/0.08	  nu(fmap#) = 1 
0.00/0.08	
0.00/0.08	Thus, we can orient the dependency pairs as follows:
0.00/0.08	
0.00/0.08	  nu(fmap#(fcons(F, X), Y)) = fcons(F, X) |> X = nu(fmap#(X, Y)) 
0.00/0.08	
0.00/0.08	By [Kop12, Thm. 7.35] and [Kop13, Thm. 5], we may replace a dependency pair problem (P_0, R_0, static, f) by ({}, R_0, static, f).  By the empty set processor [Kop12, Thm. 7.15] this problem may be immediately removed.
0.00/0.08	
0.00/0.08	As all dependency pair problems were succesfully simplified with sound (and complete) processors until nothing remained, we conclude termination.
0.00/0.08	
0.00/0.08	
0.00/0.08	+++ Citations +++
0.00/0.08	
0.00/0.08	[Kop12]  C. Kop.  Higher Order Termination.  PhD Thesis, 2012.
0.00/0.08	[Kop13]  C. Kop.  Static Dependency Pairs with Accessibility.  Unpublished manuscript, http://cl-informatik.uibk.ac.at/users/kop/static.pdf, 2013.
0.00/0.08	[KusIsoSakBla09]  K. Kusakari, Y. Isogai, M. Sakai, and F. Blanqui.  Static Dependency Pair Method Based On Strong Computability for Higher-Order Rewrite Systems.  In volume 92(10) of IEICE Transactions on Information and Systems.  2007--2015, 2009.
0.00/0.08	EOF

popout

output may be truncated. 'popout' for the full output.

job log

popout

actions all output return to Higher_Order_Rewriting_Union_Beta 2019-03-28 22.10