Higher_Order_Rewriting_Union_Beta 2019-03-28 22.10 pair #432270225

details

property	value
status	complete
benchmark	kop12thesis_sec3.3.3.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n097.star.cs.uiowa.edu
space	Kop_13

run statistics

property	value
solver	Wanda 2.1c
configuration	default
runtime (wallclock)	0.0535649 seconds
cpu usage	0.053581
user time	0.042477
system time	0.011104
max virtual memory	113176.0
max residence set size	2832.0

stage attributes

key	value
starexec-result	YES

output

0.00/0.05	YES
0.00/0.05	We consider the system theBenchmark.
0.00/0.05	
0.00/0.05	  Alphabet:
0.00/0.05	
0.00/0.05	    f : [o -> o] --> o 
0.00/0.05	    g : [] --> o -> o 
0.00/0.05	
0.00/0.05	  Rules:
0.00/0.05	
0.00/0.05	    f(g) => f(/\x.g x) 
0.00/0.05	
0.00/0.05	This AFS is converted to an AFSM simply by replacing all free variables by meta-variables (with arity 0).
0.00/0.05	
0.00/0.05	We use the dependency pair framework as described in [Kop12, Ch. 6/7], with dynamic dependency pairs.
0.00/0.05	
0.00/0.05	We thus obtain the following dependency pair problem (P_0, R_0, minimal, formative):
0.00/0.05	
0.00/0.05	  Dependency Pairs P_0:
0.00/0.05	
0.00/0.05	    0] f#(g) =#> f#(/\x.g x)   
0.00/0.05	
0.00/0.05	  Rules R_0:
0.00/0.05	
0.00/0.05	    f(g) => f(/\x.g x) 
0.00/0.05	
0.00/0.05	Thus, the original system is terminating if (P_0, R_0, minimal, formative) is finite.
0.00/0.05	
0.00/0.05	We consider the dependency pair problem (P_0, R_0, minimal, formative).
0.00/0.05	
0.00/0.05	We place the elements of P in a dependency graph approximation G (see e.g. [Kop12, Thm. 7.27, 7.29], as follows:
0.00/0.05	
0.00/0.05	    * 0 :  
0.00/0.05	
0.00/0.05	This graph has no strongly connected components.  By [Kop12, Thm. 7.31], this implies finiteness of the dependency pair problem.
0.00/0.05	
0.00/0.05	As all dependency pair problems were succesfully simplified with sound (and complete) processors until nothing remained, we conclude termination.
0.00/0.05	
0.00/0.05	
0.00/0.05	+++ Citations +++
0.00/0.05	
0.00/0.05	[Kop12]  C. Kop.  Higher Order Termination.  PhD Thesis, 2012.
0.00/0.05	EOF

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