Higher_Order_Rewriting_Union_Beta 2019-03-28 22.10 pair #432270339

details

property	value
status	complete
benchmark	gstate.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n139.star.cs.uiowa.edu
space	Hamana_17

run statistics

property	value
solver	Wanda 2.1c
configuration	default
runtime (wallclock)	36.412 seconds
cpu usage	36.4136
user time	34.4052
system time	2.00846
max virtual memory	1854236.0
max residence set size	1739800.0

stage attributes

key	value
starexec-result	MAYBE

output

36.19/36.28	MAYBE
36.19/36.28	We consider the system theBenchmark.
36.19/36.28	
36.19/36.28	  Alphabet:
36.19/36.28	
36.19/36.28	    lk : [] --> (W -> E) -> E 
36.19/36.28	    ud : [] --> W -> E -> E 
36.19/36.28	
36.19/36.28	  Rules:
36.19/36.28	
36.19/36.28	    lk (/\x.ud x y) => y 
36.19/36.28	    ud x (ud y z) => ud y z 
36.19/36.28	    ud x (lk (/\y.f y)) => ud x (f x) 
36.19/36.28	    lk (/\x.lk (/\y.f y x)) => lk (/\z.f z z) 
36.19/36.28	
36.19/36.28	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.
36.19/36.28	
36.19/36.28	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:
36.19/36.28	
36.19/36.28	  Alphabet:
36.19/36.28	
36.19/36.28	    lk : [W -> E] --> E 
36.19/36.28	    ud : [W * E] --> E 
36.19/36.28	    ~AP1 : [W -> E * W] --> E 
36.19/36.28	    ~AP2 : [W -> W -> E * W] --> W -> E 
36.19/36.28	
36.19/36.28	  Rules:
36.19/36.28	
36.19/36.28	    lk(/\x.ud(x, X)) => X 
36.19/36.28	    ud(X, ud(Y, Z)) => ud(Y, Z) 
36.19/36.28	    ud(X, lk(/\x.~AP1(F, x))) => ud(X, ~AP1(F, X)) 
36.19/36.28	    lk(/\x.lk(/\y.~AP1(~AP2(F, y), x))) => lk(/\z.~AP1(~AP2(F, z), z)) 
36.19/36.28	    ~AP1(F, X) => F X 
36.19/36.28	    ~AP2(F, X) => F X 
36.19/36.28	
36.19/36.28	
36.19/36.28	+++ Citations +++
36.19/36.28	
36.19/36.28	[Kop11]  C. Kop.  Simplifying Algebraic Functional Systems.  In Proceedings of CAI 2011, volume 6742 of LNCS.  201--215, Springer, 2011.
36.39/36.41	EOF

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