Higher_Order_Rewriting_Union_Beta 2019-03-28 22.10 pair #432270353

details

property	value
status	complete
benchmark	slml.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n073.star.cs.uiowa.edu
space	Hamana_17

run statistics

property	value
solver	Wanda 2.1c
configuration	default
runtime (wallclock)	78.5815 seconds
cpu usage	78.5435
user time	77.187
system time	1.35656
max virtual memory	1275280.0
max residence set size	1148964.0

stage attributes

key	value
starexec-result	MAYBE

output

77.89/78.48	MAYBE
78.43/78.50	We consider the system theBenchmark.
78.43/78.50	
78.43/78.50	  Alphabet:
78.43/78.50	
78.43/78.50	    abs : [] --> (a -> a) -> aa 
78.43/78.50	    app : [] --> aa -> a -> a 
78.43/78.50	    let : [] --> ta -> (a -> ta) -> ta 
78.43/78.50	    return : [] --> a -> ta 
78.43/78.50	
78.43/78.50	  Rules:
78.43/78.50	
78.43/78.50	    app (abs (/\x.f x)) y => f y 
78.43/78.50	    abs (/\x.app y x) => y 
78.43/78.50	    let (return x) (/\y.f y) => f x 
78.43/78.50	    let x (/\y.return y) => x 
78.43/78.50	    let (let x (/\y.f y)) (/\z.g z) => let x (/\u.let (f u) (/\v.g v)) 
78.43/78.50	
78.43/78.50	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.
78.43/78.50	
78.43/78.50	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:
78.43/78.50	
78.43/78.50	  Alphabet:
78.43/78.50	
78.43/78.50	    abs : [a -> a] --> aa 
78.43/78.50	    app : [aa * a] --> a 
78.43/78.50	    let : [ta * a -> ta] --> ta 
78.43/78.50	    return : [a] --> ta 
78.43/78.50	    ~AP1 : [a -> a * a] --> a 
78.43/78.50	    ~AP2 : [a -> ta * a] --> ta 
78.43/78.50	
78.43/78.50	  Rules:
78.43/78.50	
78.43/78.50	    app(abs(/\x.~AP1(F, x)), X) => ~AP1(F, X) 
78.43/78.50	    abs(/\x.app(X, x)) => X 
78.43/78.50	    let(return(X), /\x.~AP2(F, x)) => ~AP2(F, X) 
78.43/78.50	    let(X, /\x.return(x)) => X 
78.43/78.50	    let(let(X, /\x.~AP2(F, x)), /\y.~AP2(G, y)) => let(X, /\z.let(~AP2(F, z), /\u.~AP2(G, u))) 
78.43/78.50	    app(abs(/\x.app(X, x)), Y) => app(X, Y) 
78.43/78.50	    let(return(X), /\x.return(x)) => return(X) 
78.43/78.50	    let(let(X, /\x.return(x)), /\y.~AP2(F, y)) => let(X, /\z.let(return(z), /\u.~AP2(F, u))) 
78.43/78.50	    let(let(X, /\x.~AP2(F, x)), /\y.return(y)) => let(X, /\z.let(~AP2(F, z), /\u.return(u))) 
78.43/78.50	    let(let(X, /\x.return(x)), /\y.return(y)) => let(X, /\z.let(return(z), /\u.return(u))) 
78.43/78.50	    ~AP1(F, X) => F X 
78.43/78.50	    ~AP2(F, X) => F X 
78.43/78.50	
78.43/78.50	
78.43/78.50	+++ Citations +++
78.43/78.50	
78.43/78.50	[Kop11]  C. Kop.  Simplifying Algebraic Functional Systems.  In Proceedings of CAI 2011, volume 6742 of LNCS.  201--215, Springer, 2011.
78.43/78.58	EOF

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