Higher Order Rewriting Union Beta pair #487093635

details

property	value
status	complete
benchmark	h21.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n145.star.cs.uiowa.edu
space	Hamana_Kikuchi_18

run statistics

property	value
solver	Wanda 2.2a
configuration	default
runtime (wallclock)	6.73194 seconds
cpu usage	19.8392
user time	19.2773
system time	0.561829
max virtual memory	5184300.0
max residence set size	804620.0

stage attributes

key	value
starexec-result	NO

output

NO
We consider the system theBenchmark.

  Alphabet:

    0 : [] --> A 
    01 : [] --> A 
    activate : [] --> A -> A 
    app : [] --> (A -> A) -> A -> A 
    cons : [] --> A -> A -> A 
    cons1 : [] --> A -> A -> A 
    fcons : [] --> A -> A -> A 
    first : [] --> A -> A -> A 
    first1 : [] --> A -> A -> A 
    from : [] --> A -> A 
    map : [] --> (A -> A) -> A -> A 
    nil : [] --> A 
    nil1 : [] --> A 
    nxx0 : [] --> A 
    nxxcons : [] --> A -> A -> A 
    nxxfirst : [] --> A -> A -> A 
    nxxfrom : [] --> A -> A 
    nxxnil : [] --> A 
    nxxs : [] --> A -> A 
    nxxsel : [] --> A -> A -> A 
    quote : [] --> A -> A 
    quote1 : [] --> A -> A 
    s : [] --> A -> A 
    s1 : [] --> A -> A 
    sel : [] --> A -> A -> A 
    sel1 : [] --> A -> A -> A 
    unquote : [] --> A -> A 
    unquote1 : [] --> A -> A 

  Rules:

    sel (s x) (cons y z) => sel x (activate z) 
    sel 0 (cons x y) => x 
    first 0 x => nil 
    first (s x) (cons y z) => cons y (nxxfirst x (activate z)) 
    from x => cons x (nxxfrom (nxxs x)) 
    sel1 (s x) (cons y z) => sel1 x (activate z) 
    sel1 0 (cons x y) => quote x 
    first1 0 x => nil1 
    first1 (s x) (cons y z) => cons1 (quote y) (first1 x (activate z)) 
    quote nxx0 => 01 
    quote1 (nxxcons x y) => cons1 (quote (activate x)) (quote1 (activate y)) 
    quote1 nxxnil => nil1 
    quote (nxxs x) => s1 (quote (activate x)) 
    quote (nxxsel x y) => sel1 (activate x) (activate y) 
    quote1 (nxxfirst x y) => first1 (activate x) (activate y) 
    unquote 01 => 0 
    unquote (s1 x) => s (unquote x) 
    unquote1 nil1 => nil 
    unquote1 (cons1 x y) => fcons (unquote x) (unquote1 y) 
    fcons x y => cons x y 
    first x y => nxxfirst x y 
    from x => nxxfrom x 
    s x => nxxs x 
    0 => nxx0 
    cons x y => nxxcons x y 
    nil => nxxnil 
    sel x y => nxxsel x y 
    activate (nxxfirst x y) => first (activate x) (activate y) 
    activate (nxxfrom x) => from (activate x) 
    activate (nxxs x) => s (activate x) 
    activate nxx0 => 0 
    activate (nxxcons x y) => cons (activate x) y 
    activate nxxnil => nil 
    activate (nxxsel x y) => sel (activate x) (activate y) 
    activate x => x 
    map (/\x.f x) nil => nil 
    app (/\x.f x) y => f y 

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.

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:

  Alphabet:

    0 : [] --> A 
    01 : [] --> A 
    activate : [A] --> A 
    app : [A -> A * A] --> A 
    cons : [A * A] --> A 
    cons1 : [A * A] --> A 
    fcons : [A * A] --> A 
    first : [A * A] --> A 
    first1 : [A * A] --> A 
    from : [A] --> A 
    map : [A -> A * A] --> A 
    nil : [] --> A 
    nil1 : [] --> A 
    nxx0 : [] --> A 
    nxxcons : [A * A] --> A 
    nxxfirst : [A * A] --> A 
    nxxfrom : [A] --> A 
    nxxnil : [] --> A 
    nxxs : [A] --> A 
    nxxsel : [A * A] --> A

popout

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

job log

popout

actions all output return to Higher Order Rewriting Union Beta