TRS Standard pair #615296487

details

property	value
status	complete
benchmark	s.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n018.star.cs.uiowa.edu
space	Zantema_15

run statistics

property	value
solver	AutoNon 1.21
configuration	autonon
runtime (wallclock)	2.43479013443 seconds
cpu usage	8.935270703
max memory	1.1635712E9

stage attributes

key	value
output-size	2956
starexec-result	"NO"

output

/export/starexec/sandbox/solver/bin/starexec_run_autonon /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


NO

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*** AutoNon ***


AutoNon proves looping and non-looping non-termination using regular languages.

AutoNon employs SAT solving to find finite automata as certificates of non-termination.
The automata define (a) the language and (b) which rule may be applied where in a term.
By property (b), the language of the automaton does not need to be closed under rewriting.
It suffices that every term in the language admits some rewrite step to a term in the language.
Finally, we employ a quasi-order on the states of the automaton. This allows rewriting to
change the interpretation of a term (the state of the automaton) and thereby to change what
rules may be applied (the allowed rules depend on the state of the automaton).

The technique is described in the following paper:

    [EZ2015] Proving Non-Termination by Finite Automata
             by J. Endrullis and H. Zantema
             Proc. Conf. on Rewriting Techniques and Applications (RTA 2015)

For further information see <a href="http://joerg.endrullis.de/nonterm/">

       http://joerg.endrullis.de/nonterm/       

</a>

*** Input system ***

    a(a(a(S,x),y),z) -> a(a(x,z),a(y,z))



*** Non-looping non-termination using regular languages ***


Input system R is not terminating since R admits a regular language weakly closed under rewriting.


The following finite automaton witnesses non-termination:

  The states are: 0,1,...,4

  The accepting states are: 4

  The states determine the rules that may be used:

      state 0:
          a(a(a(S,x),y),z) -> a(a(x,z),a(y,z))
      state 1:
          a(a(a(S,x),y),z) -> a(a(x,z),a(y,z))
      state 2:
          a(a(a(S,x),y),z) -> a(a(x,z),a(y,z))
      state 3:
          a(a(a(S,x),y),z) -> a(a(x,z),a(y,z))
      state 4:
          a(a(a(S,x),y),z) -> a(a(x,z),a(y,z))

  Transitions for `a':

       x0  0  0  0  0  0  1  1  1  1  1  2  2  2  2  2  3  3  3  3  3  4  4  4  4  4
       x1  0  1  2  3  4  0  1  2  3  4  0  1  2  3  4  0  1  2  3  4  0  1  2  3  4
      out
        0  1                                                                        
        1  1                                                              1        1
        2        1        1                    1                          1         
        3                                      1                                    
        4                                                     1        1  1  1      

  Transitions for `S':

      out
        0  1
        1   
        2   
        3   
        4   



Hence the TRS is non-terminating.
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