TRS Standard pair #615304944

details

property	value
status	complete
benchmark	4.49.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n046.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	NTI_23
configuration	default
runtime (wallclock)	0.673928022385 seconds
cpu usage	1.532663084
max memory	7.3744384E7

stage attributes

key	value
output-size	2914
starexec-result	"NO"

output

/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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


NO

** BEGIN proof argument **
* Certificate: f(_0,_1,f(_2,_3,_4)) is non-terminating
* Description:
The following rule R was generated while unfolding
the dependency pairs of the analyzed TRS:
[iteration = 0] f^#(_0,_5,f(_2,_3,_4)) -> f^#(f(_0,_5,_2),_3,f(_0,_5,_4))
Let l be the left-hand side and r be the right-hand side of R.
Let p = epsilon, theta1 = {_5->_1} and theta2 = {_0->f(_0,_1,_2), _2->_0, _1->_3, _3->_1}.
We have r|p = f^#(f(_0,_5,_2),_3,f(_0,_5,_4))
and theta2(theta1(l)) = theta1(r|p), i.e., l semi-unifies with r|p.
So, the term theta1(l) = f(_0,_1,f(_2,_3,_4))
starts an infinite rewrite sequence w.r.t. the analyzed TRS.
** END proof argument **

** BEGIN proof description **
## Searching for a generalized rewrite rule
(a rule whose right-hand side contains a variable
that does not occur in the left-hand side)...
No generalized rewrite rule found!

## Applying the DP framework...
## 1 initial DP problem to solve.
## First, we try to decompose this problem into smaller problems.
## Round 1 [1 DP problem]:
  ## DP problem:
  Dependency pairs = [f^#(_0,_1,f(_2,_3,_4)) -> f^#(f(_0,_1,_2),_3,f(_0,_1,_4)), f^#(_0,_1,f(_2,_3,_4)) -> f^#(_0,_1,_2), f^#(_0,_1,f(_2,_3,_4)) -> f^#(_0,_1,_4)]
  TRS = {f(_0,_1,f(_2,_3,_4)) -> f(f(_0,_1,_2),_3,f(_0,_1,_4))}
    ## DP Processor: homeomorphic embeddings. 
      Using no argument filtering, i.e., applying the processor to the full problem only.
      Failed!
    ## DP Processor: lexicographic path orders. 
      Using no argument filtering, i.e., applying the processor to the full problem only.
      Failed!
    ## DP Processor: polynomial interpretations. 
      Using no argument filtering, i.e., applying the processor to the full problem only.
      Failed!
    ## DP Processor: Knuth-Bendix orders. 
      Using no argument filtering, i.e., applying the processor to the full problem only.
      Failed!
  All the DP processors have failed!
  Don't know whether this DP problem is finite.
## A DP problem could not be proved finite.
## Now, we try to prove that this problem is infinite.
    ## DP Processor: [Payet, LOPSTR'18] + [Payet, Non-termination in TRS and LP] (forward=true, backward=true, max=20). 
      # max_depth=20, unfold_variables=false:
        # Iteration 0: success, loop found, 1 unfolded rule generated.
        Here is the successful unfolding. Let IR be the TRS under analysis.
        L0 = f^#(_0,_1,f(_2,_3,_4)) -> f^#(f(_0,_1,_2),_3,f(_0,_1,_4)) [trans] is in U_IR^0.
  This DP problem is infinite.
Proof run on Linux version 3.10.0-1160.62.1.el7.x86_64 for amd64
using Java version 1.8.0_322
** END proof description **
Total number of generated unfolded rules = 2

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