TRS Standard pair #615304307

details

property	value
status	complete
benchmark	jwno4.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n135.star.cs.uiowa.edu
space	Waldmann_06

run statistics

property	value
solver	NTI_23
configuration	default
runtime (wallclock)	0.330174922943 seconds
cpu usage	0.701465791
max memory	6.1411328E7

stage attributes

key	value
output-size	3767
starexec-result	"NO"

output

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


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


NO

** BEGIN proof argument **
* Certificate: f(f(f(h(_0),_1),h(_2)),f(f(h(_3),_4),h(_5))) is non-terminating
* Description:
The following rule R was generated while unfolding
the dependency pairs of the analyzed TRS:
[iteration = 3] f^#(f(f(h(_0),_1),_6),_7) -> f^#(_7,f(f(_6,f(f(_1,f(_0,h(a))),h(a))),h(a)))
Let l be the left-hand side and r be the right-hand side of R.
Let p = epsilon, theta1 = {_6->h(_2), _7->f(f(h(_3),_4),h(_5))} and theta2 = {_3->_2, _2->_5, _1->_4, _0->_3, _4->f(f(_1,f(_0,h(a))),h(a)), _5->a}.
We have r|p = f^#(_7,f(f(_6,f(f(_1,f(_0,h(a))),h(a))),h(a)))
and theta2(theta1(l)) = theta1(r|p), i.e., l semi-unifies with r|p.
So, the term theta1(l) = f(f(f(h(_0),_1),h(_2)),f(f(h(_3),_4),h(_5)))
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^#(h(_0),_1) -> f^#(_1,f(_0,h(a))), f^#(h(_0),_1) -> f^#(_0,h(a))]
  TRS = {f(h(_0),_1) -> h(f(_1,f(_0,h(a))))}
    ## 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: infiniteness not proved, 2 unfolded rules generated.
        # Iteration 1: infiniteness not proved, 5 unfolded rules generated.
        # Iteration 2: infiniteness not proved, 7 unfolded rules generated.
        # Iteration 3: success, loop found, 5 unfolded rules generated.
        Here is the successful unfolding. Let IR be the TRS under analysis.
        L0 = f^#(h(_0),_1) -> f^#(_1,f(_0,h(a))) [trans] is in U_IR^0.
        We build a unit triple from L0.
        ==> L1 = f^#(h(_0),_1) -> f^#(_1,f(_0,h(a))) [unit] is in U_IR^1.
        Let p1 = [0].
        We unfold the rule of L1 backwards at position p1
        with the rule f(h(_0),_1) -> h(f(_1,f(_0,h(a)))).
        ==> L2 = f^#(f(h(_0),_1),_2) -> f^#(_2,f(f(_1,f(_0,h(a))),h(a))) [unit] is in U_IR^2.
        Let p2 = [0, 0].
        We unfold the rule of L2 backwards at position p2
        with the rule f(h(_0),_1) -> h(f(_1,f(_0,h(a)))).
        ==> L3 = f^#(f(f(h(_0),_1),_2),_3) -> f^#(_3,f(f(_2,f(f(_1,f(_0,h(a))),h(a))),h(a))) [unit] is in U_IR^3.
  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 = 108

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