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


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YES

** BEGIN proof argument **
All the DP problems were proved finite.
As all the involved DP processors are sound,
the TRS under analysis terminates.
** 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...
## 2 initial DP problems to solve.
## First, we try to decompose these problems into smaller problems.
## Round 1 [2 DP problems]:
  ## DP problem:
  Dependency pairs = [purge^#(.(_0,_1)) -> purge^#(remove(_0,_1))]
  TRS = {purge(nil) -> nil, purge(.(_0,_1)) -> .(_0,purge(remove(_0,_1))), remove(_0,nil) -> nil, remove(_0,.(_1,_2)) -> if(=(_0,_1),remove(_0,_2),.(_1,remove(_0,_2)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... This DP problem is too complex! Aborting!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using
      the argument filtering:
      {=:[0, 1], .:[0, 1], remove:[0, 1], if:[0], purge:[0], purge^#:[0]}
      and the  precedence:
      . > [if, =, remove, purge^#], remove > [if, =], purge > [if, =, ., remove, purge^#]
  This DP problem is finite.
  ## DP problem:
  Dependency pairs = [remove^#(_0,.(_1,_2)) -> remove^#(_0,_2), remove^#(_0,.(_1,_2)) -> remove^#(_0,_2)]
  TRS = {purge(nil) -> nil, purge(.(_0,_1)) -> .(_0,purge(remove(_0,_1))), remove(_0,nil) -> nil, remove(_0,.(_1,_2)) -> if(=(_0,_1),remove(_0,_2),.(_1,remove(_0,_2)))}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
## All the DP problems were proved finite.
As all the involved DP processors are sound,
the TRS under analysis terminates.
Proof run on Linux version 3.10.0-1160.25.1.el7.x86_64 for amd64
using Java version 1.8.0_292
** END proof description **
Total number of generated unfolded rules = 0