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


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


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...
## 3 initial DP problems to solve.
## First, we try to decompose these problems into smaller problems.
## Round 1 [3 DP problems]:
  ## DP problem:
  Dependency pairs = [qsort^#(.(_0,_1)) -> qsort^#(lowers(_0,_1)), qsort^#(.(_0,_1)) -> qsort^#(greaters(_0,_1))]
  TRS = {qsort(nil) -> nil, qsort(.(_0,_1)) -> ++(qsort(lowers(_0,_1)),.(_0,qsort(greaters(_0,_1)))), lowers(_0,nil) -> nil, lowers(_0,.(_1,_2)) -> if(<=(_1,_0),.(_1,lowers(_0,_2)),lowers(_0,_2)), greaters(_0,nil) -> nil, greaters(_0,.(_1,_2)) -> if(<=(_1,_0),greaters(_0,_2),.(_1,greaters(_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:
      {if:[0], .:[0, 1], lowers:[0, 1], greaters:[0, 1], <=:[0, 1], qsort:[0], ++:[0], qsort^#:[0]}
      and the  precedence:
      . > [++, lowers, greaters, qsort^#, <=, qsort, if], lowers > [<=, if], greaters > [<=, if]
  This DP problem is finite.
  ## DP problem:
  Dependency pairs = [greaters^#(_0,.(_1,_2)) -> greaters^#(_0,_2), greaters^#(_0,.(_1,_2)) -> greaters^#(_0,_2)]
  TRS = {qsort(nil) -> nil, qsort(.(_0,_1)) -> ++(qsort(lowers(_0,_1)),.(_0,qsort(greaters(_0,_1)))), lowers(_0,nil) -> nil, lowers(_0,.(_1,_2)) -> if(<=(_1,_0),.(_1,lowers(_0,_2)),lowers(_0,_2)), greaters(_0,nil) -> nil, greaters(_0,.(_1,_2)) -> if(<=(_1,_0),greaters(_0,_2),.(_1,greaters(_0,_2)))}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem:
  Dependency pairs = [lowers^#(_0,.(_1,_2)) -> lowers^#(_0,_2), lowers^#(_0,.(_1,_2)) -> lowers^#(_0,_2)]
  TRS = {qsort(nil) -> nil, qsort(.(_0,_1)) -> ++(qsort(lowers(_0,_1)),.(_0,qsort(greaters(_0,_1)))), lowers(_0,nil) -> nil, lowers(_0,.(_1,_2)) -> if(<=(_1,_0),.(_1,lowers(_0,_2)),lowers(_0,_2)), greaters(_0,nil) -> nil, greaters(_0,.(_1,_2)) -> if(<=(_1,_0),greaters(_0,_2),.(_1,greaters(_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