/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/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...
## 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 = [msort^#(.(_0,_1)) -> msort^#(del(min(_0,_1),.(_0,_1)))]
  TRS = {msort(nil) -> nil, msort(.(_0,_1)) -> .(min(_0,_1),msort(del(min(_0,_1),.(_0,_1)))), min(_0,nil) -> _0, min(_0,.(_1,_2)) -> if(<=(_0,_1),min(_0,_2),min(_1,_2)), del(_0,nil) -> nil, del(_0,.(_1,_2)) -> if(=(_0,_1),_2,.(_1,del(_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], if:[0], min:[0, 1], del:[0], =:[0], msort:[0], .:[0, 1], msort^#:[0]}
      and the  precedence:
      min > [<=, if], msort > [<=, =, min, nil, msort^#, if, ., del], . > [<=, =, min, nil, msort^#, if, del], del > [=, nil, if]
  This DP problem is finite.
  ## DP problem:
  Dependency pairs = [del^#(_0,.(_1,_2)) -> del^#(_0,_2)]
  TRS = {msort(nil) -> nil, msort(.(_0,_1)) -> .(min(_0,_1),msort(del(min(_0,_1),.(_0,_1)))), min(_0,nil) -> _0, min(_0,.(_1,_2)) -> if(<=(_0,_1),min(_0,_2),min(_1,_2)), del(_0,nil) -> nil, del(_0,.(_1,_2)) -> if(=(_0,_1),_2,.(_1,del(_0,_2)))}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem:
  Dependency pairs = [min^#(_0,.(_1,_2)) -> min^#(_0,_2), min^#(_0,.(_1,_2)) -> min^#(_1,_2)]
  TRS = {msort(nil) -> nil, msort(.(_0,_1)) -> .(min(_0,_1),msort(del(min(_0,_1),.(_0,_1)))), min(_0,nil) -> _0, min(_0,.(_1,_2)) -> if(<=(_0,_1),min(_0,_2),min(_1,_2)), del(_0,nil) -> nil, del(_0,.(_1,_2)) -> if(=(_0,_1),_2,.(_1,del(_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], if:[0], min:[0, 1], del:[0], =:[0], msort:[0], .:[0, 1], min^#:[0, 1]}
      and the  precedence:
      min > [<=, if], msort > [<=, =, min, nil, if, ., del, min^#], . > [<=, =, min, nil, if, del, min^#], del > [=, nil, if]
  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