/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...
## 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 = [shuffle^#(add(_0,_1)) -> shuffle^#(reverse(_1))]
  TRS = {app(nil,_0) -> _0, app(add(_0,_1),_2) -> add(_0,app(_1,_2)), reverse(nil) -> nil, reverse(add(_0,_1)) -> app(reverse(_1),add(_0,nil)), shuffle(nil) -> nil, shuffle(add(_0,_1)) -> add(_0,shuffle(reverse(_1)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations...
      The constraints are satisfied by the polynomials:
      {reverse(_0):[_0], shuffle(_0):[_0], nil:[0], app(_0,_1):[_0 + _1], add(_0,_1):[1 + _0 + _1], shuffle^#(_0):[_0]}
      for all instantiations of the variables with values greater than or equal to mu = 0.
  This DP problem is finite.
  ## DP problem:
  Dependency pairs = [reverse^#(add(_0,_1)) -> reverse^#(_1)]
  TRS = {app(nil,_0) -> _0, app(add(_0,_1),_2) -> add(_0,app(_1,_2)), reverse(nil) -> nil, reverse(add(_0,_1)) -> app(reverse(_1),add(_0,nil)), shuffle(nil) -> nil, shuffle(add(_0,_1)) -> add(_0,shuffle(reverse(_1)))}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem:
  Dependency pairs = [app^#(add(_0,_1),_2) -> app^#(_1,_2)]
  TRS = {app(nil,_0) -> _0, app(add(_0,_1),_2) -> add(_0,app(_1,_2)), reverse(nil) -> nil, reverse(add(_0,_1)) -> app(reverse(_1),add(_0,nil)), shuffle(nil) -> nil, shuffle(add(_0,_1)) -> add(_0,shuffle(reverse(_1)))}
    ## 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