/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...
## 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 = [i^#(+(_0,_1)) -> i^#(_0), i^#(+(_0,_1)) -> i^#(_1)]
  TRS = {i(0) -> 0, +(0,_0) -> _0, +(_0,0) -> _0, i(i(_0)) -> _0, +(i(_0),_0) -> 0, +(_0,i(_0)) -> 0, i(+(_0,_1)) -> +(i(_0),i(_1)), +(_0,+(_1,_2)) -> +(+(_0,_1),_2), +(+(_0,i(_1)),_1) -> _0, +(+(_0,_1),i(_1)) -> _0}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem:
  Dependency pairs = [+^#(_0,+(_1,_2)) -> +^#(+(_0,_1),_2), +^#(_0,+(_1,_2)) -> +^#(_0,_1)]
  TRS = {i(0) -> 0, +(0,_0) -> _0, +(_0,0) -> _0, i(i(_0)) -> _0, +(i(_0),_0) -> 0, +(_0,i(_0)) -> 0, i(+(_0,_1)) -> +(i(_0),i(_1)), +(_0,+(_1,_2)) -> +(+(_0,_1),_2), +(+(_0,i(_1)),_1) -> _0, +(+(_0,_1),i(_1)) -> _0}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations...
    Successfully decomposed the DP problem into 1 smaller problem to solve!
## Round 2 [1 DP problem]:
  ## DP problem:
  Dependency pairs = [+^#(_0,+(_1,_2)) -> +^#(+(_0,_1),_2)]
  TRS = {i(0) -> 0, +(0,_0) -> _0, +(_0,0) -> _0, i(i(_0)) -> _0, +(i(_0),_0) -> 0, +(_0,i(_0)) -> 0, i(+(_0,_1)) -> +(i(_0),i(_1)), +(_0,+(_1,_2)) -> +(+(_0,_1),_2), +(+(_0,i(_1)),_1) -> _0, +(+(_0,_1),i(_1)) -> _0}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations...
      The constraints are satisfied by the polynomials:
      {+(_0,_1):[_0 * _1], 0:[2], i(_0):[_0], +^#(_0,_1):[_0]}
      for all instantiations of the variables with values greater than or equal to mu = 2.
  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