/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...
## 1 initial DP problem to solve.
## First, we try to decompose this problem into smaller problems.
## Round 1 [1 DP problem]:
  ## DP problem:
  Dependency pairs = [+^#(+(_0,_1),_2) -> +^#(_0,+(_1,_2)), +^#(+(_0,_1),_2) -> +^#(_1,_2), +^#(f(_0),f(_1)) -> +^#(_0,_1), +^#(f(_0),+(f(_1),_2)) -> +^#(f(+(_0,_1)),_2), +^#(f(_0),+(f(_1),_2)) -> +^#(_0,_1)]
  TRS = {+(+(_0,_1),_2) -> +(_0,+(_1,_2)), +(f(_0),f(_1)) -> f(+(_0,_1)), +(f(_0),+(f(_1),_2)) -> +(f(+(_0,_1)),_2)}
    ## 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)), +^#(f(_0),f(_1)) -> +^#(_0,_1), +^#(f(_0),+(f(_1),_2)) -> +^#(f(+(_0,_1)),_2)]
  TRS = {+(+(_0,_1),_2) -> +(_0,+(_1,_2)), +(f(_0),f(_1)) -> f(+(_0,_1)), +(f(_0),+(f(_1),_2)) -> +(f(+(_0,_1)),_2)}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations...
    Successfully decomposed the DP problem into 1 smaller problem to solve!
## Round 3 [1 DP problem]:
  ## DP problem:
  Dependency pairs = [+^#(+(_0,_1),_2) -> +^#(_0,+(_1,_2))]
  TRS = {+(+(_0,_1),_2) -> +(_0,+(_1,_2)), +(f(_0),f(_1)) -> f(+(_0,_1)), +(f(_0),+(f(_1),_2)) -> +(f(+(_0,_1)),_2)}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations...
      The constraints are satisfied by the polynomials:
      {f(_0):[_0], +(_0,_1):[_0 * _1], +^#(_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