/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...
## 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 = [g^#(s(_0),_1) -> g^#(_0,+(_1,s(_0))), g^#(s(_0),_1) -> g^#(_0,s(+(_1,_0)))]
  TRS = {f(0) -> 1, f(s(_0)) -> g(_0,s(_0)), g(0,_0) -> _0, g(s(_0),_1) -> g(_0,+(_1,s(_0))), +(_0,0) -> _0, +(_0,s(_1)) -> s(+(_0,_1)), g(s(_0),_1) -> g(_0,s(+(_1,_0)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using
      the argument filtering:
      {g:[0, 1], +:[0, 1], s:[0], f:[0], g^#:[0, 1]}
      and the  precedence:
      g > [+, s], + > [s], 0 > [1], g^# > [+, s], f > [g, +, s]
  This DP problem is finite.
  ## DP problem:
  Dependency pairs = [+^#(_0,s(_1)) -> +^#(_0,_1)]
  TRS = {f(0) -> 1, f(s(_0)) -> g(_0,s(_0)), g(0,_0) -> _0, g(s(_0),_1) -> g(_0,+(_1,s(_0))), +(_0,0) -> _0, +(_0,s(_1)) -> s(+(_0,_1)), g(s(_0),_1) -> g(_0,s(+(_1,_0)))}
    ## 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