/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 = [s^#(f(_0,_1)) -> s^#(_1), s^#(f(_0,_1)) -> s^#(_0), s^#(g(_0,_1)) -> s^#(_0), s^#(g(_0,_1)) -> s^#(_1)]
  TRS = {s(a) -> a, s(s(_0)) -> _0, s(f(_0,_1)) -> f(s(_1),s(_0)), s(g(_0,_1)) -> g(s(_0),s(_1)), f(_0,a) -> _0, f(a,_0) -> _0, f(g(_0,_1),g(_2,_3)) -> g(f(_0,_2),f(_1,_3)), g(a,a) -> a}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem:
  Dependency pairs = [f^#(g(_0,_1),g(_2,_3)) -> f^#(_0,_2), f^#(g(_0,_1),g(_2,_3)) -> f^#(_1,_3)]
  TRS = {s(a) -> a, s(s(_0)) -> _0, s(f(_0,_1)) -> f(s(_1),s(_0)), s(g(_0,_1)) -> g(s(_0),s(_1)), f(_0,a) -> _0, f(a,_0) -> _0, f(g(_0,_1),g(_2,_3)) -> g(f(_0,_2),f(_1,_3)), g(a,a) -> a}
    ## 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