/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 = [log^#(s(s(_0))) -> log^#(s(half(_0)))]
  TRS = {half(0) -> 0, half(s(s(_0))) -> s(half(_0)), log(s(0)) -> 0, log(s(s(_0))) -> s(log(s(half(_0))))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations...
      The constraints are satisfied by the polynomials:
      {s(_0):[2 * _0], log(_0):[_0], 0:[1], half(_0):[_0], log^#(_0):[_0]}
      for all instantiations of the variables with values greater than or equal to mu = 1.
  This DP problem is finite.
  ## DP problem:
  Dependency pairs = [half^#(s(s(_0))) -> half^#(_0)]
  TRS = {half(0) -> 0, half(s(s(_0))) -> s(half(_0)), log(s(0)) -> 0, log(s(s(_0))) -> s(log(s(half(_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