/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...
## 3 initial DP problems to solve.
## First, we try to decompose these problems into smaller problems.
## Round 1 [3 DP problems]:
  ## DP problem:
  Dependency pairs = [div^#(s(_0),s(_1)) -> div^#(-(_0,_1),s(_1))]
  TRS = {-(_0,0) -> _0, -(0,s(_0)) -> 0, -(s(_0),s(_1)) -> -(_0,_1), lt(_0,0) -> false, lt(0,s(_0)) -> true, lt(s(_0),s(_1)) -> lt(_0,_1), if(true,_0,_1) -> _0, if(false,_0,_1) -> _1, div(_0,0) -> 0, div(0,_0) -> 0, div(s(_0),s(_1)) -> if(lt(_0,_1),0,s(div(-(_0,_1),s(_1))))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... This DP problem is too complex! Aborting!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using
      the argument filtering:
      {div:[0, 1], lt:[0, 1], if:[0, 1, 2], s:[0], -:[0], div^#:[0, 1]}
      and the  precedence:
      div > [true, false, if, lt, -, 0, s], 0 > [true, false], s > [true, false, -, 0]
  This DP problem is finite.
  ## DP problem:
  Dependency pairs = [lt^#(s(_0),s(_1)) -> lt^#(_0,_1)]
  TRS = {-(_0,0) -> _0, -(0,s(_0)) -> 0, -(s(_0),s(_1)) -> -(_0,_1), lt(_0,0) -> false, lt(0,s(_0)) -> true, lt(s(_0),s(_1)) -> lt(_0,_1), if(true,_0,_1) -> _0, if(false,_0,_1) -> _1, div(_0,0) -> 0, div(0,_0) -> 0, div(s(_0),s(_1)) -> if(lt(_0,_1),0,s(div(-(_0,_1),s(_1))))}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem:
  Dependency pairs = [-^#(s(_0),s(_1)) -> -^#(_0,_1)]
  TRS = {-(_0,0) -> _0, -(0,s(_0)) -> 0, -(s(_0),s(_1)) -> -(_0,_1), lt(_0,0) -> false, lt(0,s(_0)) -> true, lt(s(_0),s(_1)) -> lt(_0,_1), if(true,_0,_1) -> _0, if(false,_0,_1) -> _1, div(_0,0) -> 0, div(0,_0) -> 0, div(s(_0),s(_1)) -> if(lt(_0,_1),0,s(div(-(_0,_1),s(_1))))}
    ## 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