/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...
## 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 = [quot^#(s(_0),s(_1)) -> quot^#(min(_0,_1),s(_1))]
  TRS = {plus(0,_0) -> _0, plus(s(_0),_1) -> s(plus(_0,_1)), min(_0,0) -> _0, min(s(_0),s(_1)) -> min(_0,_1), min(min(_0,_1),Z) -> min(_0,plus(_1,Z)), quot(0,s(_0)) -> 0, quot(s(_0),s(_1)) -> s(quot(min(_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:
      {min:[0], quot:[0, 1], plus:[0, 1], s:[0], quot^#:[0, 1]}
      and the  precedence:
      quot > [s, min], plus > [s, min], s > [min]
  This DP problem is finite.
  ## DP problem:
  Dependency pairs = [min^#(s(_0),s(_1)) -> min^#(_0,_1), min^#(min(_0,_1),Z) -> min^#(_0,plus(_1,Z))]
  TRS = {plus(0,_0) -> _0, plus(s(_0),_1) -> s(plus(_0,_1)), min(_0,0) -> _0, min(s(_0),s(_1)) -> min(_0,_1), min(min(_0,_1),Z) -> min(_0,plus(_1,Z)), quot(0,s(_0)) -> 0, quot(s(_0),s(_1)) -> s(quot(min(_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:
      {min:[0], quot:[0, 1], plus:[0, 1], s:[0], min^#:[0]}
      and the  precedence:
      quot > [min^#, s, min], plus > [min^#, s, min], s > [min^#, min], min > [min^#]
  This DP problem is finite.
  ## DP problem:
  Dependency pairs = [plus^#(s(_0),_1) -> plus^#(_0,_1)]
  TRS = {plus(0,_0) -> _0, plus(s(_0),_1) -> s(plus(_0,_1)), min(_0,0) -> _0, min(s(_0),s(_1)) -> min(_0,_1), min(min(_0,_1),Z) -> min(_0,plus(_1,Z)), quot(0,s(_0)) -> 0, quot(s(_0),s(_1)) -> s(quot(min(_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