/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


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...
## 4 initial DP problems to solve.
## First, we try to decompose these problems into smaller problems.
## Round 1 [4 DP problems]:
  ## DP problem:
  Dependency pairs = [f^#(s(_0),s(_1),0) -> f^#(_0,_1,s(0)), f^#(s(_0),0,s(_1)) -> f^#(_0,s(0),_1), f^#(s(_0),s(_1),s(_2)) -> f^#(_0,_1,f(s(_0),s(_1),_2)), f^#(s(_0),s(_1),s(_2)) -> f^#(s(_0),s(_1),_2)]
  TRS = {f(_0,0,0) -> s(_0), f(0,_0,0) -> s(_0), f(0,0,_0) -> s(_0), f(s(0),_0,_1) -> f(0,s(_0),s(_1)), f(s(_0),s(_1),0) -> f(_0,_1,s(0)), f(s(_0),0,s(_1)) -> f(_0,s(0),_1), f(0,s(0),s(0)) -> s(s(0)), f(s(_0),s(_1),s(_2)) -> f(_0,_1,f(s(_0),s(_1),_2)), f(0,s(s(_0)),s(0)) -> f(0,_0,s(0)), f(0,s(0),s(s(_0))) -> f(0,s(0),_0), f(0,s(s(_0)),s(s(_1))) -> f(0,_0,f(0,s(s(_0)),s(_1)))}
    ## 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:
      {s:[0], f:[0, 1, 2], f^#:[0, 1, 2]}
      and the  precedence:
      f^# > [s, 0, f], s > [0], f > [s, 0]
  This DP problem is finite.
  ## DP problem:
  Dependency pairs = [f^#(0,s(s(_0)),s(s(_1))) -> f^#(0,_0,f(0,s(s(_0)),s(_1))), f^#(0,s(s(_0)),s(s(_1))) -> f^#(0,s(s(_0)),s(_1))]
  TRS = {f(_0,0,0) -> s(_0), f(0,_0,0) -> s(_0), f(0,0,_0) -> s(_0), f(s(0),_0,_1) -> f(0,s(_0),s(_1)), f(s(_0),s(_1),0) -> f(_0,_1,s(0)), f(s(_0),0,s(_1)) -> f(_0,s(0),_1), f(0,s(0),s(0)) -> s(s(0)), f(s(_0),s(_1),s(_2)) -> f(_0,_1,f(s(_0),s(_1),_2)), f(0,s(s(_0)),s(0)) -> f(0,_0,s(0)), f(0,s(0),s(s(_0))) -> f(0,s(0),_0), f(0,s(s(_0)),s(s(_1))) -> f(0,_0,f(0,s(s(_0)),s(_1)))}
    ## 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:
      {s:[0], f:[0, 1, 2], f^#:[0, 1, 2]}
      and the  precedence:
      f^# > [s, 0, f], s > [0], f > [s, 0]
  This DP problem is finite.
  ## DP problem:
  Dependency pairs = [f^#(0,s(0),s(s(_0))) -> f^#(0,s(0),_0)]
  TRS = {f(_0,0,0) -> s(_0), f(0,_0,0) -> s(_0), f(0,0,_0) -> s(_0), f(s(0),_0,_1) -> f(0,s(_0),s(_1)), f(s(_0),s(_1),0) -> f(_0,_1,s(0)), f(s(_0),0,s(_1)) -> f(_0,s(0),_1), f(0,s(0),s(0)) -> s(s(0)), f(s(_0),s(_1),s(_2)) -> f(_0,_1,f(s(_0),s(_1),_2)), f(0,s(s(_0)),s(0)) -> f(0,_0,s(0)), f(0,s(0),s(s(_0))) -> f(0,s(0),_0), f(0,s(s(_0)),s(s(_1))) -> f(0,_0,f(0,s(s(_0)),s(_1)))}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem:
  Dependency pairs = [f^#(0,s(s(_0)),s(0)) -> f^#(0,_0,s(0))]
  TRS = {f(_0,0,0) -> s(_0), f(0,_0,0) -> s(_0), f(0,0,_0) -> s(_0), f(s(0),_0,_1) -> f(0,s(_0),s(_1)), f(s(_0),s(_1),0) -> f(_0,_1,s(0)), f(s(_0),0,s(_1)) -> f(_0,s(0),_1), f(0,s(0),s(0)) -> s(s(0)), f(s(_0),s(_1),s(_2)) -> f(_0,_1,f(s(_0),s(_1),_2)), f(0,s(s(_0)),s(0)) -> f(0,_0,s(0)), f(0,s(0),s(s(_0))) -> f(0,s(0),_0), f(0,s(s(_0)),s(s(_1))) -> f(0,_0,f(0,s(s(_0)),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