/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...
## 1 initial DP problem to solve.
## First, we try to decompose this problem into smaller problems.
## Round 1 [1 DP problem]:
  ## DP problem:
  Dependency pairs = [plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2)), plus^#(s(_0),plus(_1,_2)) -> plus^#(s(s(_1)),_2), plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_2,plus(_1,_3)), plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_1,_3)]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations...
    Successfully decomposed the DP problem into 1 smaller problem to solve!
## Round 2 [1 DP problem]:
  ## DP problem:
  Dependency pairs = [plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2)), plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3)))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## 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], plus:[0], plus^#:[0]}
      and the  precedence:
      s > [plus, plus^#]
  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