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