/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...
## 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 = [f^#(j(_0,_1),_1) -> f^#(_0,k(_1))]
  TRS = {f(j(_0,_1),_1) -> g(f(_0,k(_1))), f(_0,h1(_1,_2)) -> h2(0,_0,h1(_1,_2)), g(h2(_0,_1,h1(_2,_3))) -> h2(s(_0),_1,h1(_2,_3)), h2(_0,j(_1,h1(_2,_3)),h1(_2,_3)) -> h2(s(_0),_1,h1(s(_2),_3)), i(f(_0,h(_1))) -> _1, i(h2(s(_0),_1,h1(_0,_2))) -> _2, k(h(_0)) -> h1(0,_0), k(h1(_0,_1)) -> h1(s(_0),_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:
      {h1:[1], i:[0], g:[0], h2:[2], j:[0, 1], s:[0], f:[0, 1], k:[0], h:[0], f^#:[0, 1]}
      and the  precedence:
      j > [g, h2, f^#, f, k], f > [h2], h > [h1]
  This DP problem is finite.
  ## DP problem:
  Dependency pairs = [h2^#(_0,j(_1,h1(_2,_3)),h1(_2,_3)) -> h2^#(s(_0),_1,h1(s(_2),_3))]
  TRS = {f(j(_0,_1),_1) -> g(f(_0,k(_1))), f(_0,h1(_1,_2)) -> h2(0,_0,h1(_1,_2)), g(h2(_0,_1,h1(_2,_3))) -> h2(s(_0),_1,h1(_2,_3)), h2(_0,j(_1,h1(_2,_3)),h1(_2,_3)) -> h2(s(_0),_1,h1(s(_2),_3)), i(f(_0,h(_1))) -> _1, i(h2(s(_0),_1,h1(_0,_2))) -> _2, k(h(_0)) -> h1(0,_0), k(h1(_0,_1)) -> h1(s(_0),_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:
      {h1:[1], i:[0], g:[0], h2:[2], j:[0, 1], s:[0], f:[0, 1], k:[0], h:[0], h2^#:[1]}
      and the  precedence:
      j > [g, h2, h2^#, f, k], f > [h2], h > [h1]
  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