/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 = [ack^#(s(_0),0) -> ack^#(_0,s(0)), ack^#(s(_0),s(_1)) -> ack^#(_0,ack(s(_0),_1)), ack^#(s(_0),s(_1)) -> ack^#(s(_0),_1)]
  TRS = {ack(0,_0) -> s(_0), ack(s(_0),0) -> ack(_0,s(0)), ack(s(_0),s(_1)) -> ack(_0,ack(s(_0),_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], ack:[0, 1], ack^#:[0, 1]}
      and the  precedence:
      s > [0], ack^# > [s, 0, ack], ack > [s, 0]
  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