/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...
## 3 initial DP problems to solve.
## First, we try to decompose these problems into smaller problems.
## Round 1 [3 DP problems]:
  ## DP problem:
  Dependency pairs = [mod^#(s(_0),s(_1)) -> if_mod^#(le(_1,_0),s(_0),s(_1)), if_mod^#(true,s(_0),s(_1)) -> mod^#(minus(_0,_1),s(_1))]
  TRS = {le(0,_0) -> true, le(s(_0),0) -> false, le(s(_0),s(_1)) -> le(_0,_1), minus(_0,0) -> _0, minus(s(_0),s(_1)) -> minus(_0,_1), mod(0,_0) -> 0, mod(s(_0),0) -> 0, mod(s(_0),s(_1)) -> if_mod(le(_1,_0),s(_0),s(_1)), if_mod(true,s(_0),s(_1)) -> mod(minus(_0,_1),s(_1)), if_mod(false,s(_0),s(_1)) -> s(_0)}
    ## 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:
      {if_mod:[1], minus:[0], mod:[0], s:[0], le:[0, 1], mod^#:[0], if_mod^#:[1]}
      and the  precedence:
      0 > [true], mod > [if_mod], mod^# > [if_mod^#], s > [0, if_mod^#, if_mod, mod, false, minus, mod^#, true]
  This DP problem is finite.
  ## DP problem:
  Dependency pairs = [minus^#(s(_0),s(_1)) -> minus^#(_0,_1)]
  TRS = {le(0,_0) -> true, le(s(_0),0) -> false, le(s(_0),s(_1)) -> le(_0,_1), minus(_0,0) -> _0, minus(s(_0),s(_1)) -> minus(_0,_1), mod(0,_0) -> 0, mod(s(_0),0) -> 0, mod(s(_0),s(_1)) -> if_mod(le(_1,_0),s(_0),s(_1)), if_mod(true,s(_0),s(_1)) -> mod(minus(_0,_1),s(_1)), if_mod(false,s(_0),s(_1)) -> s(_0)}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem:
  Dependency pairs = [le^#(s(_0),s(_1)) -> le^#(_0,_1)]
  TRS = {le(0,_0) -> true, le(s(_0),0) -> false, le(s(_0),s(_1)) -> le(_0,_1), minus(_0,0) -> _0, minus(s(_0),s(_1)) -> minus(_0,_1), mod(0,_0) -> 0, mod(s(_0),0) -> 0, mod(s(_0),s(_1)) -> if_mod(le(_1,_0),s(_0),s(_1)), if_mod(true,s(_0),s(_1)) -> mod(minus(_0,_1),s(_1)), if_mod(false,s(_0),s(_1)) -> s(_0)}
    ## 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