/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 = [*^#(O(_0),_1) -> *^#(_0,_1), *^#(I(_0),_1) -> *^#(_0,_1)]
  TRS = {O(0) -> 0, +(0,_0) -> _0, +(_0,0) -> _0, +(O(_0),O(_1)) -> O(+(_0,_1)), +(O(_0),I(_1)) -> I(+(_0,_1)), +(I(_0),O(_1)) -> I(+(_0,_1)), +(I(_0),I(_1)) -> O(+(+(_0,_1),I(0))), *(0,_0) -> 0, *(_0,0) -> 0, *(O(_0),_1) -> O(*(_0,_1)), *(I(_0),_1) -> +(O(*(_0,_1)),_1)}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem:
  Dependency pairs = [+^#(O(_0),O(_1)) -> +^#(_0,_1), +^#(O(_0),I(_1)) -> +^#(_0,_1), +^#(I(_0),O(_1)) -> +^#(_0,_1), +^#(I(_0),I(_1)) -> +^#(_0,_1), +^#(I(_0),I(_1)) -> +^#(+(_0,_1),I(0))]
  TRS = {O(0) -> 0, +(0,_0) -> _0, +(_0,0) -> _0, +(O(_0),O(_1)) -> O(+(_0,_1)), +(O(_0),I(_1)) -> I(+(_0,_1)), +(I(_0),O(_1)) -> I(+(_0,_1)), +(I(_0),I(_1)) -> O(+(+(_0,_1),I(0))), *(0,_0) -> 0, *(_0,0) -> 0, *(O(_0),_1) -> O(*(_0,_1)), *(I(_0),_1) -> +(O(*(_0,_1)),_1)}
    ## 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 = [+^#(I(_0),O(_1)) -> +^#(_0,_1), +^#(O(_0),O(_1)) -> +^#(_0,_1), +^#(O(_0),I(_1)) -> +^#(_0,_1)]
  TRS = {O(0) -> 0, +(0,_0) -> _0, +(_0,0) -> _0, +(O(_0),O(_1)) -> O(+(_0,_1)), +(O(_0),I(_1)) -> I(+(_0,_1)), +(I(_0),O(_1)) -> I(+(_0,_1)), +(I(_0),I(_1)) -> O(+(+(_0,_1),I(0))), *(0,_0) -> 0, *(_0,0) -> 0, *(O(_0),_1) -> O(*(_0,_1)), *(I(_0),_1) -> +(O(*(_0,_1)),_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