/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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NO

** BEGIN proof argument **
The following rule was generated while unfolding the analyzed TRS:
[iteration = 0] from(_0) -> from(s(_0))
Let l be the left-hand side and r be the right-hand side of this rule.
Let p = epsilon, theta1 = {} and theta2 = {_0->s(_0)}.
We have r|p = from(s(_0)) and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = from(_0) loops w.r.t. the analyzed TRS.
** 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...
## 8 initial DP problems to solve.
## First, we try to decompose these problems into smaller problems.
## Round 1 [8 DP problems]:
  ## DP problem:
  Dependency pairs = [unquote1^#(cons1(_0,_1)) -> unquote1^#(_1)]
  TRS = {sel(s(_0),cons(_1,_2)) -> sel(_0,_2), sel(0,cons(_0,_1)) -> _0, first(0,_0) -> nil, first(s(_0),cons(_1,_2)) -> cons(_1,first(_0,_2)), from(_0) -> cons(_0,from(s(_0))), sel1(s(_0),cons(_1,_2)) -> sel1(_0,_2), sel1(0,cons(_0,_1)) -> quote(_0), first1(0,_0) -> nil1, first1(s(_0),cons(_1,_2)) -> cons1(quote(_1),first1(_0,_2)), quote(0) -> 01, quote1(cons(_0,_1)) -> cons1(quote(_0),quote1(_1)), quote1(nil) -> nil1, quote(s(_0)) -> s1(quote(_0)), quote(sel(_0,_1)) -> sel1(_0,_1), quote1(first(_0,_1)) -> first1(_0,_1), unquote(01) -> 0, unquote(s1(_0)) -> s(unquote(_0)), unquote1(nil1) -> nil, unquote1(cons1(_0,_1)) -> fcons(unquote(_0),unquote1(_1)), fcons(_0,_1) -> cons(_0,_1)}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem:
  Dependency pairs = [unquote^#(s1(_0)) -> unquote^#(_0)]
  TRS = {sel(s(_0),cons(_1,_2)) -> sel(_0,_2), sel(0,cons(_0,_1)) -> _0, first(0,_0) -> nil, first(s(_0),cons(_1,_2)) -> cons(_1,first(_0,_2)), from(_0) -> cons(_0,from(s(_0))), sel1(s(_0),cons(_1,_2)) -> sel1(_0,_2), sel1(0,cons(_0,_1)) -> quote(_0), first1(0,_0) -> nil1, first1(s(_0),cons(_1,_2)) -> cons1(quote(_1),first1(_0,_2)), quote(0) -> 01, quote1(cons(_0,_1)) -> cons1(quote(_0),quote1(_1)), quote1(nil) -> nil1, quote(s(_0)) -> s1(quote(_0)), quote(sel(_0,_1)) -> sel1(_0,_1), quote1(first(_0,_1)) -> first1(_0,_1), unquote(01) -> 0, unquote(s1(_0)) -> s(unquote(_0)), unquote1(nil1) -> nil, unquote1(cons1(_0,_1)) -> fcons(unquote(_0),unquote1(_1)), fcons(_0,_1) -> cons(_0,_1)}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem:
  Dependency pairs = [quote1^#(cons(_0,_1)) -> quote1^#(_1)]
  TRS = {sel(s(_0),cons(_1,_2)) -> sel(_0,_2), sel(0,cons(_0,_1)) -> _0, first(0,_0) -> nil, first(s(_0),cons(_1,_2)) -> cons(_1,first(_0,_2)), from(_0) -> cons(_0,from(s(_0))), sel1(s(_0),cons(_1,_2)) -> sel1(_0,_2), sel1(0,cons(_0,_1)) -> quote(_0), first1(0,_0) -> nil1, first1(s(_0),cons(_1,_2)) -> cons1(quote(_1),first1(_0,_2)), quote(0) -> 01, quote1(cons(_0,_1)) -> cons1(quote(_0),quote1(_1)), quote1(nil) -> nil1, quote(s(_0)) -> s1(quote(_0)), quote(sel(_0,_1)) -> sel1(_0,_1), quote1(first(_0,_1)) -> first1(_0,_1), unquote(01) -> 0, unquote(s1(_0)) -> s(unquote(_0)), unquote1(nil1) -> nil, unquote1(cons1(_0,_1)) -> fcons(unquote(_0),unquote1(_1)), fcons(_0,_1) -> cons(_0,_1)}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem:
  Dependency pairs = [first1^#(s(_0),cons(_1,_2)) -> first1^#(_0,_2)]
  TRS = {sel(s(_0),cons(_1,_2)) -> sel(_0,_2), sel(0,cons(_0,_1)) -> _0, first(0,_0) -> nil, first(s(_0),cons(_1,_2)) -> cons(_1,first(_0,_2)), from(_0) -> cons(_0,from(s(_0))), sel1(s(_0),cons(_1,_2)) -> sel1(_0,_2), sel1(0,cons(_0,_1)) -> quote(_0), first1(0,_0) -> nil1, first1(s(_0),cons(_1,_2)) -> cons1(quote(_1),first1(_0,_2)), quote(0) -> 01, quote1(cons(_0,_1)) -> cons1(quote(_0),quote1(_1)), quote1(nil) -> nil1, quote(s(_0)) -> s1(quote(_0)), quote(sel(_0,_1)) -> sel1(_0,_1), quote1(first(_0,_1)) -> first1(_0,_1), unquote(01) -> 0, unquote(s1(_0)) -> s(unquote(_0)), unquote1(nil1) -> nil, unquote1(cons1(_0,_1)) -> fcons(unquote(_0),unquote1(_1)), fcons(_0,_1) -> cons(_0,_1)}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem:
  Dependency pairs = [sel1^#(s(_0),cons(_1,_2)) -> sel1^#(_0,_2), quote^#(sel(_0,_1)) -> sel1^#(_0,_1), quote^#(s(_0)) -> quote^#(_0), sel1^#(0,cons(_0,_1)) -> quote^#(_0)]
  TRS = {sel(s(_0),cons(_1,_2)) -> sel(_0,_2), sel(0,cons(_0,_1)) -> _0, first(0,_0) -> nil, first(s(_0),cons(_1,_2)) -> cons(_1,first(_0,_2)), from(_0) -> cons(_0,from(s(_0))), sel1(s(_0),cons(_1,_2)) -> sel1(_0,_2), sel1(0,cons(_0,_1)) -> quote(_0), first1(0,_0) -> nil1, first1(s(_0),cons(_1,_2)) -> cons1(quote(_1),first1(_0,_2)), quote(0) -> 01, quote1(cons(_0,_1)) -> cons1(quote(_0),quote1(_1)), quote1(nil) -> nil1, quote(s(_0)) -> s1(quote(_0)), quote(sel(_0,_1)) -> sel1(_0,_1), quote1(first(_0,_1)) -> first1(_0,_1), unquote(01) -> 0, unquote(s1(_0)) -> s(unquote(_0)), unquote1(nil1) -> nil, unquote1(cons1(_0,_1)) -> fcons(unquote(_0),unquote1(_1)), fcons(_0,_1) -> cons(_0,_1)}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... This DP problem is too complex! Aborting!
    ## Trying with lexicographic path orders... Too many argument filtering possibilities (279936)! Aborting!
    ## Trying with Knuth-Bendix orders... This DP problem is too complex! Aborting!
  Don't know whether this DP problem is finite.
  ## DP problem:
  Dependency pairs = [from^#(_0) -> from^#(s(_0))]
  TRS = {sel(s(_0),cons(_1,_2)) -> sel(_0,_2), sel(0,cons(_0,_1)) -> _0, first(0,_0) -> nil, first(s(_0),cons(_1,_2)) -> cons(_1,first(_0,_2)), from(_0) -> cons(_0,from(s(_0))), sel1(s(_0),cons(_1,_2)) -> sel1(_0,_2), sel1(0,cons(_0,_1)) -> quote(_0), first1(0,_0) -> nil1, first1(s(_0),cons(_1,_2)) -> cons1(quote(_1),first1(_0,_2)), quote(0) -> 01, quote1(cons(_0,_1)) -> cons1(quote(_0),quote1(_1)), quote1(nil) -> nil1, quote(s(_0)) -> s1(quote(_0)), quote(sel(_0,_1)) -> sel1(_0,_1), quote1(first(_0,_1)) -> first1(_0,_1), unquote(01) -> 0, unquote(s1(_0)) -> s(unquote(_0)), unquote1(nil1) -> nil, unquote1(cons1(_0,_1)) -> fcons(unquote(_0),unquote1(_1)), fcons(_0,_1) -> cons(_0,_1)}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... This DP problem is too complex! Aborting!
    ## Trying with lexicographic path orders... Too many argument filtering possibilities (279936)! Aborting!
    ## Trying with Knuth-Bendix orders... This DP problem is too complex! Aborting!
  Don't know whether this DP problem is finite.
  ## DP problem:
  Dependency pairs = [first^#(s(_0),cons(_1,_2)) -> first^#(_0,_2)]
  TRS = {sel(s(_0),cons(_1,_2)) -> sel(_0,_2), sel(0,cons(_0,_1)) -> _0, first(0,_0) -> nil, first(s(_0),cons(_1,_2)) -> cons(_1,first(_0,_2)), from(_0) -> cons(_0,from(s(_0))), sel1(s(_0),cons(_1,_2)) -> sel1(_0,_2), sel1(0,cons(_0,_1)) -> quote(_0), first1(0,_0) -> nil1, first1(s(_0),cons(_1,_2)) -> cons1(quote(_1),first1(_0,_2)), quote(0) -> 01, quote1(cons(_0,_1)) -> cons1(quote(_0),quote1(_1)), quote1(nil) -> nil1, quote(s(_0)) -> s1(quote(_0)), quote(sel(_0,_1)) -> sel1(_0,_1), quote1(first(_0,_1)) -> first1(_0,_1), unquote(01) -> 0, unquote(s1(_0)) -> s(unquote(_0)), unquote1(nil1) -> nil, unquote1(cons1(_0,_1)) -> fcons(unquote(_0),unquote1(_1)), fcons(_0,_1) -> cons(_0,_1)}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem:
  Dependency pairs = [sel^#(s(_0),cons(_1,_2)) -> sel^#(_0,_2)]
  TRS = {sel(s(_0),cons(_1,_2)) -> sel(_0,_2), sel(0,cons(_0,_1)) -> _0, first(0,_0) -> nil, first(s(_0),cons(_1,_2)) -> cons(_1,first(_0,_2)), from(_0) -> cons(_0,from(s(_0))), sel1(s(_0),cons(_1,_2)) -> sel1(_0,_2), sel1(0,cons(_0,_1)) -> quote(_0), first1(0,_0) -> nil1, first1(s(_0),cons(_1,_2)) -> cons1(quote(_1),first1(_0,_2)), quote(0) -> 01, quote1(cons(_0,_1)) -> cons1(quote(_0),quote1(_1)), quote1(nil) -> nil1, quote(s(_0)) -> s1(quote(_0)), quote(sel(_0,_1)) -> sel1(_0,_1), quote1(first(_0,_1)) -> first1(_0,_1), unquote(01) -> 0, unquote(s1(_0)) -> s(unquote(_0)), unquote1(nil1) -> nil, unquote1(cons1(_0,_1)) -> fcons(unquote(_0),unquote1(_1)), fcons(_0,_1) -> cons(_0,_1)}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
## Some DP problems could not be proved finite.
## Now, we try to prove that one of these problems is infinite.
    ## Trying to find a loop (forward=true, backward=true, max=20)
      # max_depth=20, unfold_variables=false:
        # Iteration 0: success, found a loop, 1 unfolded rule generated.
        Here is the successful unfolding. Let IR be the TRS under analysis.
        L0 = from^#(_0) -> from^#(s(_0)) [trans] is in U_IR^0.
  This DP problem is infinite.
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 = 10