/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 pattern rule was generated by the strategy
presented in Sect. 3 of [Emmes, Enger, Giesl, IJCAR'12]:
[iteration = 0] nats{}^n{} -> nats{}^n{}
We apply Theorem 8 of [Emmes, Enger, Giesl, IJCAR'12]
on this rule with m = 1, b = 0, pi = epsilon,
sigma' = {} and mu' = {}.
Hence the term nats, obtained from
instantiating n with 0 in the left-hand side of
the rule, starts an infinite derivation 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...
## 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 = [pairs^# -> odds^#, odds^# -> pairs^#]
  TRS = {nats -> cons(0,n__incr(nats)), pairs -> cons(0,n__incr(odds)), odds -> incr(pairs), incr(cons(_0,_1)) -> cons(s(_0),n__incr(activate(_1))), head(cons(_0,_1)) -> _0, tail(cons(_0,_1)) -> activate(_1), incr(_0) -> n__incr(_0), activate(n__incr(_0)) -> incr(_0), activate(_0) -> _0}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... This DP problem is too complex! Aborting!
    ## Trying with lexicographic path orders... Failed!
    ## Trying with Knuth-Bendix orders... Failed!
  Don't know whether this DP problem is finite.
  ## DP problem:
  Dependency pairs = [incr^#(cons(_0,_1)) -> activate^#(_1), activate^#(n__incr(_0)) -> incr^#(_0)]
  TRS = {nats -> cons(0,n__incr(nats)), pairs -> cons(0,n__incr(odds)), odds -> incr(pairs), incr(cons(_0,_1)) -> cons(s(_0),n__incr(activate(_1))), head(cons(_0,_1)) -> _0, tail(cons(_0,_1)) -> activate(_1), incr(_0) -> n__incr(_0), activate(n__incr(_0)) -> incr(_0), activate(_0) -> _0}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... This DP problem is too complex! Aborting!
    ## Trying with lexicographic path orders... Failed!
    ## Trying with Knuth-Bendix orders... Failed!
  Don't know whether this DP problem is finite.
  ## DP problem:
  Dependency pairs = [nats^# -> nats^#]
  TRS = {nats -> cons(0,n__incr(nats)), pairs -> cons(0,n__incr(odds)), odds -> incr(pairs), incr(cons(_0,_1)) -> cons(s(_0),n__incr(activate(_1))), head(cons(_0,_1)) -> _0, tail(cons(_0,_1)) -> activate(_1), incr(_0) -> n__incr(_0), activate(n__incr(_0)) -> incr(_0), activate(_0) -> _0}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... This DP problem is too complex! Aborting!
    ## Trying with lexicographic path orders... Failed!
    ## Trying with Knuth-Bendix orders... Failed!
  Don't know whether 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 prove non-looping nontermination
      # Iteration 0: success, non-looping nontermination proved, 1 unfolded rule generated.
      Here is the successful unfolding. Let IR be the TRS under analysis.
      IR contains the dependency pair nats^# -> nats^#.
      We apply (I) of [Emmes, Enger, Giesl, IJCAR'12] to this dependency pair.
      ==> P0 = nats^#{}^n{} -> nats^#{}^n{} 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 = 13