/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


NO

** BEGIN proof argument **
The following pattern rule was generated by the strategy
presented in Sect. 3 of [Emmes, Enger, Giesl, IJCAR'12]:
[iteration = 4] cond(tt,_0,_1){_0->s(_0), _1->s(_1)}^n{_0->s(0), _1->s(_2)} -> cond(tt,s(_0),s(_1)){_0->s(_0), _1->s(_1)}^n{_0->s(0), _1->s(_2)}
We apply Theorem 8 of [Emmes, Enger, Giesl, IJCAR'12]
on this rule with m = 1, b = 1, pi = epsilon,
sigma' = {} and mu' = {}.
Hence the term cond(tt,s(0),s(_2)), 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...
## 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 = [f^#(_0,_1) -> cond^#(lt(_0,_1),_0,_1), cond^#(tt,_0,_1) -> f^#(s(_0),s(_1))]
  TRS = {f(_0,_1) -> cond(lt(_0,_1),_0,_1), cond(tt,_0,_1) -> f(s(_0),s(_1)), lt(0,_0) -> tt, lt(s(_0),s(_1)) -> lt(_0,_1)}
    ## 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 = [lt^#(s(_0),s(_1)) -> lt^#(_0,_1)]
  TRS = {f(_0,_1) -> cond(lt(_0,_1),_0,_1), cond(tt,_0,_1) -> f(s(_0),s(_1)), lt(0,_0) -> tt, lt(s(_0),s(_1)) -> lt(_0,_1)}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
## A DP problem could not be proved finite.
## Now, we try to prove that this problem is infinite.
    ## Trying to prove non-looping nontermination
      # Iteration 0: non-looping nontermination not proved, 2 unfolded rules generated.
      # Iteration 1: non-looping nontermination not proved, 6 unfolded rules generated.
      # Iteration 2: non-looping nontermination not proved, 17 unfolded rules generated.
      # Iteration 3: non-looping nontermination not proved, 46 unfolded rules generated.
      # Iteration 4: success, non-looping nontermination proved, 112 unfolded rules generated.
      Here is the successful unfolding. Let IR be the TRS under analysis.
      IR contains the dependency pair cond^#(tt,_0,_1) -> f^#(s(_0),s(_1)).
      We apply (I) of [Emmes, Enger, Giesl, IJCAR'12] to this dependency pair.
      ==> P0 = cond^#(tt,_0,_1){}^n{} -> f^#(s(_0),s(_1)){}^n{} is in U_IR^0.
      We apply (VI) of [Emmes, Enger, Giesl, IJCAR'12] to this pattern rule
      at position epsilon using the pattern rule
      f(_0,_1){}^n{} -> cond(lt(_0,_1),_0,_1){}^n{}
      obtained from IR.
      ==> P1 = cond^#(tt,_0,_1){}^n{} -> cond(lt(s(_0),s(_1)),s(_0),s(_1)){}^n{} is in U_IR^1.
      We apply (VI) of [Emmes, Enger, Giesl, IJCAR'12] to this pattern rule
      at position [0] using the pattern rule
      lt(s(_0),s(_1)){_0->s(_0), _1->s(_1)}^n{_0->_2, _1->_3} -> lt(_2,_3){_0->s(_0), _1->s(_1)}^n{_0->_2, _1->_3}
      obtained from IR.
      ==> P2 = cond^#(tt,_0,_1){_0->s(_0), _1->s(_1)}^n{_0->_2, _1->_3} -> cond(lt(_2,_3),s(_0),s(_1)){_0->s(_0), _1->s(_1)}^n{_0->_2, _1->_3} is in U_IR^2.
      We apply (V) + (IX) of [Emmes, Enger, Giesl, IJCAR'12] to this pattern rule
      at position [0] using the rule
      lt(s(_0),s(_1)) -> lt(_0,_1)
      of IR.
      ==> P3 = cond^#(tt,_0,_1){_0->s(_0), _1->s(_1)}^n{_0->s(_2), _1->s(_3)} -> cond(lt(_2,_3),s(_0),s(_1)){_0->s(_0), _1->s(_1)}^n{_0->s(_2), _1->s(_3)} is in U_IR^3.
      We apply (V) + (IX) of [Emmes, Enger, Giesl, IJCAR'12] to this pattern rule
      at position [0] using the rule
      lt(0,_0) -> tt
      of IR.
      ==> P4 = cond^#(tt,_0,_1){_0->s(_0), _1->s(_1)}^n{_0->s(0), _1->s(_2)} -> cond(tt,s(_0),s(_1)){_0->s(_0), _1->s(_1)}^n{_0->s(0), _1->s(_2)} is in U_IR^4.
  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 = 485