/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 = 2] h(true,s(_0),s(_1)){_1->s(_1), _0->s(_0)}^n{_1->0, _0->s(_2)} -> h(true,s(s(_0)),s(s(_1))){_1->s(_1), _0->s(_0)}^n{_1->0, _0->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 h(true,s(s(_2)),s(0)), 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 = [h^#(true,_0,_1) -> h^#(gt(_0,_1),s(_0),s(_1))]
  TRS = {h(true,_0,_1) -> h(gt(_0,_1),s(_0),s(_1)), gt(0,_0) -> false, gt(s(_0),0) -> true, gt(s(_0),s(_1)) -> gt(_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 = [gt^#(s(_0),s(_1)) -> gt^#(_0,_1)]
  TRS = {h(true,_0,_1) -> h(gt(_0,_1),s(_0),s(_1)), gt(0,_0) -> false, gt(s(_0),0) -> true, gt(s(_0),s(_1)) -> gt(_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, 1 unfolded rule generated.
      # Iteration 1: non-looping nontermination not proved, 7 unfolded rules generated.
      # Iteration 2: success, non-looping nontermination proved, 18 unfolded rules generated.
      Here is the successful unfolding. Let IR be the TRS under analysis.
      IR contains the dependency pair h^#(true,_0,_1) -> h^#(gt(_0,_1),s(_0),s(_1)).
      We apply (I) of [Emmes, Enger, Giesl, IJCAR'12] to this dependency pair.
      ==> P0 = h^#(true,_0,_1){}^n{} -> h^#(gt(_0,_1),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 [0] using the pattern rule
      gt(s(_0),s(_1)){_0->s(_0), _1->s(_1)}^n{_0->_2, _1->_3} -> gt(_2,_3){_0->s(_0), _1->s(_1)}^n{_0->_2, _1->_3}
      obtained from IR.
      ==> P1 = h^#(true,s(_0),s(_1)){_1->s(_1), _0->s(_0)}^n{_1->_2, _0->_3} -> h^#(gt(_3,_2),s(s(_0)),s(s(_1))){_1->s(_1), _0->s(_0)}^n{_1->_2, _0->_3} is in U_IR^1.
      We apply (V) + (IX) of [Emmes, Enger, Giesl, IJCAR'12] to this pattern rule
      at position [0] using the rule
      gt(s(_0),0) -> true
      of IR.
      ==> P2 = h^#(true,s(_0),s(_1)){_1->s(_1), _0->s(_0)}^n{_1->0, _0->s(_2)} -> h^#(true,s(s(_0)),s(s(_1))){_1->s(_1), _0->s(_0)}^n{_1->0, _0->s(_2)} is in U_IR^2.
  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 = 79