/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 = 1] f(tt,nil){}^n{} -> f(tt,nil){}^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 f(tt,nil), 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...
## 1 initial DP problem to solve.
## First, we try to decompose this problem into smaller problems.
## Round 1 [1 DP problem]:
  ## DP problem:
  Dependency pairs = [f^#(tt,_0) -> f^#(isList(_0),_0)]
  TRS = {f(tt,_0) -> f(isList(_0),_0), isList(Cons(_0,xs)) -> isList(xs), isList(nil) -> tt}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders... Failed!
    ## Trying with Knuth-Bendix orders... Failed!
  Don't know whether 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: success, non-looping nontermination proved, 2 unfolded rules generated.
      Here is the successful unfolding. Let IR be the TRS under analysis.
      IR contains the dependency pair f^#(tt,_0) -> f^#(isList(_0),_0).
      We apply (I) of [Emmes, Enger, Giesl, IJCAR'12] to this dependency pair.
      ==> P0 = f^#(tt,_0){}^n{} -> f^#(isList(_0),_0){}^n{} is in U_IR^0.
      We apply (V) + (IX) of [Emmes, Enger, Giesl, IJCAR'12] to this pattern rule
      at position [0] using the rule
      isList(nil) -> tt
      of IR.
      ==> P1 = f^#(tt,nil){}^n{} -> f^#(tt,nil){}^n{} is in U_IR^1.
  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 = 9