/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] f(0){}^n{} -> f(0){}^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(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...
## 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^#(0) -> f^#(s(0)), f^#(s(0)) -> f^#(p(s(0)))]
  TRS = {f(0) -> cons(0,f(s(0))), f(s(0)) -> f(p(s(0))), p(s(0)) -> 0}
    ## 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, 2 unfolded rules generated.
      # Iteration 1: non-looping nontermination not proved, 3 unfolded rules generated.
      # Iteration 2: 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 f^#(0) -> f^#(s(0)).
      We apply (I) of [Emmes, Enger, Giesl, IJCAR'12] to this dependency pair.
      ==> P0 = f^#(0){}^n{} -> f^#(s(0)){}^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(s(0)){}^n{} -> f(p(s(0))){}^n{}
      obtained from IR.
      ==> P1 = f^#(0){}^n{} -> f(p(s(0))){}^n{} is in U_IR^1.
      We apply (IX) of [Emmes, Enger, Giesl, IJCAR'12] to this pattern rule
      at position [0] using the rule
      p(s(0)) -> 0
      of IR.
      ==> P2 = f^#(0){}^n{} -> f(0){}^n{} 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 = 10