/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 rule was generated while unfolding the analyzed TRS:
[iteration = 1] h(_0,g(_0,s(_0))) -> h(0,g(_0,s(_0)))
Let l be the left-hand side and r be the right-hand side of this rule.
Let p = epsilon, theta1 = {_0->0} and theta2 = {}.
We have r|p = h(0,g(_0,s(_0))) and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = h(0,g(0,s(0))) loops 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^#(_0,_1) -> f^#(_0,s(_0),_1), f^#(_0,_1,g(_0,_1)) -> h^#(0,g(_0,_1))]
  TRS = {h(_0,_1) -> f(_0,s(_0),_1), f(_0,_1,g(_0,_1)) -> h(0,g(_0,_1)), g(0,_0) -> 0, g(_0,s(_1)) -> g(_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 = [g^#(_0,s(_1)) -> g^#(_0,_1)]
  TRS = {h(_0,_1) -> f(_0,s(_0),_1), f(_0,_1,g(_0,_1)) -> h(0,g(_0,_1)), g(0,_0) -> 0, g(_0,s(_1)) -> g(_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 find a loop (forward=true, backward=false, max=-1)
      # max_depth=2, unfold_variables=false:
        # Iteration 0: no loop found, 2 unfolded rules generated.
        # Iteration 1: success, found a loop, 2 unfolded rules generated.
        Here is the successful unfolding. Let IR be the TRS under analysis.
        L0 = h^#(_0,_1) -> f^#(_0,s(_0),_1) [trans] is in U_IR^0.
        D = f^#(_0,_1,g(_0,_1)) -> h^#(0,g(_0,_1)) is a dependency pair of IR.
        We build a composed triple from L0 and D.
        ==> L1 = h^#(_0,g(_0,s(_0))) -> h^#(0,g(_0,s(_0))) [trans] 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 = 11