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


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NO

** BEGIN proof argument **
The following rule was generated while unfolding the analyzed TRS:
[iteration = 0] diff(_0,_1) -> diff(p(_0),_1)
Let l be the left-hand side and r be the right-hand side of this rule.
Let p = epsilon, theta1 = {} and theta2 = {_0->p(_0)}.
We have r|p = diff(p(_0),_1) and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = diff(_0,_1) 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 = [diff^#(_0,_1) -> diff^#(p(_0),_1)]
  TRS = {p(0) -> 0, p(s(_0)) -> _0, leq(0,_0) -> true, leq(s(_0),0) -> false, leq(s(_0),s(_1)) -> leq(_0,_1), if(true,_0,_1) -> activate(_0), if(false,_0,_1) -> activate(_1), diff(_0,_1) -> if(leq(_0,_1),n__0,n__s(diff(p(_0),_1))), 0 -> n__0, s(_0) -> n__s(_0), activate(n__0) -> 0, activate(n__s(_0)) -> s(_0), activate(_0) -> _0}
    ## 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 = [leq^#(s(_0),s(_1)) -> leq^#(_0,_1)]
  TRS = {p(0) -> 0, p(s(_0)) -> _0, leq(0,_0) -> true, leq(s(_0),0) -> false, leq(s(_0),s(_1)) -> leq(_0,_1), if(true,_0,_1) -> activate(_0), if(false,_0,_1) -> activate(_1), diff(_0,_1) -> if(leq(_0,_1),n__0,n__s(diff(p(_0),_1))), 0 -> n__0, s(_0) -> n__s(_0), activate(n__0) -> 0, activate(n__s(_0)) -> s(_0), activate(_0) -> _0}
    ## 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=true, max=20)
      # max_depth=20, unfold_variables=false:
        # Iteration 0: success, found a loop, 1 unfolded rule generated.
        Here is the successful unfolding. Let IR be the TRS under analysis.
        L0 = diff^#(_0,_1) -> diff^#(p(_0),_1) [trans] is in U_IR^0.
  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 = 2