/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 = 1] app(app(app(subst,_0),app(fix,_1)),_2) -> app(app(_1,app(fix,_1)),_2)
Let l be the left-hand side and r be the right-hand side of this rule.
Let p = epsilon, theta1 = {_1->app(subst,_3)} and theta2 = {_0->_3}.
We have r|p = app(app(_1,app(fix,_1)),_2) and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = app(app(app(subst,_0),app(fix,app(subst,_3))),_2) 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...
## 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 = [app^#(app(app(subst,_0),_1),_2) -> app^#(app(_0,_2),app(_1,_2)), app^#(app(app(subst,_0),_1),_2) -> app^#(_0,_2), app^#(app(app(subst,_0),_1),_2) -> app^#(_1,_2), app^#(app(fix,_0),_1) -> app^#(app(_0,app(fix,_0)),_1), app^#(app(fix,_0),_1) -> app^#(_0,app(fix,_0))]
  TRS = {app(app(const,_0),_1) -> _0, app(app(app(subst,_0),_1),_2) -> app(app(_0,_2),app(_1,_2)), app(app(fix,_0),_1) -> app(app(_0,app(fix,_0)),_1)}
    ## 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 find a loop (forward=true, backward=true, max=20)
      # max_depth=20, unfold_variables=false:
        # Iteration 0: no loop found, 5 unfolded rules generated.
        # Iteration 1: success, found a loop, 19 unfolded rules generated.
        Here is the successful unfolding. Let IR be the TRS under analysis.
        L0 = app^#(app(app(subst,_0),_1),_2) -> app^#(_1,_2) [trans] is in U_IR^0.
        D = app^#(app(fix,_0),_1) -> app^#(app(_0,app(fix,_0)),_1) is a dependency pair of IR.
        We build a composed triple from L0 and D.
        ==> L1 = app^#(app(app(subst,_0),app(fix,_1)),_2) -> app^#(app(_1,app(fix,_1)),_2) [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 = 41