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


--------------------------------------------------------------------------------


NO

** BEGIN proof argument **
The following rule was generated while unfolding the analyzed TRS:
[iteration = 0] app(app(_0,0),_1) -> app(app(cons,0),nil)
Let l be the left-hand side and r be the right-hand side of this rule.
Let p = epsilon, theta1 = {} and theta2 = {_0->cons, _1->nil}.
We have r|p = app(app(cons,0),nil) and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = app(app(_0,0),_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...
## 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(_0,0),_1) -> app^#(app(hd,app(app(map,_0),app(app(cons,0),nil))),_1), app^#(app(_0,0),_1) -> app^#(app(map,_0),app(app(cons,0),nil)), app^#(app(_0,0),_1) -> app^#(app(cons,0),nil), app^#(app(map,_0),app(app(cons,_1),_2)) -> app^#(app(cons,app(_0,_1)),app(app(map,_0),_2)), app^#(app(map,_0),app(app(cons,_1),_2)) -> app^#(_0,_1), app^#(app(map,_0),app(app(cons,_1),_2)) -> app^#(app(map,_0),_2)]
  TRS = {app(app(_0,0),_1) -> app(app(hd,app(app(map,_0),app(app(cons,0),nil))),_1), app(app(map,_0),nil) -> nil, app(app(map,_0),app(app(cons,_1),_2)) -> app(app(cons,app(_0,_1)),app(app(map,_0),_2))}
    ## 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=false, max=-1)
      # max_depth=5, unfold_variables=false:
        # Iteration 0: success, found a loop, 3 unfolded rules generated.
        Here is the successful unfolding. Let IR be the TRS under analysis.
        L0 = app^#(app(_0,0),_1) -> app^#(app(cons,0),nil) [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 = 6