/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 = 0] zeros -> zeros
Let l be the left-hand side and r be the right-hand side of this rule.
Let p = epsilon, theta1 = {} and theta2 = {}.
We have r|p = zeros and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = zeros 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...
## 3 initial DP problems to solve.
## First, we try to decompose these problems into smaller problems.
## Round 1 [3 DP problems]:
  ## DP problem:
  Dependency pairs = [zeros^# -> zeros^#]
  TRS = {incr(nil) -> nil, incr(cons(_0,_1)) -> cons(s(_0),incr(_1)), adx(nil) -> nil, adx(cons(_0,_1)) -> incr(cons(_0,adx(_1))), nats -> adx(zeros), zeros -> cons(0,zeros), head(cons(_0,_1)) -> _0, tail(cons(_0,_1)) -> _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 = [adx^#(cons(_0,_1)) -> adx^#(_1)]
  TRS = {incr(nil) -> nil, incr(cons(_0,_1)) -> cons(s(_0),incr(_1)), adx(nil) -> nil, adx(cons(_0,_1)) -> incr(cons(_0,adx(_1))), nats -> adx(zeros), zeros -> cons(0,zeros), head(cons(_0,_1)) -> _0, tail(cons(_0,_1)) -> _1}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem:
  Dependency pairs = [incr^#(cons(_0,_1)) -> incr^#(_1)]
  TRS = {incr(nil) -> nil, incr(cons(_0,_1)) -> cons(s(_0),incr(_1)), adx(nil) -> nil, adx(cons(_0,_1)) -> incr(cons(_0,adx(_1))), nats -> adx(zeros), zeros -> cons(0,zeros), head(cons(_0,_1)) -> _0, tail(cons(_0,_1)) -> _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=3, 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 = zeros^# -> zeros^# [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