/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 = 3] activate(n__incr(n__nats)) -> activate(n__incr(n__nats))
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 = activate(n__incr(n__nats)) and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = activate(n__incr(n__nats)) 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 = [odds^# -> incr^#(pairs), activate^#(n__odds) -> odds^#, incr^#(cons(_0,_1)) -> activate^#(_1), activate^#(n__incr(_0)) -> incr^#(activate(_0)), activate^#(n__incr(_0)) -> activate^#(_0)]
  TRS = {nats -> cons(0,n__incr(n__nats)), pairs -> cons(0,n__incr(n__odds)), odds -> incr(pairs), incr(cons(_0,_1)) -> cons(s(_0),n__incr(activate(_1))), head(cons(_0,_1)) -> _0, tail(cons(_0,_1)) -> activate(_1), incr(_0) -> n__incr(_0), nats -> n__nats, odds -> n__odds, activate(n__incr(_0)) -> incr(activate(_0)), activate(n__nats) -> nats, activate(n__odds) -> odds, 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.
## 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: no loop found, 5 unfolded rules generated.
        # Iteration 1: no loop found, 14 unfolded rules generated.
        # Iteration 2: no loop found, 19 unfolded rules generated.
        # Iteration 3: success, found a loop, 20 unfolded rules generated.
        Here is the successful unfolding. Let IR be the TRS under analysis.
        L0 = activate^#(n__incr(_0)) -> incr^#(activate(_0)) [trans] is in U_IR^0.
        D = incr^#(cons(_0,_1)) -> activate^#(_1) is a dependency pair of IR.
        We build a composed triple from L0 and D.
        ==> L1 = [activate^#(n__incr(_0)) -> incr^#(activate(_0)), incr^#(cons(_1,_2)) -> activate^#(_2)] [comp] is in U_IR^1.
        Let p1 = [0].
        We unfold the first rule of L1 forwards at position p1
        with the rule activate(n__nats) -> nats.
        ==> L2 = [activate^#(n__incr(n__nats)) -> incr^#(nats), incr^#(cons(_0,_1)) -> activate^#(_1)] [comp] is in U_IR^2.
        Let p2 = [0].
        We unfold the first rule of L2 forwards at position p2
        with the rule nats -> cons(0,n__incr(n__nats)).
        ==> L3 = activate^#(n__incr(n__nats)) -> activate^#(n__incr(n__nats)) [trans] is in U_IR^3.
  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 = 154