/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 = 7] length(cons(_0,n__zeros)) -> length(cons(0,n__zeros))
Let l be the left-hand side and r be the right-hand side of this rule.
Let p = epsilon, theta1 = {} and theta2 = {_0->0}.
We have r|p = length(cons(0,n__zeros)) and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = length(cons(_0,n__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...
## 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 = [U11^#(tt,_0) -> U12^#(tt,activate(_0)), length^#(cons(_0,_1)) -> U11^#(tt,activate(_1)), U12^#(tt,_0) -> length^#(activate(_0))]
  TRS = {zeros -> cons(0,n__zeros), U11(tt,_0) -> U12(tt,activate(_0)), U12(tt,_0) -> s(length(activate(_0))), length(nil) -> 0, length(cons(_0,_1)) -> U11(tt,activate(_1)), zeros -> n__zeros, activate(n__zeros) -> zeros, 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, 3 unfolded rules generated.
        # Iteration 1: no loop found, 5 unfolded rules generated.
        # Iteration 2: no loop found, 16 unfolded rules generated.
        # Iteration 3: no loop found, 30 unfolded rules generated.
        # Iteration 4: no loop found, 36 unfolded rules generated.
        # Iteration 5: no loop found, 5 unfolded rules generated.
        # Iteration 6: no loop found, 9 unfolded rules generated.
        # Iteration 7: success, found a loop, 1 unfolded rule generated.
        Here is the successful unfolding. Let IR be the TRS under analysis.
        L0 = length^#(cons(_0,_1)) -> U11^#(tt,activate(_1)) [trans] is in U_IR^0.
        D = U11^#(tt,_0) -> U12^#(tt,activate(_0)) is a dependency pair of IR.
        We build a composed triple from L0 and D.
        ==> L1 = [length^#(cons(_0,_1)) -> U11^#(tt,activate(_1)), U11^#(tt,_2) -> U12^#(tt,activate(_2))] [comp] is in U_IR^1.
        Let p1 = [1].
        We unfold the first rule of L1 forwards at position p1
        with the rule activate(n__zeros) -> zeros.
        ==> L2 = length^#(cons(_0,n__zeros)) -> U12^#(tt,activate(zeros)) [trans] is in U_IR^2.
        D = U12^#(tt,_0) -> length^#(activate(_0)) is a dependency pair of IR.
        We build a composed triple from L2 and D.
        ==> L3 = length^#(cons(_0,n__zeros)) -> length^#(activate(activate(zeros))) [trans] is in U_IR^3.
        We build a unit triple from L3.
        ==> L4 = length^#(cons(_0,n__zeros)) -> length^#(activate(activate(zeros))) [unit] is in U_IR^4.
        Let p4 = [0].
        We unfold the rule of L4 forwards at position p4
        with the rule activate(_0) -> _0.
        ==> L5 = length^#(cons(_0,n__zeros)) -> length^#(activate(zeros)) [unit] is in U_IR^5.
        Let p5 = [0].
        We unfold the rule of L5 forwards at position p5
        with the rule activate(_0) -> _0.
        ==> L6 = length^#(cons(_0,n__zeros)) -> length^#(zeros) [unit] is in U_IR^6.
        Let p6 = [0].
        We unfold the rule of L6 forwards at position p6
        with the rule zeros -> cons(0,n__zeros).
        ==> L7 = length^#(cons(_0,n__zeros)) -> length^#(cons(0,n__zeros)) [unit] is in U_IR^7.
  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 = 532