/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 = 5] activate(n__zWadr(cons(_0,_1),n__prefix(_2))) -> activate(n__zWadr(_2,n__prefix(_2)))
Let l be the left-hand side and r be the right-hand side of this rule.
Let p = epsilon, theta1 = {_2->cons(_3,_4)} and theta2 = {_1->_4, _0->_3}.
We have r|p = activate(n__zWadr(_2,n__prefix(_2))) and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = activate(n__zWadr(cons(_0,_1),n__prefix(cons(_3,_4)))) 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^#(cons(_0,_1),_2) -> activate^#(_1), activate^#(n__app(_0,_1)) -> app^#(activate(_0),activate(_1)), zWadr^#(cons(_0,_1),cons(_2,_3)) -> app^#(_2,cons(_0,n__nil)), activate^#(n__zWadr(_0,_1)) -> zWadr^#(activate(_0),activate(_1)), activate^#(n__app(_0,_1)) -> activate^#(_0), activate^#(n__app(_0,_1)) -> activate^#(_1), activate^#(n__from(_0)) -> activate^#(_0), activate^#(n__s(_0)) -> activate^#(_0), activate^#(n__zWadr(_0,_1)) -> activate^#(_0), activate^#(n__zWadr(_0,_1)) -> activate^#(_1), activate^#(n__prefix(_0)) -> activate^#(_0), zWadr^#(cons(_0,_1),cons(_2,_3)) -> activate^#(_3), zWadr^#(cons(_0,_1),cons(_2,_3)) -> activate^#(_1)]
  TRS = {app(nil,_0) -> _0, app(cons(_0,_1),_2) -> cons(_0,n__app(activate(_1),_2)), from(_0) -> cons(_0,n__from(n__s(_0))), zWadr(nil,_0) -> nil, zWadr(_0,nil) -> nil, zWadr(cons(_0,_1),cons(_2,_3)) -> cons(app(_2,cons(_0,n__nil)),n__zWadr(activate(_1),activate(_3))), prefix(_0) -> cons(nil,n__zWadr(_0,n__prefix(_0))), app(_0,_1) -> n__app(_0,_1), from(_0) -> n__from(_0), s(_0) -> n__s(_0), nil -> n__nil, zWadr(_0,_1) -> n__zWadr(_0,_1), prefix(_0) -> n__prefix(_0), activate(n__app(_0,_1)) -> app(activate(_0),activate(_1)), activate(n__from(_0)) -> from(activate(_0)), activate(n__s(_0)) -> s(activate(_0)), activate(n__nil) -> nil, activate(n__zWadr(_0,_1)) -> zWadr(activate(_0),activate(_1)), activate(n__prefix(_0)) -> prefix(activate(_0)), activate(_0) -> _0}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... This DP problem is too complex! Aborting!
    ## Trying with lexicographic path orders... Too many argument filtering possibilities (31104)! Aborting!
    ## 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, 13 unfolded rules generated.
        # Iteration 1: no loop found, 172 unfolded rules generated.
        # Iteration 2: no loop found, 545 unfolded rules generated.
        # Iteration 3: no loop found, 284 unfolded rules generated.
        # Iteration 4: no loop found, 791 unfolded rules generated.
        # Iteration 5: success, found a loop, 1140 unfolded rules generated.
        Here is the successful unfolding. Let IR be the TRS under analysis.
        L0 = activate^#(n__zWadr(_0,_1)) -> zWadr^#(activate(_0),activate(_1)) [trans] is in U_IR^0.
        D = zWadr^#(cons(_0,_1),cons(_2,_3)) -> activate^#(_3) is a dependency pair of IR.
        We build a composed triple from L0 and D.
        ==> L1 = [activate^#(n__zWadr(_0,_1)) -> zWadr^#(activate(_0),activate(_1)), zWadr^#(cons(_2,_3),cons(_4,_5)) -> activate^#(_5)] [comp] is in U_IR^1.
        Let p1 = [0].
        We unfold the first rule of L1 forwards at position p1
        with the rule activate(_0) -> _0.
        ==> L2 = [activate^#(n__zWadr(_0,_1)) -> zWadr^#(_0,activate(_1)), zWadr^#(cons(_2,_3),cons(_4,_5)) -> activate^#(_5)] [comp] is in U_IR^2.
        Let p2 = [1].
        We unfold the first rule of L2 forwards at position p2
        with the rule activate(n__prefix(_0)) -> prefix(activate(_0)).
        ==> L3 = [activate^#(n__zWadr(_0,n__prefix(_1))) -> zWadr^#(_0,prefix(activate(_1))), zWadr^#(cons(_2,_3),cons(_4,_5)) -> activate^#(_5)] [comp] is in U_IR^3.
        Let p3 = [1, 0].
        We unfold the first rule of L3 forwards at position p3
        with the rule activate(_0) -> _0.
        ==> L4 = [activate^#(n__zWadr(_0,n__prefix(_1))) -> zWadr^#(_0,prefix(_1)), zWadr^#(cons(_2,_3),cons(_4,_5)) -> activate^#(_5)] [comp] is in U_IR^4.
        Let p4 = [1].
        We unfold the first rule of L4 forwards at position p4
        with the rule prefix(_0) -> cons(nil,n__zWadr(_0,n__prefix(_0))).
        ==> L5 = activate^#(n__zWadr(cons(_0,_1),n__prefix(_2))) -> activate^#(n__zWadr(_2,n__prefix(_2))) [trans] is in U_IR^5.
  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 = 10794