NO

Prover = TRS(tech=GUIDED_UNF_TRIPLES, nb_unfoldings=unlimited, unfold_variables=false, max_nb_coefficients=12, max_nb_unfolded_rules=-1, strategy=LEFTMOST_NE)

** 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...
## Round 1:
  ## 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... Too many coefficients (37)! Aborting!
    ## Trying with lexicographic path orders... Too many argument filtering possibilities (31104)! Aborting!
    ## Trying to prove nontermination by unfolding the dependency pairs with the rules of the TRS
      # max_depth=3, unfold_variables=false:
        # Iteration 0: nontermination not detected, 13 unfolded rules generated.
        # Iteration 1: nontermination not detected, 172 unfolded rules generated.
        # Iteration 2: nontermination not detected, 537 unfolded rules generated.
        # Iteration 3: nontermination not detected, 168 unfolded rules generated.
        # Iteration 4: nontermination not detected, 517 unfolded rules generated.
        # Iteration 5: nontermination detected, 833 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.

** END proof description **

Proof stopped at iteration 5
Number of unfolded rules generated by this proof = 2240
Number of unfolded rules generated by all the parallel proofs = 9864