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 = 8] isNatList(n__cons(n__0,n__zeros)) -> isNatList(n__cons(n__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 = {}.
We have r|p = isNatList(n__cons(n__0,n__zeros)) and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = isNatList(n__cons(n__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...
## Round 1:
  ## DP problem: 
  Dependency pairs = [U11^#(tt,_0) -> length^#(activate(_0)), length^#(cons(_0,_1)) -> U11^#(and(isNatList(activate(_1)),n__isNat(_0)),activate(_1)), activate^#(n__length(_0)) -> length^#(_0), and^#(tt,_0) -> activate^#(_0), length^#(cons(_0,_1)) -> and^#(isNatList(activate(_1)),n__isNat(_0)), isNatList^#(n__cons(_0,_1)) -> and^#(isNat(activate(_0)),n__isNatList(activate(_1))), isNatIList^#(n__cons(_0,_1)) -> and^#(isNat(activate(_0)),n__isNatIList(activate(_1))), activate^#(n__isNatIList(_0)) -> isNatIList^#(_0), isNat^#(n__length(_0)) -> activate^#(_0), isNat^#(n__s(_0)) -> isNat^#(activate(_0)), isNatList^#(n__cons(_0,_1)) -> isNat^#(activate(_0)), isNat^#(n__length(_0)) -> isNatList^#(activate(_0)), activate^#(n__isNat(_0)) -> isNat^#(_0), isNatList^#(n__cons(_0,_1)) -> activate^#(_0), activate^#(n__isNatList(_0)) -> isNatList^#(_0), length^#(cons(_0,_1)) -> activate^#(_1), length^#(cons(_0,_1)) -> activate^#(_1), isNatList^#(n__cons(_0,_1)) -> activate^#(_1), length^#(cons(_0,_1)) -> isNatList^#(activate(_1)), isNatIList^#(_0) -> isNatList^#(activate(_0)), isNatIList^#(n__cons(_0,_1)) -> activate^#(_1), isNatIList^#(n__cons(_0,_1)) -> activate^#(_0), isNatIList^#(_0) -> activate^#(_0), isNat^#(n__s(_0)) -> activate^#(_0), isNatIList^#(n__cons(_0,_1)) -> isNat^#(activate(_0)), U11^#(tt,_0) -> activate^#(_0)]
  TRS = {zeros -> cons(0,n__zeros), U11(tt,_0) -> s(length(activate(_0))), and(tt,_0) -> activate(_0), isNat(n__0) -> tt, isNat(n__length(_0)) -> isNatList(activate(_0)), isNat(n__s(_0)) -> isNat(activate(_0)), isNatIList(_0) -> isNatList(activate(_0)), isNatIList(n__zeros) -> tt, isNatIList(n__cons(_0,_1)) -> and(isNat(activate(_0)),n__isNatIList(activate(_1))), isNatList(n__nil) -> tt, isNatList(n__cons(_0,_1)) -> and(isNat(activate(_0)),n__isNatList(activate(_1))), length(nil) -> 0, length(cons(_0,_1)) -> U11(and(isNatList(activate(_1)),n__isNat(_0)),activate(_1)), zeros -> n__zeros, 0 -> n__0, length(_0) -> n__length(_0), s(_0) -> n__s(_0), cons(_0,_1) -> n__cons(_0,_1), isNatIList(_0) -> n__isNatIList(_0), nil -> n__nil, isNatList(_0) -> n__isNatList(_0), isNat(_0) -> n__isNat(_0), activate(n__zeros) -> zeros, activate(n__0) -> 0, activate(n__length(_0)) -> length(_0), activate(n__s(_0)) -> s(_0), activate(n__cons(_0,_1)) -> cons(_0,_1), activate(n__isNatIList(_0)) -> isNatIList(_0), activate(n__nil) -> nil, activate(n__isNatList(_0)) -> isNatList(_0), activate(n__isNat(_0)) -> isNat(_0), activate(_0) -> _0}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Too many coefficients (46)! Aborting!
    ## Trying with lexicographic path orders... Too many argument filtering possibilities (165888)! Aborting!
    ## Trying to prove nontermination by unfolding the dependency pairs with the rules of the TRS
      # max_depth=4, unfold_variables=false:
        # Iteration 0: nontermination not detected, 26 unfolded rules generated.
        # Iteration 1: nontermination not detected, 160 unfolded rules generated.
        # Iteration 2: nontermination not detected, 767 unfolded rules generated.
        # Iteration 3: nontermination not detected, 1600 unfolded rules generated.
        # Iteration 4: nontermination not detected, 5118 unfolded rules generated.
        # Iteration 5: nontermination not detected, 13497 unfolded rules generated.
        # Iteration 6: nontermination not detected, 43566 unfolded rules generated.
        # Iteration 7: nontermination not detected, 108019 unfolded rules generated.
        # Iteration 8: nontermination detected, 95061 unfolded rules generated.
        Here is the successful unfolding. Let IR be the TRS under analysis.
        L0 = isNatList^#(n__cons(_0,_1)) -> and^#(isNat(activate(_0)),n__isNatList(activate(_1))) [trans] is in U_IR^0.
        D = and^#(tt,_0) -> activate^#(_0) is a dependency pair of IR.
        We build a composed triple from L0 and D.
        ==> L1 = [isNatList^#(n__cons(_0,_1)) -> and^#(isNat(activate(_0)),n__isNatList(activate(_1))), and^#(tt,_2) -> activate^#(_2)] [comp] is in U_IR^1.
        Let p1 = [0, 0].
        We unfold the first rule of L1 forwards at position p1
        with the rule activate(_0) -> _0.
        ==> L2 = [isNatList^#(n__cons(_0,_1)) -> and^#(isNat(_0),n__isNatList(activate(_1))), and^#(tt,_2) -> activate^#(_2)] [comp] is in U_IR^2.
        Let p2 = [0].
        We unfold the first rule of L2 forwards at position p2
        with the rule isNat(n__0) -> tt.
        ==> L3 = [isNatList^#(n__cons(n__0,_0)) -> and^#(tt,n__isNatList(activate(_0))), and^#(tt,_1) -> activate^#(_1)] [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(n__zeros) -> zeros.
        ==> L4 = [isNatList^#(n__cons(n__0,n__zeros)) -> and^#(tt,n__isNatList(zeros)), and^#(tt,_0) -> activate^#(_0)] [comp] is in U_IR^4.
        Let p4 = [1, 0].
        We unfold the first rule of L4 forwards at position p4
        with the rule zeros -> cons(0,n__zeros).
        ==> L5 = [isNatList^#(n__cons(n__0,n__zeros)) -> and^#(tt,n__isNatList(cons(0,n__zeros))), and^#(tt,_0) -> activate^#(_0)] [comp] is in U_IR^5.
        Let p5 = [1, 0].
        We unfold the first rule of L5 forwards at position p5
        with the rule cons(_0,_1) -> n__cons(_0,_1).
        ==> L6 = [isNatList^#(n__cons(n__0,n__zeros)) -> and^#(tt,n__isNatList(n__cons(0,n__zeros))), and^#(tt,_0) -> activate^#(_0)] [comp] is in U_IR^6.
        Let p6 = [1, 0, 0].
        We unfold the first rule of L6 forwards at position p6
        with the rule 0 -> n__0.
        ==> L7 = isNatList^#(n__cons(n__0,n__zeros)) -> activate^#(n__isNatList(n__cons(n__0,n__zeros))) [trans] is in U_IR^7.
        D = activate^#(n__isNatList(_0)) -> isNatList^#(_0) is a dependency pair of IR.
        We build a composed triple from L7 and D.
        ==> L8 = isNatList^#(n__cons(n__0,n__zeros)) -> isNatList^#(n__cons(n__0,n__zeros)) [trans] is in U_IR^8.
  This DP problem is infinite.

** END proof description **

Proof stopped at iteration 8
Number of unfolded rules generated by this proof = 267814
Number of unfolded rules generated by all the parallel proofs = 1227179