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 = 6] a__f(_0,_0) -> a__f(b,b)
Let l be the left-hand side and r be the right-hand side of this rule.
Let p = epsilon, theta1 = {} and theta2 = {_0->b}.
We have r|p = a__f(b,b) and theta2(theta1(l)) = theta1(r|p).
Hence, the term theta1(l) = a__f(_0,_0) 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 = [a__h^#(_0) -> a__g^#(mark(_0),_0), a__f^#(_0,_0) -> a__h^#(a__a), mark^#(f(_0,_1)) -> a__f^#(mark(_0),_1), a__g^#(a,_0) -> a__f^#(b,_0), mark^#(g(_0,_1)) -> a__g^#(mark(_0),_1), a__h^#(_0) -> mark^#(_0), mark^#(h(_0)) -> a__h^#(mark(_0)), mark^#(h(_0)) -> mark^#(_0), mark^#(g(_0,_1)) -> mark^#(_0), mark^#(f(_0,_1)) -> mark^#(_0)]
  TRS = {a__h(_0) -> a__g(mark(_0),_0), a__g(a,_0) -> a__f(b,_0), a__f(_0,_0) -> a__h(a__a), a__a -> b, mark(h(_0)) -> a__h(mark(_0)), mark(g(_0,_1)) -> a__g(mark(_0),_1), mark(a) -> a__a, mark(f(_0,_1)) -> a__f(mark(_0),_1), mark(b) -> b, a__h(_0) -> h(_0), a__g(_0,_1) -> g(_0,_1), a__a -> a, a__f(_0,_1) -> f(_0,_1)}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Too many coefficients (26)! Aborting!
    ## Trying with lexicographic path orders... Failed!
    ## Trying to prove nontermination by unfolding the dependency pairs with the rules of the TRS
      # max_depth=2, unfold_variables=false:
        # Iteration 0: nontermination not detected, 10 unfolded rules generated.
        # Iteration 1: nontermination not detected, 39 unfolded rules generated.
        # Iteration 2: nontermination not detected, 56 unfolded rules generated.
        # Iteration 3: nontermination not detected, 63 unfolded rules generated.
        # Iteration 4: nontermination not detected, 79 unfolded rules generated.
        # Iteration 5: nontermination not detected, 87 unfolded rules generated.
        # Iteration 6: nontermination detected, 5 unfolded rules generated.
        Here is the successful unfolding. Let IR be the TRS under analysis.
        L0 = a__f^#(_0,_0) -> a__h^#(a__a) [trans] is in U_IR^0.
        D = a__h^#(_0) -> a__g^#(mark(_0),_0) is a dependency pair of IR.
        We build a composed triple from L0 and D.
        ==> L1 = a__f^#(_0,_0) -> a__g^#(mark(a__a),a__a) [trans] is in U_IR^1.
        D = a__g^#(a,_0) -> a__f^#(b,_0) is a dependency pair of IR.
        We build a composed triple from L1 and D.
        ==> L2 = [a__f^#(_0,_0) -> a__g^#(mark(a__a),a__a), a__g^#(a,_1) -> a__f^#(b,_1)] [comp] is in U_IR^2.
        Let p2 = [0, 0].
        We unfold the first rule of L2 forwards at position p2
        with the rule a__a -> a.
        ==> L3 = [a__f^#(_0,_0) -> a__g^#(mark(a),a__a), a__g^#(a,_1) -> a__f^#(b,_1)] [comp] is in U_IR^3.
        Let p3 = [0].
        We unfold the first rule of L3 forwards at position p3
        with the rule mark(a) -> a__a.
        ==> L4 = [a__f^#(_0,_0) -> a__g^#(a__a,a__a), a__g^#(a,_1) -> a__f^#(b,_1)] [comp] is in U_IR^4.
        Let p4 = [0].
        We unfold the first rule of L4 forwards at position p4
        with the rule a__a -> a.
        ==> L5 = [a__f^#(_0,_0) -> a__g^#(a,a__a), a__g^#(a,_1) -> a__f^#(b,_1)] [comp] is in U_IR^5.
        Let p5 = [1].
        We unfold the first rule of L5 forwards at position p5
        with the rule a__a -> b.
        ==> L6 = a__f^#(_0,_0) -> a__f^#(b,b) [trans] is in U_IR^6.
  This DP problem is infinite.

** END proof description **

Proof stopped at iteration 6
Number of unfolded rules generated by this proof = 339
Number of unfolded rules generated by all the parallel proofs = 1830