YES

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 **
All the DP problems were proved finite.
As all the involved DP processors are sound,
the TRS under analysis terminates.
** 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 = [f^#(j(_0,_1),_1) -> f^#(_0,k(_1))]
  TRS = {f(j(_0,_1),_1) -> g(f(_0,k(_1))), f(_0,h1(_1,_2)) -> h2(0,_0,h1(_1,_2)), g(h2(_0,_1,h1(_2,_3))) -> h2(s(_0),_1,h1(_2,_3)), h2(_0,j(_1,h1(_2,_3)),h1(_2,_3)) -> h2(s(_0),_1,h1(s(_2),_3)), i(f(_0,h(_1))) -> _1, i(h2(s(_0),_1,h1(_0,_2))) -> _2, k(h(_0)) -> h1(0,_0), k(h1(_0,_1)) -> h1(s(_0),_1)}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Too many coefficients (32)! Aborting!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      j > [f, k, h2, g], f > [h2], h > [h1]
      and the argument filtering:
      {j:[0, 1], f:[0, 1], k:[0], h2:[2], s:[0], g:[0], h1:[1], i:[0], h:[0], f^#:[0, 1]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [h2^#(_0,j(_1,h1(_2,_3)),h1(_2,_3)) -> h2^#(s(_0),_1,h1(s(_2),_3))]
  TRS = {f(j(_0,_1),_1) -> g(f(_0,k(_1))), f(_0,h1(_1,_2)) -> h2(0,_0,h1(_1,_2)), g(h2(_0,_1,h1(_2,_3))) -> h2(s(_0),_1,h1(_2,_3)), h2(_0,j(_1,h1(_2,_3)),h1(_2,_3)) -> h2(s(_0),_1,h1(s(_2),_3)), i(f(_0,h(_1))) -> _1, i(h2(s(_0),_1,h1(_0,_2))) -> _2, k(h(_0)) -> h1(0,_0), k(h1(_0,_1)) -> h1(s(_0),_1)}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Too many coefficients (32)! Aborting!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      j > [f, k, h2, g], f > [h2], h > [h1]
      and the argument filtering:
      {j:[0, 1], f:[0, 1], k:[0], h2:[2], s:[0], g:[0], h1:[1], i:[0], h:[0], h2^#:[1]}
  This DP problem is finite.

** END proof description **

Proof stopped at iteration 0
Number of unfolded rules generated by this proof = 0
Number of unfolded rules generated by all the parallel proofs = 130