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 = [plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2)), plus^#(s(_0),plus(_1,_2)) -> plus^#(s(s(_1)),_2), plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_2,plus(_1,_3)), plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_1,_3)]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations...
    Successfully decomposed the DP problem into smaller problems to solve!
## Round 2:
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),plus(_1,plus(_2,_3))) -> plus^#(_0,plus(_2,plus(_1,_3))), plus^#(s(_0),plus(_1,_2)) -> plus^#(_0,plus(s(s(_1)),_2))]
  TRS = {plus(s(_0),plus(_1,_2)) -> plus(_0,plus(s(s(_1)),_2)), plus(s(_0),plus(_1,plus(_2,_3))) -> plus(_0,plus(_2,plus(_1,_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [plus]
      and the argument filtering:
      {plus:[0], s:[0], plus^#:[0]}
  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 = 1670018