code: def enumerate(semiring, edge):
      ssize = semiring.size()
      batch, N, K, C, _ = edge.shape
      edge = semiring.convert(edge)
      chains = {}
      chains[0] = [
          (
              [(c, 0)],
              semiring.fill(
                  torch.zeros(ssize, batch),
                  torch.tensor(True),
                  semiring.one,
              ),
          )
          for c in range(C)
      ]
  
      for n in range(1, N + 1):
          chains[n] = []
          for k in range(1, K):
              if n - k not in chains:
                  continue
              for chain, score in chains[n - k]:
                  for c in range(C):
                      chains[n].append(
                          (
                              chain + [(c, k)],
                              semiring.mul(
                                  score,
                                  edge[:, :, n - k, k, c, chain[-1][0]],
                              ),
                          )
                      )
      ls = [s for (_, s) in chains[N]]
      return (
          semiring.unconvert(
              semiring.sum(torch.stack(ls, dim=1), dim=1)
          ),
          ls,
      )
  
imports: import torch_struct
  import torch
  from torch_struct import LogSemiring
  import itertools
  from hypothesis.strategies import integers, composite, floats
  from hypothesis.extra.numpy import arrays
  import numpy
label_desc: Use image node_id 2 for calling the SemiMarkovTest obj's underlying member method code with example usage: obj.enumerate(semiring, edge) and returns: semiring,  ls