ceta_eq: termination proof not accepted
1: error below switch to dependency pairs
1.1: error below the dependency graph processor
 1.1.2: error when applying the reduction pair processor with usable rules to remove from the DP problem
  pairs:
  
  .#(.(x, y), z) -> .#(x, .(y, z))
  .#(.(x, y), z) -> .#(y, z)
  rules:
  
  .(1, x) -> x
  .(x, 1) -> x
  .(i(x), x) -> 1
  .(x, i(x)) -> 1
  .(i(y), .(y, z)) -> z
  .(y, .(i(y), z)) -> z
  .(.(x, y), z) -> .(x, .(y, z))
  i(1) -> 1
  i(i(x)) -> x
  i(.(x, y)) -> .(i(y), i(x))
  
   the pairs 
  .#(.(x, y), z) -> .#(x, .(y, z))
  .#(.(x, y), z) -> .#(y, z)
  
  could not apply the generic root reduction pair processor with the following
  SCNP-version with mu = MS and the level mapping defined by 
  pi(.#) = [(epsilon,0),(1,2)]
  Argument Filter: 
  pi(.#/2) = []
  pi(./2) = [2,1]
  pi(1/0) = []
  pi(i/1) = [1]
  
  RPO with the following precedence
  precedence(.#[2]) = 1
  precedence(.[2]) = 0
  precedence(1[0]) = 2
  precedence(i[1]) = 3
  
  precedence(_) = 0
  and the following status
  status(.#[2]) = lex
  status(.[2]) = lex
  status(1[0]) = lex
  status(i[1]) = lex
  
  status(_) = lex
  
  problem when orienting DPs
  cannot orient pair .#(.(x, y), z) -> .#(x, .(y, z)) strictly:
  [(.#(.(x, y), z),0),(.(x, y),2)] >mu [(.#(x, .(y, z)),0),(x,2)] could not be ensured