ceta_eq: termination proof not accepted
1: error below switch to dependency pairs
1.1: error below the dependency graph processor
 1.1.1: error when applying the reduction pair processor with usable rules to remove from the DP problem
  pairs:
  
  app#(app(map, f), app(app(cons, x), xs)) -> app#(f, x)
  app#(app(map, f), app(app(cons, x), xs)) -> app#(app(map, f), xs)
  app#(app(filter, f), app(app(cons, x), xs)) -> app#(app(app(app(filter2, app(f, x)), f), x), xs)
  app#(app(filter, f), app(app(cons, x), xs)) -> app#(f, x)
  app#(app(app(app(filter2, true), f), x), xs) -> app#(app(filter, f), xs)
  app#(app(app(app(filter2, false), f), x), xs) -> app#(app(filter, f), xs)
  rules:
  
  app(app(., 1), x) -> x
  app(app(., x), 1) -> x
  app(app(., app(i, x)), x) -> 1
  app(app(., x), app(i, x)) -> 1
  app(app(., app(i, y)), app(app(., y), z)) -> z
  app(app(., y), app(app(., app(i, y)), z)) -> z
  app(app(., app(app(., x), y)), z) -> app(app(., x), app(app(., y), z))
  app(i, 1) -> 1
  app(i, app(i, x)) -> x
  app(i, app(app(., x), y)) -> app(app(., app(i, y)), app(i, x))
  app(app(map, f), nil) -> nil
  app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs))
  app(app(filter, f), nil) -> nil
  app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs)
  app(app(app(app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs))
  app(app(app(app(filter2, false), f), x), xs) -> app(app(filter, f), xs)
  
   the pairs 
  app#(app(map, f), app(app(cons, x), xs)) -> app#(f, x)
  app#(app(map, f), app(app(cons, x), xs)) -> app#(app(map, f), xs)
  app#(app(filter, f), app(app(cons, x), xs)) -> app#(app(app(app(filter2, app(f, x)), f), x), xs)
  app#(app(filter, f), app(app(cons, x), xs)) -> app#(f, x)
  
  could not apply the generic root reduction pair processor with the following
  SCNP-version with mu = MS and the level mapping defined by 
  pi(app#) = [(epsilon,0),(2,2)]
  Argument Filter: 
  pi(app#/2) = []
  pi(app/2) = [1,2]
  pi(map/0) = []
  pi(cons/0) = []
  pi(filter/0) = []
  pi(filter2/0) = []
  pi(true/0) = []
  pi(false/0) = []
  pi(./0) = []
  pi(1/0) = []
  pi(i/0) = []
  pi(nil/0) = []
  
  RPO with the following precedence
  precedence(i[0]) = 0
  precedence(.[0]) = 1
  precedence(cons[0]) = 2
  precedence(app#[2]) = 3
  precedence(true[0]) = 4
  precedence(map[0]) = 5
  precedence(false[0]) = 6
  precedence(app[2]) = 7
  precedence(filter2[0]) = 8
  precedence(1[0]) = 9
  precedence(nil[0]) = 10
  precedence(filter[0]) = 11
  
  precedence(_) = 0
  and the following status
  status(i[0]) = lex
  status(.[0]) = lex
  status(cons[0]) = lex
  status(app#[2]) = lex
  status(true[0]) = lex
  status(map[0]) = lex
  status(false[0]) = lex
  status(app[2]) = lex
  status(filter2[0]) = lex
  status(1[0]) = lex
  status(nil[0]) = lex
  status(filter[0]) = lex
  
  status(_) = lex
  
  problem when orienting DPs
  cannot orient pair app#(app(app(app(filter2, true), f), x), xs) -> app#(app(filter, f), xs) weakly:
  [(app#(app(app(app(filter2, true), f), x), xs),0),(xs,2)] >=mu [(app#(app(filter, f), xs),0),(xs,2)] could not be ensured