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:
  
  app#(app(app(f, 0), 1), x) -> app#(app(app(f, app(s, x)), x), x)
  app#(app(app(f, x), y), app(s, z)) -> app#(app(app(f, 0), 1), z)
  rules:
  
  app(app(app(f, 0), 1), x) -> app(app(app(f, app(s, x)), x), x)
  app(app(app(f, x), y), app(s, z)) -> app(s, app(app(app(f, 0), 1), z))
  app(app(map, fun), nil) -> nil
  app(app(map, fun), app(app(cons, x), xs)) -> app(app(cons, app(fun, x)), app(app(map, fun), xs))
  app(app(filter, fun), nil) -> nil
  app(app(filter, fun), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(fun, x)), fun), x), xs)
  app(app(app(app(filter2, true), fun), x), xs) -> app(app(cons, x), app(app(filter, fun), xs))
  app(app(app(app(filter2, false), fun), x), xs) -> app(app(filter, fun), xs)
  
   the pairs 
  app#(app(app(f, x), y), app(s, z)) -> app#(app(app(f, 0), 1), 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(app#) = [(epsilon,0),(2,1)]
  Argument Filter: 
  pi(app#/2) = []
  pi(app/2) = [2,1]
  pi(f/0) = []
  pi(s/0) = []
  pi(0/0) = []
  pi(1/0) = []
  
  RPO with the following precedence
  precedence(app#[2]) = 4
  precedence(app[2]) = 3
  precedence(f[0]) = 2
  precedence(s[0]) = 2
  precedence(0[0]) = 1
  precedence(1[0]) = 0
  
  precedence(_) = 0
  and the following status
  status(app#[2]) = lex
  status(app[2]) = lex
  status(f[0]) = lex
  status(s[0]) = lex
  status(0[0]) = lex
  status(1[0]) = lex
  
  status(_) = lex
  
  problem when orienting DPs
  cannot orient pair app#(app(app(f, 0), 1), x) -> app#(app(app(f, app(s, x)), x), x) weakly:
  [(app#(app(app(f, 0), 1), x),0),(x,1)] >=mu [(app#(app(app(f, app(s, x)), x), x),0),(x,1)] could not be ensured