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, fun), app(app(cons, x), xs)) -> app#(fun, x)
  app#(app(map, fun), app(app(cons, x), xs)) -> app#(app(map, fun), xs)
  app#(app(filter, fun), app(app(cons, x), xs)) -> app#(fun, x)
  app#(app(app(app(filter2, true), fun), x), xs) -> app#(app(filter, fun), xs)
  app#(app(app(app(filter2, false), fun), x), xs) -> app#(app(filter, fun), xs)
  rules:
  
  app(f, a) -> app(f, b)
  app(g, b) -> app(g, a)
  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(map, fun), app(app(cons, x), xs)) -> app#(fun, 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)]
  polynomial interpretration over naturals with negative constants
  Pol(app#(x_1, x_2)) = x_1
  Pol(app(x_1, x_2)) = x_2 + x_1
  Pol(map) = 1
  Pol(cons) = 0
  Pol(filter) = 0
  Pol(filter2) = 0
  Pol(true) = 0
  Pol(false) = 0
  problem when orienting DPs
  cannot orient pair app#(app(map, fun), app(app(cons, x), xs)) -> app#(app(map, fun), xs) weakly:
  [(app#(app(map, fun), app(app(cons, x), xs)),0),(app(app(cons, x), xs),2)] >=mu [(app#(app(map, fun), xs),0),(xs,2)] could not be ensured