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(ack, app(succ, x)), y) -> app#(app(ack, x), app(succ, 0))
  app#(app(ack, app(succ, x)), app(succ, y)) -> app#(app(ack, x), app(app(ack, app(succ, x)), y))
  app#(app(ack, app(succ, x)), app(succ, y)) -> app#(app(ack, app(succ, x)), y)
  rules:
  
  app(app(ack, 0), y) -> app(succ, y)
  app(app(ack, app(succ, x)), y) -> app(app(ack, x), app(succ, 0))
  app(app(ack, app(succ, x)), app(succ, y)) -> app(app(ack, x), app(app(ack, app(succ, x)), y))
  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(ack, app(succ, x)), y) -> app#(app(ack, x), app(succ, 0))
  app#(app(ack, app(succ, x)), app(succ, y)) -> app#(app(ack, x), app(app(ack, app(succ, x)), y))
  
  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),(1,1)]
  Argument Filter: 
  pi(app#/2) = []
  pi(app/2) = [1,2]
  pi(ack/0) = []
  pi(succ/0) = []
  pi(0/0) = []
  
  RPO with the following precedence
  precedence(app#[2]) = 1
  precedence(app[2]) = 0
  precedence(ack[0]) = 1
  precedence(succ[0]) = 0
  precedence(0[0]) = 1
  
  precedence(_) = 0
  and the following status
  status(app#[2]) = mul
  status(app[2]) = mul
  status(ack[0]) = mul
  status(succ[0]) = mul
  status(0[0]) = mul
  
  status(_) = lex
  
  problem when orienting DPs
  cannot orient pair app#(app(ack, app(succ, x)), app(succ, y)) -> app#(app(ack, app(succ, x)), y) weakly:
  [(app#(app(ack, app(succ, x)), app(succ, y)),0),(app(ack, app(succ, x)),1)] >=mu [(app#(app(ack, app(succ, x)), y),0),(app(ack, app(succ, x)),1)] could not be ensured