ceta_eq: termination proof not accepted
1: error below switch to dependency pairs
1.1: error below the dependency graph processor
 1.1.4: error when applying the reduction pair processor with usable rules to remove from the DP problem
  pairs:
  
  first#(mark(X1), X2) -> first#(X1, X2)
  first#(X1, mark(X2)) -> first#(X1, X2)
  first#(ok(X1), ok(X2)) -> first#(X1, X2)
  rules:
  
  active(first(0, X)) -> mark(nil)
  active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
  active(from(X)) -> mark(cons(X, from(s(X))))
  active(first(X1, X2)) -> first(active(X1), X2)
  active(first(X1, X2)) -> first(X1, active(X2))
  active(s(X)) -> s(active(X))
  active(cons(X1, X2)) -> cons(active(X1), X2)
  active(from(X)) -> from(active(X))
  cons(mark(X1), X2) -> mark(cons(X1, X2))
  cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
  first(mark(X1), X2) -> mark(first(X1, X2))
  first(X1, mark(X2)) -> mark(first(X1, X2))
  first(ok(X1), ok(X2)) -> ok(first(X1, X2))
  from(mark(X)) -> mark(from(X))
  from(ok(X)) -> ok(from(X))
  proper(first(X1, X2)) -> first(proper(X1), proper(X2))
  proper(0) -> ok(0)
  proper(nil) -> ok(nil)
  proper(s(X)) -> s(proper(X))
  proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
  proper(from(X)) -> from(proper(X))
  s(mark(X)) -> mark(s(X))
  s(ok(X)) -> ok(s(X))
  top(mark(X)) -> top(proper(X))
  top(ok(X)) -> top(active(X))
  
   the pairs 
  first#(mark(X1), X2) -> first#(X1, X2)
  first#(X1, mark(X2)) -> first#(X1, X2)
  
  could not apply the generic root reduction pair processor with the following
  SCNP-version with mu = MS and the level mapping defined by 
  pi(first#) = [(1,0),(2,2)]
  Argument Filter: 
  pi(first#/2) = []
  pi(mark/1) = [1]
  pi(ok/1) = 1
  
  RPO with the following precedence
  precedence(first#[2]) = 0
  precedence(mark[1]) = 1
  
  precedence(_) = 0
  and the following status
  status(first#[2]) = lex
  status(mark[1]) = lex
  
  status(_) = lex
  
  problem when orienting DPs
  cannot orient pair first#(ok(X1), ok(X2)) -> first#(X1, X2) weakly:
  [(ok(X1),0),(ok(X2),2)] >=mu [(X1,0),(X2,2)] could not be ensured