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:
  
  first#(mark(X1), X2) -> first#(X1, X2)
  first#(X1, mark(X2)) -> first#(X1, X2)
  first#(active(X1), X2) -> first#(X1, X2)
  first#(X1, active(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))))
  cons(mark(X1), X2) -> cons(X1, X2)
  cons(X1, mark(X2)) -> cons(X1, X2)
  cons(active(X1), X2) -> cons(X1, X2)
  cons(X1, active(X2)) -> cons(X1, X2)
  first(mark(X1), X2) -> first(X1, X2)
  first(X1, mark(X2)) -> first(X1, X2)
  first(active(X1), X2) -> first(X1, X2)
  first(X1, active(X2)) -> first(X1, X2)
  from(mark(X)) -> from(X)
  from(active(X)) -> from(X)
  mark(first(X1, X2)) -> active(first(mark(X1), mark(X2)))
  mark(0) -> active(0)
  mark(nil) -> active(nil)
  mark(s(X)) -> active(s(mark(X)))
  mark(cons(X1, X2)) -> active(cons(mark(X1), X2))
  mark(from(X)) -> active(from(mark(X)))
  s(mark(X)) -> s(X)
  s(active(X)) -> s(X)
  
   the pairs 
  first#(active(X1), 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#) = [(epsilon,0),(1,1)]
  Argument Filter: 
  pi(first#/2) = []
  pi(mark/1) = 1
  pi(active/1) = [1]
  
  RPO with the following precedence
  precedence(first#[2]) = 0
  precedence(active[1]) = 1
  
  precedence(_) = 0
  and the following status
  status(first#[2]) = lex
  status(active[1]) = lex
  
  status(_) = lex
  
  problem when orienting DPs
  cannot orient pair first#(mark(X1), X2) -> first#(X1, X2) weakly:
  [(first#(mark(X1), X2),0),(mark(X1),1)] >=mu [(first#(X1, X2),0),(X1,1)] could not be ensured