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