ceta_eq: termination proof not accepted
1: error below switch to dependency pairs
1.1: error below the dependency graph processor
 1.1.3: error when applying the reduction pair processor with usable rules to remove from the DP problem
  pairs:
  
  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)
  rules:
  
  active(terms(N)) -> mark(cons(recip(sqr(N)), terms(s(N))))
  active(sqr(0)) -> mark(0)
  active(sqr(s(X))) -> mark(s(add(sqr(X), dbl(X))))
  active(dbl(0)) -> mark(0)
  active(dbl(s(X))) -> mark(s(s(dbl(X))))
  active(add(0, X)) -> mark(X)
  active(add(s(X), Y)) -> mark(s(add(X, Y)))
  active(first(0, X)) -> mark(nil)
  active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
  add(mark(X1), X2) -> add(X1, X2)
  add(X1, mark(X2)) -> add(X1, X2)
  add(active(X1), X2) -> add(X1, X2)
  add(X1, active(X2)) -> add(X1, X2)
  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)
  dbl(mark(X)) -> dbl(X)
  dbl(active(X)) -> dbl(X)
  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)
  mark(terms(X)) -> active(terms(mark(X)))
  mark(cons(X1, X2)) -> active(cons(mark(X1), X2))
  mark(recip(X)) -> active(recip(mark(X)))
  mark(sqr(X)) -> active(sqr(mark(X)))
  mark(s(X)) -> active(s(mark(X)))
  mark(0) -> active(0)
  mark(add(X1, X2)) -> active(add(mark(X1), mark(X2)))
  mark(dbl(X)) -> active(dbl(mark(X)))
  mark(first(X1, X2)) -> active(first(mark(X1), mark(X2)))
  mark(nil) -> active(nil)
  recip(mark(X)) -> recip(X)
  recip(active(X)) -> recip(X)
  s(mark(X)) -> s(X)
  s(active(X)) -> s(X)
  sqr(mark(X)) -> sqr(X)
  sqr(active(X)) -> sqr(X)
  terms(mark(X)) -> terms(X)
  terms(active(X)) -> terms(X)
  
   the pairs 
  cons#(active(X1), X2) -> cons#(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(cons#) = [(epsilon,0),(1,1)]
  Argument Filter: 
  pi(cons#/2) = []
  pi(mark/1) = 1
  pi(active/1) = [1]
  
  RPO with the following precedence
  precedence(cons#[2]) = 0
  precedence(active[1]) = 1
  
  precedence(_) = 0
  and the following status
  status(cons#[2]) = lex
  status(active[1]) = lex
  
  status(_) = lex
  
  problem when orienting DPs
  cannot orient pair cons#(mark(X1), X2) -> cons#(X1, X2) weakly:
  [(cons#(mark(X1), X2),0),(mark(X1),1)] >=mu [(cons#(X1, X2),0),(X1,1)] could not be ensured