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 below the reduction pair processor
  1.1.2.1: error below the reduction pair processor
   1.1.2.1.1: error below the reduction pair processor
    1.1.2.1.1.1: error when applying the reduction pair processor with usable rules to remove from the DP problem
     pairs:
     
     active#(recip(X)) -> active#(X)
     active#(s(X)) -> active#(X)
     active#(dbl(X)) -> active#(X)
     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)))
     active(terms(X)) -> terms(active(X))
     active(cons(X1, X2)) -> cons(active(X1), X2)
     active(recip(X)) -> recip(active(X))
     active(sqr(X)) -> sqr(active(X))
     active(s(X)) -> s(active(X))
     active(add(X1, X2)) -> add(active(X1), X2)
     active(add(X1, X2)) -> add(X1, active(X2))
     active(dbl(X)) -> dbl(active(X))
     active(first(X1, X2)) -> first(active(X1), X2)
     active(first(X1, X2)) -> first(X1, active(X2))
     add(mark(X1), X2) -> mark(add(X1, X2))
     add(X1, mark(X2)) -> mark(add(X1, X2))
     add(ok(X1), ok(X2)) -> ok(add(X1, X2))
     cons(mark(X1), X2) -> mark(cons(X1, X2))
     cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
     dbl(mark(X)) -> mark(dbl(X))
     dbl(ok(X)) -> ok(dbl(X))
     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))
     proper(terms(X)) -> terms(proper(X))
     proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     proper(recip(X)) -> recip(proper(X))
     proper(sqr(X)) -> sqr(proper(X))
     proper(s(X)) -> s(proper(X))
     proper(0) -> ok(0)
     proper(add(X1, X2)) -> add(proper(X1), proper(X2))
     proper(dbl(X)) -> dbl(proper(X))
     proper(first(X1, X2)) -> first(proper(X1), proper(X2))
     proper(nil) -> ok(nil)
     recip(mark(X)) -> mark(recip(X))
     recip(ok(X)) -> ok(recip(X))
     s(mark(X)) -> mark(s(X))
     s(ok(X)) -> ok(s(X))
     sqr(mark(X)) -> mark(sqr(X))
     sqr(ok(X)) -> ok(sqr(X))
     terms(mark(X)) -> mark(terms(X))
     terms(ok(X)) -> ok(terms(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
     
      the pairs 
     active#(s(X)) -> active#(X)
     
     could not apply the generic root reduction pair processor with the following
     SCNP-version with mu = MS and the level mapping defined by 
     pi(active#) = [(epsilon,0),(1,0)]
     Argument Filter: 
     pi(active#/1) = []
     pi(recip/1) = 1
     pi(s/1) = [1]
     pi(dbl/1) = 1
     
     RPO with the following precedence
     precedence(active#[1]) = 0
     precedence(s[1]) = 1
     
     precedence(_) = 0
     and the following status
     status(active#[1]) = lex
     status(s[1]) = lex
     
     status(_) = lex
     
     problem when orienting DPs
     cannot orient pair active#(recip(X)) -> active#(X) weakly:
     [(active#(recip(X)),0),(recip(X),0)] >=mu [(active#(X),0),(X,0)] could not be ensured