ceta_equiv: termination proof not accepted
1: error below switch to dependency pairs
1.1: error below the dependency graph processor
 1.1.1: error when applying the reduction pair processor with usable rules to remove from the DP problem
  pairs:
  
  top#(mark(X)) -> top#(proper(X))
  top#(ok(X)) -> top#(active(X))
  rules:
  
  active(and(true, X)) -> mark(X)
  active(and(false, Y)) -> mark(false)
  active(if(true, X, Y)) -> mark(X)
  active(if(false, X, Y)) -> mark(Y)
  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(from(X)) -> mark(cons(X, from(s(X))))
  active(and(X1, X2)) -> and(active(X1), X2)
  active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
  active(add(X1, X2)) -> add(active(X1), X2)
  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(ok(X1), ok(X2)) -> ok(add(X1, X2))
  and(mark(X1), X2) -> mark(and(X1, X2))
  and(ok(X1), ok(X2)) -> ok(and(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(ok(X)) -> ok(from(X))
  if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
  if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
  proper(and(X1, X2)) -> and(proper(X1), proper(X2))
  proper(true) -> ok(true)
  proper(false) -> ok(false)
  proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
  proper(add(X1, X2)) -> add(proper(X1), proper(X2))
  proper(0) -> ok(0)
  proper(s(X)) -> s(proper(X))
  proper(first(X1, X2)) -> first(proper(X1), proper(X2))
  proper(nil) -> ok(nil)
  proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
  proper(from(X)) -> from(proper(X))
  s(ok(X)) -> ok(s(X))
  top(mark(X)) -> top(proper(X))
  top(ok(X)) -> top(active(X))
  
   the pairs 
  top#(mark(X)) -> top#(proper(X))
  
  could not apply the generic reduction pair processor with the following
  Argument Filter: 
  pi(top#/1) = [1]
  pi(ok/1) = 1
  pi(active/1) = 1
  pi(mark/1) = [1]
  pi(proper/1) = 1
  pi(and/2) = [1,2]
  pi(true/0) = []
  pi(false/0) = []
  pi(if/3) = [1,3,2]
  pi(add/2) = [1,2]
  pi(0/0) = []
  pi(s/1) = []
  pi(first/2) = [2,1]
  pi(nil/0) = []
  pi(cons/2) = []
  pi(from/1) = [1]
  
  RPO with the following precedence
  precedence(top#[1]) = 1
  precedence(mark[1]) = 2
  precedence(and[2]) = 3
  precedence(true[0]) = 4
  precedence(false[0]) = 0
  precedence(if[3]) = 5
  precedence(add[2]) = 8
  precedence(0[0]) = 6
  precedence(s[1]) = 7
  precedence(first[2]) = 6
  precedence(nil[0]) = 6
  precedence(cons[2]) = 0
  precedence(from[1]) = 2
  
  precedence(_) = 0
  and the following status
  status(top#[1]) = lex
  status(mark[1]) = mul
  status(and[2]) = mul
  status(true[0]) = mul
  status(false[0]) = mul
  status(if[3]) = lex
  status(add[2]) = lex
  status(0[0]) = mul
  status(s[1]) = mul
  status(first[2]) = lex
  status(nil[0]) = mul
  status(cons[2]) = mul
  status(from[1]) = mul
  
  status(_) = lex
  
  problem when orienting (usable) rules
  could not orient active(from(X)) >= mark(cons(X, from(s(X))))
  pi( active(from(X)) ) = from(X)
  pi( mark(cons(X, from(s(X)))) ) = mark(cons)
  could not orient from(X) >=RPO mark(cons)