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:
  
  and#(mark(X1), X2) -> and#(X1, X2)
  and#(X1, mark(X2)) -> and#(X1, X2)
  and#(active(X1), X2) -> and#(X1, X2)
  and#(X1, active(X2)) -> and#(X1, X2)
  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))))
  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)
  and(mark(X1), X2) -> and(X1, X2)
  and(X1, mark(X2)) -> and(X1, X2)
  and(active(X1), X2) -> and(X1, X2)
  and(X1, active(X2)) -> and(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)
  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)
  if(mark(X1), X2, X3) -> if(X1, X2, X3)
  if(X1, mark(X2), X3) -> if(X1, X2, X3)
  if(X1, X2, mark(X3)) -> if(X1, X2, X3)
  if(active(X1), X2, X3) -> if(X1, X2, X3)
  if(X1, active(X2), X3) -> if(X1, X2, X3)
  if(X1, X2, active(X3)) -> if(X1, X2, X3)
  mark(and(X1, X2)) -> active(and(mark(X1), X2))
  mark(true) -> active(true)
  mark(false) -> active(false)
  mark(if(X1, X2, X3)) -> active(if(mark(X1), X2, X3))
  mark(add(X1, X2)) -> active(add(mark(X1), X2))
  mark(0) -> active(0)
  mark(s(X)) -> active(s(X))
  mark(first(X1, X2)) -> active(first(mark(X1), mark(X2)))
  mark(nil) -> active(nil)
  mark(cons(X1, X2)) -> active(cons(X1, X2))
  mark(from(X)) -> active(from(X))
  s(mark(X)) -> s(X)
  s(active(X)) -> s(X)
  
   the pairs 
  and#(active(X1), X2) -> and#(X1, X2)
  and#(X1, active(X2)) -> and#(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(and#) = [(1,3),(2,1)]
  Argument Filter: 
  pi(and#/2) = 1
  pi(mark/1) = 1
  pi(active/1) = [1]
  
  RPO with the following precedence
  precedence(active[1]) = 0
  
  precedence(_) = 0
  and the following status
  status(active[1]) = lex
  
  status(_) = lex
  
  problem when orienting DPs
  cannot orient pair and#(mark(X1), X2) -> and#(X1, X2) weakly:
  [(mark(X1),3),(X2,1)] >=mu [(X1,3),(X2,1)] could not be ensured