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 below the reduction pair processor
  1.1.1.1: error when applying the reduction pair processor with usable rules to remove from the DP problem
   pairs:
   
   ren#(x, y, apply(t, s)) -> ren#(x, y, t)
   ren#(x, y, apply(t, s)) -> ren#(x, y, s)
   ren#(x, y, lambda(z, t)) -> ren#(x, y, ren(z, var(cons(x, cons(y, cons(lambda(z, t), nil)))), t))
   rules:
   
   and(true, y) -> y
   and(false, y) -> false
   eq(nil, nil) -> true
   eq(cons(t, l), nil) -> false
   eq(nil, cons(t, l)) -> false
   eq(cons(t, l), cons(t', l')) -> and(eq(t, t'), eq(l, l'))
   eq(var(l), var(l')) -> eq(l, l')
   eq(var(l), apply(t, s)) -> false
   eq(var(l), lambda(x, t)) -> false
   eq(apply(t, s), var(l)) -> false
   eq(apply(t, s), apply(t', s')) -> and(eq(t, t'), eq(s, s'))
   eq(apply(t, s), lambda(x, t)) -> false
   eq(lambda(x, t), var(l)) -> false
   eq(lambda(x, t), apply(t, s)) -> false
   eq(lambda(x, t), lambda(x', t')) -> and(eq(x, x'), eq(t, t'))
   if(true, var(k), var(l')) -> var(k)
   if(false, var(k), var(l')) -> var(l')
   ren(var(l), var(k), var(l')) -> if(eq(l, l'), var(k), var(l'))
   ren(x, y, apply(t, s)) -> apply(ren(x, y, t), ren(x, y, s))
   ren(x, y, lambda(z, t)) -> lambda(var(cons(x, cons(y, cons(lambda(z, t), nil)))), ren(x, y, ren(z, var(cons(x, cons(y, cons(lambda(z, t), nil)))), t)))
   
    the pairs 
   ren#(x, y, apply(t, s)) -> ren#(x, y, t)
   ren#(x, y, apply(t, s)) -> ren#(x, y, s)
   ren#(x, y, lambda(z, t)) -> ren#(x, y, ren(z, var(cons(x, cons(y, cons(lambda(z, t), nil)))), t))
   
   could not apply the generic root reduction pair processor with the following
   SCNP-version with mu = DMS and the level mapping defined by 
   pi(ren#) = [(1,2),(3,0)]
   Argument Filter: 
   pi(ren#/3) = [1,2,3]
   pi(apply/2) = [1,2]
   pi(lambda/2) = [1,2]
   pi(ren/3) = 3
   pi(var/1) = []
   pi(cons/2) = []
   pi(nil/0) = []
   pi(if/3) = 2
   pi(eq/2) = [1,2]
   pi(true/0) = []
   pi(false/0) = []
   pi(and/2) = [1]
   
   RPO with the following precedence
   precedence(ren#[3]) = 2
   precedence(apply[2]) = 3
   precedence(lambda[2]) = 2
   precedence(var[1]) = 0
   precedence(cons[2]) = 2
   precedence(nil[0]) = 2
   precedence(eq[2]) = 1
   precedence(true[0]) = 4
   precedence(false[0]) = 5
   precedence(and[2]) = 1
   
   precedence(_) = 0
   and the following status
   status(ren#[3]) = mul
   status(apply[2]) = lex
   status(lambda[2]) = mul
   status(var[1]) = lex
   status(cons[2]) = mul
   status(nil[0]) = mul
   status(eq[2]) = mul
   status(true[0]) = mul
   status(false[0]) = mul
   status(and[2]) = mul
   
   status(_) = lex
   
   problem when orienting (usable) rules
   could not orient ren(x, y, lambda(z, t)) >= lambda(var(cons(x, cons(y, cons(lambda(z, t), nil)))), ren(x, y, ren(z, var(cons(x, cons(y, cons(lambda(z, t), nil)))), t)))
   pi( ren(x, y, lambda(z, t)) ) = lambda(z, t)
   pi( lambda(var(cons(x, cons(y, cons(lambda(z, t), nil)))), ren(x, y, ren(z, var(cons(x, cons(y, cons(lambda(z, t), nil)))), t))) ) = lambda(var, t)
   could not orient lambda(z, t) >=RPO lambda(var, t)