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 below the reduction pair processor
   1.1.1.1.1: error below the reduction pair processor
    1.1.1.1.1.1: error below the reduction pair processor
     1.1.1.1.1.1.1: error below the reduction pair processor
      1.1.1.1.1.1.1.1: error below the reduction pair processor
       1.1.1.1.1.1.1.1.1: error below the reduction pair processor
        1.1.1.1.1.1.1.1.1.1: error below the reduction pair processor
         1.1.1.1.1.1.1.1.1.1.1: error below the reduction pair processor
          1.1.1.1.1.1.1.1.1.1.1.1: error when applying the reduction pair processor to remove from the DP problem
           pairs:
           
           active#(if(false, X, Y)) -> mark#(Y)
           mark#(and(X1, X2)) -> active#(and(mark(X1), X2))
           mark#(if(X1, X2, X3)) -> active#(if(mark(X1), X2, X3))
           mark#(if(X1, X2, X3)) -> mark#(X1)
           mark#(add(X1, X2)) -> active#(add(mark(X1), X2))
           mark#(first(X1, X2)) -> active#(first(mark(X1), mark(X2)))
           mark#(cons(X1, X2)) -> active#(cons(X1, X2))
           mark#(from(X)) -> active#(from(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))))
           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 
           active#(if(false, X, Y)) -> mark#(Y)
           
           could not apply the generic root reduction pair processor with the following
           SCNP-version with mu = MS and the level mapping defined by 
           pi(mark#) = [(epsilon,0),(1,0)]
           pi(active#) = [(epsilon,0),(1,0)]
           polynomial interpretration over naturals with negative constants
           Pol(mark#(x_1)) = 1
           Pol(and(x_1, x_2)) = x_2 + x_1
           Pol(active#(x_1)) = 1
           Pol(mark(x_1)) = x_1
           Pol(if(x_1, x_2, x_3)) = x_3 + x_2 + x_1
           Pol(add(x_1, x_2)) = 1 + x_2 + x_1
           Pol(false) = 1
           Pol(first(x_1, x_2)) = 1 + x_2 + x_1
           Pol(cons(x_1, x_2)) = x_1
           Pol(from(x_1)) = x_1
           Pol(active(x_1)) = x_1
           Pol(true) = 1
           Pol(s(x_1)) = 1 + x_1
           Pol(0) = 0
           Pol(nil) = 0
           problem when orienting DPs
           cannot orient pair mark#(if(X1, X2, X3)) -> mark#(X1) weakly:
           [(mark#(if(X1, X2, X3)),0),(if(X1, X2, X3),0)] >=mu [(mark#(X1),0),(X1,0)] could not be ensured