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#(first(X1, X2)) -> active#(X1)
     active#(first(X1, X2)) -> active#(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))))
     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 
     active#(first(X1, X2)) -> active#(X1)
     active#(first(X1, X2)) -> active#(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(active#) = [(epsilon,0),(1,0)]
     polynomial interpretration over naturals with negative constants
     Pol(active#(x_1)) = 1
     Pol(first(x_1, x_2)) = 1 + x_2 + x_1
     problem when orienting DPs
     cannot orient pair active#(first(X1, X2)) -> active#(X1) strictly:
     [(active#(first(X1, X2)),0),(first(X1, X2),0)] >mu [(active#(X1),0),(X1,0)] could not be ensured