ceta_eq: 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 when applying the reduction pair processor with usable rules to remove from the DP problem
    pairs:
    
    mark#(take(X1, X2)) -> mark#(X1)
    mark#(take(X1, X2)) -> mark#(X2)
    rules:
    
    a__eq(0, 0) -> true
    a__eq(s(X), s(Y)) -> a__eq(X, Y)
    a__eq(X, Y) -> false
    a__eq(X1, X2) -> eq(X1, X2)
    a__inf(X) -> cons(X, inf(s(X)))
    a__inf(X) -> inf(X)
    a__length(nil) -> 0
    a__length(cons(X, L)) -> s(length(L))
    a__length(X) -> length(X)
    a__take(0, X) -> nil
    a__take(s(X), cons(Y, L)) -> cons(Y, take(X, L))
    a__take(X1, X2) -> take(X1, X2)
    mark(eq(X1, X2)) -> a__eq(X1, X2)
    mark(inf(X)) -> a__inf(mark(X))
    mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
    mark(length(X)) -> a__length(mark(X))
    mark(0) -> 0
    mark(true) -> true
    mark(s(X)) -> s(X)
    mark(false) -> false
    mark(cons(X1, X2)) -> cons(X1, X2)
    mark(nil) -> nil
    
     the pairs 
    mark#(take(X1, X2)) -> mark#(X1)
    mark#(take(X1, X2)) -> mark#(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(mark#) = [(epsilon,0),(1,0)]
    polynomial interpretration over naturals with negative constants
    Pol(mark#(x_1)) = 1
    Pol(take(x_1, x_2)) = 1 + x_2 + x_1
    problem when orienting DPs
    cannot orient pair mark#(take(X1, X2)) -> mark#(X1) strictly:
    [(mark#(take(X1, X2)),0),(take(X1, X2),0)] >mu [(mark#(X1),0),(X1,0)] could not be ensured