ceta_equiv: 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 when applying the reduction pair processor with usable rules to remove from the DP problem
   pairs:
   
   eq#(cons(T, L), cons(Tp, Lp)) -> eq#(T, Tp)
   eq#(cons(T, L), cons(Tp, Lp)) -> eq#(L, Lp)
   eq#(apply(T, S), apply(Tp, Sp)) -> eq#(T, Tp)
   eq#(apply(T, S), apply(Tp, Sp)) -> eq#(S, Sp)
   eq#(lambda(X, T), lambda(Xp, Tp)) -> eq#(T, Tp)
   eq#(lambda(X, T), lambda(Xp, Tp)) -> eq#(X, Xp)
   rules:
   
   and(false, false) -> false
   and(true, false) -> false
   and(false, true) -> false
   and(true, true) -> true
   eq(nil, nil) -> true
   eq(cons(T, L), nil) -> false
   eq(nil, cons(T, L)) -> false
   eq(cons(T, L), cons(Tp, Lp)) -> and(eq(T, Tp), eq(L, Lp))
   eq(var(L), var(Lp)) -> eq(L, Lp)
   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(Tp, Sp)) -> and(eq(T, Tp), eq(S, Sp))
   eq(apply(T, S), lambda(X, Tp)) -> false
   eq(lambda(X, T), var(L)) -> false
   eq(lambda(X, T), apply(Tp, Sp)) -> false
   eq(lambda(X, T), lambda(Xp, Tp)) -> and(eq(T, Tp), eq(X, Xp))
   if(true, var(K), var(L)) -> var(K)
   if(false, var(K), var(L)) -> var(L)
   ren(var(L), var(K), var(Lp)) -> if(eq(L, Lp), var(K), var(Lp))
   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 
   eq#(apply(T, S), apply(Tp, Sp)) -> eq#(T, Tp)
   eq#(apply(T, S), apply(Tp, Sp)) -> eq#(S, Sp)
   
   could not apply the generic root reduction pair processor with the following
   SCNP-version with mu = MS and the level mapping defined by 
   pi(eq#) = [(epsilon,0),(1,0)]
   polynomial interpretration over naturals with negative constants
   Pol(eq#(x_1, x_2)) = 1
   Pol(cons(x_1, x_2)) = x_2 + x_1
   Pol(apply(x_1, x_2)) = 1 + x_2 + x_1
   Pol(lambda(x_1, x_2)) = x_2 + x_1
   problem when orienting DPs
   cannot orient pair eq#(cons(T, L), cons(Tp, Lp)) -> eq#(T, Tp) weakly:
   [(eq#(cons(T, L), cons(Tp, Lp)),0),(cons(T, L),0)] >=mu [(eq#(T, Tp),0),(T,0)] could not be ensured