Input TRS:
    1: 2nd(cons1(X,cons(Y,Z))) -> Y
    2: 2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
    3: from(X) -> cons(X,n__from(n__s(X)))
    4: from(X) -> n__from(X)
    5: s(X) -> n__s(X)
    6: activate(n__from(X)) -> from(activate(X))
    7: activate(n__s(X)) -> s(activate(X))
    8: activate(X) -> X
Number of strict rules: 8
Direct Order(PosReal,>,Poly) ... failed.
Freezing 2nd
1: 2nd❆1_cons1(X,cons(Y,Z)) -> Y
2: 2nd❆1_cons(X,X1) -> 2nd❆1_cons1(X,activate(X1))
3: from(X) -> cons(X,n__from(n__s(X)))
4: from(X) -> n__from(X)
5: s(X) -> n__s(X)
6: activate(n__from(X)) -> from(activate(X))
7: activate(n__s(X)) -> s(activate(X))
8: activate(X) -> X
9: 2nd(cons(_1,_2)) ->= 2nd❆1_cons(_1,_2)
10: 2nd(cons1(_1,_2)) ->= 2nd❆1_cons1(_1,_2)
Number of strict rules: 8
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #2nd❆1_cons(X,X1) -> #2nd❆1_cons1(X,activate(X1))
   #2: #2nd❆1_cons(X,X1) -> #activate(X1)
   #3: #activate(n__from(X)) -> #from(activate(X))
   #4: #activate(n__from(X)) -> #activate(X)
   #5: #2nd(cons(_1,_2)) ->? #2nd❆1_cons(_1,_2)
   #6: #activate(n__s(X)) -> #s(activate(X))
   #7: #activate(n__s(X)) -> #activate(X)
   #8: #2nd(cons1(_1,_2)) ->? #2nd❆1_cons1(_1,_2)
Number of SCCs: 1, DPs: 2, edges: 4
	SCC { #4 #7 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#2nd❆1_cons(x1,x2)	weight: 0
     s(x1)	weight: 0
activate(x1)	weight: 0
n__from(x1)	weight: (/ 1 2) + x1
#activate(x1)	weight: x1
   2nd(x1)	weight: 0
2nd❆1_cons(x1,x2)	weight: 0
  n__s(x1)	weight: (/ 1 2) + x1
 cons1(x1,x2)	weight: 0
  from(x1)	weight: 0
   #s(x1)	weight: 0
 #2nd(x1)	weight: 0
#from(x1)	weight: 0
  cons(x1,x2)	weight: 0
#2nd❆1_cons1(x1,x2)	weight: 0
2nd❆1_cons1(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #4 #7
Number of SCCs: 0, DPs: 0, edges: 0
YES