Termination Proof Script

Consider the TRS R consisting of the rewrite rules
1:    from(X)  → cons(X,n__from(s(X)))
2:    length(n__nil)  → 0
3:    length(n__cons(X,Y))  → s(length1(activate(Y)))
4:    length1(X)  → length(activate(X))
5:    from(X)  → n__from(X)
6:    nil  → n__nil
7:    cons(X1,X2)  → n__cons(X1,X2)
8:    activate(n__from(X))  → from(X)
9:    activate(n__nil)  → nil
10:    activate(n__cons(X1,X2))  → cons(X1,X2)
11:    activate(X)  → X
There are 8 dependency pairs:
12:    FROM(X)  → CONS(X,n__from(s(X)))
13:    LENGTH(n__cons(X,Y))  → LENGTH1(activate(Y))
14:    LENGTH(n__cons(X,Y))  → ACTIVATE(Y)
15:    LENGTH1(X)  → LENGTH(activate(X))
16:    LENGTH1(X)  → ACTIVATE(X)
17:    ACTIVATE(n__from(X))  → FROM(X)
18:    ACTIVATE(n__nil)  → NIL
19:    ACTIVATE(n__cons(X1,X2))  → CONS(X1,X2)
The approximated dependency graph contains one SCC: {13,15}.
Tyrolean Termination Tool  (0.09 seconds)   ---  May 3, 2006