Termination Proof Script

Consider the TRS R consisting of the rewrite rules
1:    first(0,X)  → nil
2:    first(s(X),cons(Y,Z))  → cons(Y,n__first(X,activate(Z)))
3:    from(X)  → cons(X,n__from(n__s(X)))
4:    first(X1,X2)  → n__first(X1,X2)
5:    from(X)  → n__from(X)
6:    s(X)  → n__s(X)
7:    activate(n__first(X1,X2))  → first(activate(X1),activate(X2))
8:    activate(n__from(X))  → from(activate(X))
9:    activate(n__s(X))  → s(activate(X))
10:    activate(X)  → X
There are 8 dependency pairs:
11:    FIRST(s(X),cons(Y,Z))  → ACTIVATE(Z)
12:    ACTIVATE(n__first(X1,X2))  → FIRST(activate(X1),activate(X2))
13:    ACTIVATE(n__first(X1,X2))  → ACTIVATE(X1)
14:    ACTIVATE(n__first(X1,X2))  → ACTIVATE(X2)
15:    ACTIVATE(n__from(X))  → FROM(activate(X))
16:    ACTIVATE(n__from(X))  → ACTIVATE(X)
17:    ACTIVATE(n__s(X))  → S(activate(X))
18:    ACTIVATE(n__s(X))  → ACTIVATE(X)
The approximated dependency graph contains one SCC: {11-14,16,18}.
Tyrolean Termination Tool  (1.50 seconds)   ---  May 3, 2006