Termination Proof Script

Consider the TRS R consisting of the rewrite rules
1:    a__from(X)  → cons(mark(X),from(s(X)))
2:    a__length(nil)  → 0
3:    a__length(cons(X,Y))  → s(a__length1(Y))
4:    a__length1(X)  → a__length(X)
5:    mark(from(X))  → a__from(mark(X))
6:    mark(length(X))  → a__length(X)
7:    mark(length1(X))  → a__length1(X)
8:    mark(cons(X1,X2))  → cons(mark(X1),X2)
9:    mark(s(X))  → s(mark(X))
10:    mark(nil)  → nil
11:    mark(0)  → 0
12:    a__from(X)  → from(X)
13:    a__length(X)  → length(X)
14:    a__length1(X)  → length1(X)
There are 9 dependency pairs:
15:    A__FROM(X)  → MARK(X)
16:    A__LENGTH(cons(X,Y))  → A__LENGTH1(Y)
17:    A__LENGTH1(X)  → A__LENGTH(X)
18:    MARK(from(X))  → A__FROM(mark(X))
19:    MARK(from(X))  → MARK(X)
20:    MARK(length(X))  → A__LENGTH(X)
21:    MARK(length1(X))  → A__LENGTH1(X)
22:    MARK(cons(X1,X2))  → MARK(X1)
23:    MARK(s(X))  → MARK(X)
The approximated dependency graph contains 2 SCCs: {16,17} and {15,18,19,22,23}.
Tyrolean Termination Tool  (0.16 seconds)   ---  May 3, 2006