Termination Proof Script

Consider the TRS R consisting of the rewrite rules
1:    a__first(0,X)  → nil
2:    a__first(s(X),cons(Y,Z))  → cons(mark(Y),first(X,Z))
3:    a__from(X)  → cons(mark(X),from(s(X)))
4:    mark(first(X1,X2))  → a__first(mark(X1),mark(X2))
5:    mark(from(X))  → a__from(mark(X))
6:    mark(0)  → 0
7:    mark(nil)  → nil
8:    mark(s(X))  → s(mark(X))
9:    mark(cons(X1,X2))  → cons(mark(X1),X2)
10:    a__first(X1,X2)  → first(X1,X2)
11:    a__from(X)  → from(X)
There are 9 dependency pairs:
12:    A__FIRST(s(X),cons(Y,Z))  → MARK(Y)
13:    A__FROM(X)  → MARK(X)
14:    MARK(first(X1,X2))  → A__FIRST(mark(X1),mark(X2))
15:    MARK(first(X1,X2))  → MARK(X1)
16:    MARK(first(X1,X2))  → MARK(X2)
17:    MARK(from(X))  → A__FROM(mark(X))
18:    MARK(from(X))  → MARK(X)
19:    MARK(s(X))  → MARK(X)
20:    MARK(cons(X1,X2))  → MARK(X1)
Consider the SCC {12-20}. The constraints could not be solved.
Tyrolean Termination Tool  (0.70 seconds)   ---  May 3, 2006