Termination Proof Script

Consider the TRS R consisting of the rewrite rules
1:    del(x . (y . z))  → f(x = y,x,y,z)
2:    f(true,x,y,z)  → del(y . z)
3:    f(false,x,y,z)  → x . del(y . z)
4:    nil = nil  → true
5:    (x . y) = nil  → false
6:    nil = (y . z)  → false
7:    (x . y) = (u . v)  → and(x = u,y = v)
There are 6 dependency pairs:
8:    DEL(x . (y . z))  → F(x = y,x,y,z)
9:    DEL(x . (y . z))  → x =# y
10:    F(true,x,y,z)  → DEL(y . z)
11:    F(false,x,y,z)  → DEL(y . z)
12:    (x . y) =# (u . v)  → x =# u
13:    (x . y) =# (u . v)  → y =# v
The approximated dependency graph contains one SCC: {8,10,11}.
Tyrolean Termination Tool  (0.22 seconds)   ---  May 3, 2006