Termination Proof Script

Consider the TRS R consisting of the rewrite rules
1:    app(not,app(not,x))  → x
2:    app(not,app(app(or,x),y))  → app(app(and,app(not,x)),app(not,y))
3:    app(not,app(app(and,x),y))  → app(app(or,app(not,x)),app(not,y))
4:    app(app(and,x),app(app(or,y),z))  → app(app(or,app(app(and,x),y)),app(app(and,x),z))
5:    app(app(and,app(app(or,y),z)),x)  → app(app(or,app(app(and,x),y)),app(app(and,x),z))
There are 17 dependency pairs:
6:    APP(not,app(app(or,x),y))  → APP(app(and,app(not,x)),app(not,y))
7:    APP(not,app(app(or,x),y))  → APP(and,app(not,x))
8:    APP(not,app(app(or,x),y))  → APP(not,x)
9:    APP(not,app(app(or,x),y))  → APP(not,y)
10:    APP(not,app(app(and,x),y))  → APP(app(or,app(not,x)),app(not,y))
11:    APP(not,app(app(and,x),y))  → APP(or,app(not,x))
12:    APP(not,app(app(and,x),y))  → APP(not,x)
13:    APP(not,app(app(and,x),y))  → APP(not,y)
14:    APP(app(and,x),app(app(or,y),z))  → APP(app(or,app(app(and,x),y)),app(app(and,x),z))
15:    APP(app(and,x),app(app(or,y),z))  → APP(or,app(app(and,x),y))
16:    APP(app(and,x),app(app(or,y),z))  → APP(app(and,x),y)
17:    APP(app(and,x),app(app(or,y),z))  → APP(app(and,x),z)
18:    APP(app(and,app(app(or,y),z)),x)  → APP(app(or,app(app(and,x),y)),app(app(and,x),z))
19:    APP(app(and,app(app(or,y),z)),x)  → APP(or,app(app(and,x),y))
20:    APP(app(and,app(app(or,y),z)),x)  → APP(app(and,x),y)
21:    APP(app(and,app(app(or,y),z)),x)  → APP(app(and,x),z)
22:    APP(app(and,app(app(or,y),z)),x)  → APP(and,x)
The approximated dependency graph contains one SCC: {6,8-10,12-14,16-18,20,21}.
Tyrolean Termination Tool  (0.13 seconds)   ---  May 3, 2006