Termination Proof Script

Consider the TRS R consisting of the rewrite rules
1:    app(app(app(app(rec,t),u),v),0)  → t
2:    app(app(app(app(rec,t),u),v),app(s,x))  → app(app(u,x),app(app(app(app(rec,t),u),v),x))
3:    app(app(app(app(rec,t),u),v),app(lim,f))  → app(app(v,f),app(app(app(app(rectuv,t),u),v),app(f,n)))
4:    app(app(app(app(rectuv,t),u),v),n)  → app(app(app(app(rec,t),u),v),n)
There are 14 dependency pairs:
5:    APP(app(app(app(rec,t),u),v),app(s,x))  → APP(app(u,x),app(app(app(app(rec,t),u),v),x))
6:    APP(app(app(app(rec,t),u),v),app(s,x))  → APP(u,x)
7:    APP(app(app(app(rec,t),u),v),app(s,x))  → APP(app(app(app(rec,t),u),v),x)
8:    APP(app(app(app(rec,t),u),v),app(lim,f))  → APP(app(v,f),app(app(app(app(rectuv,t),u),v),app(f,n)))
9:    APP(app(app(app(rec,t),u),v),app(lim,f))  → APP(v,f)
10:    APP(app(app(app(rec,t),u),v),app(lim,f))  → APP(app(app(app(rectuv,t),u),v),app(f,n))
11:    APP(app(app(app(rec,t),u),v),app(lim,f))  → APP(app(app(rectuv,t),u),v)
12:    APP(app(app(app(rec,t),u),v),app(lim,f))  → APP(app(rectuv,t),u)
13:    APP(app(app(app(rec,t),u),v),app(lim,f))  → APP(rectuv,t)
14:    APP(app(app(app(rec,t),u),v),app(lim,f))  → APP(f,n)
15:    APP(app(app(app(rectuv,t),u),v),n)  → APP(app(app(app(rec,t),u),v),n)
16:    APP(app(app(app(rectuv,t),u),v),n)  → APP(app(app(rec,t),u),v)
17:    APP(app(app(app(rectuv,t),u),v),n)  → APP(app(rec,t),u)
18:    APP(app(app(app(rectuv,t),u),v),n)  → APP(rec,t)
The approximated dependency graph contains one SCC: {5-12,14-17}.
Tyrolean Termination Tool  (0.68 seconds)   ---  May 3, 2006