Termination Proof Script

Consider the TRS R consisting of the rewrite rules
1:    circ(cons(a,s),t)  → cons(msubst(a,t),circ(s,t))
2:    circ(cons(lift,s),cons(a,t))  → cons(a,circ(s,t))
3:    circ(cons(lift,s),cons(lift,t))  → cons(lift,circ(s,t))
4:    circ(circ(s,t),u)  → circ(s,circ(t,u))
5:    circ(s,id)  → s
6:    circ(id,s)  → s
7:    circ(cons(lift,s),circ(cons(lift,t),u))  → circ(cons(lift,circ(s,t)),u)
8:    subst(a,id)  → a
9:    msubst(a,id)  → a
10:    msubst(msubst(a,s),t)  → msubst(a,circ(s,t))
There are 10 dependency pairs:
11:    CIRC(cons(a,s),t)  → MSUBST(a,t)
12:    CIRC(cons(a,s),t)  → CIRC(s,t)
13:    CIRC(cons(lift,s),cons(a,t))  → CIRC(s,t)
14:    CIRC(cons(lift,s),cons(lift,t))  → CIRC(s,t)
15:    CIRC(circ(s,t),u)  → CIRC(s,circ(t,u))
16:    CIRC(circ(s,t),u)  → CIRC(t,u)
17:    CIRC(cons(lift,s),circ(cons(lift,t),u))  → CIRC(cons(lift,circ(s,t)),u)
18:    CIRC(cons(lift,s),circ(cons(lift,t),u))  → CIRC(s,t)
19:    MSUBST(msubst(a,s),t)  → MSUBST(a,circ(s,t))
20:    MSUBST(msubst(a,s),t)  → CIRC(s,t)
The approximated dependency graph contains one SCC: {11-20}.
Tyrolean Termination Tool  (0.08 seconds)   ---  May 3, 2006