Termination Proof Script

Consider the TRS R consisting of the rewrite rules
1:    sortSu(circ(sortSu(cons(te(a),sortSu(s))),sortSu(t)))  → sortSu(cons(te(msubst(te(a),sortSu(t))),sortSu(circ(sortSu(s),sortSu(t)))))
2:    sortSu(circ(sortSu(cons(sop(lift),sortSu(s))),sortSu(cons(te(a),sortSu(t)))))  → sortSu(cons(te(a),sortSu(circ(sortSu(s),sortSu(t)))))
3:    sortSu(circ(sortSu(cons(sop(lift),sortSu(s))),sortSu(cons(sop(lift),sortSu(t)))))  → sortSu(cons(sop(lift),sortSu(circ(sortSu(s),sortSu(t)))))
4:    sortSu(circ(sortSu(circ(sortSu(s),sortSu(t))),sortSu(u)))  → sortSu(circ(sortSu(s),sortSu(circ(sortSu(t),sortSu(u)))))
5:    sortSu(circ(sortSu(s),sortSu(id)))  → sortSu(s)
6:    sortSu(circ(sortSu(id),sortSu(s)))  → sortSu(s)
7:    sortSu(circ(sortSu(cons(sop(lift),sortSu(s))),sortSu(circ(sortSu(cons(sop(lift),sortSu(t))),sortSu(u)))))  → sortSu(circ(sortSu(cons(sop(lift),sortSu(circ(sortSu(s),sortSu(t))))),sortSu(u)))
8:    te(subst(te(a),sortSu(id)))  → te(a)
9:    te(msubst(te(a),sortSu(id)))  → te(a)
10:    te(msubst(te(msubst(te(a),sortSu(s))),sortSu(t)))  → te(msubst(te(a),sortSu(circ(sortSu(s),sortSu(t)))))
There are 14 dependency pairs:
11:    SORTSU(circ(sortSu(cons(te(a),sortSu(s))),sortSu(t)))  → SORTSU(cons(te(msubst(te(a),sortSu(t))),sortSu(circ(sortSu(s),sortSu(t)))))
12:    SORTSU(circ(sortSu(cons(te(a),sortSu(s))),sortSu(t)))  → TE(msubst(te(a),sortSu(t)))
13:    SORTSU(circ(sortSu(cons(te(a),sortSu(s))),sortSu(t)))  → SORTSU(circ(sortSu(s),sortSu(t)))
14:    SORTSU(circ(sortSu(cons(sop(lift),sortSu(s))),sortSu(cons(te(a),sortSu(t)))))  → SORTSU(cons(te(a),sortSu(circ(sortSu(s),sortSu(t)))))
15:    SORTSU(circ(sortSu(cons(sop(lift),sortSu(s))),sortSu(cons(te(a),sortSu(t)))))  → SORTSU(circ(sortSu(s),sortSu(t)))
16:    SORTSU(circ(sortSu(cons(sop(lift),sortSu(s))),sortSu(cons(sop(lift),sortSu(t)))))  → SORTSU(cons(sop(lift),sortSu(circ(sortSu(s),sortSu(t)))))
17:    SORTSU(circ(sortSu(cons(sop(lift),sortSu(s))),sortSu(cons(sop(lift),sortSu(t)))))  → SORTSU(circ(sortSu(s),sortSu(t)))
18:    SORTSU(circ(sortSu(circ(sortSu(s),sortSu(t))),sortSu(u)))  → SORTSU(circ(sortSu(s),sortSu(circ(sortSu(t),sortSu(u)))))
19:    SORTSU(circ(sortSu(circ(sortSu(s),sortSu(t))),sortSu(u)))  → SORTSU(circ(sortSu(t),sortSu(u)))
20:    SORTSU(circ(sortSu(cons(sop(lift),sortSu(s))),sortSu(circ(sortSu(cons(sop(lift),sortSu(t))),sortSu(u)))))  → SORTSU(circ(sortSu(cons(sop(lift),sortSu(circ(sortSu(s),sortSu(t))))),sortSu(u)))
21:    SORTSU(circ(sortSu(cons(sop(lift),sortSu(s))),sortSu(circ(sortSu(cons(sop(lift),sortSu(t))),sortSu(u)))))  → SORTSU(cons(sop(lift),sortSu(circ(sortSu(s),sortSu(t)))))
22:    SORTSU(circ(sortSu(cons(sop(lift),sortSu(s))),sortSu(circ(sortSu(cons(sop(lift),sortSu(t))),sortSu(u)))))  → SORTSU(circ(sortSu(s),sortSu(t)))
23:    TE(msubst(te(msubst(te(a),sortSu(s))),sortSu(t)))  → TE(msubst(te(a),sortSu(circ(sortSu(s),sortSu(t)))))
24:    TE(msubst(te(msubst(te(a),sortSu(s))),sortSu(t)))  → SORTSU(circ(sortSu(s),sortSu(t)))
The approximated dependency graph contains one SCC: {12,13,15,17-20,22-24}.
Tyrolean Termination Tool  (9.42 seconds)   ---  May 3, 2006