Certification Problem
Input (TPDB SRS_Standard/Zantema_04/z065)
The rewrite relation of the following TRS is considered.
|
0(*(x1)) |
→ |
*(1(x1)) |
(1) |
|
1(*(x1)) |
→ |
0(#(x1)) |
(2) |
|
#(0(x1)) |
→ |
0(#(x1)) |
(3) |
|
#(1(x1)) |
→ |
1(#(x1)) |
(4) |
|
#($(x1)) |
→ |
*($(x1)) |
(5) |
|
#(#(x1)) |
→ |
#(x1) |
(6) |
|
#(*(x1)) |
→ |
*(x1) |
(7) |
Property / Task
Prove or disprove termination.Answer / Result
Yes.Proof (by ttt2 @ termCOMP 2023)
1 Rule Removal
Using the
Knuth Bendix order with w0 = 1 and the following precedence and weight functions
| prec($) |
= |
7 |
|
weight($) |
= |
2 |
|
|
|
| prec(#) |
= |
3 |
|
weight(#) |
= |
5 |
|
|
|
| prec(1) |
= |
2 |
|
weight(1) |
= |
1 |
|
|
|
| prec(0) |
= |
1 |
|
weight(0) |
= |
1 |
|
|
|
| prec(*) |
= |
0 |
|
weight(*) |
= |
5 |
|
|
|
all of the following rules can be deleted.
|
0(*(x1)) |
→ |
*(1(x1)) |
(1) |
|
1(*(x1)) |
→ |
0(#(x1)) |
(2) |
|
#(0(x1)) |
→ |
0(#(x1)) |
(3) |
|
#(1(x1)) |
→ |
1(#(x1)) |
(4) |
|
#($(x1)) |
→ |
*($(x1)) |
(5) |
|
#(#(x1)) |
→ |
#(x1) |
(6) |
|
#(*(x1)) |
→ |
*(x1) |
(7) |
1.1 R is empty
There are no rules in the TRS. Hence, it is terminating.