YES
Termination Proof
Termination Proof
by ttt2 (version ttt2 1.15)
Input
The rewrite relation of the following TRS is considered.
|
0(x0) |
→ |
1(x0) |
|
4(5(4(5(x0)))) |
→ |
4(4(5(5(x0)))) |
|
5(5(5(5(5(5(4(4(4(4(4(4(x0)))))))))))) |
→ |
2(x0) |
Proof
1 Rule Removal
Using the
linear polynomial interpretation over the arctic semiring over the integers
| [2(x1)] |
= |
0 ·
x1 +
-∞
|
| [1(x1)] |
= |
0 ·
x1 +
-∞
|
| [4(x1)] |
= |
2 ·
x1 +
-∞
|
| [0(x1)] |
= |
2 ·
x1 +
-∞
|
| [5(x1)] |
= |
3 ·
x1 +
-∞
|
the
rule
|
4(5(4(5(x0)))) |
→ |
4(4(5(5(x0)))) |
remains.
1.1 Rule Removal
Using the
Knuth Bendix order with w0 = 1 and the following precedence and weight function
| prec(4) |
= |
0 |
|
weight(4) |
= |
1 |
|
|
|
| prec(5) |
= |
1 |
|
weight(5) |
= |
1 |
|
|
|
all rules could be removed.
1.1.1 R is empty
There are no rules in the TRS. Hence, it is terminating.