YES
Termination Proof
Termination Proof
by ttt2 (version ttt2 1.15)
Input
The rewrite relation of the following TRS is considered.
|
1(0(x0)) |
→ |
0(0(0(1(x0)))) |
|
0(1(x0)) |
→ |
1(x0) |
|
1(1(x0)) |
→ |
0(0(0(0(x0)))) |
|
0(0(x0)) |
→ |
0(x0) |
Proof
1 Rule Removal
Using the
linear polynomial interpretation over the arctic semiring over the integers
| [1(x1)] |
= |
4 ·
x1 +
-∞
|
| [0(x1)] |
= |
0 ·
x1 +
-∞
|
the
rules
|
1(0(x0)) |
→ |
0(0(0(1(x0)))) |
|
0(1(x0)) |
→ |
1(x0) |
|
0(0(x0)) |
→ |
0(x0) |
remain.
1.1 Rule Removal
Using the
linear polynomial interpretation over the naturals
| [1(x1)] |
= |
4 ·
x1 + 0 |
| [0(x1)] |
= |
1 ·
x1 + 4 |
all rules could be removed.
1.1.1 R is empty
There are no rules in the TRS. Hence, it is terminating.