Certification Problem
Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-541)
The rewrite relation of the following TRS is considered.
|
a(b(x1)) |
→ |
x1 |
(1) |
|
a(b(x1)) |
→ |
b(c(x1)) |
(2) |
|
a(c(x1)) |
→ |
c(b(a(a(x1)))) |
(3) |
Property / Task
Prove or disprove termination.Answer / Result
Yes.Proof (by AProVE @ termCOMP 2023)
1 Dependency Pair Transformation
The following set of initial dependency pairs has been identified.
|
a#(c(x1)) |
→ |
a#(a(x1)) |
(4) |
|
a#(c(x1)) |
→ |
a#(x1) |
(5) |
1.1 Reduction Pair Processor
Using the linear polynomial interpretation over the naturals
| [a#(x1)] |
= |
x1 |
| [a(x1)] |
= |
2 + x1
|
| [b(x1)] |
= |
-2 + x1
|
| [c(x1)] |
= |
2 + x1
|
the
pair
could be deleted.
1.1.1 Reduction Pair Processor
Using the linear polynomial interpretation over the rationals with delta = 16
| [a#(x1)] |
= |
0 + 4 · x1
|
| [c(x1)] |
= |
4 + 2 · x1
|
| [a(x1)] |
= |
0 + 2 · x1
|
| [b(x1)] |
= |
2 + 1/2 · x1
|
the
pair
|
a#(c(x1)) |
→ |
a#(a(x1)) |
(4) |
could be deleted.
1.1.1.1 P is empty
There are no pairs anymore.