Certification Problem
Input (TPDB TRS_Standard/Rubio_04/bn122)
The rewrite relation of the following TRS is considered.
|
plus(plus(X,Y),Z) |
→ |
plus(X,plus(Y,Z)) |
(1) |
|
times(X,s(Y)) |
→ |
plus(X,times(Y,X)) |
(2) |
Property / Task
Prove or disprove termination.Answer / Result
Yes.Proof (by AProVE @ termCOMP 2023)
1 Rule Removal
Using the
linear polynomial interpretation over the naturals
| [plus(x1, x2)] |
= |
1 · x1 + 1 · x2
|
| [times(x1, x2)] |
= |
2 · x1 + 1 · x2
|
| [s(x1)] |
= |
2 + 2 · x1
|
all of the following rules can be deleted.
|
times(X,s(Y)) |
→ |
plus(X,times(Y,X)) |
(2) |
1.1 Rule Removal
Using the
Knuth Bendix order with w0 = 1 and the following precedence and weight functions
| prec(plus) |
= |
0 |
|
weight(plus) |
= |
0 |
|
|
|
all of the following rules can be deleted.
|
plus(plus(X,Y),Z) |
→ |
plus(X,plus(Y,Z)) |
(1) |
1.1.1 R is empty
There are no rules in the TRS. Hence, it is terminating.