Certification Problem
Input (TPDB TRS_Standard/Strategy_removed_mixed_05/bn111)
The rewrite relation of the following TRS is considered.
|
f(f(X,Y),Z) |
→ |
f(X,f(Y,Z)) |
(1) |
|
f(X,f(Y,Z)) |
→ |
f(Y,Y) |
(2) |
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.
|
f#(f(X,Y),Z) |
→ |
f#(X,f(Y,Z)) |
(3) |
|
f#(f(X,Y),Z) |
→ |
f#(Y,Z) |
(4) |
|
f#(X,f(Y,Z)) |
→ |
f#(Y,Y) |
(5) |
1.1 Reduction Pair Processor
Using the non-linear polynomial interpretation over the naturals
| [f#(x1, x2)] |
= |
2 · x2 + 1 · x1 · x2 + 2 · x1 · x1
|
| [f(x1, x2)] |
= |
2 + 2 · x1 + 2 · x2 + 1 · x1 · x2 + 2 · x1 · x1
|
the
pairs
|
f#(f(X,Y),Z) |
→ |
f#(X,f(Y,Z)) |
(3) |
|
f#(f(X,Y),Z) |
→ |
f#(Y,Z) |
(4) |
|
f#(X,f(Y,Z)) |
→ |
f#(Y,Y) |
(5) |
could be deleted.
1.1.1 P is empty
There are no pairs anymore.