Certification Problem
Input (TPDB TRS_Standard/Strategy_removed_CSR_05/Ex1_GM99)
The rewrite relation of the following TRS is considered.
|
f(a,b,X) |
→ |
f(X,X,X) |
(1) |
| c |
→ |
a |
(2) |
| c |
→ |
b |
(3) |
Property / Task
Prove or disprove termination.Answer / Result
No.Proof (by AProVE @ termCOMP 2023)
1 Dependency Pair Transformation
The following set of initial dependency pairs has been identified.
|
f#(a,b,X) |
→ |
f#(X,X,X) |
(4) |
It remains to prove infiniteness of the resulting DP problem.
1.1 Loop
The following loop proves infiniteness of the DP problem.
| t0
|
= |
f#(c,c,c) |
|
→R
|
f#(c,b,c) |
|
→R
|
f#(a,b,c) |
|
→P
|
f#(c,c,c) |
|
= |
t3
|
where t3 =
t0