Certification Problem
Input (TPDB TRS_Standard/Strategy_removed_CSR_05/Ex24_GM04)
The rewrite relation of the following TRS is considered.
|
f(X,g(X),Y) |
→ |
f(Y,Y,Y) |
(1) |
|
g(b) |
→ |
c |
(2) |
| b |
→ |
c |
(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#(X,g(X),Y) |
→ |
f#(Y,Y,Y) |
(4) |
It remains to prove infiniteness of the resulting DP problem.
1.1 Instantiation Processor
The pairs are instantiated to the following pairs.
|
f#(x0,g(x0),g(y_1)) |
→ |
f#(g(y_1),g(y_1),g(y_1)) |
(5) |
1.1.1 Loop
The following loop proves infiniteness of the DP problem.
| t0
|
= |
f#(g(b),g(b),g(b)) |
|
→R
|
f#(g(b),g(c),g(b)) |
|
→R
|
f#(c,g(c),g(b)) |
|
→P
|
f#(g(b),g(b),g(b)) |
|
= |
t3
|
where t3 =
t0