Certification Problem
Input (TPDB TRS_Standard/HirokawaMiddeldorp_04/n007)
The rewrite relation of the following TRS is considered.
|
f(x,y) |
→ |
f(x,x) |
(1) |
|
f(s(x),y) |
→ |
f(y,x) |
(2) |
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,y) |
→ |
f#(x,x) |
(3) |
|
f#(s(x),y) |
→ |
f#(y,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#(x,y) |
|
→P
|
f#(x,x) |
|
= |
t1
|
where t1 =
t0σ
and
σ =
{x/x, y/x}