Certification Problem
Input (TPDB TRS_Standard/Strategy_removed_AG01/#4.12a)
The rewrite relation of the following TRS is considered.
|
h(x,y) |
→ |
f(x,y,x) |
(1) |
|
f(0,1,x) |
→ |
h(x,x) |
(2) |
|
g(x,y) |
→ |
x |
(3) |
|
g(x,y) |
→ |
y |
(4) |
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.
|
h#(x,y) |
→ |
f#(x,y,x) |
(5) |
|
f#(0,1,x) |
→ |
h#(x,x) |
(6) |
It remains to prove infiniteness of the resulting DP problem.
1.1 Loop
The following loop proves infiniteness of the DP problem.
| t0
|
= |
f#(g(0,1),g(0,1),g(0,1)) |
|
→R
|
f#(g(0,1),1,g(0,1)) |
|
→R
|
f#(0,1,g(0,1)) |
|
→P
|
h#(g(0,1),g(0,1)) |
|
→P
|
f#(g(0,1),g(0,1),g(0,1)) |
|
= |
t4
|
where t4 =
t0