Certification Problem
Input (TPDB TRS_Standard/Strategy_removed_CSR_05/Ex4_Zan97)
The rewrite relation of the following TRS is considered.
|
f(X) |
→ |
cons(X,f(g(X))) |
(1) |
|
g(0) |
→ |
s(0) |
(2) |
|
g(s(X)) |
→ |
s(s(g(X))) |
(3) |
|
sel(0,cons(X,Y)) |
→ |
X |
(4) |
|
sel(s(X),cons(Y,Z)) |
→ |
sel(X,Z) |
(5) |
Property / Task
Prove or disprove termination.Answer / Result
No.Proof (by ttt2 @ termCOMP 2023)
1 Loop
The following loop proves nontermination.
| t0
|
= |
f(X) |
|
→
|
cons(X,f(g(X))) |
|
= |
t1
|
where t1 =
C[t0σ]
and
σ =
{X/g(X)}
and
C = cons(X,☐)