Certification Problem
Input (TPDB TRS_Standard/Strategy_removed_CSR_05/Ex8_BLR02)
The rewrite relation of the following TRS is considered.
|
fib(N) |
→ |
sel(N,fib1(s(0),s(0))) |
(1) |
|
fib1(X,Y) |
→ |
cons(X,fib1(Y,add(X,Y))) |
(2) |
|
add(0,X) |
→ |
X |
(3) |
|
add(s(X),Y) |
→ |
s(add(X,Y)) |
(4) |
|
sel(0,cons(X,XS)) |
→ |
X |
(5) |
|
sel(s(N),cons(X,XS)) |
→ |
sel(N,XS) |
(6) |
Property / Task
Prove or disprove termination.Answer / Result
No.Proof (by ttt2 @ termCOMP 2023)
1 Loop
The following loop proves nontermination.
| t0
|
= |
fib1(X,Y) |
|
→
|
cons(X,fib1(Y,add(X,Y))) |
|
= |
t1
|
where t1 =
C[t0σ]
and
σ =
{Y/add(X,Y), X/Y}
and
C = cons(X,☐)