Certification Problem
Input (TPDB SRS_Standard/Mixed_SRS/07-oppelt08)
The rewrite relation of the following TRS is considered.
|
R(b(x1)) |
→ |
b(R(x1)) |
(1) |
|
R(c(x1)) |
→ |
L(c(x1)) |
(2) |
|
b(L(x1)) |
→ |
L(b(x1)) |
(3) |
|
a(L(x1)) |
→ |
a(b(R(x1))) |
(4) |
Property / Task
Prove or disprove termination.Answer / Result
No.Proof (by AProVE @ termCOMP 2023)
1 Infinite derivation
There is a self-embedding derivation structure which implies nontermination.
a
(b)n L c →+ a
(b)n + 1 L c
The derivation can be derived as follows.
-
b L →+ L b:
This is an original rule (OC1).
-
(b)n L →+ L
(b)n:
The derivation pattern is obtained from the following self-overlapping overlap closure (type 1)
-
a L →+ a b R:
This is an original rule (OC1).
-
a
(b)n L →+ a b R
(b)n:
The derivation pattern is obtained from overlapping the following two derivation patterns (DP OC 1.2)
-
(b)n L →+ L
(b)n
-
a L →+ a b R
-
R b →+ b R:
This is an original rule (OC1).
-
R
(b)n →+
(b)n R:
The derivation pattern is obtained from the following self-overlapping overlap closure (type 2)
-
a
(b)n L →+ a b
(b)n R:
The derivation pattern is obtained from overlapping the following two derivation patterns (DP DP 1.2)
-
a
(b)n L →+ a b R
(b)n
-
R
(b)n →+
(b)n R
-
a
(b)n L →+ a
(b)n + 1 R:
The derivation pattern is equivalent to the following derivation pattern.
-
R c →+ L c:
This is an original rule (OC1).
-
a
(b)n L c →+ a
(b)n + 1 L c:
The derivation pattern is obtained from overlapping the following two derivation patterns (DP OC 3.2)
-
a
(b)n L →+ a
(b)n + 1 R
-
R c →+ L c