Certification Problem
Input (TPDB TRS_Standard/Transformed_CSR_04/Ex1_Zan97_GM)
The rewrite relation of the following TRS is considered.
|
a__g(X) |
→ |
a__h(X) |
(1) |
| a__c |
→ |
d |
(2) |
|
a__h(d) |
→ |
a__g(c) |
(3) |
|
mark(g(X)) |
→ |
a__g(X) |
(4) |
|
mark(h(X)) |
→ |
a__h(X) |
(5) |
|
mark(c) |
→ |
a__c |
(6) |
|
mark(d) |
→ |
d |
(7) |
|
a__g(X) |
→ |
g(X) |
(8) |
|
a__h(X) |
→ |
h(X) |
(9) |
| a__c |
→ |
c |
(10) |
Property / Task
Prove or disprove termination.Answer / Result
Yes.Proof (by NaTT @ termCOMP 2023)
1 Dependency Pair Transformation
The following set of initial dependency pairs has been identified.
|
mark#(h(X)) |
→ |
a__h#(X) |
(11) |
|
mark#(g(X)) |
→ |
a__g#(X) |
(12) |
|
a__h#(d) |
→ |
a__g#(c) |
(13) |
|
mark#(c) |
→ |
a__c# |
(14) |
|
a__g#(X) |
→ |
a__h#(X) |
(15) |
1.1 Dependency Graph Processor
The dependency pairs are split into 1
component.