Certification Problem
Input (TPDB TRS_Standard/Transformed_CSR_04/Ex23_Luc06_FR)
The rewrite relation of the following TRS is considered.
|
f(f(a)) |
→ |
c(n__f(n__g(n__f(n__a)))) |
(1) |
|
f(X) |
→ |
n__f(X) |
(2) |
|
g(X) |
→ |
n__g(X) |
(3) |
| a |
→ |
n__a |
(4) |
|
activate(n__f(X)) |
→ |
f(activate(X)) |
(5) |
|
activate(n__g(X)) |
→ |
g(activate(X)) |
(6) |
|
activate(n__a) |
→ |
a |
(7) |
|
activate(X) |
→ |
X |
(8) |
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.
|
activate#(n__g(X)) |
→ |
activate#(X) |
(9) |
|
activate#(n__f(X)) |
→ |
activate#(X) |
(10) |
|
activate#(n__a) |
→ |
a# |
(11) |
|
activate#(n__g(X)) |
→ |
g#(activate(X)) |
(12) |
|
activate#(n__f(X)) |
→ |
f#(activate(X)) |
(13) |
1.1 Dependency Graph Processor
The dependency pairs are split into 1
component.