Certification Problem
Input (TPDB TRS_Standard/Transformed_CSR_04/Ex25_Luc06_Z)
The rewrite relation of the following TRS is considered.
f(f(X)) |
→ |
c(n__f(g(n__f(X)))) |
(1) |
c(X) |
→ |
d(activate(X)) |
(2) |
h(X) |
→ |
c(n__d(X)) |
(3) |
f(X) |
→ |
n__f(X) |
(4) |
d(X) |
→ |
n__d(X) |
(5) |
activate(n__f(X)) |
→ |
f(X) |
(6) |
activate(n__d(X)) |
→ |
d(X) |
(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.
c#(X) |
→ |
activate#(X) |
(9) |
f#(f(X)) |
→ |
c#(n__f(g(n__f(X)))) |
(10) |
h#(X) |
→ |
c#(n__d(X)) |
(11) |
activate#(n__f(X)) |
→ |
f#(X) |
(12) |
c#(X) |
→ |
d#(activate(X)) |
(13) |
activate#(n__d(X)) |
→ |
d#(X) |
(14) |
1.1 Dependency Graph Processor
The dependency pairs are split into 1
component.