Certification Problem
Input (TPDB TRS_Standard/Transformed_CSR_04/Ex4_Zan97_Z)
The rewrite relation of the following TRS is considered.
f(X) |
→ |
cons(X,n__f(g(X))) |
(1) |
g(0) |
→ |
s(0) |
(2) |
g(s(X)) |
→ |
s(s(g(X))) |
(3) |
sel(0,cons(X,Y)) |
→ |
X |
(4) |
sel(s(X),cons(Y,Z)) |
→ |
sel(X,activate(Z)) |
(5) |
f(X) |
→ |
n__f(X) |
(6) |
activate(n__f(X)) |
→ |
f(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.
sel#(s(X),cons(Y,Z)) |
→ |
sel#(X,activate(Z)) |
(9) |
f#(X) |
→ |
g#(X) |
(10) |
sel#(s(X),cons(Y,Z)) |
→ |
activate#(Z) |
(11) |
activate#(n__f(X)) |
→ |
f#(X) |
(12) |
g#(s(X)) |
→ |
g#(X) |
(13) |
1.1 Dependency Graph Processor
The dependency pairs are split into 2
components.