Certification Problem
Input (TPDB TRS_Standard/Transformed_CSR_04/Ex1_Luc02b_Z)
The rewrite relation of the following TRS is considered.
from(X) |
→ |
cons(X,n__from(s(X))) |
(1) |
first(0,Z) |
→ |
nil |
(2) |
first(s(X),cons(Y,Z)) |
→ |
cons(Y,n__first(X,activate(Z))) |
(3) |
sel(0,cons(X,Z)) |
→ |
X |
(4) |
sel(s(X),cons(Y,Z)) |
→ |
sel(X,activate(Z)) |
(5) |
from(X) |
→ |
n__from(X) |
(6) |
first(X1,X2) |
→ |
n__first(X1,X2) |
(7) |
activate(n__from(X)) |
→ |
from(X) |
(8) |
activate(n__first(X1,X2)) |
→ |
first(X1,X2) |
(9) |
activate(X) |
→ |
X |
(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.
sel#(s(X),cons(Y,Z)) |
→ |
sel#(X,activate(Z)) |
(11) |
activate#(n__from(X)) |
→ |
from#(X) |
(12) |
sel#(s(X),cons(Y,Z)) |
→ |
activate#(Z) |
(13) |
activate#(n__first(X1,X2)) |
→ |
first#(X1,X2) |
(14) |
first#(s(X),cons(Y,Z)) |
→ |
activate#(Z) |
(15) |
1.1 Dependency Graph Processor
The dependency pairs are split into 2
components.