Certification Problem
Input (TPDB TRS_Standard/Transformed_CSR_04/Ex2_Luc03b_Z)
The rewrite relation of the following TRS is considered.
fst(0,Z) |
→ |
nil |
(1) |
fst(s(X),cons(Y,Z)) |
→ |
cons(Y,n__fst(activate(X),activate(Z))) |
(2) |
from(X) |
→ |
cons(X,n__from(s(X))) |
(3) |
add(0,X) |
→ |
X |
(4) |
add(s(X),Y) |
→ |
s(n__add(activate(X),Y)) |
(5) |
len(nil) |
→ |
0 |
(6) |
len(cons(X,Z)) |
→ |
s(n__len(activate(Z))) |
(7) |
fst(X1,X2) |
→ |
n__fst(X1,X2) |
(8) |
from(X) |
→ |
n__from(X) |
(9) |
add(X1,X2) |
→ |
n__add(X1,X2) |
(10) |
len(X) |
→ |
n__len(X) |
(11) |
activate(n__fst(X1,X2)) |
→ |
fst(X1,X2) |
(12) |
activate(n__from(X)) |
→ |
from(X) |
(13) |
activate(n__add(X1,X2)) |
→ |
add(X1,X2) |
(14) |
activate(n__len(X)) |
→ |
len(X) |
(15) |
activate(X) |
→ |
X |
(16) |
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.
fst#(s(X),cons(Y,Z)) |
→ |
activate#(Z) |
(17) |
len#(cons(X,Z)) |
→ |
activate#(Z) |
(18) |
add#(s(X),Y) |
→ |
activate#(X) |
(19) |
activate#(n__add(X1,X2)) |
→ |
add#(X1,X2) |
(20) |
activate#(n__from(X)) |
→ |
from#(X) |
(21) |
fst#(s(X),cons(Y,Z)) |
→ |
activate#(X) |
(22) |
activate#(n__len(X)) |
→ |
len#(X) |
(23) |
activate#(n__fst(X1,X2)) |
→ |
fst#(X1,X2) |
(24) |
1.1 Dependency Graph Processor
The dependency pairs are split into 1
component.