Certification Problem
Input (TPDB TRS_Standard/Transformed_CSR_04/Ex4_7_15_Bor03_FR)
The rewrite relation of the following TRS is considered.
f(0) |
→ |
cons(0,n__f(n__s(n__0))) |
(1) |
f(s(0)) |
→ |
f(p(s(0))) |
(2) |
p(s(0)) |
→ |
0 |
(3) |
f(X) |
→ |
n__f(X) |
(4) |
s(X) |
→ |
n__s(X) |
(5) |
0 |
→ |
n__0 |
(6) |
activate(n__f(X)) |
→ |
f(activate(X)) |
(7) |
activate(n__s(X)) |
→ |
s(activate(X)) |
(8) |
activate(n__0) |
→ |
0 |
(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.
f#(s(0)) |
→ |
p#(s(0)) |
(11) |
activate#(n__s(X)) |
→ |
s#(activate(X)) |
(12) |
activate#(n__s(X)) |
→ |
activate#(X) |
(13) |
activate#(n__f(X)) |
→ |
activate#(X) |
(14) |
activate#(n__0) |
→ |
0# |
(15) |
f#(s(0)) |
→ |
f#(p(s(0))) |
(16) |
activate#(n__f(X)) |
→ |
f#(activate(X)) |
(17) |
1.1 Dependency Graph Processor
The dependency pairs are split into 2
components.