Certification Problem
Input (TPDB TRS_Standard/Transformed_CSR_04/PEANO_nosorts-noand_FR)
The rewrite relation of the following TRS is considered.
U11(tt,M,N) |
→ |
U12(tt,activate(M),activate(N)) |
(1) |
U12(tt,M,N) |
→ |
s(plus(activate(N),activate(M))) |
(2) |
plus(N,0) |
→ |
N |
(3) |
plus(N,s(M)) |
→ |
U11(tt,M,N) |
(4) |
activate(X) |
→ |
X |
(5) |
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.
U12#(tt,M,N) |
→ |
activate#(N) |
(6) |
U11#(tt,M,N) |
→ |
activate#(N) |
(7) |
plus#(N,s(M)) |
→ |
U11#(tt,M,N) |
(8) |
U11#(tt,M,N) |
→ |
activate#(M) |
(9) |
U12#(tt,M,N) |
→ |
activate#(M) |
(10) |
U12#(tt,M,N) |
→ |
plus#(activate(N),activate(M)) |
(11) |
U11#(tt,M,N) |
→ |
U12#(tt,activate(M),activate(N)) |
(12) |
1.1 Dependency Graph Processor
The dependency pairs are split into 1
component.