Certification Problem
Input (TPDB TRS_Standard/AProVE_04/forward_instantiation2)
The rewrite relation of the following TRS is considered.
|
f(x,y,z) |
→ |
g(x,y,z) |
(1) |
|
g(0,1,x) |
→ |
f(x,x,x) |
(2) |
| a |
→ |
b |
(3) |
| a |
→ |
c |
(4) |
Property / Task
Prove or disprove termination.Answer / Result
Yes.Proof (by AProVE @ termCOMP 2023)
1 Dependency Pair Transformation
The following set of initial dependency pairs has been identified.
|
f#(x,y,z) |
→ |
g#(x,y,z) |
(5) |
|
g#(0,1,x) |
→ |
f#(x,x,x) |
(6) |
1.1 Forward Instantiation Processor
We instantiate the pair
to the following set of pairs
|
f#(0,1,x2) |
→ |
g#(0,1,x2) |
(7) |
1.1.1 Dependency Graph Processor
The dependency pairs are split into 0
components.