Certification Problem
Input (TPDB TRS_Innermost/AG01_innermost/#4.21)
The rewrite relation of the following TRS is considered.
|
f(1) |
→ |
f(g(1)) |
(1) |
|
f(f(x)) |
→ |
f(x) |
(2) |
|
g(0) |
→ |
g(f(0)) |
(3) |
|
g(g(x)) |
→ |
g(x) |
(4) |
The evaluation strategy is innermost.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#(1) |
→ |
f#(g(1)) |
(5) |
|
f#(1) |
→ |
g#(1) |
(6) |
|
g#(0) |
→ |
g#(f(0)) |
(7) |
|
g#(0) |
→ |
f#(0) |
(8) |
1.1 Dependency Graph Processor
The dependency pairs are split into 0
components.