Certification Problem
Input (TPDB TRS_Standard/Strategy_removed_AG01/#4.20)
The rewrite relation of the following TRS is considered.
|
f(f(x)) |
→ |
f(x) |
(1) |
|
g(0) |
→ |
g(f(0)) |
(2) |
Property / Task
Prove or disprove termination.Answer / Result
Yes.Proof (by AProVE @ termCOMP 2023)
1 Constant to Unary
Every constant is turned into a unary function symbol to obtain the TRS
|
f(f(x)) |
→ |
f(x) |
(1) |
|
g(0'(x)) |
→ |
g(f(0'(x))) |
(3) |
1.1 String Reversal
Since only unary symbols occur, one can reverse all terms and obtains the TRS
|
f(f(x)) |
→ |
f(x) |
(1) |
|
0'(g(x)) |
→ |
0'(f(g(x))) |
(4) |
1.1.1 Dependency Pair Transformation
The following set of initial dependency pairs has been identified.
|
0'#(g(x)) |
→ |
0'#(f(g(x))) |
(5) |
|
0'#(g(x)) |
→ |
f#(g(x)) |
(6) |
1.1.1.1 Dependency Graph Processor
The dependency pairs are split into 0
components.