Certification Problem
Input (TPDB SRS_Standard/Zantema_04/z013)
The rewrite relation of the following TRS is considered.
|
g(c(x1)) |
→ |
g(f(c(x1))) |
(1) |
|
g(f(c(x1))) |
→ |
g(f(f(c(x1)))) |
(2) |
|
g(g(x1)) |
→ |
g(f(g(x1))) |
(3) |
|
f(f(g(x1))) |
→ |
g(f(x1)) |
(4) |
Property / Task
Prove or disprove termination.Answer / Result
Yes.Proof (by matchbox @ termCOMP 2023)
1 String Reversal
Since only unary symbols occur, one can reverse all terms and obtains the TRS
|
c(g(x1)) |
→ |
c(f(g(x1))) |
(5) |
|
c(f(g(x1))) |
→ |
c(f(f(g(x1)))) |
(6) |
|
g(g(x1)) |
→ |
g(f(g(x1))) |
(3) |
|
g(f(f(x1))) |
→ |
f(g(x1)) |
(7) |
1.1 Dependency Pair Transformation
The following set of initial dependency pairs has been identified.
|
g#(g(x1)) |
→ |
g#(f(g(x1))) |
(8) |
|
g#(f(f(x1))) |
→ |
g#(x1) |
(9) |
|
c#(g(x1)) |
→ |
c#(f(g(x1))) |
(10) |
|
c#(f(g(x1))) |
→ |
c#(f(f(g(x1)))) |
(11) |
1.1.1 Dependency Graph Processor
The dependency pairs are split into 1
component.