YES
Termination Proof
Termination Proof
by ttt2 (version ttt2 1.15)
Input
The rewrite relation of the following TRS is considered.
|
a(x0) |
→ |
x0 |
|
a(b(x0)) |
→ |
b(a(c(x0))) |
|
b(x0) |
→ |
x0 |
|
c(c(x0)) |
→ |
b(a(x0)) |
Proof
1 String Reversal
Since only unary symbols occur, one can reverse all terms and obtains the TRS
|
a(x0) |
→ |
x0 |
|
b(a(x0)) |
→ |
c(a(b(x0))) |
|
b(x0) |
→ |
x0 |
|
c(c(x0)) |
→ |
a(b(x0)) |
1.1 Dependency Pair Transformation
The following set of initial dependency pairs has been identified.
|
b#(a(x0)) |
→ |
b#(x0) |
|
b#(a(x0)) |
→ |
a#(b(x0)) |
|
b#(a(x0)) |
→ |
c#(a(b(x0))) |
|
c#(c(x0)) |
→ |
b#(x0) |
|
c#(c(x0)) |
→ |
a#(b(x0)) |
1.1.1 Dependency Graph Processor
The dependency pairs are split into 1
component.