The rewrite relation of the following TRS is considered.
| a(x1) | → | x1 | (1) |
| a(b(x1)) | → | c(b(x1)) | (2) |
| b(x1) | → | a(a(c(x1))) | (3) |
| c(c(x1)) | → | b(x1) | (4) |
| a#(b(x1)) | → | c#(b(x1)) | (5) |
| b#(x1) | → | a#(a(c(x1))) | (6) |
| b#(x1) | → | a#(c(x1)) | (7) |
| b#(x1) | → | c#(x1) | (8) |
| c#(c(x1)) | → | b#(x1) | (9) |
| [a#(x1)] | = |
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| [b(x1)] | = |
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| [c#(x1)] | = |
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| [b#(x1)] | = |
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| [a(x1)] | = |
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| [c(x1)] | = |
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| a#(b(x1)) | → | c#(b(x1)) | (5) |
The dependency pairs are split into 1 component.
| b#(x1) | → | c#(x1) | (8) |
| c#(c(x1)) | → | b#(x1) | (9) |
| [c(x1)] | = | 1 · x1 |
| [c#(x1)] | = | 1 · x1 |
| [b#(x1)] | = | 1 · x1 |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
| c#(c(x1)) | → | b#(x1) | (9) |
| 1 | > | 1 | |
| b#(x1) | → | c#(x1) | (8) |
| 1 | ≥ | 1 |
As there is no critical graph in the transitive closure, there are no infinite chains.