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.