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