The rewrite relation of the following TRS is considered.
a(x1) | → | x1 | (1) |
a(a(b(x1))) | → | c(a(b(b(a(a(x1)))))) | (2) |
b(c(x1)) | → | x1 | (3) |
a#(a(b(x1))) | → | a#(x1) | (4) |
a#(a(b(x1))) | → | a#(a(x1)) | (5) |
a#(a(b(x1))) | → | b#(a(a(x1))) | (6) |
a#(a(b(x1))) | → | b#(b(a(a(x1)))) | (7) |
a#(a(b(x1))) | → | a#(b(b(a(a(x1))))) | (8) |
The dependency pairs are split into 1 component.
a#(a(b(x1))) | → | a#(b(b(a(a(x1))))) | (8) |
a#(a(b(x1))) | → | a#(x1) | (4) |
a#(a(b(x1))) | → | a#(a(x1)) | (5) |
[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) | → | x1 | (1) |
a(a(b(x1))) | → | c(a(b(b(a(a(x1)))))) | (2) |
b(c(x1)) | → | x1 | (3) |
a#(a(b(x1))) | → | a#(b(b(a(a(x1))))) | (8) |
[b(x1)] | = | 0 · x1 + 2 |
[a#(x1)] | = | 0 · x1 + -∞ |
[a(x1)] | = | 1 · x1 + 0 |
[c(x1)] | = | -∞ · x1 + 2 |
a(x1) | → | x1 | (1) |
a(a(b(x1))) | → | c(a(b(b(a(a(x1)))))) | (2) |
a#(a(b(x1))) | → | a#(x1) | (4) |
[b(x1)] | = | 1 · x1 + 5 |
[a#(x1)] | = | 0 · x1 + 0 |
[a(x1)] | = | 0 · x1 + 4 |
[c(x1)] | = | -∞ · x1 + 1 |
a(x1) | → | x1 | (1) |
a(a(b(x1))) | → | c(a(b(b(a(a(x1)))))) | (2) |
a#(a(b(x1))) | → | a#(a(x1)) | (5) |
There are no pairs anymore.