#2057 ⟨a, b | abababba=ab⟩
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- Properties
- Rewriting system
- Presentation has sum-of-sides 10
- Infinite non-cancellative non-commutative monoid
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ (ba)2b2a = ab and a ⋅ b = ab, however (ba)2b2a ≠ b
- Enveloping group: ⟨a, b | aabab-1⟩
- Auxiliary generators:
- c = ab
- d = cb
- Reduction order:
- Right-to-left recursive path with deg(a) = deg(c) = 0, a < c; deg(d) = deg(b) = 1, d < b
- Certificate: derivations of all rewriting rules from the defining relations.
- Morphocompletion: how the auxiliary generators were found.
# ab:abababba=ab reversed:ac/db ab=c,cb=d morph:2/0,2/0
ccda=c
ccdc=d
ab=c
cb=d
dda=ccd
dcda=d
ddc=ccccdd
dcdc=ccdd
db=ccdd