#2609 ⟨a, b | ababba=baba⟩
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- Properties
- Rewriting system
- Presentation has sum-of-sides 10
- Infinite non-cancellative non-commutative monoid
- Not right cancellative, because right multiplication by a is not injective:
-
abab2 ⋅ a = (ba)2 and bab ⋅ a = (ba)2, however abab2 ≠ bab
- Enveloping group: ⟨a, b | aaba-1b-1⟩
- Auxiliary generators:
- c = ba
- d = bcc
- Reduction order:
- Left-to-right recursive path with deg(c) = 0; deg(a) = deg(d) = deg(b) = 1, a < d < b
- Certificate: derivations of all rewriting rules from the defining relations.
- Morphocompletion: how the auxiliary generators were found.
# ab:ababba=baba c/adb ba=c,bcc=d morph:2/0,3/0
ccd=dc
bcc=d
ccbc=d
acd=ccc
acbc=cc
ba=c
bd=dbc
bcd=dcbc