#2609 ⟨a, b | ababba=baba⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not right cancellative, because right multiplication by c is not injective:
- acb ⋅ c = c² and c ⋅ c = c², however acb ≠ c

Format:	Pretty Plain
Word:
	Enter a word above to compute its normal form. Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Strategy:	Leftmost Rightmost
Result:	1 1

Auxiliary generators:
1. c = ba
2. 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