#1925 ⟨a, b | aaabbbaa=ba⟩

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 a is not injective:
- a³b³a ⋅ a = ba and b ⋅ a = ba, however a³b³a ≠ b

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 = bbba
Reduction order:
- Right-to-left recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

# ab:aaabbbaa=ba reversed:ac/b bbba=c morph:4/0
aaacc=caaca
aaacaaacaaaca=c
ba=aaaca
bc=caaca