⟨a, b, c | aba=b, acb=1⟩

Up:

Sum of relation sides is 7

Infinite non-cancellative non-commutative monoid

Element a has infinite order

Not left cancellative, because left multiplication by c is not injective:

Not right cancellative, because right multiplication by b is not injective:

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

# abc:aba=b,acb=1 b/dac ab=d morph:2/0 bbd=dbb ab=d bba=db cbb=ba bcb=d dd=bb da=b ad=dcb acb=1 cdb=baa cbd=b bcd=dcb cba=1 acd=cb

#358 ⟨a, b, c | aba=b, acb=1⟩