#7225 ⟨a, b, c | aa=1, bacb=bc⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element ab has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ adb = bd and b ⋅ d = bd, however adb ≠ d

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

# abc:aa=1,bacb=bc abd/c cb=d morph:2/1
aa=1
badb=bd
dadb=dd
cb=d
bc=bad
dc=dad