#3486 ⟨a, b, c | bb=aa, aca=a⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element ba has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ ca = a and a ⋅ 1 = a, however ca ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- ac ⋅ a = a and 1 ⋅ a = a, however ac ≠ 1

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

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

# abc:bb=aa,aca=a bc/a - -
bbcbbbb=bbbbcbb
bbcbbcbb=bbbb
abb=bbcbb
acbb=bb
bba=bbcbb
bbca=bb
aa=bb
aca=a