#1780 ⟨a, b, c | aab=cc, bba=1⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ bab = b and b ⋅ 1 = b, however bab ≠ 1
Not right cancellative, because right multiplication by ba is not injective:
- bab ⋅ ba = ba and 1 ⋅ ba = ba, however bab ≠ 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:
- Right-to-left recursive path with deg(b) = deg(a) = 0, b < a; deg(c) = 1
Certificate: derivations of all rewriting rules from the defining relations.

# abc:aab=cc,bba=1 reversed:ba/c - -
bba=1
caa=aabcba
bcbab=bc
cc=aab