#3254 ⟨a, b, c | bb=aa, acbc=1⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ b(cbc)²b = b and b ⋅ 1 = b, however b(cbc)²b ≠ 1
Not right cancellative, because right multiplication by b(cbc)² is not injective:
- b(cbc)²b ⋅ b(cbc)² = b(cbc)² and 1 ⋅ b(cbc)² = b(cbc)², however b(cbc)²b ≠ 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(c) = deg(b) = 0, c < b; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.

# abc:bb=aa,acbc=1 cb/a - -
bbbbcbc=bbcbcbb
bbcbccbc=1
bbcbcbbcbc=bb
a=bbcbc