#7280 ⟨a, b, c | ab=1, aaaa=cb⟩

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 c is not injective:
- c ⋅ b⁵c = c and c ⋅ 1 = c, however b⁵c ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- cb²c ⋅ b = cbcb² and (cb)² ⋅ b = cbcb², however cb²c ≠ (cb)²

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:ab=1,aaaa=cb cb/a - -
cbbcb=cbcbb
cbbbcb=cbcbbb
cbbbbb=1
cbbbbcb=cbcbbbb
a=cbbbb