#3243 ⟨a, b, c | bb=aa, aaac=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(b²c)²b = b and b ⋅ 1 = b, however b(b²c)²b ≠ 1
Not right cancellative, because right multiplication by b(b²c)² is not injective:
- b(b²c)²b ⋅ b(b²c)² = b(b²c)² and 1 ⋅ b(b²c)² = b(b²c)², however b(b²c)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,aaac=1 cb/a - -
bbbbbbc=bbbbcbb
bbbbcbbc=1
bbbbcbbbbc=bb
a=bbbbc

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

2 total

Σ	#	Presentation	Mapping
8	3244	⟨a, b, c \| bb=aa, aabc=1⟩	φ(a) = b, φ(b) = bbbbc, φ(c) = c
8	3249	⟨a, b, c \| bb=aa, abbc=1⟩	φ(a) = bbbbc, φ(b) = b, φ(c) = c