#6169 ⟨a, b, c | aa=1, abbcbc=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(cb)²)² = b and b ⋅ 1 = b, however (b(cb)²)² ≠ 1
Not right cancellative, because right multiplication by bc(bcb)²c is not injective:
- (b(cb)²)² ⋅ bc(bcb)²c = bc(bcb)²c and 1 ⋅ bc(bcb)²c = bc(bcb)²c, however (b(cb)²)² ≠ 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.

#	Rule	Proof
1.	(b(bc)²)² ⇒ 1	[4]
2.	a ⇒ b(bc)²	[3]

# abc:aa=1,abbcbc=1 bc/a - -
bbcbcbbcbc=1
a=bbcbc

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

1 total

Σ	#	Presentation	Mapping
8	6760	⟨a, b, c \| aa=1, bbcbc=a⟩	φ(a) = bbcbc, φ(b) = b, φ(c) = c