#1080 ⟨a, b, c | aa=1, abbcc=1⟩

Properties

Sum of relation sides is 7
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ (bc²b)² = b and b ⋅ 1 = b, however (bc²b)² ≠ 1
Not right cancellative, because right multiplication by bc²b²c² is not injective:
- (bc²b)² ⋅ bc²b²c² = bc²b²c² and 1 ⋅ bc²b²c² = bc²b²c², however (bc²b)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.	(b²c²)² ⇒ 1	[4]
2.	a ⇒ b²c²	[3]

# abc:aa=1,abbcc=1 bc/a - -
bbccbbcc=1
a=bbcc

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

2 total

Σ	#	Presentation	Mapping
7	1268	⟨a, b, c \| aa=1, bbcc=a⟩	φ(a) = bbcc, φ(b) = b, φ(c) = c
8	2548	⟨a, b, c \| aab=c, cbcb=1⟩	φ(a) = b, φ(b) = c, φ(c) = bbc