#7145 ⟨a, b, c | aa=1, abab=cb⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element ab has infinite order
Not right cancellative, because right multiplication by b is not injective:
- c ⋅ b = (ab)² and aba ⋅ b = (ab)², however c ≠ aba

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(a) = deg(b) = 0, a < b; deg(c) = 1
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	a² ⇒ 1	[1]
2.	cb ⇒ (ab)²	[2]

# abc:aa=1,abab=cb ab/c - -
aa=1
cb=abab

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

1 total

Σ	#	Presentation	Mapping
8	7640	⟨a, b, c \| aa=1, bab=acb⟩	φ(a) = a, φ(b) = b, φ(c) = c