#2976 ⟨a, b, c | aab=c, baa=c⟩

Properties

Sum of relation sides is 8
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaba^-1a^-1b^-1⟩
- Embedding: φ(a) = a, φ(b) = a^-1a^-1b^-1, φ(c) = b^-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(a) = deg(b) = 0, a < b; deg(c) = 1
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	ba² ⇒ a²b	[2]
2.	c ⇒ a²b	[1]

# abc:aab=c,baa=c ab/c - -
baa=aab
c=aab

8 unique, 14 total

Σ	#	Presentation	Properties	φ
7	533	⟨a, b, c \| ba=ab, cc=a⟩	Can Inf
8	2199	⟨a, b, c \| aabc=1, acba=1⟩	Grp Inf	5
8	3072	⟨a, b, c \| abc=b, cba=b⟩	Can Inf
8	3431	⟨a, b, c \| ba=ab, cac=b⟩	Can Inf
8	3587	⟨a, b, c \| ba=ab, cc=ab⟩	Can Inf	1
8	3592	⟨a, b, c \| ba=ac, ca=ab⟩	Can Inf
8	3596	⟨a, b, c \| ba=ac, cc=bb⟩	Can Inf
8	6088	⟨a, b, c \| ab=c, bca=cc⟩	Can Inf

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

2 total

Σ	#	Presentation	Mapping
8	5676	⟨a, b, c \| aa=b, aac=cb⟩	φ(a) = a, φ(b) = aa, φ(c) = b
8	6058	⟨a, b, c \| ab=c, baa=ac⟩	φ(a) = a, φ(b) = b, φ(c) = ab