#162 ⟨a, b, c | aa=1, abac=1⟩

Properties

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

#	Rule	Proof
1.	a² ⇒ 1	[1]
2.	bac ⇒ a	[3]

# abc:aa=1,abac=1 abc - -
aa=1
bac=a

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

13 total

Σ	#	Presentation	Mapping
6	218	⟨a, b, c \| aa=1, bac=a⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	2299	⟨a, b, c \| aaa=a, abac=1⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	2418	⟨a, b, c \| aab=b, abac=1⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	2434	⟨a, b, c \| aab=b, baca=1⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	2771	⟨a, b, c \| abc=b, abcb=1⟩	φ(a) = b, φ(b) = a, φ(c) = c
8	6114	⟨a, b, c \| aa=1, aaabac=1⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	6121	⟨a, b, c \| aa=1, aabaca=1⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	6138	⟨a, b, c \| aa=1, abaaac=1⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	6623	⟨a, b, c \| aa=1, aabac=a⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	6649	⟨a, b, c \| aa=1, abaca=a⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	6697	⟨a, b, c \| aa=1, baaac=a⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7147	⟨a, b, c \| aa=1, abac=aa⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7642	⟨a, b, c \| aa=1, bac=aaa⟩	φ(a) = a, φ(b) = b, φ(c) = c