#2032 ⟨a, b, c | aaaa=1, aabc=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.	bc ⇒ a²	[3]
2.	a⁴ ⇒ 1	[1]

# abc:aaaa=1,aabc=1 abc - -
bc=aa
aaaa=1

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

7 total

Σ	#	Presentation	Mapping
8	2035	⟨a, b, c \| aaaa=1, abca=1⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	2216	⟨a, b, c \| aabc=1, bcbc=1⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	2250	⟨a, b, c \| abab=1, cabc=1⟩	φ(a) = b, φ(b) = c, φ(c) = a
8	3281	⟨a, b, c \| bb=ac, acac=1⟩	φ(a) = b, φ(b) = a, φ(c) = c
8	3283	⟨a, b, c \| bb=ac, acbb=1⟩	φ(a) = b, φ(b) = a, φ(c) = c
8	3291	⟨a, b, c \| bb=ac, bacb=1⟩	φ(a) = b, φ(b) = a, φ(c) = c
8	3295	⟨a, b, c \| bb=ac, bbbb=1⟩	φ(a) = b, φ(b) = a, φ(c) = c