Certificate for #7291 ⟨a, b, c | ab=1, aaac=bb⟩

Back:⟨a, b, c | ab=1, aaac=bb⟩

Completion settings:

[1] ab=1

Axiom: ab=1.

Referenced by [3], [5].

[2] bb=aaac

Axiom: aaac=bb.

Flip LHS and RHS.

Referenced by [3], [4].

[3] b=aaaac

Overlap of [1] ab=1 with [2] bb=aaac:

a b bb

Critical pair: aaaac=b.

Flip LHS and RHS.

Defines rule #3.

Referenced by [4], [5].

[4] aaacaaaac=aaaacaaac

Overlap of [2] bb=aaac with [2] bb=aaac:

b b bb

Critical pair: baaac=aaacb.

Reduce LHS:

[3](b)aaac
⇒ aaaacaaac

Reduce RHS:

[3]aaac(b)
⇒ aaacaaaac

Flip LHS and RHS.

Defines rule #2.

[5] aaaaac=1

Overlap of [1] ab=1 with [3] b=aaaac:

a b b

Critical pair: aaaaac=1.

Defines rule #1.