Certificate for #3770 ⟨a, b | aaaa=bb, aabb=1⟩

Back:⟨a, b | aaaa=bb, aabb=1⟩

Completion settings:

[1] bb=aaaa

Axiom: aaaa=bb.

Flip LHS and RHS.

Defines rule #3.

Referenced by [2], [3].

[2] aaaaaa=1

Axiom: aabb=1.

Reduce LHS:

[1]aa(bb)
⇒ aaaaaa

Defines rule #1.

Referenced by [4], [5].

[3] aaaab=baaaa

Overlap of [1] bb=aaaa with [1] bb=aaaa:

b b bb

Critical pair: baaaa=aaaab.

Flip LHS and RHS.

Referenced by [4], [5].

[4] aabaaaa=b

Overlap of [2] aaaaaa=1 with [3] aaaab=baaaa:

aa aaaa aaaab

Critical pair: aabaaaa=b.

Referenced by [5].

[5] aab=baa

Overlap of [3] aaaab=baaaa with [4] aabaaaa=b:

aa aab aabaaaa

Critical pair: aab=baaaaaaaa.

Reduce RHS:

[2]b(aaaaaa)aa
⇒ baa

Defines rule #2.