Certificate for #6665 ⟨a, b | aab=b, aaaa=bb⟩

Back:⟨a, b | aab=b, aaaa=bb⟩

Completion settings:

[1] aab=b

Axiom: aab=b.

Defines rule #3.

Referenced by [3], [4].

[2] bb=aaaa

Axiom: aaaa=bb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [3], [4].

[3] aaaaaa=aaaa

Overlap of [1] aab=b with [2] bb=aaaa:

aa b bb

Critical pair: aaaaaa=bb.

Reduce RHS:

[2](bb)
⇒ aaaa

Defines rule #1.

Referenced by [5].

[4] baaaa=b

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

b b bb

Critical pair: baaaa=aaaab.

Reduce RHS:

[1]aa(aab)
[1]⇒ (aab)
⇒ b

Referenced by [5].

[5] baa=b

Overlap of [4] baaaa=b with [3] aaaaaa=aaaa:

b aaaa aaaaaa

Critical pair: baaaa=baa.

Reduce LHS:

[4](baaaa)
⇒ b

Flip LHS and RHS.

Defines rule #2.