Certificate for #16274 ⟨a, b | aab=bb, aaaa=ab⟩

Back:⟨a, b | aab=bb, aaaa=ab⟩

Completion settings:

[1] bb=aab

Axiom: aab=bb.

Flip LHS and RHS.

Referenced by [3].

[2] ab=aaaa

Axiom: aaaa=ab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [3], [4], [5].

[3] bb=aaaaa

Simplify [1] bb=aab.

Reduce RHS:

[2]a(ab)
⇒ aaaaa

Defines rule #4.

Referenced by [4], [5].

[4] baaaaa=aaaaaaaa

Overlap of [3] bb=aaaaa with [3] bb=aaaaa:

b b bb

Critical pair: baaaaa=aaaaab.

Reduce RHS:

[2]aaaa(ab)
⇒ aaaaaaaa

Referenced by [6].

[5] aaaaaaa=aaaaaa

Overlap of [2] ab=aaaa with [3] bb=aaaaa:

a b bb

Critical pair: aaaaaa=aaaab.

Reduce RHS:

[2]aaa(ab)
⇒ aaaaaaa

Flip LHS and RHS.

Defines rule #1.

Referenced by [6].

[6] baaaaa=aaaaaa

Simplify [4] baaaaa=aaaaaaaa.

Reduce RHS:

[5](aaaaaaa)a
[5]⇒ (aaaaaaa)
⇒ aaaaaa

Defines rule #2.