Certificate for #5414 ⟨a, b | aab=bb, bba=aa⟩

Back:⟨a, b | aab=bb, bba=aa⟩

Completion settings:

[1] bb=aab

Axiom: aab=bb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [2], [3], [5].

[2] aaba=aa

Axiom: bba=aa.

Reduce LHS:

[1](bb)a
⇒ aaba

Defines rule #3.

Referenced by [4], [5].

[3] baab=aaaab

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

b b bb

Critical pair: baab=aabb.

Reduce RHS:

[1]aa(bb)
⇒ aaaab

Referenced by [4].

[4] baa=aaaa

Overlap of [3] baab=aaaab with [2] aaba=aa:

b aab aaba

Critical pair: baa=aaaaba.

Reduce RHS:

[2]aa(aaba)
⇒ aaaa

Defines rule #2.

Referenced by [5].

[5] aaaaaa=aaa

Overlap of [1] bb=aab with [4] baa=aaaa:

b b baa

Critical pair: baaaa=aabaa.

Reduce LHS:

[4](baa)aa
⇒ aaaaaa

Reduce RHS:

[2](aaba)a
⇒ aaa

Defines rule #1.