Certificate for #188 ⟨a, b | aab=1, bbbb=1⟩

Back:⟨a, b | aab=1, bbbb=1⟩

Completion settings:

[1] aab=1

Axiom: aab=1.

Referenced by [3], [4], [6].

[2] bbbb=1

Axiom: bbbb=1.

Referenced by [3], [5].

[3] bbb=aa

Overlap of [1] aab=1 with [2] bbbb=1:

aa b bbbb

Critical pair: aa=bbb.

Flip LHS and RHS.

Referenced by [4], [5], [6].

[4] bb=aaaa

Overlap of [1] aab=1 with [3] bbb=aa:

aa b bbb

Critical pair: aaaa=bb.

Flip LHS and RHS.

Referenced by [5].

[5] b=aaaaaa

Overlap of [2] bbbb=1 with [3] bbb=aa:

bb bb bbb

Critical pair: bbaa=b.

Reduce LHS:

[4](bb)aa
⇒ aaaaaa

Flip LHS and RHS.

Defines rule #2.

Referenced by [6].

[6] aaaaaaaa=1

Overlap of [3] bbb=aa with [3] bbb=aa:

b bb bbb

Critical pair: baa=aab.

Reduce LHS:

[5](b)aa
⇒ aaaaaaaa

Reduce RHS:

[1](aab)
⇒ 1

Defines rule #1.