Certificate for #7803 ⟨a, b | aaa=1, abbbb=bb⟩

Back:⟨a, b | aaa=1, abbbb=bb⟩

Completion settings:

[1] aaa=1

Axiom: aaa=1.

Defines rule #3.

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

[2] abbbb=bb

Axiom: abbbb=bb.

Referenced by [3].

[3] aabb=bbbb

Overlap of [1] aaa=1 with [2] abbbb=bb:

aa a abbbb

Critical pair: aabb=bbbb.

Referenced by [4], [5].

[4] abb=bbbbbb

Overlap of [1] aaa=1 with [3] aabb=bbbb:

aa a aabb

Critical pair: aabbbb=abb.

Reduce LHS:

[3](aabb)bb
⇒ bbbbbb

Flip LHS and RHS.

Defines rule #2.

Referenced by [5].

[5] bbbbbbbb=bb

Overlap of [1] aaa=1 with [4] abb=bbbbbb:

aa a abb

Critical pair: aabbbbbb=bb.

Reduce LHS:

[3](aabb)bbbb
⇒ bbbbbbbb

Defines rule #1.