Certificate for #6496 ⟨a, b | aba=b, aabab=a⟩

Back:⟨a, b | aba=b, aabab=a⟩

Completion settings:

[1] aba=b

Axiom: aba=b.

Defines rule #1.

Referenced by [2], [3], [4].

[2] abb=a

Axiom: aabab=a.

Reduce LHS:

[1]a(aba)b
⇒ abb

Defines rule #2.

Referenced by [3], [4].

[3] bba=a

Overlap of [1] aba=b with [1] aba=b:

ab a aba

Critical pair: abb=bba.

Reduce LHS:

[2](abb)
⇒ a

Flip LHS and RHS.

Defines rule #3.

[4] bbb=b

Overlap of [1] aba=b with [2] abb=a:

ab a abb

Critical pair: aba=bbb.

Reduce LHS:

[1](aba)
⇒ b

Flip LHS and RHS.

Defines rule #4.