Certificate for #2073 ⟨a, b | aab=b, baba=b⟩

Back:⟨a, b | aab=b, baba=b⟩

Completion settings:

[1] aab=b

Axiom: aab=b.

Defines rule #2.

Referenced by [3].

[2] baba=b

Axiom: baba=b.

Referenced by [3], [4], [5], [7].

[3] babb=bab

Overlap of [2] baba=b with [1] aab=b:

bab a aab

Critical pair: babb=bab.

Referenced by [5].

[4] bba=bab

Overlap of [2] baba=b with [2] baba=b:

ba ba baba

Critical pair: bab=bba.

Flip LHS and RHS.

Referenced by [5], [6].

[5] bb=b

Overlap of [4] bba=bab with [2] baba=b:

b ba baba

Critical pair: bb=babba.

Reduce RHS:

[3](babb)a
[2]⇒ (baba)
⇒ b

Defines rule #1.

Referenced by [6], [7].

[6] bab=ba

Overlap of [4] bba=bab with [5] bb=b:

bba bb

Critical pair: ba=bab.

Flip LHS and RHS.

Defines rule #4.

Referenced by [7].

[7] baa=b

Overlap of [5] bb=b with [2] baba=b:

b b baba

Critical pair: bb=baba.

Reduce LHS:

[5](bb)
⇒ b

Reduce RHS:

[6](bab)a
⇒ baa

Flip LHS and RHS.

Defines rule #3.