Certificate for #2063 ⟨a, b | aab=b, abab=b⟩

Back:⟨a, b | aab=b, abab=b⟩

Completion settings:

[1] aab=b

Axiom: aab=b.

Defines rule #2.

Referenced by [3], [5].

[2] abab=b

Axiom: abab=b.

Referenced by [3], [4].

[3] bab=ab

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

a ab abab

Critical pair: ab=bab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [4].

[4] abb=ab

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

ab ab abab

Critical pair: abb=bab.

Reduce RHS:

[3](bab)
⇒ ab

Referenced by [5].

[5] bb=b

Overlap of [1] aab=b with [4] abb=ab:

a ab abb

Critical pair: aab=bb.

Reduce LHS:

[1](aab)
⇒ b

Flip LHS and RHS.

Defines rule #1.