Certificate for #19260 ⟨a, b | aaa=a, aabbb=ba⟩

Completion settings:

• Reduction order:
  • Left-to-right shortlex with b < a

Axiom: aaa=a.

Defines rule #1.

Referenced by [3], [4], [8].

Axiom: aabbb=ba.

Referenced by [3], [4], [5], [6], [7], [8].

Overlap of [1] aaa=a with [2] aabbb=ba:

Critical pair: aba=abbb.

Flip LHS and RHS.

Defines rule #4.

Overlap of [1] aaa=a with [2] aabbb=ba:

Critical pair: aaba=aabbb.

Reduce RHS:

Defines rule #5.

Referenced by [5], [6].

Overlap of [4] aaba=ba with [2] aabbb=ba:

Critical pair: aabba=baabbb.

Reduce RHS:

Defines rule #7.

Referenced by [6], [7].

Overlap of [4] aaba=ba with [5] aabba=bba:

Critical pair: aabbba=baabba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [7], [8].

Overlap of [5] aabba=bba with [5] aabba=bba:

Critical pair: aabbbba=bbaabba.

Reduce LHS:

Reduce RHS:

Defines rule #3.

Overlap of [2] aabbb=ba with [6] bbba=baa:

Critical pair: aabbbaa=babba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.