Certificate for #6251 ⟨a, b | aaa=a, aabba=b⟩

Completion settings:

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

Axiom: aaa=a.

Defines rule #4.

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

Axiom: aabba=b.

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

Overlap of [1] aaa=a with [2] aabba=b:

Critical pair: ab=abba.

Flip LHS and RHS.

Referenced by [6].

Overlap of [1] aaa=a with [2] aabba=b:

Critical pair: aab=aabba.

Reduce RHS:

Defines rule #3.

Referenced by [5], [6], [7].

Overlap of [2] aabba=b with [1] aaa=a:

Critical pair: aabba=baa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [8].

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

Critical pair: aabbb=babba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [9].

Overlap of [2] aabba=b with [4] aab=b:

Critical pair: bba=b.

Referenced by [8], [9], [10].

Simplify [5] baa=bba.

Reduce RHS:

Referenced by [9], [10].

Overlap of [6] bab=bbb with [8] baa=b:

Critical pair: bab=bbbaa.

Reduce LHS:

Reduce RHS:

Defines rule #2.

Overlap of [7] bba=b with [8] baa=b:

Critical pair: bb=ba.

Flip LHS and RHS.

Defines rule #1.