Certificate for #14301 ⟨a, b | abba=b, aabaab=1⟩

Completion settings:

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

Axiom: abba=b.

Defines rule #1.

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

Axiom: aabaab=1.

Defines rule #9.

Referenced by [4].

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

Critical pair: abbb=bbba.

Flip LHS and RHS.

Defines rule #5.

Referenced by [9].

Overlap of [2] aabaab=1 with [1] abba=b:

Critical pair: aabab=ba.

Defines rule #6.

Referenced by [5], [7], [10].

Overlap of [4] aabab=ba with [1] abba=b:

Critical pair: aabb=baba.

Flip LHS and RHS.

Defines rule #3.

Referenced by [6], [7].

Overlap of [1] abba=b with [5] baba=aabb:

Critical pair: abaabb=bba.

Defines rule #10.

Overlap of [4] aabab=ba with [5] baba=aabb:

Critical pair: aaaabb=baa.

Defines rule #8.

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

Overlap of [7] aaaabb=baa with [1] abba=b:

Critical pair: aaab=baaa.

Flip LHS and RHS.

Defines rule #2.

Referenced by [10].

Overlap of [7] aaaabb=baa with [3] bbba=abbb:

Critical pair: aaaaabbb=baaba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.

Overlap of [8] baaa=aaab with [7] aaaabb=baa:

Critical pair: bbaa=aaababb.

Reduce RHS:

Defines rule #4.