Certificate for #12591 ⟨a, b | abba=ba, bbaa=b⟩

Completion settings:

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

Axiom: abba=ba.

Referenced by [3], [4], [5], [6], [7], [9].

Axiom: bbaa=b.

Referenced by [4], [8], [11], [13].

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

Critical pair: abbba=babba.

Reduce RHS:

Referenced by [6].

Overlap of [1] abba=ba with [2] bbaa=b:

Critical pair: ab=baa.

Flip LHS and RHS.

Referenced by [5], [6], [9], [10], [12], [13], [14].

Overlap of [1] abba=ba with [4] baa=ab:

Critical pair: abab=baa.

Reduce RHS:

Referenced by [7], [8], [9], [10], [12].

Overlap of [4] baa=ab with [1] abba=ba:

Critical pair: baba=abbba.

Reduce RHS:

Referenced by [7].

Overlap of [1] abba=ba with [5] abab=ab:

Critical pair: abbab=babab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [8], [11].

Overlap of [2] bbaa=b with [5] abab=ab:

Critical pair: bbaab=bbab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [9], [11], [12].

Overlap of [4] baa=ab with [5] abab=ab:

Critical pair: baab=abbab.

Reduce LHS:

Reduce RHS:

Referenced by [10].

Overlap of [5] abab=ab with [4] baa=ab:

Critical pair: abaab=abaa.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [11], [12], [13].

Overlap of [2] bbaa=b with [10] aab=bb:

Critical pair: bbabb=bab.

Reduce LHS:

Reduce RHS:

Referenced by [12].

Overlap of [4] baa=ab with [10] aab=bb:

Critical pair: babb=abab.

Reduce LHS:

Reduce RHS:

Referenced by [13], [15].

Overlap of [2] bbaa=b with [12] bb=ab:

Critical pair: abaa=b.

Reduce LHS:

Defines rule #1.

Referenced by [14], [15].

Simplify [4] baa=ab.

Reduce RHS:

Defines rule #3.

Simplify [12] bb=ab.

Reduce RHS:

Defines rule #2.