Certificate for #16185 ⟨a, b | aab=ab, baba=aa⟩

Completion settings:

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

Axiom: aab=ab.

Defines rule #2.

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

Axiom: baba=aa.

Referenced by [3], [4], [5], [7], [8], [9].

Overlap of [1] aab=ab with [2] baba=aa:

Critical pair: aaaa=ababa.

Reduce RHS:

Referenced by [5].

Overlap of [2] baba=aa with [2] baba=aa:

Critical pair: baaa=aaba.

Reduce RHS:

Referenced by [5], [6].

Overlap of [2] baba=aa with [4] baaa=aba:

Critical pair: baaba=aaaa.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Overlap of [4] baaa=aba with [1] aab=ab:

Critical pair: baab=abab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [7], [9].

Overlap of [2] baba=aa with [6] abab=bab:

Critical pair: bbab=aab.

Reduce RHS:

Defines rule #4.

Referenced by [8], [10].

Overlap of [7] bbab=ab with [2] baba=aa:

Critical pair: baa=aba.

Flip LHS and RHS.

Defines rule #1.

Referenced by [9].

Overlap of [6] abab=bab with [8] aba=baa:

Critical pair: abbaa=baba.

Reduce RHS:

Referenced by [10].

Overlap of [7] bbab=ab with [9] abbaa=aa:

Critical pair: bbaa=abbaa.

Reduce RHS:

Defines rule #5.