Certificate for #13103 ⟨a, b | bab=aba, aaab=b⟩

Completion settings:

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

Axiom: bab=aba.

Defines rule #1.

Referenced by [3], [4], [5], [7], [9], [11].

Axiom: aaab=b.

Defines rule #2.

Referenced by [4], [5], [6], [7], [8], [9], [10], [11], [12].

Overlap of [1] bab=aba with [1] bab=aba:

Critical pair: baaba=abaab.

Defines rule #6.

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

Overlap of [1] bab=aba with [3] baaba=abaab:

Critical pair: baabaab=abaaaba.

Reduce LHS:

Reduce RHS:

Referenced by [6].

Overlap of [3] baaba=abaab with [1] bab=aba:

Critical pair: baaaba=abaabb.

Reduce LHS:

Flip LHS and RHS.

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

Overlap of [3] baaba=abaab with [3] baaba=abaab:

Critical pair: baaabaab=abaababa.

Reduce LHS:

Reduce RHS:

Defines rule #9.

Overlap of [1] bab=aba with [5] abaabb=bba:

Critical pair: bbba=abaaabb.

Reduce RHS:

Defines rule #3.

Referenced by [9], [11].

Overlap of [2] aaab=b with [5] abaabb=bba:

Critical pair: aabba=baabb.

Flip LHS and RHS.

Defines rule #7.

Overlap of [5] abaabb=bba with [7] bbba=abbb:

Critical pair: abaaabbb=bbaba.

Reduce LHS:

Reduce RHS:

Referenced by [10].

Overlap of [2] aaab=b with [9] abbbb=abaaa:

Critical pair: aaabaaa=bbbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [11], [12].

Overlap of [10] bbbb=baaa with [7] bbba=abbb:

Critical pair: babbb=baaaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Overlap of [10] bbbb=baaa with [10] bbbb=baaa:

Critical pair: bbaaa=baaab.

Reduce RHS:

Defines rule #8.