Certificate for #12448 ⟨a, b | aabb=aa, bbab=a⟩

Completion settings:

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

Axiom: aabb=aa.

Defines rule #3.

Referenced by [4], [5].

Axiom: bbab=a.

Defines rule #1.

Referenced by [3], [4], [5], [6], [8], [9].

Overlap of [2] bbab=a with [2] bbab=a:

Critical pair: bbaa=abab.

Flip LHS and RHS.

Defines rule #2.

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

Overlap of [1] aabb=aa with [2] bbab=a:

Critical pair: aaa=aaab.

Flip LHS and RHS.

Defines rule #4.

Referenced by [7].

Overlap of [1] aabb=aa with [2] bbab=a:

Critical pair: aaba=aabab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [8].

Overlap of [2] bbab=a with [3] abab=bbaa:

Critical pair: bbbbaa=aab.

Defines rule #7.

Overlap of [3] abab=bbaa with [3] abab=bbaa:

Critical pair: abbbaa=bbaaab.

Reduce RHS:

Defines rule #9.

Overlap of [2] bbab=a with [5] abbaa=aaba:

Critical pair: bbaaba=abaa.

Defines rule #8.

Referenced by [9].

Overlap of [8] bbaaba=abaa with [3] abab=bbaa:

Critical pair: bbabbaa=abaab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.