Certificate for #15727 ⟨a, b | aab=ba, bbabb=a⟩

Completion settings:

• Reduction order:
  • Left-to-right recursive path with deg(a) = 0; deg(b) = 1

Axiom: aab=ba.

Referenced by [3], [4], [5], [6], [10], [12].

Axiom: bbabb=a.

Referenced by [3], [4], [8], [10].

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

Critical pair: bbaa=aabb.

Reduce RHS:

Flip LHS and RHS.

Referenced by [4], [6], [10].

Overlap of [2] bbabb=a with [3] bab=bbaa:

Critical pair: bbabbbaa=aab.

Reduce LHS:

Reduce RHS:

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

Overlap of [1] aab=ba with [4] abaa=ba:

Critical pair: aba=baaa.

Referenced by [7].

Overlap of [4] abaa=ba with [1] aab=ba:

Critical pair: abba=bab.

Reduce RHS:

Referenced by [8].

Overlap of [4] abaa=ba with [5] aba=baaa:

Critical pair: baaaa=ba.

Referenced by [9].

Overlap of [2] bbabb=a with [6] abba=bbaa:

Critical pair: bbbbaa=aa.

Referenced by [9].

Overlap of [8] bbbbaa=aa with [7] baaaa=ba:

Critical pair: bbbba=aaaa.

Referenced by [10], [11].

Overlap of [2] bbabb=a with [3] bab=bbaa:

Critical pair: bbbaab=a.

Reduce LHS:

Defines rule #1.

Referenced by [11], [12].

Simplify [9] bbbba=aaaa.

Reduce RHS:

Defines rule #3.

Overlap of [10] aaaa=a with [1] aab=ba:

Critical pair: aaba=ab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.