Certificate for #19558 ⟨a, b | aab=b, abbab=ba⟩

Completion settings:

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

Axiom: aab=b.

Defines rule #4.

Referenced by [3], [6], [9], [12].

Axiom: abbab=ba.

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

Overlap of [1] aab=b with [2] abbab=ba:

Critical pair: aba=bbab.

Defines rule #5.

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

Overlap of [2] abbab=ba with [2] abbab=ba:

Critical pair: abbba=babab.

Reduce RHS:

Defines rule #7.

Referenced by [7].

Overlap of [2] abbab=ba with [3] aba=bbab:

Critical pair: abbbbab=baa.

Flip LHS and RHS.

Referenced by [9], [13].

Overlap of [3] aba=bbab with [1] aab=b:

Critical pair: abb=bbabab.

Reduce RHS:

Flip LHS and RHS.

Referenced by [7], [10], [11].

Overlap of [3] aba=bbab with [2] abbab=ba:

Critical pair: abba=bbabbbab.

Reduce RHS:

Defines rule #6.

Referenced by [8].

Overlap of [2] abbab=ba with [7] abba=babbb:

Critical pair: babbbb=ba.

Defines rule #2.

Referenced by [9], [10].

Overlap of [8] babbbb=ba with [8] babbbb=ba:

Critical pair: babbbba=baabbbb.

Reduce LHS:

Reduce RHS:

Referenced by [13].

Overlap of [6] bbbbabb=abb with [8] babbbb=ba:

Critical pair: bbbba=abbbb.

Defines rule #3.

Referenced by [11].

Overlap of [6] bbbbabb=abb with [10] bbbba=abbbb:

Critical pair: abbbbbb=abb.

Referenced by [12].

Overlap of [1] aab=b with [11] abbbbbb=abb:

Critical pair: aabb=bbbbbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Simplify [5] baa=abbbbab.

Reduce RHS:

Defines rule #8.