Certificate for #27121 ⟨a, b | aa=1, ababbab=bb⟩

Completion settings:

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

Axiom: aa=1.

Defines rule #1.

Referenced by [3], [10].

Axiom: ababbab=bb.

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

Overlap of [1] aa=1 with [2] ababbab=bb:

Critical pair: abb=babbab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [4], [5], [7], [10].

Overlap of [2] ababbab=bb with [3] babbab=abb:

Critical pair: abababb=bbbab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [8], [9], [10].

Overlap of [3] babbab=abb with [2] ababbab=bb:

Critical pair: babbbb=abbabbab.

Reduce RHS:

Defines rule #5.

Referenced by [6], [7], [8], [9].

Overlap of [2] ababbab=bb with [5] babbbb=ababb:

Critical pair: ababababb=bbbbb.

Referenced by [8].

Overlap of [3] babbab=abb with [5] babbbb=ababb:

Critical pair: babababb=abbbbb.

Defines rule #7.

Referenced by [9].

Overlap of [5] babbbb=ababb with [4] bbbab=abababb:

Critical pair: bababababb=ababbab.

Reduce LHS:

Reduce RHS:

Defines rule #8.

Referenced by [9].

Overlap of [8] bbbbbb=bb with [4] bbbab=abababb:

Critical pair: bbbabababb=bbab.

Reduce LHS:

Defines rule #6.

Referenced by [10].

Overlap of [9] bababbb=bbab with [4] bbbab=abababb:

Critical pair: babaabababb=bbabab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.