Certificate for #4199 ⟨a, b | bba=abb, bbb=b⟩

Completion settings:

• Auxiliary generators:
  1. c = baa
• Reduction order:
  • Left-to-right recursive path with deg(b) = deg(c) = 0, b < c; deg(a) = 1

Axiom: bba=abb.

Defines rule #6.

Referenced by [5], [6], [7], [8].

Axiom: bbb=b.

Defines rule #1.

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

Axiom: baa=c.

Defines rule #9.

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

Overlap of [2] bbb=b with [3] baa=c:

Critical pair: bbc=baa.

Reduce RHS:

Defines rule #2.

Referenced by [11].

Overlap of [1] bba=abb with [3] baa=c:

Critical pair: bc=abba.

Reduce RHS:

Flip LHS and RHS.

Referenced by [9], [10], [11].

Overlap of [2] bbb=b with [1] bba=abb:

Critical pair: babb=ba.

Defines rule #4.

Referenced by [7].

Overlap of [6] babb=ba with [1] bba=abb:

Critical pair: baabb=baa.

Reduce LHS:

Reduce RHS:

Defines rule #3.

Referenced by [8].

Overlap of [7] cbb=c with [1] bba=abb:

Critical pair: cabb=ca.

Referenced by [9].

Overlap of [3] baa=c with [5] aabb=bc:

Critical pair: babc=cabb.

Reduce RHS:

Flip LHS and RHS.

Defines rule #5.

Overlap of [5] aabb=bc with [2] bbb=b:

Critical pair: aab=bcb.

Defines rule #7.

Overlap of [5] aabb=bc with [4] bbc=c:

Critical pair: aac=bcc.

Defines rule #8.