Certificate for #4277 ⟨a, b | abaabbaba=ba⟩

Completion settings:

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

Axiom: abaabbaba=ba.

Referenced by [3].

Axiom: bba=c.

Defines rule #2.

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

Overlap of [1] abaabbaba=ba with [2] bba=c:

Critical pair: abaacba=ba.

Defines rule #5.

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

Overlap of [2] bba=c with [3] abaacba=ba:

Critical pair: bbba=cbaacba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #8.

Referenced by [9], [10].

Overlap of [3] abaacba=ba with [3] abaacba=ba:

Critical pair: abaacbba=babaacba.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Referenced by [6], [7].

Overlap of [2] bba=c with [5] abaacc=c:

Critical pair: bbc=cbaacc.

Defines rule #3.

Referenced by [8].

Overlap of [3] abaacba=ba with [5] abaacc=c:

Critical pair: abaacbc=babaacc.

Reduce RHS:

Defines rule #6.

Referenced by [8].

Overlap of [2] bba=c with [7] abaacbc=bc:

Critical pair: bbbc=cbaacbc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #9.

Overlap of [3] abaacba=ba with [4] cbaacba=bc:

Critical pair: abaabc=baacba.

Defines rule #4.

Overlap of [4] cbaacba=bc with [4] cbaacba=bc:

Critical pair: cbaabc=bcacba.

Defines rule #7.