Certificate for #4157 ⟨a, b | aabbaaaba=ba⟩

Completion settings:

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

Axiom: aabbaaaba=ba.

Referenced by [3].

Axiom: bba=c.

Defines rule #6.

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

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

Critical pair: aacaaba=ba.

Defines rule #4.

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

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

Critical pair: bbba=cacaaba.

Reduce LHS:

Defines rule #5.

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

Critical pair: aacaabba=baacaaba.

Reduce LHS:

Reduce RHS:

Defines rule #2.

Referenced by [6], [7].

Overlap of [5] aacaac=c with [3] aacaaba=ba:

Critical pair: aacba=caaba.

Defines rule #3.

Overlap of [5] aacaac=c with [5] aacaac=c:

Critical pair: aacc=caac.

Defines rule #1.