Certificate for #4204 ⟨a, b | aabbbabba=ba⟩

Completion settings:

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

Axiom: aabbbabba=ba.

Referenced by [3].

Axiom: bbba=c.

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

Overlap of [1] aabbbabba=ba with [2] bbba=c:

Critical pair: aacbba=ba.

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

Overlap of [2] bbba=c with [3] aacbba=ba:

Critical pair: bbbba=cacbba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [6].

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

Critical pair: aacbbba=baacbba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

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

Simplify [4] cacbba=bc.

Reduce LHS:

Flip LHS and RHS.

Referenced by [11], [12].

Overlap of [2] bbba=c with [5] bba=aacc:

Critical pair: baacc=c.

Referenced by [10].

Overlap of [3] aacbba=ba with [5] bba=aacc:

Critical pair: aacaacc=ba.

Flip LHS and RHS.

Defines rule #3.

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

Overlap of [5] bba=aacc with [8] ba=aacaacc:

Critical pair: baacaacc=aacc.

Reduce LHS:

Referenced by [11].

Simplify [7] baacc=c.

Reduce LHS:

Defines rule #2.

Referenced by [11].

Overlap of [8] ba=aacaacc with [10] aacaaccacc=c:

Critical pair: bc=aacaaccacaaccacc.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Referenced by [12].

Simplify [6] bc=cacaacc.

Reduce RHS:

Defines rule #4.