Certificate for #1971 ⟨a, b | aababbaa=ba⟩

Completion settings:

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

Axiom: aababbaa=ba.

Referenced by [3].

Axiom: ba=c.

Defines rule #1.

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

Simplify [1] aababbaa=ba.

Reduce RHS:

Referenced by [4].

Overlap of [3] aababbaa=c with [2] ba=c:

Critical pair: aacbbaa=c.

Reduce LHS:

Defines rule #7.

Referenced by [5], [6], [7], [8], [10].

Overlap of [2] ba=c with [4] aacbca=c:

Critical pair: bc=cacbca.

Flip LHS and RHS.

Defines rule #3.

Referenced by [6], [7], [8], [9], [11].

Overlap of [4] aacbca=c with [4] aacbca=c:

Critical pair: aacbcc=cacbca.

Reduce RHS:

Defines rule #4.

Referenced by [10], [11].

Overlap of [4] aacbca=c with [5] cacbca=bc:

Critical pair: aacbbc=ccbca.

Referenced by [12].

Overlap of [5] cacbca=bc with [4] aacbca=c:

Critical pair: cacbcc=bcacbca.

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [9], [12].

Overlap of [5] cacbca=bc with [5] cacbca=bc:

Critical pair: cacbbc=bccbca.

Reduce LHS:

Defines rule #5.

Overlap of [4] aacbca=c with [6] aacbcc=bc:

Critical pair: aacbcbc=cacbcc.

Defines rule #9.

Overlap of [5] cacbca=bc with [6] aacbcc=bc:

Critical pair: cacbcbc=bcacbcc.

Defines rule #6.

Simplify [7] aacbbc=ccbca.

Reduce LHS:

Defines rule #8.