Certificate for #1053 ⟨a, b | aaabba=baa⟩

Completion settings:

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

Axiom: aaabba=baa.

Referenced by [4].

Axiom: bb=c.

Defines rule #10.

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

Axiom: caa=d.

Defines rule #4.

Referenced by [6], [7], [8], [9], [10], [11].

Overlap of [1] aaabba=baa with [2] bb=c:

Critical pair: aaaca=baa.

Flip LHS and RHS.

Defines rule #7.

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

Overlap of [2] bb=c with [2] bb=c:

Critical pair: bc=cb.

Flip LHS and RHS.

Defines rule #9.

Referenced by [7].

Overlap of [2] bb=c with [4] baa=aaaca:

Critical pair: baaaca=caa.

Reduce LHS:

Reduce RHS:

Defines rule #2.

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

Overlap of [5] cb=bc with [4] baa=aaaca:

Critical pair: caaaca=bcaa.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [8].

Overlap of [2] bb=c with [7] bd=daca:

Critical pair: bdaca=cd.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Overlap of [3] caa=d with [6] aaadca=d:

Critical pair: cad=daadca.

Defines rule #5.

Overlap of [4] baa=aaaca with [6] aaadca=d:

Critical pair: bad=aaacaaadca.

Reduce RHS:

Defines rule #8.

Overlap of [6] aaadca=d with [3] caa=d:

Critical pair: aaadd=da.

Defines rule #1.