Certificate for #26090 ⟨a, b | aa=1, abbabbabb=1⟩

Completion settings:

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

Axiom: aa=1.

Defines rule #1.

Referenced by [6], [10].

Axiom: abbabbabb=1.

Referenced by [4].

Axiom: bab=c.

Defines rule #5.

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

Overlap of [2] abbabbabb=1 with [3] bab=c:

Critical pair: abcbabb=1.

Reduce LHS:

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

Overlap of [3] bab=c with [3] bab=c:

Critical pair: bac=cab.

Flip LHS and RHS.

Defines rule #3.

Overlap of [1] aa=1 with [4] abccb=1:

Critical pair: a=bccb.

Flip LHS and RHS.

Referenced by [8], [9].

Overlap of [3] bab=c with [4] abccb=1:

Critical pair: b=cccb.

Flip LHS and RHS.

Referenced by [9].

Overlap of [4] abccb=1 with [6] bccb=a:

Critical pair: abcca=ccb.

Flip LHS and RHS.

Defines rule #4.

Overlap of [7] cccb=b with [6] bccb=a:

Critical pair: ccca=bccb.

Reduce RHS:

Referenced by [10].

Overlap of [9] ccca=a with [1] aa=1:

Critical pair: ccc=aa.

Reduce RHS:

Defines rule #2.