Certificate for #969 ⟨a, b | abaaaab=ba⟩

Completion settings:

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

Axiom: abaaaab=ba.

Referenced by [3].

Axiom: baaaa=c.

Referenced by [3], [4].

Overlap of [1] abaaaab=ba with [2] baaaa=c:

Critical pair: acb=ba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [4], [5], [6], [7].

Overlap of [2] baaaa=c with [3] ba=acb:

Critical pair: acbaaa=c.

Reduce LHS:

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

Overlap of [3] ba=acb with [4] acacacacb=c:

Critical pair: bc=acbcacacacb.

Flip LHS and RHS.

Referenced by [7].

Overlap of [4] acacacacb=c with [3] ba=acb:

Critical pair: acacacacacb=ca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [7], [8].

Simplify [5] acbcacacacb=bc.

Reduce LHS:

Referenced by [9].

Overlap of [4] acacacacb=c with [6] ca=acc:

Critical pair: aacccacacb=c.

Reduce LHS:

Defines rule #4.

Referenced by [9].

Overlap of [7] aaaacccccccccccccccbcccccccccccccccb=bc with [8] aaaacccccccccccccccb=c:

Critical pair: ccccccccccccccccb=bc.

Defines rule #1.