Certificate for #3806 ⟨a, b | abbaabaaab=b⟩

Completion settings:

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

Axiom: abbaabaaab=b.

Referenced by [3].

Axiom: aab=c.

Referenced by [3], [4], [8].

Overlap of [1] abbaabaaab=b with [2] aab=c:

Critical pair: abbcaaab=b.

Reduce LHS:

Referenced by [4], [5].

Overlap of [2] aab=c with [3] abbcac=b:

Critical pair: ab=cbcac.

Defines rule #2.

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

Overlap of [3] abbcac=b with [4] ab=cbcac:

Critical pair: cbcacbcac=b.

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

Overlap of [5] cbcacbcac=b with [5] cbcacbcac=b:

Critical pair: cbcab=bbcac.

Reduce LHS:

Referenced by [7].

Overlap of [6] cbccbcac=bbcac with [5] cbcacbcac=b:

Critical pair: cbcb=bbcacbcac.

Flip LHS and RHS.

Referenced by [10].

Overlap of [2] aab=c with [4] ab=cbcac:

Critical pair: acbcac=c.

Defines rule #3.

Referenced by [9], [10].

Overlap of [5] cbcacbcac=b with [8] acbcac=c:

Critical pair: cbcc=b.

Defines rule #1.

Referenced by [11].

Overlap of [7] bbcacbcac=cbcb with [8] acbcac=c:

Critical pair: bbcc=cbcb.

Flip LHS and RHS.

Defines rule #5.

Referenced by [11].

Overlap of [10] cbcb=bbcc with [9] cbcc=b:

Critical pair: cbb=bbcccc.

Defines rule #4.