Certificate for #1986 ⟨a, b | aabbaaba=ab⟩

Completion settings:

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

Axiom: aabbaaba=ab.

Referenced by [3].

Axiom: abb=c.

Defines rule #4.

Referenced by [3], [4], [5], [7].

Overlap of [1] aabbaaba=ab with [2] abb=c:

Critical pair: acaaba=ab.

Defines rule #1.

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

Overlap of [3] acaaba=ab with [2] abb=c:

Critical pair: acaabc=abbb.

Reduce RHS:

Defines rule #2.

Referenced by [6], [7], [8], [9], [11], [12], [13].

Overlap of [3] acaaba=ab with [3] acaaba=ab:

Critical pair: acaabab=abcaaba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

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

Overlap of [3] acaaba=ab with [4] acaabc=cb:

Critical pair: acaabcb=abcaabc.

Reduce LHS:

Defines rule #6.

Overlap of [3] acaaba=ab with [5] abcaaba=c:

Critical pair: acaabc=abbcaaba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [11].

Overlap of [4] acaabc=cb with [5] abcaaba=c:

Critical pair: acac=cbaaba.

Flip LHS and RHS.

Defines rule #7.

Referenced by [12].

Overlap of [5] abcaaba=c with [4] acaabc=cb:

Critical pair: abcaabcb=ccaabc.

Defines rule #10.

Overlap of [5] abcaaba=c with [5] abcaaba=c:

Critical pair: abcaabc=cbcaaba.

Flip LHS and RHS.

Defines rule #8.

Referenced by [13].

Overlap of [7] ccaaba=cb with [4] acaabc=cb:

Critical pair: ccaabcb=cbcaabc.

Defines rule #9.

Overlap of [8] cbaaba=acac with [4] acaabc=cb:

Critical pair: cbaabcb=acaccaabc.

Defines rule #11.

Overlap of [10] cbcaaba=abcaabc with [4] acaabc=cb:

Critical pair: cbcaabcb=abcaabccaabc.

Defines rule #12.