Certificate for #2005 ⟨a, b | aabbbaba=ab⟩

Completion settings:

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

Axiom: aabbbaba=ab.

Referenced by [3].

Axiom: abbb=c.

Defines rule #9.

Referenced by [3], [4], [7], [10], [12], [14].

Overlap of [1] aabbbaba=ab with [2] abbb=c:

Critical pair: acaba=ab.

Defines rule #1.

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

Overlap of [3] acaba=ab with [2] abbb=c:

Critical pair: acabc=abbbb.

Reduce RHS:

Defines rule #2.

Referenced by [6], [8], [9], [11], [13], [15].

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

Critical pair: acabab=abcaba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

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

Overlap of [3] acaba=ab with [4] acabc=cb:

Critical pair: acabcb=abcabc.

Reduce LHS:

Defines rule #5.

Referenced by [11], [12].

Overlap of [3] acaba=ab with [5] abcaba=abb:

Critical pair: acababb=abbcaba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #10.

Overlap of [4] acabc=cb with [5] abcaba=abb:

Critical pair: acabb=cbaba.

Defines rule #7.

Referenced by [14].

Overlap of [5] abcaba=abb with [4] acabc=cb:

Critical pair: abcabcb=abbcabc.

Defines rule #11.

Referenced by [12].

Overlap of [5] abcaba=abb with [5] abcaba=abb:

Critical pair: abcababb=abbbcaba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [11], [12], [13].

Overlap of [4] acabc=cb with [10] ccaba=cb:

Critical pair: acabcb=cbcaba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [15].

Overlap of [10] ccaba=cb with [2] abbb=c:

Critical pair: ccabc=cbbbb.

Reduce RHS:

Flip LHS and RHS.

Defines rule #14.

Overlap of [10] ccaba=cb with [4] acabc=cb:

Critical pair: ccabcb=cbcabc.

Defines rule #8.

Overlap of [8] acabb=cbaba with [2] abbb=c:

Critical pair: acc=cbabab.

Flip LHS and RHS.

Defines rule #12.

Overlap of [11] cbcaba=abcabc with [4] acabc=cb:

Critical pair: cbcabcb=abcabccabc.

Defines rule #13.