Certificate for #1978 ⟨a, b | aababbba=ab⟩

Completion settings:

• Auxiliary generators:
  1. c = abbb
• Reduction order:
  • Left-to-right shortlex with a < b < c

Axiom: aababbba=ab.

Referenced by [3].

Axiom: abbb=c.

Defines rule #1.

Referenced by [3], [4], [7], [9], [12], [13].

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

Critical pair: aabca=ab.

Defines rule #2.

Referenced by [4], [5], [6], [7], [10].

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

Critical pair: aabcc=abbbb.

Reduce RHS:

Defines rule #3.

Referenced by [6], [8], [11], [14].

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

Critical pair: aabcab=ababca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #8.

Referenced by [7], [8], [9], [12], [15].

Overlap of [3] aabca=ab with [4] aabcc=cb:

Critical pair: aabccb=ababcc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #10.

Referenced by [8], [21], [22].

Overlap of [3] aabca=ab with [5] ababca=abb:

Critical pair: aabcabb=abbabca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #14.

Referenced by [17], [18], [19].

Overlap of [5] ababca=abb with [4] aabcc=cb:

Critical pair: ababccb=abbabcc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #16.

Referenced by [19].

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

Critical pair: ababcabb=abbbabca.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [10], [11], [12], [13], [14], [15], [16], [17], [18], [20], [21].

Overlap of [3] aabca=ab with [9] cabca=cb:

Critical pair: aabcb=abbca.

Flip LHS and RHS.

Defines rule #4.

Overlap of [4] aabcc=cb with [9] cabca=cb:

Critical pair: aabccb=cbabca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #11.

Referenced by [22], [23].

Overlap of [5] ababca=abb with [9] cabca=cb:

Critical pair: ababcb=abbbca.

Reduce RHS:

Defines rule #9.

Referenced by [19], [20], [23].

Overlap of [9] cabca=cb with [2] abbb=c:

Critical pair: cabcc=cbbbb.

Flip LHS and RHS.

Defines rule #6.

Overlap of [9] cabca=cb with [4] aabcc=cb:

Critical pair: cabccb=cbabcc.

Flip LHS and RHS.

Defines rule #12.

Referenced by [22], [23].

Overlap of [9] cabca=cb with [5] ababca=abb:

Critical pair: cabcabb=cbbabca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #17.

Overlap of [9] cabca=cb with [9] cabca=cb:

Critical pair: cabcb=cbbca.

Flip LHS and RHS.

Defines rule #7.

Overlap of [7] abbabca=c with [9] cabca=cb:

Critical pair: abbabcb=cbca.

Defines rule #15.

Overlap of [9] cabca=cb with [7] abbabca=c:

Critical pair: cabcc=cbbbabca.

Flip LHS and RHS.

Defines rule #20.

Overlap of [7] abbabca=c with [12] ababcb=cca:

Critical pair: abbabccca=cbabcb.

Reduce LHS:

Defines rule #13.

Overlap of [9] cabca=cb with [12] ababcb=cca:

Critical pair: cabccca=cbbabcb.

Flip LHS and RHS.

Defines rule #18.

Overlap of [9] cabca=cb with [6] ababcc=cbb:

Critical pair: cabccbb=cbbabcc.

Flip LHS and RHS.

Defines rule #19.

Overlap of [11] cbabca=cbb with [6] ababcc=cbb:

Critical pair: cbabccbb=cbbbabcc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #22.

Overlap of [11] cbabca=cbb with [12] ababcb=cca:

Critical pair: cbabccca=cbbbabcb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #21.