Certificate for #945 ⟨a, b | aababba=ab⟩

Completion settings:

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

Axiom: aababba=ab.

Referenced by [3].

Axiom: abb=c.

Defines rule #3.

Referenced by [3], [4], [5], [7], [10].

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

Critical pair: aabca=ab.

Defines rule #7.

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

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

Critical pair: aabcc=abbb.

Reduce RHS:

Defines rule #1.

Referenced by [6], [7], [8], [12].

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

Critical pair: aabcab=ababca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #13.

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

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

Critical pair: aabccb=ababcc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #9.

Referenced by [8], [9], [16].

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

Critical pair: aabcc=abbabca.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [10], [11], [12], [13], [14], [15].

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

Critical pair: ababccb=cabcc.

Reduce LHS:

Defines rule #6.

Referenced by [16].

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

Critical pair: ababcc=cbabca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #10.

Referenced by [17].

Overlap of [3] aabca=ab with [7] cabca=cb:

Critical pair: aabcb=abbca.

Reduce RHS:

Defines rule #8.

Referenced by [15], [17].

Overlap of [5] ababca=c with [7] cabca=cb:

Critical pair: ababcb=cbca.

Defines rule #14.

Overlap of [7] cabca=cb with [4] aabcc=cb:

Critical pair: cabccb=cbabcc.

Flip LHS and RHS.

Defines rule #4.

Referenced by [17].

Overlap of [7] cabca=cb with [5] ababca=c:

Critical pair: cabcc=cbbabca.

Flip LHS and RHS.

Defines rule #15.

Overlap of [7] cabca=cb with [7] cabca=cb:

Critical pair: cabcb=cbbca.

Flip LHS and RHS.

Defines rule #5.

Overlap of [7] cabca=cb with [10] aabcb=cca:

Critical pair: cabccca=cbabcb.

Flip LHS and RHS.

Defines rule #11.

Overlap of [6] ababcc=cbb with [8] cbbb=cabcc:

Critical pair: ababccabcc=cbbbbb.

Reduce LHS:

Reduce RHS:

Defines rule #12.

Overlap of [9] cbabca=cbb with [10] aabcb=cca:

Critical pair: cbabccca=cbbabcb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #16.