Certificate for #462 ⟨a, b | aabbba=ab⟩

Completion settings:

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

Axiom: aabbba=ab.

Referenced by [4], [5], [6], [8], [15], [16].

Axiom: bbabbba=c.

Referenced by [3], [5], [7], [8], [11], [12], [15], [17].

Overlap of [2] bbabbba=c with [2] bbabbba=c:

Critical pair: bbabc=cbbba.

Referenced by [9].

Overlap of [1] aabbba=ab with [1] aabbba=ab:

Critical pair: aabbbab=ababbba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [15], [18].

Overlap of [2] bbabbba=c with [1] aabbba=ab:

Critical pair: bbabbbab=cabbba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [6], [7], [13], [14], [19].

Overlap of [5] cabbba=cb with [1] aabbba=ab:

Critical pair: cabbbab=cbabbba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [8], [20].

Overlap of [5] cabbba=cb with [2] bbabbba=c:

Critical pair: cabc=cbbbba.

Referenced by [10].

Overlap of [6] cbabbba=cbb with [1] aabbba=ab:

Critical pair: cbabbbab=cbbabbba.

Reduce LHS:

Reduce RHS:

Defines rule #2.

Referenced by [9], [10], [11], [12], [26], [27], [30], [31], [32].

Overlap of [3] bbabc=cbbba with [8] cbbb=cc:

Critical pair: bbabcc=cbbbabbb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [11], [13].

Overlap of [7] cabc=cbbbba with [8] cbbb=cc:

Critical pair: cabcc=cbbbbabbb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [12], [14].

Overlap of [8] cbbb=cc with [2] bbabbba=c:

Critical pair: cbc=ccabbba.

Reduce RHS:

Flip LHS and RHS.

Referenced by [13].

Overlap of [8] cbbb=cc with [2] bbabbba=c:

Critical pair: cbbc=ccbabbba.

Reduce RHS:

Flip LHS and RHS.

Referenced by [14].

Overlap of [9] ccabbb=ccac with [5] cabbba=cb:

Critical pair: ccb=ccaca.

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [14], [21].

Overlap of [13] cbc=ccb with [5] cabbba=cb:

Critical pair: cbcb=ccbabbba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [28].

Overlap of [1] aabbba=ab with [4] ababbba=abb:

Critical pair: aabbbabb=abbabbba.

Reduce LHS:

Reduce RHS:

Defines rule #11.

Referenced by [16], [17], [18], [19], [20], [22], [23].

Overlap of [1] aabbba=ab with [15] abbb=ac:

Critical pair: aaca=ab.

Defines rule #20.

Referenced by [25], [29].

Overlap of [2] bbabbba=c with [15] abbb=ac:

Critical pair: bbaca=c.

Defines rule #14.

Referenced by [22], [23], [24].

Overlap of [4] ababbba=abb with [15] abbb=ac:

Critical pair: abaca=abb.

Defines rule #21.

Overlap of [5] cabbba=cb with [15] abbb=ac:

Critical pair: caca=cb.

Defines rule #13.

Referenced by [21], [22], [24], [25], [28].

Overlap of [6] cbabbba=cbb with [15] abbb=ac:

Critical pair: cbaca=cbb.

Defines rule #15.

Referenced by [23], [28].

Overlap of [19] caca=cb with [19] caca=cb:

Critical pair: cacb=cbca.

Reduce RHS:

Defines rule #4.

Referenced by [26].

Overlap of [15] abbb=ac with [17] bbaca=c:

Critical pair: abc=acaca.

Reduce RHS:

Defines rule #7.

Referenced by [25], [29].

Overlap of [15] abbb=ac with [17] bbaca=c:

Critical pair: abbc=acbaca.

Reduce RHS:

Defines rule #12.

Overlap of [17] bbaca=c with [19] caca=cb:

Critical pair: bbacb=cca.

Defines rule #5.

Referenced by [27].

Overlap of [16] aaca=ab with [19] caca=cb:

Critical pair: aacb=abca.

Reduce RHS:

Defines rule #16.

Referenced by [29], [30].

Overlap of [21] cacb=ccba with [8] cbbb=cc:

Critical pair: cacc=ccbabb.

Defines rule #8.

Overlap of [24] bbacb=cca with [8] cbbb=cc:

Critical pair: bbacc=ccabb.

Defines rule #9.

Overlap of [20] cbaca=cbb with [19] caca=cb:

Critical pair: cbacb=cbbca.

Reduce RHS:

Defines rule #6.

Referenced by [31].

Overlap of [16] aaca=ab with [25] aacb=acba:

Critical pair: aacacba=abacb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #17.

Referenced by [32].

Overlap of [25] aacb=acba with [8] cbbb=cc:

Critical pair: aacc=acbabb.

Defines rule #18.

Overlap of [28] cbacb=ccbba with [8] cbbb=cc:

Critical pair: cbacc=ccbbabb.

Defines rule #10.

Overlap of [29] abacb=acbba with [8] cbbb=cc:

Critical pair: abacc=acbbabb.

Defines rule #19.