Certificate for #4312 ⟨a, b | ababbabba=ba⟩

Completion settings:

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

Axiom: ababbabba=ba.

Defines rule #6.

Referenced by [3], [4], [5], [6], [9].

Axiom: bbbbba=c.

Referenced by [4], [7], [9], [10], [11], [16], [17].

Overlap of [1] ababbabba=ba with [1] ababbabba=ba:

Critical pair: ababbabbba=bababbabba.

Reduce RHS:

Defines rule #10.

Referenced by [6], [7], [8], [10], [12], [14], [16].

Overlap of [2] bbbbba=c with [1] ababbabba=ba:

Critical pair: bbbbbba=cbabbabba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #8.

Referenced by [5], [8], [9], [13], [15].

Overlap of [4] cbabbabba=bc with [1] ababbabba=ba:

Critical pair: cbabbabbba=bcbabbabba.

Reduce RHS:

Defines rule #14.

Referenced by [8], [10], [16].

Overlap of [1] ababbabba=ba with [3] ababbabbba=bba:

Critical pair: ababbabbbba=bababbabbba.

Reduce RHS:

Referenced by [18].

Overlap of [3] ababbabbba=bba with [3] ababbabbba=bba:

Critical pair: ababbabbbbba=bbababbabbba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [8], [9], [10], [17], [18].

Overlap of [4] cbabbabba=bc with [3] ababbabbba=bba:

Critical pair: cbabbabbbba=bcbabbabbba.

Reduce LHS:

Reduce RHS:

Defines rule #16.

Overlap of [7] bbbba=ababbac with [1] ababbabba=ba:

Critical pair: bbbbba=ababbacbabbabba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #4.

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

Overlap of [7] bbbba=ababbac with [3] ababbabbba=bba:

Critical pair: bbbbbba=ababbacbabbabbba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #7.

Referenced by [14], [15].

Overlap of [2] bbbbba=c with [9] ababbabc=c:

Critical pair: bbbbbc=cbabbabc.

Referenced by [19].

Overlap of [3] ababbabbba=bba with [9] ababbabc=c:

Critical pair: ababbabbbc=bbababbabc.

Reduce RHS:

Defines rule #11.

Overlap of [4] cbabbabba=bc with [9] ababbabc=c:

Critical pair: cbabbabbc=bcbabbabc.

Referenced by [15], [20].

Overlap of [3] ababbabbba=bba with [10] ababbabbc=bc:

Critical pair: ababbabbbbc=bbababbabbc.

Reduce RHS:

Referenced by [21].

Overlap of [4] cbabbabba=bc with [10] ababbabbc=bc:

Critical pair: cbabbabbbc=bcbabbabbc.

Reduce RHS:

Referenced by [22].

Overlap of [5] cbabbabbba=bbc with [3] ababbabbba=bba:

Critical pair: cbabbabbbbba=bbcbabbabbba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [19], [21].

Overlap of [2] bbbbba=c with [7] bbbba=ababbac:

Critical pair: bababbac=c.

Defines rule #3.

Overlap of [6] ababbabbbba=bbba with [7] bbbba=ababbac:

Critical pair: ababbaababbac=bbba.

Defines rule #12.

Overlap of [11] bbbbbc=cbabbabc with [16] bbbbc=cbabbac:

Critical pair: bcbabbac=cbabbabc.

Flip LHS and RHS.

Defines rule #5.

Referenced by [20], [22].

Simplify [13] cbabbabbc=bcbabbabc.

Reduce RHS:

Defines rule #9.

Overlap of [14] ababbabbbbc=bbbc with [16] bbbbc=cbabbac:

Critical pair: ababbacbabbac=bbbc.

Defines rule #13.

Simplify [15] cbabbabbbc=bbcbabbabc.

Reduce RHS:

Defines rule #15.