Certificate for #4849 ⟨a, b | ababbbba=baa⟩

Completion settings:

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

Axiom: ababbbba=baa.

Referenced by [3].

Axiom: baa=c.

Defines rule #3.

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

Simplify [1] ababbbba=baa.

Reduce RHS:

Defines rule #11.

Referenced by [4], [5], [6], [7], [8].

Overlap of [3] ababbbba=c with [3] ababbbba=c:

Critical pair: ababbbbc=cbabbbba.

Flip LHS and RHS.

Referenced by [6], [13].

Overlap of [3] ababbbba=c with [2] baa=c:

Critical pair: ababbbc=ca.

Defines rule #1.

Referenced by [7], [10].

Overlap of [2] baa=c with [3] ababbbba=c:

Critical pair: bac=cbabbbba.

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [7], [8], [9], [11], [13], [14].

Overlap of [3] ababbbba=c with [5] ababbbc=ca:

Critical pair: ababbbbca=cbabbbc.

Reduce LHS:

Defines rule #5.

Referenced by [10], [11], [12].

Overlap of [3] ababbbba=c with [6] ababbbbc=bac:

Critical pair: ababbbbbac=cbabbbbc.

Defines rule #12.

Overlap of [2] baa=c with [6] ababbbbc=bac:

Critical pair: babac=cbabbbbc.

Defines rule #4.

Referenced by [12].

Overlap of [7] baca=cbabbbc with [5] ababbbc=ca:

Critical pair: bacca=cbabbbcbabbbc.

Flip LHS and RHS.

Defines rule #9.

Overlap of [7] baca=cbabbbc with [6] ababbbbc=bac:

Critical pair: bacbac=cbabbbcbabbbbc.

Flip LHS and RHS.

Defines rule #10.

Overlap of [9] babac=cbabbbbc with [7] baca=cbabbbc:

Critical pair: bacbabbbc=cbabbbbca.

Flip LHS and RHS.

Defines rule #8.

Simplify [4] cbabbbba=ababbbbc.

Reduce RHS:

Defines rule #6.

Referenced by [14].

Overlap of [13] cbabbbba=bac with [6] ababbbbc=bac:

Critical pair: cbabbbbbac=bacbabbbbc.

Defines rule #7.