Certificate for #3784 ⟨a, b | ababbabaab=b⟩

Completion settings:

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

Axiom: ababbabaab=b.

Referenced by [3].

Axiom: abaab=c.

Defines rule #2.

Referenced by [3], [4], [5], [8].

Overlap of [1] ababbabaab=b with [2] abaab=c:

Critical pair: ababbc=b.

Defines rule #4.

Referenced by [5], [6], [7], [9], [10], [12], [14], [15].

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

Critical pair: abac=caab.

Flip LHS and RHS.

Defines rule #1.

Referenced by [6], [8].

Overlap of [2] abaab=c with [3] ababbc=b:

Critical pair: abab=cabbc.

Flip LHS and RHS.

Defines rule #3.

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

Overlap of [3] ababbc=b with [4] caab=abac:

Critical pair: ababbabac=baab.

Defines rule #10.

Referenced by [11].

Overlap of [3] ababbc=b with [5] cabbc=abab:

Critical pair: ababbabab=babbc.

Defines rule #14.

Referenced by [13], [15].

Overlap of [5] cabbc=abab with [4] caab=abac:

Critical pair: cabbabac=ababaab.

Reduce RHS:

Defines rule #7.

Referenced by [10], [11].

Overlap of [5] cabbc=abab with [5] cabbc=abab:

Critical pair: cabbabab=abababbc.

Reduce RHS:

Defines rule #12.

Referenced by [12], [13], [14].

Overlap of [3] ababbc=b with [8] cabbabac=abc:

Critical pair: ababbabc=babbabac.

Defines rule #9.

Overlap of [5] cabbc=abab with [8] cabbabac=abc:

Critical pair: cabbabc=abababbabac.

Reduce RHS:

Defines rule #6.

Overlap of [3] ababbc=b with [9] cabbabab=abb:

Critical pair: ababbabb=babbabab.

Defines rule #13.

Overlap of [5] cabbc=abab with [9] cabbabab=abb:

Critical pair: cabbabb=abababbabab.

Reduce RHS:

Defines rule #11.

Overlap of [9] cabbabab=abb with [3] ababbc=b:

Critical pair: cabbb=abbbc.

Defines rule #5.

Overlap of [7] ababbabab=babbc with [3] ababbc=b:

Critical pair: ababbb=babbcbc.

Defines rule #8.