Certificate for #5374 ⟨a, b | ababbba=baab⟩

Completion settings:

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

Axiom: ababbba=baab.

Referenced by [4].

Axiom: bba=c.

Defines rule #5.

Referenced by [4], [5], [6], [8], [11], [12], [15].

Axiom: ababc=d.

Defines rule #6.

Referenced by [4], [8], [9], [10], [13], [16].

Overlap of [1] ababbba=baab with [2] bba=c:

Critical pair: ababc=baab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #8.

Referenced by [5], [6], [7], [9], [14], [17].

Overlap of [2] bba=c with [4] baab=d:

Critical pair: bd=cab.

Defines rule #1.

Referenced by [8].

Overlap of [4] baab=d with [2] bba=c:

Critical pair: baac=dba.

Defines rule #3.

Overlap of [4] baab=d with [4] baab=d:

Critical pair: baad=daab.

Defines rule #7.

Overlap of [2] bba=c with [3] ababc=d:

Critical pair: bbd=cbabc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [10], [11].

Overlap of [4] baab=d with [3] ababc=d:

Critical pair: bad=dabc.

Defines rule #2.

Overlap of [3] ababc=d with [8] cbabc=bcab:

Critical pair: ababbcab=dbabc.

Defines rule #16.

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

Overlap of [8] cbabc=bcab with [8] cbabc=bcab:

Critical pair: cbabbcab=bcabbabc.

Reduce RHS:

Defines rule #14.

Referenced by [15], [16], [17].

Overlap of [10] ababbcab=dbabc with [2] bba=c:

Critical pair: ababbcac=dbabcba.

Defines rule #12.

Overlap of [10] ababbcab=dbabc with [3] ababc=d:

Critical pair: ababbcd=dbabcabc.

Defines rule #11.

Overlap of [10] ababbcab=dbabc with [4] baab=d:

Critical pair: ababbcad=dbabcaab.

Defines rule #15.

Overlap of [11] cbabbcab=bcacbc with [2] bba=c:

Critical pair: cbabbcac=bcacbcba.

Defines rule #10.

Overlap of [11] cbabbcab=bcacbc with [3] ababc=d:

Critical pair: cbabbcd=bcacbcabc.

Defines rule #9.

Overlap of [11] cbabbcab=bcacbc with [4] baab=d:

Critical pair: cbabbcad=bcacbcaab.

Defines rule #13.