Certificate for #5201 ⟨a, b | aababba=baba⟩

Completion settings:

• Reduction order:
  • Right-to-left shortlex with b < a < c
• Auxiliary generators:
  1. baba=c

Axiom: aababba=baba.

Referenced by [3].

Axiom: baba=c.

Defines rule #2.

Referenced by [3], [4], [6], [7].

Simplify [1] aababba=baba.

Reduce RHS:

Defines rule #5.

Referenced by [5], [6], [7], [8], [9], [11], [13].

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

Critical pair: bac=cba.

Defines rule #1.

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

Critical pair: aababbc=cababba.

Referenced by [8], [10].

Overlap of [3] aababba=c with [2] baba=c:

Critical pair: aababc=cba.

Defines rule #3.

Referenced by [8].

Overlap of [2] baba=c with [3] aababba=c:

Critical pair: babc=cababba.

Flip LHS and RHS.

Defines rule #6.

Referenced by [8], [9], [10], [12], [14].

Overlap of [3] aababba=c with [6] aababc=cba:

Critical pair: aababbcba=cababc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Overlap of [7] cababba=babc with [3] aababba=c:

Critical pair: cababbc=babcababba.

Reduce RHS:

Flip LHS and RHS.

Defines rule #8.

Referenced by [13], [14].

Simplify [5] aababbc=cababba.

Reduce RHS:

Defines rule #7.

Referenced by [11], [12].

Overlap of [3] aababba=c with [10] aababbc=babc:

Critical pair: aababbbabc=cababbc.

Defines rule #11.

Overlap of [7] cababba=babc with [10] aababbc=babc:

Critical pair: cababbbabc=babcababbc.

Defines rule #12.

Overlap of [3] aababba=c with [9] babbabc=cababbc:

Critical pair: aacababbc=cbc.

Defines rule #9.

Overlap of [7] cababba=babc with [9] babbabc=cababbc:

Critical pair: cacababbc=babcbc.

Defines rule #10.