Certificate for #5619 ⟨a, b | aaabba=babba⟩

Completion settings:

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

Axiom: aaabba=babba.

Referenced by [3].

Axiom: babba=c.

Defines rule #2.

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

Simplify [1] aaabba=babba.

Reduce RHS:

Defines rule #9.

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

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

Critical pair: babc=cbba.

Defines rule #1.

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

Critical pair: aaabbc=caabba.

Referenced by [8], [10].

Overlap of [3] aaabba=c with [2] babba=c:

Critical pair: aaabc=cbba.

Defines rule #6.

Referenced by [8].

Overlap of [2] babba=c with [3] aaabba=c:

Critical pair: babbc=caabba.

Flip LHS and RHS.

Defines rule #5.

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

Overlap of [3] aaabba=c with [6] aaabc=cbba:

Critical pair: aaabbcbba=caabc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Overlap of [7] caabba=babbc with [3] aaabba=c:

Critical pair: caabbc=babbcaabba.

Reduce RHS:

Flip LHS and RHS.

Defines rule #4.

Simplify [5] aaabbc=caabba.

Reduce RHS:

Defines rule #7.

Referenced by [11], [12].

Overlap of [3] aaabba=c with [10] aaabbc=babbc:

Critical pair: aaabbbabbc=caabbc.

Defines rule #10.

Overlap of [7] caabba=babbc with [10] aaabbc=babbc:

Critical pair: caabbbabbc=babbcaabbc.

Defines rule #8.