Certificate for #4828 ⟨a, b | abababba=bab⟩

Completion settings:

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

Axiom: abababba=bab.

Referenced by [3].

Axiom: ababba=c.

Referenced by [3], [4].

Overlap of [1] abababba=bab with [2] ababba=c:

Critical pair: abc=bab.

Flip LHS and RHS.

Defines rule #1.

Referenced by [4], [5], [6], [9], [10], [11], [12], [14], [15].

Overlap of [2] ababba=c with [3] bab=abc:

Critical pair: aabcba=c.

Defines rule #2.

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

Overlap of [3] bab=abc with [3] bab=abc:

Critical pair: baabc=abcab.

Defines rule #4.

Referenced by [8], [9], [15].

Overlap of [4] aabcba=c with [3] bab=abc:

Critical pair: aabcabc=cb.

Defines rule #5.

Referenced by [9], [13].

Overlap of [4] aabcba=c with [4] aabcba=c:

Critical pair: aabcbc=cabcba.

Defines rule #3.

Overlap of [5] baabc=abcab with [4] aabcba=c:

Critical pair: bc=abcabba.

Flip LHS and RHS.

Defines rule #8.

Referenced by [10].

Overlap of [5] baabc=abcab with [6] aabcabc=cb:

Critical pair: bcb=abcababc.

Reduce RHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [11], [14].

Overlap of [3] bab=abc with [8] abcabba=bc:

Critical pair: bbc=abccabba.

Flip LHS and RHS.

Defines rule #9.

Referenced by [12], [13], [14], [15].

Overlap of [3] bab=abc with [9] abcaabcc=bcb:

Critical pair: bbcb=abccaabcc.

Defines rule #7.

Overlap of [3] bab=abc with [10] abccabba=bbc:

Critical pair: bbbc=abcccabba.

Defines rule #10.

Overlap of [6] aabcabc=cb with [10] abccabba=bbc:

Critical pair: aabcbbc=cbcabba.

Defines rule #11.

Overlap of [9] abcaabcc=bcb with [10] abccabba=bbc:

Critical pair: abcabbc=bcbabba.

Reduce RHS:

Defines rule #12.

Overlap of [10] abccabba=bbc with [5] baabc=abcab:

Critical pair: abccababcab=bbcabc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #13.