Certificate for #4212 ⟨a, b | aabbbbaba=ba⟩

Completion settings:

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

Axiom: aabbbbaba=ba.

Referenced by [3].

Axiom: bbba=c.

Defines rule #6.

Referenced by [3], [4], [7], [8], [9].

Overlap of [1] aabbbbaba=ba with [2] bbba=c:

Critical pair: aabcba=ba.

Defines rule #2.

Referenced by [4], [5], [6], [7].

Overlap of [2] bbba=c with [3] aabcba=ba:

Critical pair: bbbba=cabcba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [6], [8], [10], [12].

Overlap of [3] aabcba=ba with [3] aabcba=ba:

Critical pair: aabcbba=baabcba.

Reduce RHS:

Defines rule #8.

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

Overlap of [4] cabcba=bc with [3] aabcba=ba:

Critical pair: cabcbba=bcabcba.

Reduce RHS:

Defines rule #10.

Referenced by [8].

Overlap of [3] aabcba=ba with [5] aabcbba=bba:

Critical pair: aabcbbba=baabcbba.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Referenced by [10], [11].

Overlap of [4] cabcba=bc with [5] aabcbba=bba:

Critical pair: cabcbbba=bcabcbba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #7.

Overlap of [5] aabcbba=bba with [5] aabcbba=bba:

Critical pair: aabcbbbba=bbaabcbba.

Reduce LHS:

Reduce RHS:

Defines rule #3.

Referenced by [12].

Overlap of [4] cabcba=bc with [7] aabcc=c:

Critical pair: cabcbc=bcabcc.

Defines rule #5.

Referenced by [12].

Overlap of [5] aabcbba=bba with [7] aabcc=c:

Critical pair: aabcbbc=bbaabcc.

Reduce RHS:

Defines rule #9.

Overlap of [4] cabcba=bc with [9] aabcbc=bc:

Critical pair: cabcbbc=bcabcbc.

Reduce RHS:

Defines rule #11.