Certificate for #27647 ⟨a, b | aa=1, ababba=bab⟩

Completion settings:

• Reduction order:
  • Left-to-right shortlex with a < b

Axiom: aa=1.

Defines rule #1.

Referenced by [3], [4], [6], [7], [8], [10].

Axiom: ababba=bab.

Referenced by [3], [4], [5], [7].

Overlap of [1] aa=1 with [2] ababba=bab:

Critical pair: abab=babba.

Flip LHS and RHS.

Referenced by [5], [7], [9].

Overlap of [2] ababba=bab with [1] aa=1:

Critical pair: ababb=baba.

Referenced by [5], [6], [7], [8], [10].

Overlap of [2] ababba=bab with [2] ababba=bab:

Critical pair: ababbbab=babbabba.

Reduce LHS:

Reduce RHS:

Referenced by [7], [8].

Overlap of [1] aa=1 with [4] ababb=baba:

Critical pair: ababa=babb.

Referenced by [7], [8], [10].

Overlap of [2] ababba=bab with [6] ababa=babb:

Critical pair: ababbbabb=babbaba.

Reduce LHS:

Reduce RHS:

Referenced by [8].

Overlap of [4] ababb=baba with [7] bbabb=bab:

Critical pair: ababbab=babababb.

Reduce LHS:

Reduce RHS:

Defines rule #3.

Referenced by [9], [10].

Simplify [3] babba=abab.

Reduce LHS:

Defines rule #2.

Referenced by [10].

Overlap of [9] baba=abab with [9] baba=abab:

Critical pair: baabab=ababba.

Reduce LHS:

Reduce RHS:

Defines rule #4.