Certificate for #4623 ⟨a, b | aaaa=a, abba=b⟩

Completion settings:

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

Axiom: aaaa=a.

Defines rule #3.

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

Axiom: abba=b.

Referenced by [3], [4], [5], [6], [10].

Overlap of [1] aaaa=a with [2] abba=b:

Critical pair: aaab=abba.

Reduce RHS:

Defines rule #4.

Referenced by [5], [9].

Overlap of [2] abba=b with [1] aaaa=a:

Critical pair: abba=baaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [6], [10].

Overlap of [3] aaab=b with [2] abba=b:

Critical pair: aab=bba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [7], [8].

Overlap of [2] abba=b with [4] baaa=b:

Critical pair: abb=baa.

Flip LHS and RHS.

Defines rule #1.

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

Overlap of [5] bba=aab with [6] baa=abb:

Critical pair: babb=aaba.

Defines rule #5.

Referenced by [8].

Overlap of [7] babb=aaba with [5] bba=aab:

Critical pair: babaab=aababa.

Reduce LHS:

Referenced by [9], [10].

Overlap of [3] aaab=b with [8] abbbbb=aababa:

Critical pair: aaaababa=bbbbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [10].

Overlap of [4] baaa=b with [8] abbbbb=aababa:

Critical pair: baaaababa=bbbbbb.

Reduce LHS:

Reduce RHS:

Defines rule #7.