Certificate for #8628 ⟨a, b | aa=a, bababb=a⟩

Completion settings:

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

Axiom: aa=a.

Defines rule #1.

Referenced by [3], [4], [6], [9].

Axiom: bababb=a.

Referenced by [3], [4], [5], [7], [9].

Overlap of [2] bababb=a with [2] bababb=a:

Critical pair: bababa=aababb.

Reduce RHS:

Referenced by [4], [8].

Overlap of [3] bababa=ababb with [3] bababa=ababb:

Critical pair: baababb=ababbba.

Reduce LHS:

Flip LHS and RHS.

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

Overlap of [2] bababb=a with [4] ababbba=a:

Critical pair: ba=aba.

Flip LHS and RHS.

Defines rule #2.

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

Overlap of [4] ababbba=a with [1] aa=a:

Critical pair: ababbba=aa.

Reduce LHS:

Reduce RHS:

Referenced by [8].

Overlap of [4] ababbba=a with [2] bababb=a:

Critical pair: ababba=ababb.

Reduce LHS:

Reduce RHS:

Referenced by [8].

Overlap of [4] ababbba=a with [3] bababa=ababb:

Critical pair: ababbababb=ababa.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [9].

Overlap of [2] bababb=a with [8] bba=abb:

Critical pair: babaabb=aa.

Reduce LHS:

Reduce RHS:

Defines rule #4.