Certificate for #12236 ⟨a, b | aaab=aa, bbab=a⟩

Completion settings:

• Reduction order:
  • Left-to-right recursive path with deg(a) = 0; deg(b) = 1

Axiom: aaab=aa.

Referenced by [4], [5], [7], [8].

Axiom: bbab=a.

Defines rule #5.

Referenced by [3], [4], [6], [9], [11].

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

Critical pair: bbaa=abab.

Flip LHS and RHS.

Referenced by [4], [5], [6], [7], [12].

Overlap of [1] aaab=aa with [2] bbab=a:

Critical pair: aaaa=aabab.

Reduce RHS:

Flip LHS and RHS.

Referenced by [5], [9].

Overlap of [1] aaab=aa with [3] abab=bbaa:

Critical pair: aabbaa=aaab.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Referenced by [8].

Overlap of [2] bbab=a with [3] abab=bbaa:

Critical pair: bbbbaa=aab.

Referenced by [10].

Overlap of [3] abab=bbaa with [3] abab=bbaa:

Critical pair: abbbaa=bbaaab.

Reduce RHS:

Referenced by [11].

Overlap of [5] aaaaa=aa with [1] aaab=aa:

Critical pair: aaaa=aab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [10].

Overlap of [2] bbab=a with [4] abbaa=aaaa:

Critical pair: bbaaaa=abaa.

Referenced by [11].

Simplify [6] bbbbaa=aab.

Reduce RHS:

Referenced by [11].

Overlap of [2] bbab=a with [10] bbbbaa=aaaa:

Critical pair: bbaaaaa=abbbaa.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [12].

Simplify [3] abab=bbaa.

Reduce RHS:

Defines rule #4.