Certificate for #12413 ⟨a, b | aaba=bb, abbb=b⟩

Completion settings:

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

Axiom: aaba=bb.

Flip LHS and RHS.

Referenced by [2], [3], [6], [7], [8], [9], [10], [11], [12].

Axiom: abbb=b.

Reduce LHS:

Referenced by [4].

Overlap of [1] bb=aaba with [1] bb=aaba:

Critical pair: baaba=aabab.

Flip LHS and RHS.

Referenced by [4], [9].

Simplify [2] aaabab=b.

Reduce LHS:

Referenced by [5], [6], [7], [9].

Overlap of [4] abaaba=b with [4] abaaba=b:

Critical pair: abab=baba.

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

Overlap of [5] abab=baba with [1] bb=aaba:

Critical pair: abaaaba=babab.

Reduce RHS:

Referenced by [7], [10].

Overlap of [5] abab=baba with [4] abaaba=b:

Critical pair: abb=babaaaba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [8], [9], [10].

Overlap of [1] bb=aaba with [7] bab=aaaba:

Critical pair: baaaba=aabaab.

Flip LHS and RHS.

Referenced by [10].

Overlap of [7] bab=aaaba with [1] bb=aaba:

Critical pair: baaaba=aaabab.

Reduce RHS:

Referenced by [10], [11].

Overlap of [7] bab=aaaba with [5] abab=baba:

Critical pair: bbaba=aaabaab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [11], [12].

Simplify [9] baaaba=b.

Reduce LHS:

Defines rule #1.

Simplify [1] bb=aaba.

Reduce RHS:

Defines rule #3.