Certificate for #16437 ⟨a, b | aba=bb, aaaa=aa⟩

Completion settings:

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

Axiom: aba=bb.

Flip LHS and RHS.

Defines rule #2.

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

Axiom: aaaa=aa.

Defines rule #1.

Referenced by [8].

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

Critical pair: baba=abab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [4], [6].

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

Critical pair: abbaba=babaab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [5], [6].

Overlap of [1] bb=aba with [4] babaab=aabaaba:

Critical pair: baabaaba=abaabaab.

Flip LHS and RHS.

Defines rule #6.

Overlap of [3] abab=baba with [4] babaab=aabaaba:

Critical pair: aaabaaba=babaaab.

Flip LHS and RHS.

Defines rule #5.

Referenced by [7].

Overlap of [1] bb=aba with [6] babaaab=aaabaaba:

Critical pair: baaabaaba=abaabaaab.

Flip LHS and RHS.

Defines rule #7.

Referenced by [8].

Overlap of [2] aaaa=aa with [7] abaabaaab=baaabaaba:

Critical pair: aaabaaabaaba=aabaabaaab.

Reduce RHS:

Defines rule #8.