Certificate for #20242 ⟨a, b | aba=a, bbbb=aaa⟩

Completion settings:

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

Axiom: aba=a.

Defines rule #3.

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

Axiom: bbbb=aaa.

Defines rule #5.

Referenced by [3], [6].

Overlap of [2] bbbb=aaa with [2] bbbb=aaa:

Critical pair: baaa=aaab.

Flip LHS and RHS.

Referenced by [4], [5], [7], [10].

Overlap of [1] aba=a with [3] aaab=baaa:

Critical pair: abbaaa=aaab.

Reduce RHS:

Referenced by [7].

Overlap of [3] aaab=baaa with [1] aba=a:

Critical pair: aaa=baaaa.

Flip LHS and RHS.

Referenced by [6], [8].

Overlap of [2] bbbb=aaa with [5] baaaa=aaa:

Critical pair: bbbaaa=aaaaaaa.

Referenced by [7].

Overlap of [4] abbaaa=baaa with [3] aaab=baaa:

Critical pair: abbbaaa=baaab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [8].

Overlap of [7] bbaaa=aaaaaaaa with [5] baaaa=aaa:

Critical pair: baaa=aaaaaaaaa.

Defines rule #2.

Referenced by [9], [10].

Overlap of [1] aba=a with [8] baaa=aaaaaaaaa:

Critical pair: aaaaaaaaaa=aaa.

Defines rule #1.

Simplify [3] aaab=baaa.

Reduce RHS:

Defines rule #4.