Certificate for #5521 ⟨a, b | aaab=1, bbbbbb=1⟩

Completion settings:

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

Axiom: aaab=1.

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

Axiom: bbbbbb=1.

Referenced by [3].

Overlap of [1] aaab=1 with [2] bbbbbb=1:

Critical pair: aaa=bbbbb.

Flip LHS and RHS.

Referenced by [4], [5].

Overlap of [1] aaab=1 with [3] bbbbb=aaa:

Critical pair: aaaaaa=bbbb.

Flip LHS and RHS.

Referenced by [6].

Overlap of [3] bbbbb=aaa with [3] bbbbb=aaa:

Critical pair: baaa=aaab.

Reduce RHS:

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

Overlap of [4] bbbb=aaaaaa with [5] baaa=1:

Critical pair: bbb=aaaaaaaaa.

Referenced by [7].

Overlap of [6] bbb=aaaaaaaaa with [5] baaa=1:

Critical pair: bb=aaaaaaaaaaaa.

Referenced by [8].

Overlap of [7] bb=aaaaaaaaaaaa with [5] baaa=1:

Critical pair: b=aaaaaaaaaaaaaaa.

Defines rule #2.

Referenced by [9].

Overlap of [5] baaa=1 with [8] b=aaaaaaaaaaaaaaa:

Critical pair: aaaaaaaaaaaaaaaaaa=1.

Defines rule #1.