Certificate for #5218 ⟨a, b | aab=bb, bbba=a⟩

Completion settings:

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

Axiom: aab=bb.

Flip LHS and RHS.

Defines rule #3.

Referenced by [2], [3], [6], [7].

Axiom: bbba=a.

Reduce LHS:

Referenced by [4], [5], [6], [8].

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

Critical pair: baab=aabb.

Reduce RHS:

Referenced by [4], [6].

Overlap of [3] baab=aaaab with [3] baab=aaaab:

Critical pair: baaaaaab=aaaabaab.

Reduce RHS:

Referenced by [5].

Overlap of [4] baaaaaab=aab with [2] aaaaba=a:

Critical pair: baaa=aaba.

Flip LHS and RHS.

Referenced by [6], [7].

Overlap of [3] baab=aaaab with [5] aaba=baaa:

Critical pair: bbaaa=aaaaba.

Reduce LHS:

Reduce RHS:

Referenced by [7], [8].

Overlap of [1] bb=aab with [6] baaaaa=a:

Critical pair: ba=aabaaaaa.

Reduce RHS:

Defines rule #2.

Referenced by [8].

Overlap of [6] baaaaa=a with [2] aaaaba=a:

Critical pair: baaaaa=aaaaba.

Reduce LHS:

Reduce RHS:

Defines rule #1.