Certificate for #12322 ⟨a, b | aaab=bb, bbba=a⟩

Completion settings:

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

Axiom: aaab=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=aaab with [1] bb=aaab:

Critical pair: baaab=aaabb.

Reduce RHS:

Referenced by [4], [6].

Overlap of [3] baaab=aaaaaab with [3] baaab=aaaaaab:

Critical pair: baaaaaaaaab=aaaaaabaaab.

Reduce RHS:

Referenced by [5].

Overlap of [4] baaaaaaaaab=aaab with [2] aaaaaaba=a:

Critical pair: baaaa=aaaba.

Flip LHS and RHS.

Referenced by [6], [7].

Overlap of [3] baaab=aaaaaab with [5] aaaba=baaaa:

Critical pair: bbaaaa=aaaaaaba.

Reduce LHS:

Reduce RHS:

Referenced by [7], [8].

Overlap of [1] bb=aaab with [6] baaaaaaa=a:

Critical pair: ba=aaabaaaaaaa.

Reduce RHS:

Defines rule #2.

Referenced by [8].

Overlap of [6] baaaaaaa=a with [2] aaaaaaba=a:

Critical pair: baaaaaaa=aaaaaaba.

Reduce LHS:

Reduce RHS:

Defines rule #1.