Certificate for #4671 ⟨a, b | aaab=a, bbab=a⟩

Completion settings:

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

Axiom: aaab=a.

Referenced by [3], [5], [6], [7], [8], [9].

Axiom: bbab=a.

Referenced by [3], [4].

Overlap of [1] aaab=a with [2] bbab=a:

Critical pair: aaaa=abab.

Flip LHS and RHS.

Referenced by [4].

Overlap of [2] bbab=a with [2] bbab=a:

Critical pair: bbaa=abab.

Reduce RHS:

Referenced by [5].

Overlap of [4] bbaa=aaaa with [1] aaab=a:

Critical pair: bba=aaaaab.

Reduce RHS:

Defines rule #3.

Referenced by [6].

Overlap of [1] aaab=a with [5] bba=aaa:

Critical pair: aaaaaa=aba.

Flip LHS and RHS.

Referenced by [7], [8].

Overlap of [1] aaab=a with [6] aba=aaaaaa:

Critical pair: aaaaaaaa=aa.

Referenced by [8].

Overlap of [6] aba=aaaaaa with [1] aaab=a:

Critical pair: aba=aaaaaaaab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [9], [10].

Overlap of [1] aaab=a with [8] aab=aaaaaa:

Critical pair: aaaaaaa=a.

Defines rule #1.

Referenced by [10].

Overlap of [9] aaaaaaa=a with [8] aab=aaaaaa:

Critical pair: aaaaaaaaaaa=ab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.