Certificate for #3771 ⟨a, b | aaaa=bb, abab=1⟩

Completion settings:

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

Axiom: aaaa=bb.

Flip LHS and RHS.

Defines rule #3.

Referenced by [3], [4], [7], [9], [13].

Axiom: abab=1.

Referenced by [4], [10], [11], [13].

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

Critical pair: baaaa=aaaab.

Flip LHS and RHS.

Referenced by [5], [6], [7], [9], [11], [13].

Overlap of [2] abab=1 with [1] bb=aaaa:

Critical pair: abaaaaa=b.

Referenced by [5], [6], [7].

Overlap of [3] aaaab=baaaa with [4] abaaaaa=b:

Critical pair: aaab=baaaaaaaaa.

Referenced by [7].

Overlap of [4] abaaaaa=b with [3] aaaab=baaaa:

Critical pair: abaabaaaa=bab.

Referenced by [8].

Overlap of [4] abaaaaa=b with [3] aaaab=baaaa:

Critical pair: abaaabaaaa=baab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [8].

Simplify [6] abaabaaaa=bab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [9], [10], [11].

Overlap of [1] bb=aaaa with [8] bab=aaaaaaaaaaaaaaaaaaaaaaa:

Critical pair: baaaaaaaaaaaaaaaaaaaaaaa=aaaaab.

Reduce RHS:

Flip LHS and RHS.

Referenced by [10].

Overlap of [2] abab=1 with [8] bab=aaaaaaaaaaaaaaaaaaaaaaa:

Critical pair: abaaaaaaaaaaaaaaaaaaaaaaaa=ab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [12].

Overlap of [8] bab=aaaaaaaaaaaaaaaaaaaaaaa with [2] abab=1:

Critical pair: b=aaaaaaaaaaaaaaaaaaaaaaaab.

Reduce RHS:

Flip LHS and RHS.

Referenced by [12].

Simplify [10] ab=baaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa.

Reduce RHS:

Defines rule #2.

Referenced by [13].

Overlap of [2] abab=1 with [12] ab=baaaaaaaaaaaaaaaaaaa:

Critical pair: baaaaaaaaaaaaaaaaaaaab=1.

Reduce LHS:

Defines rule #1.