Certificate for #14463 ⟨a, b | aaab=a, bbabb=a⟩

Completion settings:

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

Axiom: aaab=a.

Referenced by [4], [5], [6], [7], [8], [12], [13].

Axiom: bbabb=a.

Referenced by [3], [5].

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

Critical pair: bbaa=aabb.

Flip LHS and RHS.

Referenced by [4], [5], [9].

Overlap of [1] aaab=a with [3] aabb=bbaa:

Critical pair: abbaa=ab.

Referenced by [6], [7], [10].

Overlap of [3] aabb=bbaa with [2] bbabb=a:

Critical pair: aaa=bbaaabb.

Reduce RHS:

Flip LHS and RHS.

Referenced by [10].

Overlap of [1] aaab=a with [4] abbaa=ab:

Critical pair: aaab=abaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [8], [11], [14].

Overlap of [4] abbaa=ab with [1] aaab=a:

Critical pair: abba=abab.

Flip LHS and RHS.

Referenced by [9], [11].

Overlap of [6] abaa=a with [1] aaab=a:

Critical pair: aba=aab.

Flip LHS and RHS.

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

Overlap of [3] aabb=bbaa with [8] aab=aba:

Critical pair: abab=bbaa.

Reduce LHS:

Referenced by [10], [12].

Overlap of [4] abbaa=ab with [8] aab=aba:

Critical pair: abbaba=abb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [11].

Overlap of [6] abaa=a with [8] aab=aba:

Critical pair: ababa=ab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [12], [14].

Simplify [9] abba=bbaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [13].

Overlap of [12] bbaa=aaaaaa with [1] aaab=a:

Critical pair: bba=aaaaaaab.

Reduce RHS:

Defines rule #3.

Overlap of [6] abaa=a with [11] ab=aaaaaaa:

Critical pair: aaaaaaaaa=a.

Defines rule #1.