Certificate for #13109 ⟨a, b | bab=aba, abba=b⟩

Completion settings:

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

Axiom: bab=aba.

Defines rule #4.

Referenced by [3], [4], [5], [6].

Axiom: abba=b.

Referenced by [4], [8].

Overlap of [1] bab=aba with [1] bab=aba:

Critical pair: baaba=abaab.

Flip LHS and RHS.

Defines rule #5.

Overlap of [1] bab=aba with [2] abba=b:

Critical pair: bb=ababa.

Reduce RHS:

Defines rule #3.

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

Overlap of [1] bab=aba with [4] bb=aabaa:

Critical pair: baaabaa=abab.

Reduce RHS:

Referenced by [7].

Overlap of [4] bb=aabaa with [1] bab=aba:

Critical pair: baba=aabaaab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [7].

Overlap of [6] aabaaab=abaa with [5] baaabaa=aaba:

Critical pair: aaaaba=abaaaa.

Referenced by [9].

Overlap of [2] abba=b with [4] bb=aabaa:

Critical pair: aaabaaa=b.

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

Overlap of [7] aaaaba=abaaaa with [8] aaabaaa=b:

Critical pair: ab=abaaaaaa.

Flip LHS and RHS.

Referenced by [10].

Overlap of [8] aaabaaa=b with [9] abaaaaaa=ab:

Critical pair: aaab=baaa.

Defines rule #2.

Referenced by [11].

Overlap of [8] aaabaaa=b with [10] aaab=baaa:

Critical pair: baaaaaa=b.

Defines rule #1.