Certificate for #14861 ⟨a, b | abba=b, baaab=a⟩

Completion settings:

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

Axiom: abba=b.

Referenced by [3], [5], [7], [8], [11].

Axiom: baaab=a.

Defines rule #6.

Referenced by [3], [4], [10], [12].

Overlap of [1] abba=b with [2] baaab=a:

Critical pair: aba=baab.

Flip LHS and RHS.

Defines rule #5.

Referenced by [5], [6], [7], [9], [10].

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

Critical pair: baaaa=aaaab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [9], [10], [12].

Overlap of [1] abba=b with [3] baab=aba:

Critical pair: ababa=bab.

Referenced by [6].

Overlap of [3] baab=aba with [5] ababa=bab:

Critical pair: babab=abaaba.

Reduce RHS:

Referenced by [7].

Overlap of [1] abba=b with [6] babab=aabaa:

Critical pair: abaabaa=bbab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [8].

Overlap of [1] abba=b with [7] bbab=aabaaa:

Critical pair: aaabaaa=bb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [9], [10].

Overlap of [3] baab=aba with [8] bb=aaabaaa:

Critical pair: baaaaabaaa=abab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.

Overlap of [8] bb=aaabaaa with [2] baaab=a:

Critical pair: ba=aaabaaaaaab.

Reduce RHS:

Flip LHS and RHS.

Referenced by [11], [12].

Overlap of [1] abba=b with [10] baaaaaaaaa=ba:

Critical pair: abba=baaaaaaaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Overlap of [10] baaaaaaaaa=ba with [4] aaaab=baaaa:

Critical pair: baaaaaaabaaaa=baaab.

Reduce LHS:

Reduce RHS:

Defines rule #1.