Certificate for #5442 ⟨a, b | aaaa=1, ababbb=1⟩

Completion settings:

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

Axiom: aaaa=1.

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

Axiom: ababbb=1.

Referenced by [3], [6], [7], [8], [14], [15], [16].

Overlap of [1] aaaa=1 with [2] ababbb=1:

Critical pair: aaa=babbb.

Defines rule #5.

Referenced by [4], [9], [13], [15].

Overlap of [1] aaaa=1 with [3] aaa=babbb:

Critical pair: babbba=1.

Referenced by [5], [9].

Overlap of [4] babbba=1 with [4] babbba=1:

Critical pair: babb=bbba.

Flip LHS and RHS.

Referenced by [6], [7], [8], [11], [13], [14].

Overlap of [2] ababbb=1 with [5] bbba=babb:

Critical pair: abababb=a.

Referenced by [9].

Overlap of [2] ababbb=1 with [5] bbba=babb:

Critical pair: ababbabb=ba.

Referenced by [12].

Overlap of [2] ababbb=1 with [5] bbba=babb:

Critical pair: ababbbabb=bba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [10], [12], [13], [15].

Overlap of [1] aaaa=1 with [6] abababb=a:

Critical pair: aaaa=bababb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [10].

Overlap of [9] bababb=1 with [8] bba=abb:

Critical pair: babaabb=a.

Referenced by [11].

Overlap of [10] babaabb=a with [5] bbba=babb:

Critical pair: babaababb=aba.

Referenced by [15].

Simplify [7] ababbabb=ba.

Reduce LHS:

Referenced by [13], [14].

Overlap of [12] abaabbbb=ba with [5] bbba=babb:

Critical pair: abaabbabb=baa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [15].

Overlap of [12] abaabbbb=ba with [5] bbba=babb:

Critical pair: abaabbbabb=baba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [15].

Overlap of [11] babaababb=aba with [14] baba=abab:

Critical pair: ababababb=aba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [16].

Overlap of [2] ababbb=1 with [15] aba=bbbbbbbbbbbbb:

Critical pair: bbbbbbbbbbbbbbbb=1.

Defines rule #1.