Certificate for #24168 ⟨a, b | aa=a, bababbb=a⟩

Completion settings:

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

Axiom: aa=a.

Defines rule #3.

Referenced by [3], [4], [5], [7], [8], [10], [11], [12], [13].

Axiom: bababbb=a.

Referenced by [3], [4], [6], [7], [10], [11], [12], [13], [14].

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

Critical pair: bababba=aababbb.

Reduce RHS:

Referenced by [4], [5], [6], [9], [11], [12], [13].

Overlap of [2] bababbb=a with [3] bababba=ababbb:

Critical pair: bababbababbb=aababba.

Reduce LHS:

Reduce RHS:

Referenced by [6].

Overlap of [3] bababba=ababbb with [1] aa=a:

Critical pair: bababba=ababbba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [15].

Overlap of [3] bababba=ababbb with [2] bababbb=a:

Critical pair: bababa=ababbbbabbb.

Reduce RHS:

Referenced by [7], [12].

Overlap of [6] bababa=ababba with [2] bababbb=a:

Critical pair: baa=ababbabbb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [8], [9], [10], [11], [12], [14].

Overlap of [1] aa=a with [7] ababbabbb=ba:

Critical pair: aba=ababbabbb.

Reduce RHS:

Referenced by [9], [10], [11], [12], [13], [14], [15].

Overlap of [3] bababba=ababbb with [7] ababbabbb=ba:

Critical pair: bba=ababbbbbb.

Reduce RHS:

Referenced by [10], [11], [12], [13], [14].

Overlap of [7] ababbabbb=ba with [2] bababbb=a:

Critical pair: ababbabba=baababbb.

Reduce LHS:

Reduce RHS:

Referenced by [16].

Overlap of [7] ababbabbb=ba with [3] bababba=ababbb:

Critical pair: ababbabbababbb=baababba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [12], [13].

Overlap of [7] ababbabbb=ba with [6] bababa=ababba:

Critical pair: ababbabbababba=baababa.

Reduce LHS:

Reduce RHS:

Referenced by [13].

Overlap of [3] bababba=ababbb with [8] aba=ba:

Critical pair: bababbba=ababbbba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [15].

Overlap of [7] ababbabbb=ba with [8] aba=ba:

Critical pair: babbabbb=ba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [15], [16].

Simplify [5] ababbba=ababbb.

Reduce LHS:

Reduce RHS:

Referenced by [16].

Simplify [10] babbbbbbbbbbbbbbbbbbbbbbbb=a.

Reduce LHS:

Defines rule #1.