Certificate for #22799 ⟨a, b | aaa=1, ababb=bab⟩

Completion settings:

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

Axiom: aaa=1.

Defines rule #7.

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

Axiom: ababb=bab.

Referenced by [3], [5], [9].

Overlap of [1] aaa=1 with [2] ababb=bab:

Critical pair: aabab=babb.

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

Overlap of [1] aaa=1 with [3] aabab=babb:

Critical pair: aababb=abab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [6], [7], [8], [9], [10], [11].

Overlap of [3] aabab=babb with [2] ababb=bab:

Critical pair: aabbab=babbabb.

Defines rule #8.

Referenced by [8], [9].

Overlap of [1] aaa=1 with [4] abab=babbb:

Critical pair: aababbb=bab.

Reduce LHS:

Defines rule #1.

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

Overlap of [4] abab=babbb with [4] abab=babbb:

Critical pair: abbabbb=babbbab.

Flip LHS and RHS.

Defines rule #5.

Referenced by [9], [10].

Overlap of [5] aabbab=babbabb with [4] abab=babbb:

Critical pair: aabbbabbb=babbabbab.

Flip LHS and RHS.

Referenced by [14].

Overlap of [2] ababb=bab with [7] babbbab=abbabbb:

Critical pair: abababbabbb=bababbbab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [10], [14].

Overlap of [9] bbabbab=abbbabb with [7] babbbab=abbabbb:

Critical pair: bbababbabbb=abbbabbbbab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [11], [12].

Overlap of [6] babbbb=bab with [10] abbbbabbb=bbbbabb:

Critical pair: bbbbbabb=bababbb.

Reduce RHS:

Referenced by [13].

Overlap of [10] abbbbabbb=bbbbabb with [6] babbbb=bab:

Critical pair: abbbbab=bbbbabbb.

Defines rule #4.

Overlap of [11] bbbbbabb=bbabb with [6] babbbb=bab:

Critical pair: bbbbbab=bbabbbb.

Reduce RHS:

Defines rule #2.

Overlap of [8] babbabbab=aabbbabbb with [9] bbabbab=abbbabb:

Critical pair: baabbbabb=aabbbabbb.

Referenced by [15].

Overlap of [14] baabbbabb=aabbbabbb with [6] babbbb=bab:

Critical pair: baabbbab=aabbbabbbbb.

Reduce RHS:

Defines rule #9.