Certificate for #23309 ⟨a, b | aaa=1, babb=abab⟩

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], [11].

Axiom: babb=abab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [3], [4], [5], [6], [8], [9], [10], [11], [13].

Overlap of [1] aaa=1 with [2] abab=babb:

Critical pair: aababb=bab.

Reduce LHS:

Defines rule #1.

Referenced by [7], [9], [11], [12], [13], [14].

Overlap of [2] abab=babb with [2] abab=babb:

Critical pair: abbabb=babbab.

Flip LHS and RHS.

Defines rule #5.

Referenced by [5], [6], [9], [10], [11].

Overlap of [2] abab=babb with [4] babbab=abbabb:

Critical pair: aabbabb=babbbab.

Referenced by [7].

Overlap of [4] babbab=abbabb with [4] babbab=abbabb:

Critical pair: bababbabb=abbabbbab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #9.

Referenced by [9], [10].

Overlap of [5] aabbabb=babbbab with [3] babbbb=bab:

Critical pair: aabbab=babbbabbb.

Defines rule #8.

Referenced by [8].

Overlap of [7] aabbab=babbbabbb with [2] abab=babb:

Critical pair: aabbbabb=babbbabbbab.

Flip LHS and RHS.

Referenced by [10], [15].

Overlap of [4] babbab=abbabb with [6] abbabbbab=bbabbbabb:

Critical pair: bbbabbbabb=abbabbbbab.

Reduce RHS:

Referenced by [11], [12].

Overlap of [6] abbabbbab=bbabbbabb with [4] babbab=abbabb:

Critical pair: abbabbabbabb=bbabbbabbbab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [11].

Overlap of [4] babbab=abbabb with [9] bbbabbbabb=abbbabb:

Critical pair: babbaabbbabb=abbabbbbabbbabb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [13], [14].

Overlap of [9] bbbabbbabb=abbbabb with [3] babbbb=bab:

Critical pair: bbbabbbab=abbbabbbb.

Reduce RHS:

Defines rule #6.

Referenced by [15].

Overlap of [3] babbbb=bab with [11] abbbbabbb=bbbbab:

Critical pair: bbbbbab=bababbb.

Reduce RHS:

Defines rule #2.

Overlap of [11] abbbbabbb=bbbbab with [3] babbbb=bab:

Critical pair: abbbbab=bbbbabb.

Defines rule #4.

Overlap of [8] babbbabbbab=aabbbabb with [12] bbbabbbab=abbbab:

Critical pair: baabbbab=aabbbabb.

Defines rule #10.