Certificate for #10664 ⟨a, b | aaaa=bbb, abab=1⟩

Completion settings:

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

Axiom: aaaa=bbb.

Flip LHS and RHS.

Referenced by [3], [4].

Axiom: abab=1.

Referenced by [4], [5], [6], [10], [16].

Overlap of [1] bbb=aaaa with [1] bbb=aaaa:

Critical pair: baaaa=aaaab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [6], [7], [8], [9], [11], [12], [14], [15], [16], [18].

Overlap of [2] abab=1 with [1] bbb=aaaa:

Critical pair: abaaaaa=bb.

Flip LHS and RHS.

Defines rule #3.

Referenced by [5], [7], [11], [12], [14], [15], [16].

Overlap of [2] abab=1 with [4] bb=abaaaaa:

Critical pair: abaabaaaaa=b.

Referenced by [8], [9], [10].

Overlap of [3] aaaab=baaaa with [2] abab=1:

Critical pair: aaa=baaaaab.

Reduce RHS:

Flip LHS and RHS.

Referenced by [7].

Overlap of [6] babaaaa=aaa with [3] aaaab=baaaa:

Critical pair: babbaaaa=aaab.

Reduce LHS:

Referenced by [11].

Overlap of [5] abaabaaaaa=b with [3] aaaab=baaaa:

Critical pair: abaabaabaaaa=bab.

Referenced by [10].

Overlap of [5] abaabaaaaa=b with [3] aaaab=baaaa:

Critical pair: abaabaaabaaaa=baab.

Referenced by [12], [13].

Overlap of [8] abaabaabaaaa=bab with [5] abaabaaaaa=b:

Critical pair: abab=baba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [14], [15], [17], [18].

Overlap of [7] baabaaaaaaaaa=aaab with [3] aaaab=baaaa:

Critical pair: baabaaaaaaaabaaaa=aaabaaab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [12], [14].

Overlap of [9] abaabaaabaaaa=baab with [3] aaaab=baaaa:

Critical pair: abaabaaabaaabaaaa=baabaaab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [13].

Overlap of [9] abaabaaabaaaa=baab with [12] baabaaab=aabaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa:

Critical pair: aaabaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa=baab.

Flip LHS and RHS.

Defines rule #5.

Referenced by [16].

Overlap of [10] baba=1 with [11] aaabaaab=baaabaaaaaaaaaaaaaaaaa:

Critical pair: babbaaabaaaaaaaaaaaaaaaaa=aabaaab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [15].

Overlap of [10] baba=1 with [14] aabaaab=baaabaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa:

Critical pair: babbaaabaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa=abaaab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Overlap of [13] baab=aaabaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa with [2] abab=1:

Critical pair: ba=aaabaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaab.

Reduce RHS:

Flip LHS and RHS.

Referenced by [17], [18].

Overlap of [10] baba=1 with [16] baaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa=ba:

Critical pair: baba=aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Overlap of [16] baaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa=ba with [3] aaaab=baaaa:

Critical pair: baaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaabaaaa=bab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.