Certificate for #2930 ⟨a, b | aaababaabaa=1⟩

Completion settings:

• Reduction order:
  • Left-to-right recursive path with deg(c) = deg(a) = 0, c < a; deg(b) = 1
• Auxiliary generators:
  1. babaab=c

Axiom: aaababaabaa=1.

Referenced by [3].

Axiom: babaab=c.

Defines rule #9.

Referenced by [3], [5], [17], [18], [22].

Overlap of [1] aaababaabaa=1 with [2] babaab=c:

Critical pair: aaacaa=1.

Referenced by [4], [6], [7].

Overlap of [3] aaacaa=1 with [3] aaacaa=1:

Critical pair: aaac=acaa.

Referenced by [6], [7], [9].

Overlap of [2] babaab=c with [2] babaab=c:

Critical pair: babaac=cabaab.

Flip LHS and RHS.

Referenced by [11].

Overlap of [3] aaacaa=1 with [4] aaac=acaa:

Critical pair: acaaaa=1.

Referenced by [7], [8], [10].

Overlap of [3] aaacaa=1 with [4] aaac=acaa:

Critical pair: aaacaacaa=aac.

Reduce LHS:

Flip LHS and RHS.

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

Overlap of [7] aac=caa with [6] acaaaa=1:

Critical pair: a=caaaaaa.

Flip LHS and RHS.

Referenced by [9].

Overlap of [8] caaaaaa=a with [4] aaac=acaa:

Critical pair: caaaacaa=ac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [10], [13], [15], [17], [18], [19], [22], [23], [25], [27].

Overlap of [6] acaaaa=1 with [9] ac=ca:

Critical pair: caaaaa=1.

Defines rule #2.

Referenced by [15], [16], [19], [20], [24], [25], [26], [28].

Simplify [5] cabaab=babaac.

Reduce RHS:

Defines rule #4.

Referenced by [12], [13].

Overlap of [7] aac=caa with [11] cabaab=babcaa:

Critical pair: aababcaa=caaabaab.

Flip LHS and RHS.

Defines rule #7.

Overlap of [9] ac=ca with [11] cabaab=babcaa:

Critical pair: ababcaa=caabaab.

Flip LHS and RHS.

Defines rule #5.

Referenced by [14].

Overlap of [7] aac=caa with [13] caabaab=ababcaa:

Critical pair: aaababcaa=caaaabaab.

Flip LHS and RHS.

Referenced by [15], [20], [25].

Overlap of [9] ac=ca with [14] caaaabaab=aaababcaa:

Critical pair: aaaababcaa=caaaaabaab.

Reduce RHS:

Referenced by [16].

Overlap of [15] aaaababcaa=baab with [10] caaaaa=1:

Critical pair: aaaabab=baabaaa.

Referenced by [17], [18].

Overlap of [16] aaaabab=baabaaa with [2] babaab=c:

Critical pair: aaaac=baabaaaaab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [19].

Overlap of [16] aaaabab=baabaaa with [2] babaab=c:

Critical pair: aaaabac=baabaaaabaab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [26].

Overlap of [17] baabaaaaab=caaaa with [17] baabaaaaab=caaaa:

Critical pair: baabaaaaacaaaa=caaaaaabaaaaab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [20], [21].

Overlap of [10] caaaaa=1 with [19] abaaaaab=baabaaaa:

Critical pair: caaaabaabaaaa=baaaaab.

Reduce LHS:

Referenced by [22], [23].

Overlap of [19] abaaaaab=baabaaaa with [19] abaaaaab=baabaaaa:

Critical pair: abaaaabaabaaaa=baabaaaaaaaaab.

Referenced by [27].

Overlap of [20] aaababa=baaaaab with [2] babaab=c:

Critical pair: aaabac=baaaaabbaab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [26].

Overlap of [20] aaababa=baaaaab with [9] ac=ca:

Critical pair: aaababca=baaaaabc.

Referenced by [24].

Overlap of [23] aaababca=baaaaabc with [10] caaaaa=1:

Critical pair: aaabab=baaaaabcaaaa.

Defines rule #6.

Referenced by [25].

Simplify [14] caaaabaab=aaababcaa.

Reduce RHS:

Defines rule #8.

Overlap of [22] baaaaabbaab=aaabca with [18] baabaaaabaab=aaaabca:

Critical pair: baaaaabaaaabca=aaabcaaaaabaab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #11.

Overlap of [21] abaaaabaabaaaa=baabaaaaaaaaab with [9] ac=ca:

Critical pair: abaaaabaabaaaca=baabaaaaaaaaabc.

Reduce LHS:

Referenced by [28].

Overlap of [27] abaaaabaabcaaaa=baabaaaaaaaaabc with [10] caaaaa=1:

Critical pair: abaaaabaab=baabaaaaaaaaabca.

Defines rule #10.