Certificate for #4855 ⟨a, b | abbaaaab=aba⟩

Completion settings:

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

Axiom: abbaaaab=aba.

Referenced by [3].

Axiom: baaaa=c.

Defines rule #9.

Referenced by [3], [4], [5], [7], [14], [16], [17], [21], [25].

Overlap of [1] abbaaaab=aba with [2] baaaa=c:

Critical pair: abcb=aba.

Defines rule #1.

Referenced by [4], [5], [6], [9].

Overlap of [2] baaaa=c with [3] abcb=aba:

Critical pair: baaaaba=cbcb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [6], [7], [8], [10], [11], [13], [18].

Overlap of [3] abcb=aba with [2] baaaa=c:

Critical pair: abcc=abaaaaa.

Reduce RHS:

Defines rule #5.

Referenced by [9].

Overlap of [3] abcb=aba with [4] cbcb=cba:

Critical pair: abcba=abacb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

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

Overlap of [4] cbcb=cba with [2] baaaa=c:

Critical pair: cbcc=cbaaaaa.

Reduce RHS:

Defines rule #8.

Referenced by [9], [10], [12], [15], [19], [22], [23], [24], [26], [27], [28].

Overlap of [4] cbcb=cba with [4] cbcb=cba:

Critical pair: cbcba=cbacb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [13], [14], [15], [16], [20].

Overlap of [3] abcb=aba with [7] cbcc=cca:

Critical pair: abcca=abacc.

Reduce LHS:

Defines rule #11.

Referenced by [17], [20].

Overlap of [4] cbcb=cba with [7] cbcc=cca:

Critical pair: cbcca=cbacc.

Reduce LHS:

Defines rule #14.

Referenced by [23], [25].

Overlap of [6] abacb=abaa with [4] cbcb=cba:

Critical pair: abacba=abaacb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #10.

Overlap of [6] abacb=abaa with [7] cbcc=cca:

Critical pair: abacca=abaacc.

Defines rule #17.

Referenced by [17].

Overlap of [4] cbcb=cba with [8] cbacb=cbaa:

Critical pair: cbcbaa=cbaacb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #13.

Overlap of [6] abacb=abaa with [8] cbacb=cbaa:

Critical pair: abacbaa=abaaacb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #16.

Referenced by [17], [18], [19], [20].

Overlap of [8] cbacb=cbaa with [7] cbcc=cca:

Critical pair: cbacca=cbaacc.

Defines rule #20.

Referenced by [25].

Overlap of [8] cbacb=cbaa with [8] cbacb=cbaa:

Critical pair: cbacbaa=cbaaacb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #19.

Referenced by [25], [26].

Overlap of [14] abaaacb=ac with [2] baaaa=c:

Critical pair: abaaacc=acaaaa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #22.

Overlap of [14] abaaacb=ac with [4] cbcb=cba:

Critical pair: abaaacba=accb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [21], [22].

Overlap of [14] abaaacb=ac with [7] cbcc=cca:

Critical pair: abaaacca=accc.

Defines rule #26.

Overlap of [14] abaaacb=ac with [8] cbacb=cbaa:

Critical pair: abaaacbaa=acacb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #12.

Referenced by [27].

Overlap of [2] baaaa=c with [18] accb=aca:

Critical pair: baaaaca=cccb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.

Referenced by [23], [24].

Overlap of [18] accb=aca with [7] cbcc=cca:

Critical pair: accca=acacc.

Defines rule #18.

Overlap of [7] cbcc=cca with [21] cccb=cca:

Critical pair: cbcca=ccacb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #15.

Referenced by [28].

Overlap of [21] cccb=cca with [7] cbcc=cca:

Critical pair: cccca=ccacc.

Defines rule #21.

Overlap of [16] cbaaacb=cc with [2] baaaa=c:

Critical pair: cbaaacc=ccaaaa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #24.

Overlap of [16] cbaaacb=cc with [7] cbcc=cca:

Critical pair: cbaaacca=cccc.

Defines rule #27.

Overlap of [20] acacb=abacc with [7] cbcc=cca:

Critical pair: acacca=abacccc.

Defines rule #23.

Overlap of [23] ccacb=cbacc with [7] cbcc=cca:

Critical pair: ccacca=cbacccc.

Defines rule #25.