Certificate for #2345 ⟨a, b | abbaaab=aba⟩

Completion settings:

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

Axiom: abbaaab=aba.

Referenced by [3].

Axiom: baaa=c.

Defines rule #3.

Referenced by [3], [4], [5], [7], [11], [13], [16], [21].

Overlap of [1] abbaaab=aba with [2] baaa=c:

Critical pair: abcb=aba.

Defines rule #1.

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

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

Critical pair: baaaba=cbcb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [6], [7], [8], [10], [11], [14], [17].

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

Critical pair: abcc=abaaaa.

Reduce RHS:

Defines rule #6.

Referenced by [9].

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

Critical pair: abcba=abacb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [11], [12].

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

Critical pair: cbcc=cbaaaa.

Reduce RHS:

Defines rule #9.

Referenced by [9], [10], [12], [15], [18], [19], [20], [22], [23], [24].

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

Critical pair: cbcba=cbacb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.

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

Critical pair: abcca=abacc.

Reduce LHS:

Defines rule #11.

Referenced by [17].

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

Critical pair: cbcca=cbacc.

Reduce LHS:

Defines rule #14.

Referenced by [19], [21].

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

Critical pair: abacba=abaacb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #10.

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

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

Critical pair: abacca=abaacc.

Defines rule #16.

Overlap of [2] baaa=c with [11] abaacb=ac:

Critical pair: baaac=cbaacb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #13.

Referenced by [21], [22].

Overlap of [11] abaacb=ac with [4] cbcb=cba:

Critical pair: abaacba=accb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [16], [17], [18].

Overlap of [11] abaacb=ac with [7] cbcc=cca:

Critical pair: abaacca=accc.

Defines rule #20.

Overlap of [2] baaa=c with [14] accb=aca:

Critical pair: baaaca=cccb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #8.

Referenced by [19], [20].

Overlap of [14] accb=aca with [4] cbcb=cba:

Critical pair: accba=acacb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #12.

Referenced by [23].

Overlap of [14] accb=aca with [7] cbcc=cca:

Critical pair: accca=acacc.

Defines rule #17.

Overlap of [7] cbcc=cca with [16] cccb=cca:

Critical pair: cbcca=ccacb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #15.

Referenced by [24].

Overlap of [16] cccb=cca with [7] cbcc=cca:

Critical pair: cccca=ccacc.

Defines rule #19.

Overlap of [13] cbaacb=cc with [2] baaa=c:

Critical pair: cbaacc=ccaaa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #18.

Overlap of [13] cbaacb=cc with [7] cbcc=cca:

Critical pair: cbaacca=cccc.

Defines rule #22.

Overlap of [17] acacb=abacc with [7] cbcc=cca:

Critical pair: acacca=abacccc.

Defines rule #21.

Overlap of [19] ccacb=cbacc with [7] cbcc=cca:

Critical pair: ccacca=cbacccc.

Defines rule #23.