Certificate for #4836 ⟨a, b | ababbaab=bab⟩

Completion settings:

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

Axiom: ababbaab=bab.

Referenced by [3].

Axiom: bba=c.

Defines rule #7.

Referenced by [3], [4], [5], [6], [7], [8].

Overlap of [1] ababbaab=bab with [2] bba=c:

Critical pair: abacab=bab.

Defines rule #4.

Referenced by [4], [5], [6], [8], [9], [11], [15], [17].

Overlap of [2] bba=c with [3] abacab=bab:

Critical pair: bbbab=cbacab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [9], [10], [12], [13], [16], [18], [20], [21], [22], [23], [24].

Overlap of [3] abacab=bab with [2] bba=c:

Critical pair: abacac=babba.

Reduce RHS:

Defines rule #1.

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

Overlap of [3] abacab=bab with [3] abacab=bab:

Critical pair: abacbab=babacab.

Reduce RHS:

Defines rule #13.

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

Overlap of [2] bba=c with [5] abacac=bac:

Critical pair: bbbac=cbacac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [10], [14].

Overlap of [3] abacab=bab with [5] abacac=bac:

Critical pair: abacbac=babacac.

Reduce RHS:

Defines rule #8.

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

Overlap of [4] cbacab=bcb with [3] abacab=bab:

Critical pair: cbacbab=bcbacab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #14.

Overlap of [4] cbacab=bcb with [5] abacac=bac:

Critical pair: cbacbac=bcbacac.

Reduce RHS:

Flip LHS and RHS.

Defines rule #9.

Referenced by [15].

Overlap of [3] abacab=bab with [8] abacbac=cc:

Critical pair: abaccc=babacbac.

Reduce RHS:

Defines rule #3.

Referenced by [15], [16].

Overlap of [4] cbacab=bcb with [8] abacbac=cc:

Critical pair: cbaccc=bcbacbac.

Flip LHS and RHS.

Defines rule #18.

Overlap of [8] abacbac=cc with [4] cbacab=bcb:

Critical pair: ababcb=ccab.

Defines rule #15.

Referenced by [22].

Overlap of [8] abacbac=cc with [7] cbacac=bcc:

Critical pair: ababcc=ccac.

Defines rule #10.

Referenced by [21].

Overlap of [3] abacab=bab with [11] abaccc=bcc:

Critical pair: abacbcc=babaccc.

Reduce RHS:

Defines rule #11.

Referenced by [23].

Overlap of [4] cbacab=bcb with [11] abaccc=bcc:

Critical pair: cbacbcc=bcbaccc.

Flip LHS and RHS.

Defines rule #12.

Overlap of [3] abacab=bab with [6] abacbab=cb:

Critical pair: abaccb=babacbab.

Reduce RHS:

Defines rule #6.

Referenced by [20].

Overlap of [4] cbacab=bcb with [6] abacbab=cb:

Critical pair: cbaccb=bcbacbab.

Flip LHS and RHS.

Defines rule #21.

Overlap of [6] abacbab=cb with [6] abacbab=cb:

Critical pair: abacbcb=cbacbab.

Defines rule #16.

Referenced by [24].

Overlap of [4] cbacab=bcb with [17] abaccb=bcb:

Critical pair: cbacbcb=bcbaccb.

Flip LHS and RHS.

Defines rule #17.

Overlap of [4] cbacab=bcb with [14] ababcc=ccac:

Critical pair: cbacccac=bcbabcc.

Flip LHS and RHS.

Defines rule #19.

Overlap of [4] cbacab=bcb with [13] ababcb=ccab:

Critical pair: cbacccab=bcbabcb.

Flip LHS and RHS.

Defines rule #22.

Overlap of [4] cbacab=bcb with [15] abacbcc=cbacbac:

Critical pair: cbaccbacbac=bcbacbcc.

Flip LHS and RHS.

Defines rule #20.

Overlap of [4] cbacab=bcb with [19] abacbcb=cbacbab:

Critical pair: cbaccbacbab=bcbacbcb.

Flip LHS and RHS.

Defines rule #23.