Certificate for #4808 ⟨a, b | abaabbba=bab⟩

Completion settings:

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

Axiom: abaabbba=bab.

Referenced by [3].

Axiom: abbba=c.

Defines rule #7.

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

Overlap of [1] abaabbba=bab with [2] abbba=c:

Critical pair: abac=bab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [5], [6], [7], [8], [9], [10], [13], [14], [16], [17], [20].

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

Critical pair: abbbc=cbbba.

Defines rule #6.

Referenced by [9], [11].

Overlap of [2] abbba=c with [3] bab=abac:

Critical pair: abbabac=cb.

Reduce LHS:

Defines rule #1.

Referenced by [18].

Overlap of [3] bab=abac with [2] abbba=c:

Critical pair: bc=abacbba.

Flip LHS and RHS.

Defines rule #8.

Referenced by [8].

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

Critical pair: baabac=abacab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [10], [11], [12], [18].

Overlap of [3] bab=abac with [6] abacbba=bc:

Critical pair: bbc=abacacbba.

Flip LHS and RHS.

Defines rule #11.

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

Overlap of [3] bab=abac with [4] abbbc=cbbba:

Critical pair: bcbbba=abacbbc.

Defines rule #16.

Referenced by [16], [21].

Overlap of [3] bab=abac with [7] abacab=baabac:

Critical pair: bbaabac=abacacab.

Defines rule #5.

Referenced by [15], [16], [19], [22].

Overlap of [7] abacab=baabac with [4] abbbc=cbbba:

Critical pair: abaccbbba=baabacbbc.

Defines rule #19.

Overlap of [7] abacab=baabac with [7] abacab=baabac:

Critical pair: abacbaabac=baabacacab.

Defines rule #10.

Overlap of [3] bab=abac with [8] abacacbba=bbc:

Critical pair: bbbc=abacacacbba.

Flip LHS and RHS.

Defines rule #13.

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

Overlap of [8] abacacbba=bbc with [3] bab=abac:

Critical pair: abacacbabac=bbcb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [20], [21], [22], [23], [24].

Overlap of [8] abacacbba=bbc with [10] bbaabac=abacacab:

Critical pair: abacacabacacab=bbcabac.

Defines rule #12.

Referenced by [25].

Overlap of [9] bcbbba=abacbbc with [10] bbaabac=abacacab:

Critical pair: bcbabacacab=abacbbcabac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #18.

Overlap of [3] bab=abac with [13] abacacacbba=bbbc:

Critical pair: bbbbc=abacacacacbba.

Defines rule #14.

Referenced by [24].

Overlap of [7] abacab=baabac with [13] abacacacbba=bbbc:

Critical pair: abacbbbc=baabacacacacbba.

Reduce RHS:

Defines rule #17.

Overlap of [13] abacacacbba=bbbc with [10] bbaabac=abacacab:

Critical pair: abacacacabacacab=bbbcabac.

Flip LHS and RHS.

Defines rule #15.

Overlap of [3] bab=abac with [14] bbcb=abacacabacac:

Critical pair: baabacacabacac=abacbcb.

Flip LHS and RHS.

Defines rule #9.

Overlap of [14] bbcb=abacacabacac with [9] bcbbba=abacbbc:

Critical pair: bbcabacbbc=abacacabacaccbbba.

Flip LHS and RHS.

Defines rule #24.

Overlap of [14] bbcb=abacacabacac with [10] bbaabac=abacacab:

Critical pair: bbcabacacab=abacacabacacbaabac.

Flip LHS and RHS.

Defines rule #22.

Overlap of [14] bbcb=abacacabacac with [14] bbcb=abacacabacac:

Critical pair: bbcabacacabacac=abacacabacacbcb.

Flip LHS and RHS.

Defines rule #21.

Overlap of [14] bbcb=abacacabacac with [17] bbbbc=abacacacacbba:

Critical pair: bbcabacacacacbba=abacacabacacbbbc.

Flip LHS and RHS.

Defines rule #23.

Overlap of [15] abacacabacacab=bbcabac with [15] abacacabacacab=bbcabac:

Critical pair: abacacbbcabac=bbcabacacacab.

Defines rule #20.