Input = − 1 + k_{1} u_{5} + k_{2} k_{10} + u_{1} k_{8} k_{1} k_{6} + k_{2} u_{7} + u_{1} k_{9} k_{1} k_{7} + k_{2} k_{11} + u_{1} u_{6} k_{3} u_{5} + k_{4} k_{10} + u_{2} k_{8} − 1 + k_{3} k_{6} + k_{4} u_{7} + u_{2} k_{9} k_{3} k_{7} + k_{4} k_{11} + u_{2} u_{6} k_{5} k_{8} + u_{3} u_{5} + u_{4} k_{10} k_{5} k_{9} + u_{3} k_{6} + u_{4} u_{7} − 1 + k_{5} u_{6} + u_{3} k_{7} + u_{4} k_{11} − 1 + k_{6} k_{3} + k_{7} u_{3} + u_{5} k_{1} k_{6} u_{2} + k_{7} k_{5} + u_{5} u_{1} k_{6} k_{4} + k_{7} u_{4} + u_{5} k_{2} k_{8} k_{1} + k_{9} k_{3} + u_{6} u_{3} − 1 + k_{8} u_{1} + k_{9} u_{2} + u_{6} k_{5} k_{8} k_{2} + k_{9} k_{4} + u_{6} u_{4} k_{10} k_{1} + k_{11} u_{3} + u_{7} k_{3} k_{10} u_{1} + k_{11} k_{5} + u_{7} u_{2} − 1 + k_{10} k_{2} + k_{11} u_{4} + u_{7} k_{4} k_{1} k_{1}^{−1} == 1 k_{1}^{−1} k_{1} == 1 k_{2} k_{2}^{−1} == 1 k_{2}^{−1} k_{2} == 1 k_{3} k_{3}^{−1} == 1 k_{3}^{−1} k_{3} == 1 k_{4} k_{4}^{−1} == 1 k_{4}^{−1} k_{4} == 1 k_{5} k_{5}^{−1} == 1 k_{5}^{−1} k_{5} == 1 k_{6} k_{6}^{−1} == 1 k_{6}^{−1} k_{6} == 1 k_{7} k_{7}^{−1} == 1 k_{7}^{−1} k_{7} == 1 k_{8} k_{8}^{−1} == 1 k_{8}^{−1} k_{8} == 1 k_{9} k_{9}^{−1} == 1 k_{9}^{−1} k_{9} == 1 k_{10} k_{10}^{−1} == 1 k_{10}^{−1} k_{10} == 1 k_{11} k_{11}^{−1} == 1 k_{11}^{−1} k_{11} == 1 File Name = thms/WoerdOutput-13805 NCMakeGB Iterations = 2 NCMakeGB on Digested Iterations = 2 SmallBasis Iterations = 1 SmallBasis on Knowns Iterations = 1 Deselect→ {} UserSelect→ {} UserUnknowns→ {} NCShortFormulas→-1 RR→True RRByCat→False SB→True SBByCat→False DegreeCap→18 DegreeSumCap→26 DegreeCapSB→19 DegreeSumCapSB→27 NCCV→False THE ORDER IS NOW THE FOLLOWING: k_{1} < k_{1}^{−1} < k_{2} < k_{2}^{−1} < k_{3} < k_{3}^{−1} < k_{4} < k_{4}^{−1} < k_{5} < k_{5}^{−1} < k_{6} < k_{6}^{−1} < k_{7} < k_{7}^{−1} < k_{8} < k_{8}^{−1} < k_{9} < k_{9}^{−1} < k_{10} < k_{10}^{−1} < k_{11} < k_{11}^{−1} ≪ u_{1} ≪ u_{2} ≪ u_{3} ≪ u_{4} ≪ u_{5} ≪ u_{6} ≪ u_{7}

YOUR SESSION HAS DIGESTED THE FOLLOWING RELATIONS

THE FOLLOWING VARIABLES HAVE BEEN SOLVED FOR: {u_{2}, u_{3}, u_{4}, u_{5}, u_{6}, u_{7}} The corresponding rules are the following: u_{2} → k_{3} k_{1}^{−1} u_{1} − k_{3} k_{1}^{−1} k_{8}^{−1} − k_{4} k_{10} k_{8}^{−1} + k_{3} k_{1}^{−1} k_{2} k_{10} k_{8}^{−1} u_{3} → −1 k_{7}^{−1} k_{6} k_{3} + k_{7}^{−1} k_{1}^{−1} k_{2} k_{10} k_{1} + k_{7}^{−1} k_{1}^{−1} u_{1} k_{8} k_{1} u_{4} → −1 k_{7}^{−1} k_{6} k_{4} − k_{7}^{−1} k_{1}^{−1} k_{2} + k_{7}^{−1} k_{1}^{−1} k_{2} k_{10} k_{2} + k_{7}^{−1} k_{1}^{−1} u_{1} k_{8} k_{2} u_{5} → k_{1}^{−1} − k_{1}^{−1} k_{2} k_{10} − k_{1}^{−1} u_{1} k_{8}

{u_{6} → \atop k_{5}^{−1} − k_{8} u_{1} k_{5}^{−1} − k_{9} k_{3} k_{1}^{−1} u_{1} k_{5}^{−1} + k_{9} k_{3} k_{1}^{−1} k_{8}^{−1} k_{5}^{−1} + k_{9} k_{4} k_{10} k_{8}^{−1} k_{5}^{−1} − k_{9} k_{3} k_{1}^{−1} k_{2} k_{10} k_{8}^{−1} k_{5}^{−1}}

u_{7} → −1 k_{2}^{−1} k_{1} k_{6} − k_{2}^{−1} u_{1} k_{9}

The expressions with unknown variables {} and knowns {k_{1}, k_{10}, k_{11}, k_{2}, k_{3}, k_{4}, k_{5}, k_{6}, k_{7}, k_{8}, k_{9}, k_{1}^{−1}, k_{10}^{−1}, k_{11}^{−1}, k_{2}^{−1}, k_{3}^{−1}, k_{4}^{−1}, k_{5}^{−1}, k_{6}^{−1}, k_{7}^{−1}, k_{8}^{−1}, k_{9}^{−1}} k_{1} k_{1}^{−1} → 1 k_{10} k_{10}^{−1} → 1 k_{11} k_{11}^{−1} → 1 k_{2} k_{2}^{−1} → 1 k_{3} k_{3}^{−1} → 1 k_{4} k_{4}^{−1} → 1 k_{5} k_{5}^{−1} → 1 k_{6} k_{6}^{−1} → 1 k_{7} k_{7}^{−1} → 1 k_{8} k_{8}^{−1} → 1 k_{9} k_{9}^{−1} → 1 k_{1}^{−1} k_{1} → 1 k_{10}^{−1} k_{10} → 1 k_{11}^{−1} k_{11} → 1 k_{2}^{−1} k_{2} → 1 k_{3}^{−1} k_{3} → 1 k_{4}^{−1} k_{4} → 1 k_{5}^{−1} k_{5} → 1

k_{6}^{−1} k_{6} → 1

k_{7}^{−1} k_{7} → 1

k_{8}^{−1} k_{8} → 1

k_{9}^{−1} k_{9} → 1

USER CREATIONS APPEAR BELOW

SOME RELATIONS WHICH APPEAR BELOW MAY BE UNDIGESTED

THE FOLLOWING VARIABLES HAVE NOT BEEN SOLVED FOR: {k_{1}, k_{10}, k_{11}, k_{2}, k_{3}, k_{4}, k_{5}, k_{6}, k_{7}, k_{8}, k_{9}, u_{1}, k_{1}^{−1}, k_{10}^{−1}, k_{11}^{−1}, k_{2}^{−1}, k_{3}^{−1}, k_{4}^{−1}, k_{5}^{−1}, k_{6}^{−1}, k_{7}^{−1}, k_{8}^{−1}, k_{9}^{−1}}

The expressions with unknown variables {u_{1}} and knowns {k_{1}, k_{10}, k_{11}, k_{2}, k_{3}, k_{4}, k_{5}, k_{6}, k_{7}, k_{8}, k_{9}, k_{1}^{−1}, k_{11}^{−1}, k_{2}^{−1}, k_{5}^{−1}, k_{7}^{−1}, k_{8}^{−1}, k_{9}^{−1}}

{k_{4} k_{2}^{−1} u_{1} → −1 k_{9}^{−1} + k_{3} k_{6} k_{9}^{−1} + k_{3} k_{1}^{−1} u_{1} − k_{3} k_{1}^{−1} k_{8}^{−1} − k_{4} k_{10} k_{8}^{−1} + k_{3} k_{1}^{−1} k_{2} k_{10} k_{8}^{−1} − \atop k_{4} k_{2}^{−1} k_{1} k_{6} k_{9}^{−1}}

{k_{1}^{−1} u_{1} k_{8} u_{1} → k_{7} k_{5} + k_{1}^{−1} u_{1} + k_{6} k_{3} k_{1}^{−1} u_{1} − k_{6} k_{3} k_{1}^{−1} k_{8}^{−1} − k_{6} k_{4} k_{10} k_{8}^{−1} − k_{1}^{−1} k_{2} k_{10} u_{1} + \atop k_{6} k_{3} k_{1}^{−1} k_{2} k_{10} k_{8}^{−1}}

{u_{1} k_{9} k_{3} k_{1}^{−1} u_{1} → u_{1} + k_{1} k_{7} k_{5} + k_{2} k_{11} k_{5} − u_{1} k_{8} u_{1} + u_{1} k_{9} k_{3} k_{1}^{−1} k_{8}^{−1} + u_{1} k_{9} k_{4} k_{10} k_{8}^{−1} − \atop u_{1} k_{9} k_{3} k_{1}^{−1} k_{2} k_{10} k_{8}^{−1}}

k_{11}^{−1} k_{2}^{−1} u_{1} k_{9} k_{3} → k_{11}^{−1} k_{10} k_{1} − k_{7}^{−1} k_{6} k_{3} − k_{11}^{−1} k_{2}^{−1} k_{1} k_{6} k_{3} + k_{7}^{−1} k_{1}^{−1} k_{2} k_{10} k_{1} + k_{7}^{−1} k_{1}^{−1} u_{1} k_{8} k_{1}

{k_{11}^{−1} k_{2}^{−1} u_{1} k_{9} k_{4} → −1 k_{11}^{−1}+k_{11}^{−1} k_{10} k_{2}−k_{7}^{−1} k_{6} k_{4}−k_{7}^{−1} k_{1}^{−1} k_{2}−k_{11}^{−1} k_{2}^{−1} k_{1} k_{6} k_{4}+k_{7}^{−1} k_{1}^{−1} k_{2} k_{10} k_{2}+ \atop k_{7}^{−1} k_{1}^{−1} u_{1} k_{8} k_{2}}

{k_{2}^{−1} u_{1} k_{8} u_{1} k_{8} → −1 k_{10} u_{1} k_{8} + k_{2}^{−1} u_{1} k_{8} − k_{2}^{−1} k_{1} k_{6} k_{3} k_{1}^{−1} − k_{2}^{−1} k_{1} k_{6} k_{4} k_{10} + k_{2}^{−1} k_{1} k_{7} k_{5} k_{8} + \atop k_{2}^{−1} k_{1} k_{6} k_{3} k_{1}^{−1} k_{2} k_{10} + k_{2}^{−1} k_{1} k_{6} k_{3} k_{1}^{−1} u_{1} k_{8}}

{k_{2}^{−1} u_{1} k_{8} u_{1} k_{9} → −1 k_{10} u_{1} k_{9} + k_{2}^{−1} u_{1} k_{9} + k_{2}^{−1} k_{1} k_{7} k_{5} k_{9} + k_{2}^{−1} k_{1} k_{6} k_{3} k_{1}^{−1} u_{1} k_{9} − \atop k_{2}^{−1} k_{1} k_{6} k_{3} k_{1}^{−1} k_{8}^{−1} k_{9} − k_{2}^{−1} k_{1} k_{6} k_{4} k_{10} k_{8}^{−1} k_{9} + k_{2}^{−1} k_{1} k_{6} k_{3} k_{1}^{−1} k_{2} k_{10} k_{8}^{−1} k_{9}}

k_{11} k_{5} k_{9} k_{3} k_{1}^{−1} u_{1} → k_{11} k_{5} − k_{10} k_{1} k_{7} k_{5} − k_{10} k_{2} k_{11} k_{5} − k_{11} k_{5} k_{8} u_{1} + k_{11} k_{5} k_{9} k_{3} k_{1}^{−1} k_{8}^{−1} + k_{11} k_{5} k_{9} k_{4} k_{10} k_{8}^{−1} + k_{2}^{−1} k_{1} k_{6} k_{3} k_{7} k_{5} + k_{2}^{−1} k_{1} k_{6} k_{4} k_{11} k_{5} + k_{2}^{−1} u_{1} k_{9} k_{3} k_{7} k_{5} + k_{2}^{−1} u_{1} k_{9} k_{4} k_{11} k_{5} − k_{11} k_{5} k_{9} k_{3} k_{1}^{−1} k_{2} k_{10} k_{8}^{−1}

k_{11} k_{7}^{−1} k_{1}^{−1} u_{1} k_{8} k_{1} → −1 k_{10} k_{1} + k_{11} k_{7}^{−1} k_{6} k_{3} + k_{2}^{−1} k_{1} k_{6} k_{3} + k_{2}^{−1} u_{1} k_{9} k_{3} − k_{11} k_{7}^{−1} k_{1}^{−1} k_{2} k_{10} k_{1}

{k_{11} k_{7}^{−1} k_{1}^{−1} u_{1} k_{8} k_{2} → 1 − k_{10} k_{2} + k_{11} k_{7}^{−1} k_{6} k_{4} + k_{11} k_{7}^{−1} k_{1}^{−1} k_{2} + k_{2}^{−1} k_{1} k_{6} k_{4} + k_{2}^{−1} u_{1} k_{9} k_{4} − \atop k_{11} k_{7}^{−1} k_{1}^{−1} k_{2} k_{10} k_{2}}

k_{7} k_{5} k_{9} k_{3} k_{1}^{−1} u_{1} → −1 k_{6} k_{3} k_{7} k_{5} − k_{6} k_{4} k_{11} k_{5} − k_{7} k_{5} k_{8} u_{1} − k_{1}^{−1} k_{2} k_{11} k_{5} + k_{7} k_{5} k_{9} k_{3} k_{1}^{−1} k_{8}^{−1} + k_{7} k_{5} k_{9} k_{4} k_{10} k_{8}^{−1} +k_{1}^{−1} k_{2} k_{10} k_{1} k_{7} k_{5} +k_{1}^{−1} k_{2} k_{10} k_{2} k_{11} k_{5} +k_{1}^{−1} u_{1} k_{8} k_{1} k_{7} k_{5} +k_{1}^{−1} u_{1} k_{8} k_{2} k_{11} k_{5} − k_{7} k_{5} k_{9} k_{3} k_{1}^{−1} k_{2} k_{10} k_{8}^{−1}

k_{7}^{−1} k_{1}^{−1} u_{1} k_{8} k_{2} k_{11}  →  k_{5} k_{8} u_{1} k_{5}^{−1}  +  k_{7}^{−1} k_{6} k_{3} k_{7}  +

k_{7}^{−1} k_{6} k_{4} k_{11} + k_{7}^{−1} k_{1}^{−1} k_{2} k_{11} + k_{5} k_{9} k_{3} k_{1}^{−1} u_{1} k_{5}^{−1} − k_{5} k_{9} k_{3} k_{1}^{−1} k_{8}^{−1} k_{5}^{−1} − k_{5} k_{9} k_{4} k_{10} k_{8}^{−1} k_{5}^{−1} − k_{7}^{−1} k_{1}^{−1} k_{2} k_{10} k_{1} k_{7} − k_{7}^{−1} k_{1}^{−1} k_{2} k_{10} k_{2} k_{11} − k_{7}^{−1} k_{1}^{−1} u_{1} k_{8} k_{1} k_{7} + k_{5} k_{9} k_{3} k_{1}^{−1} k_{2} k_{10} k_{8}^{−1} k_{5}^{−1}

k_{5}^{−1} k_{7}^{−1} k_{1}^{−1} u_{1} k_{8} k_{1} k_{7} k_{11}^{−1} → k_{8} u_{1} k_{5}^{−1} k_{11}^{−1} +k_{5}^{−1} k_{7}^{−1} k_{6} k_{4} +k_{5}^{−1} k_{7}^{−1} k_{1}^{−1} k_{2} +k_{9} k_{3} k_{1}^{−1} u_{1} k_{5}^{−1} k_{11}^{−1} − k_{9} k_{3} k_{1}^{−1} k_{8}^{−1} k_{5}^{−1} k_{11}^{−1} − k_{9} k_{4} k_{10} k_{8}^{−1} k_{5}^{−1} k_{11}^{−1} + k_{5}^{−1} k_{7}^{−1} k_{6} k_{3} k_{7} k_{11}^{−1} − k_{5}^{−1} k_{7}^{−1} k_{1}^{−1} k_{2} k_{10} k_{2} − k_{5}^{−1} k_{7}^{−1} k_{1}^{−1} u_{1} k_{8} k_{2} + k_{9} k_{3} k_{1}^{−1} k_{2} k_{10} k_{8}^{−1} k_{5}^{−1} k_{11}^{−1} − k_{5}^{−1} k_{7}^{−1} k_{1}^{−1} k_{2} k_{10} k_{1} k_{7} k_{11}^{−1} k_{9} k_{3} k_{1}^{−1} u_{1} k_{5}^{−1} k_{7}^{−1} k_{1}^{−1} u_{1} k_{8} k_{1} → k_{8} k_{1} + k_{9} k_{3} − k_{5}^{−1} k_{7}^{−1} k_{6} k_{3} + k_{8} u_{1} k_{5}^{−1} k_{7}^{−1} k_{6} k_{3} + k_{5}^{−1} k_{7}^{−1} k_{1}^{−1} k_{2} k_{10} k_{1}+k_{5}^{−1} k_{7}^{−1} k_{1}^{−1} u_{1} k_{8} k_{1}−k_{8} u_{1} k_{5}^{−1} k_{7}^{−1} k_{1}^{−1} k_{2} k_{10} k_{1}−k_{8} u_{1} k_{5}^{−1} k_{7}^{−1} k_{1}^{−1} u_{1} k_{8} k_{1}+ k_{9} k_{3} k_{1}^{−1} u_{1} k_{5}^{−1} k_{7}^{−1} k_{6} k_{3} − k_{9} k_{3} k_{1}^{−1} k_{8}^{−1} k_{5}^{−1} k_{7}^{−1} k_{6} k_{3} − k_{9} k_{4} k_{10} k_{8}^{−1} k_{5}^{−1} k_{7}^{−1} k_{6} k_{3} + k_{9} k_{3} k_{1}^{−1} k_{2} k_{10} k_{8}^{−1} k_{5}^{−1} k_{7}^{−1} k_{6} k_{3} − k_{9} k_{3} k_{1}^{−1} u_{1} k_{5}^{−1} k_{7}^{−1} k_{1}^{−1} k_{2} k_{10} k_{1} +

k_{9} k_{3} k_{1}^{−1} k_{8}^{−1} k_{5}^{−1} k_{7}^{−1} k_{1}^{−1} k_{2} k_{10} k_{1}  +  k_{9} k_{3} k_{1}^{−1} k_{8}^{−1} k_{5}^{−1} k_{7}^{−1} k_{1}^{−1} u_{1} k_{8} k_{1}  +
k_{9} k_{4} k_{10} k_{8}^{−1} k_{5}^{−1} k_{7}^{−1} k_{1}^{−1} k_{2} k_{10} k_{1}  +  k_{9} k_{4} k_{10} k_{8}^{−1} k_{5}^{−1} k_{7}^{−1} k_{1}^{−1} u_{1} k_{8} k_{1}  −

k_{9} k_{3} k_{1}^{−1} k_{2} k_{10} k_{8}^{−1} k_{5}^{−1} k_{7}^{−1} k_{1}^{−1} k_{2} k_{10} k_{1} − k_{9} k_{3} k_{1}^{−1} k_{2} k_{10} k_{8}^{−1} k_{5}^{−1} k_{7}^{−1} k_{1}^{−1} u_{1} k_{8} k_{1}

k_{9} k_{3} k_{1}^{−1} k_{2} k_{10} k_{8}^{−1} k_{9} k_{3} k_{1}^{−1} u_{1} k_{5}^{−1} k_{11}^{−1}  →  k_{9} k_{4}  −  k_{9} k_{3} k_{1}^{−1} k_{2}  +

k_{9} k_{3} k_{1}^{−1} u_{1} k_{5}^{−1} k_{11}^{−1} − k_{9} k_{3} k_{1}^{−1} k_{8}^{−1} k_{5}^{−1} k_{11}^{−1} + k_{9} k_{4} k_{10} u_{1} k_{5}^{−1} k_{11}^{−1} − k_{9} k_{4} k_{10} k_{8}^{−1} k_{5}^{−1} k_{11}^{−1} − k_{9} k_{3} k_{1}^{−1} k_{2} k_{10} u_{1} k_{5}^{−1} k_{11}^{−1} + k_{9} k_{3} k_{1}^{−1} k_{2} k_{10} k_{8}^{−1} k_{5}^{−1} k_{11}^{−1} + k_{9} k_{3} k_{1}^{−1} k_{8}^{−1} k_{9} k_{3} k_{1}^{−1} u_{1} k_{5}^{−1} k_{11}^{−1} −

k_{9} k_{3} k_{1}^{−1} k_{8}^{−1} k_{9} k_{3} k_{1}^{−1} k_{8}^{−1} k_{5}^{−1} k_{11}^{−1}  −  k_{9} k_{3} k_{1}^{−1} k_{8}^{−1} k_{9} k_{4} k_{10} k_{8}^{−1} k_{5}^{−1} k_{11}^{−1}  +
k_{9} k_{4} k_{10} k_{8}^{−1} k_{9} k_{3} k_{1}^{−1} u_{1} k_{5}^{−1} k_{11}^{−1}  −  k_{9} k_{4} k_{10} k_{8}^{−1} k_{9} k_{3} k_{1}^{−1} k_{8}^{−1} k_{5}^{−1} k_{11}^{−1}  −
k_{9} k_{4} k_{10} k_{8}^{−1} k_{9} k_{4} k_{10} k_{8}^{−1} k_{5}^{−1} k_{11}^{−1}  +  k_{9} k_{3} k_{1}^{−1} k_{2} k_{10} k_{8}^{−1} k_{9} k_{3} k_{1}^{−1} k_{8}^{−1} k_{5}^{−1} k_{11}^{−1}  +
k_{9} k_{3} k_{1}^{−1} k_{2} k_{10} k_{8}^{−1} k_{9} k_{4} k_{10} k_{8}^{−1} k_{5}^{−1} k_{11}^{−1}  +  k_{9} k_{3} k_{1}^{−1} k_{8}^{−1} k_{9} k_{3} k_{1}^{−1} k_{2} k_{10} k_{8}^{−1} k_{5}^{−1} k_{11}^{−1}  +

k_{9} k_{4} k_{10} k_{8}^{−1} k_{9} k_{3} k_{1}^{−1} k_{2} k_{10} k_{8}^{−1} k_{5}^{−1} k_{11}^{−1} − k_{9} k_{3} k_{1}^{−1} k_{2} k_{10} k_{8}^{−1} k_{9} k_{3} k_{1}^{−1} k_{2} k_{10} k_{8}^{−1} k_{5}^{−1} k_{11}^{−1}

The time for preliminaries was 0:00:00 The time for NCMakeGB 1 was 0:00:00 The time for Remove Redundant 1 was 0:00:00 The time for the main NCMakeGB was 0:00:01 The time for Remove Redundant 2 was 0:00:00 The time for reducing unknowns was 0:00:00 The time for clean up basis was 0:00:00 The time for SmallBasis was 0:00:05 The time for CreateCategories was 0:00:08 The time for NCCV was 0:00:00 The time for RegularOutput was 0:00:06 The time for everything so far was 0:00:22