WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f1_0_main_Load\' : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ 2*x39_1>0 && arg2>0 && 1-2*x40_1+2*x39_1==1 && x39_1>-1 && arg1>0 && x41_1>2 && arg1==arg1P_1 && arg2==arg2P_1 ], cost: 1 1: f1_0_main_Load\' -> f723_0_init_GE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ 2*x45_1>0 && arg2>0 && 1-2*x46_1+2*x45_1==1 && x45_1>-1 && arg1>0 && arg1P_2>2 && 1-2*x46_1+2*x45_1<2 && 1-2*x46_1+2*x45_1>=0 && 0==arg2P_2 && 1+2*x45_1==arg3P_2 ], cost: 1 2: f723_0_init_GE -> f873_0_init_GE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ arg1P_3<=arg1 && arg2<3 && arg1>2 && arg1P_3>2 && 4+arg3<=arg1 && arg2==arg2P_3 && 0==arg3P_3 && arg3==arg4P_3 ], cost: 1 5: f723_0_init_GE -> f723_0_init_GE\' : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, [ arg3>1 && arg2>2 && arg3>x50_1 && arg3>x51_1 && x52_1<=arg1 && arg1>2 && x52_1>2 && 4+arg3<=arg1 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1 3: f873_0_init_GE -> f723_0_init_GE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg1>=arg1P_4 && arg3>2 && arg1>2 && arg1P_4>2 && arg1>=4+arg4 && 1+arg2==arg2P_4 && arg4==arg3P_4 ], cost: 1 4: f873_0_init_GE -> f873_0_init_GE : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg4>arg2 && arg3<3 && x18_1>arg3 && x18_1>-1 && arg1P_5<=arg1 && arg1>2 && arg1P_5>2 && 4+arg4<=arg1 && arg2==arg2P_5 && 1+arg3==arg3P_5 && arg4==arg4P_5 ], cost: 1 6: f723_0_init_GE\' -> f1037_0_imprimer_GE : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [ arg3>1 && arg2>2 && arg3>x57_1 && arg3>x58_1 && arg1P_7<=arg1 && arg1>2 && arg1P_7>2 && 4+arg3<=arg1 && arg3-2*x57_1>=0 && arg3-2*x57_1<2 && -2*x58_1+arg3<2 && -2*x58_1+arg3>=0 && 0==arg2P_7 && arg3==arg3P_7 ], cost: 1 7: f1037_0_imprimer_GE -> f1074_0_imprimer_GE : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, [ arg1P_8<=arg1 && arg3>arg2 && arg1>2 && arg1P_8>2 && 4+arg3<=arg1 && arg2==arg2P_8 && 0==arg3P_8 && arg3==arg4P_8 ], cost: 1 8: f1074_0_imprimer_GE -> f1037_0_imprimer_GE : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, [ arg1P_9<=arg1 && arg4<=arg3 && arg1>2 && arg1P_9>2 && 4+arg4<=arg1 && 1+arg2==arg2P_9 && arg4==arg3P_9 ], cost: 1 9: f1074_0_imprimer_GE -> f1074_0_imprimer_GE : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, [ arg1P_10<=arg1 && arg4>arg3 && arg1>2 && arg1P_10>2 && 4+arg4<=arg1 && arg2==arg2P_10 && 1+arg3==arg3P_10 && arg4==arg4P_10 ], cost: 1 10: __init -> f1_0_main_Load : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 10: __init -> f1_0_main_Load : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f1_0_main_Load\' : arg3'=arg3P_1, arg4'=arg4P_1, [ 2*x39_1>0 && arg2>0 && arg1>0 ], cost: 1 1: f1_0_main_Load\' -> f723_0_init_GE : arg1'=arg1P_2, arg2'=0, arg3'=1+2*x45_1, arg4'=arg4P_2, [ 2*x45_1>0 && arg2>0 && arg1>0 && arg1P_2>2 ], cost: 1 2: f723_0_init_GE -> f873_0_init_GE : arg1'=arg1P_3, arg3'=0, arg4'=arg3, [ arg1P_3<=arg1 && arg2<3 && arg1>2 && arg1P_3>2 && 4+arg3<=arg1 ], cost: 1 5: f723_0_init_GE -> f723_0_init_GE\' : arg4'=arg4P_6, [ arg3>1 && arg2>2 && arg1>2 && 4+arg3<=arg1 ], cost: 1 3: f873_0_init_GE -> f723_0_init_GE : arg1'=arg1P_4, arg2'=1+arg2, arg3'=arg4, arg4'=arg4P_4, [ arg1>=arg1P_4 && arg3>2 && arg1>2 && arg1P_4>2 && arg1>=4+arg4 ], cost: 1 4: f873_0_init_GE -> f873_0_init_GE : arg1'=arg1P_5, arg3'=1+arg3, [ arg4>arg2 && arg3<3 && arg1P_5<=arg1 && arg1>2 && arg1P_5>2 && 4+arg4<=arg1 ], cost: 1 6: f723_0_init_GE\' -> f1037_0_imprimer_GE : arg1'=arg1P_7, arg2'=0, arg4'=arg4P_7, [ arg3>1 && arg2>2 && arg3>x58_1 && arg1P_7<=arg1 && arg1>2 && arg1P_7>2 && 4+arg3<=arg1 && arg3-2*x57_1>=0 && arg3-2*x57_1<2 && -2*x58_1+arg3<2 && -2*x58_1+arg3>=0 ], cost: 1 7: f1037_0_imprimer_GE -> f1074_0_imprimer_GE : arg1'=arg1P_8, arg3'=0, arg4'=arg3, [ arg1P_8<=arg1 && arg3>arg2 && arg1>2 && arg1P_8>2 && 4+arg3<=arg1 ], cost: 1 8: f1074_0_imprimer_GE -> f1037_0_imprimer_GE : arg1'=arg1P_9, arg2'=1+arg2, arg3'=arg4, arg4'=arg4P_9, [ arg1P_9<=arg1 && arg4<=arg3 && arg1>2 && arg1P_9>2 && 4+arg4<=arg1 ], cost: 1 9: f1074_0_imprimer_GE -> f1074_0_imprimer_GE : arg1'=arg1P_10, arg3'=1+arg3, [ arg1P_10<=arg1 && arg4>arg3 && arg1>2 && arg1P_10>2 && 4+arg4<=arg1 ], cost: 1 10: __init -> f1_0_main_Load : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 3. Accelerating the following rules: 4: f873_0_init_GE -> f873_0_init_GE : arg1'=arg1P_5, arg3'=1+arg3, [ arg4>arg2 && arg3<3 && arg1P_5<=arg1 && arg1>2 && arg1P_5>2 && 4+arg4<=arg1 ], cost: 1 During metering: Instantiating temporary variables by {arg1P_5==arg1} Accelerated rule 4 with metering function 3-arg3, yielding the new rule 11. Removing the simple loops: 4. Accelerating simple loops of location 6. Accelerating the following rules: 9: f1074_0_imprimer_GE -> f1074_0_imprimer_GE : arg1'=arg1P_10, arg3'=1+arg3, [ arg1P_10<=arg1 && arg4>arg3 && arg1>2 && arg1P_10>2 && 4+arg4<=arg1 ], cost: 1 During metering: Instantiating temporary variables by {arg1P_10==arg1} Accelerated rule 9 with metering function -arg3+arg4, yielding the new rule 12. Removing the simple loops: 9. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f1_0_main_Load\' : arg3'=arg3P_1, arg4'=arg4P_1, [ 2*x39_1>0 && arg2>0 && arg1>0 ], cost: 1 1: f1_0_main_Load\' -> f723_0_init_GE : arg1'=arg1P_2, arg2'=0, arg3'=1+2*x45_1, arg4'=arg4P_2, [ 2*x45_1>0 && arg2>0 && arg1>0 && arg1P_2>2 ], cost: 1 2: f723_0_init_GE -> f873_0_init_GE : arg1'=arg1P_3, arg3'=0, arg4'=arg3, [ arg1P_3<=arg1 && arg2<3 && arg1>2 && arg1P_3>2 && 4+arg3<=arg1 ], cost: 1 5: f723_0_init_GE -> f723_0_init_GE\' : arg4'=arg4P_6, [ arg3>1 && arg2>2 && arg1>2 && 4+arg3<=arg1 ], cost: 1 3: f873_0_init_GE -> f723_0_init_GE : arg1'=arg1P_4, arg2'=1+arg2, arg3'=arg4, arg4'=arg4P_4, [ arg1>=arg1P_4 && arg3>2 && arg1>2 && arg1P_4>2 && arg1>=4+arg4 ], cost: 1 11: f873_0_init_GE -> f873_0_init_GE : arg1'=arg1, arg3'=3, [ arg4>arg2 && arg3<3 && arg1>2 && 4+arg4<=arg1 ], cost: 3-arg3 6: f723_0_init_GE\' -> f1037_0_imprimer_GE : arg1'=arg1P_7, arg2'=0, arg4'=arg4P_7, [ arg3>1 && arg2>2 && arg3>x58_1 && arg1P_7<=arg1 && arg1>2 && arg1P_7>2 && 4+arg3<=arg1 && arg3-2*x57_1>=0 && arg3-2*x57_1<2 && -2*x58_1+arg3<2 && -2*x58_1+arg3>=0 ], cost: 1 7: f1037_0_imprimer_GE -> f1074_0_imprimer_GE : arg1'=arg1P_8, arg3'=0, arg4'=arg3, [ arg1P_8<=arg1 && arg3>arg2 && arg1>2 && arg1P_8>2 && 4+arg3<=arg1 ], cost: 1 8: f1074_0_imprimer_GE -> f1037_0_imprimer_GE : arg1'=arg1P_9, arg2'=1+arg2, arg3'=arg4, arg4'=arg4P_9, [ arg1P_9<=arg1 && arg4<=arg3 && arg1>2 && arg1P_9>2 && 4+arg4<=arg1 ], cost: 1 12: f1074_0_imprimer_GE -> f1074_0_imprimer_GE : arg1'=arg1, arg3'=arg4, [ arg4>arg3 && arg1>2 && 4+arg4<=arg1 ], cost: -arg3+arg4 10: __init -> f1_0_main_Load : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f1_0_main_Load\' : arg3'=arg3P_1, arg4'=arg4P_1, [ 2*x39_1>0 && arg2>0 && arg1>0 ], cost: 1 1: f1_0_main_Load\' -> f723_0_init_GE : arg1'=arg1P_2, arg2'=0, arg3'=1+2*x45_1, arg4'=arg4P_2, [ 2*x45_1>0 && arg2>0 && arg1>0 && arg1P_2>2 ], cost: 1 2: f723_0_init_GE -> f873_0_init_GE : arg1'=arg1P_3, arg3'=0, arg4'=arg3, [ arg1P_3<=arg1 && arg2<3 && arg1>2 && arg1P_3>2 && 4+arg3<=arg1 ], cost: 1 5: f723_0_init_GE -> f723_0_init_GE\' : arg4'=arg4P_6, [ arg3>1 && arg2>2 && arg1>2 && 4+arg3<=arg1 ], cost: 1 13: f723_0_init_GE -> f873_0_init_GE : arg1'=arg1P_3, arg3'=3, arg4'=arg3, [ arg1P_3<=arg1 && arg2<3 && arg1>2 && arg1P_3>2 && 4+arg3<=arg1 && arg3>arg2 && 4+arg3<=arg1P_3 ], cost: 4 3: f873_0_init_GE -> f723_0_init_GE : arg1'=arg1P_4, arg2'=1+arg2, arg3'=arg4, arg4'=arg4P_4, [ arg1>=arg1P_4 && arg3>2 && arg1>2 && arg1P_4>2 && arg1>=4+arg4 ], cost: 1 6: f723_0_init_GE\' -> f1037_0_imprimer_GE : arg1'=arg1P_7, arg2'=0, arg4'=arg4P_7, [ arg3>1 && arg2>2 && arg3>x58_1 && arg1P_7<=arg1 && arg1>2 && arg1P_7>2 && 4+arg3<=arg1 && arg3-2*x57_1>=0 && arg3-2*x57_1<2 && -2*x58_1+arg3<2 && -2*x58_1+arg3>=0 ], cost: 1 7: f1037_0_imprimer_GE -> f1074_0_imprimer_GE : arg1'=arg1P_8, arg3'=0, arg4'=arg3, [ arg1P_8<=arg1 && arg3>arg2 && arg1>2 && arg1P_8>2 && 4+arg3<=arg1 ], cost: 1 14: f1037_0_imprimer_GE -> f1074_0_imprimer_GE : arg1'=arg1P_8, arg4'=arg3, [ arg1P_8<=arg1 && arg3>arg2 && arg1>2 && arg1P_8>2 && 4+arg3<=arg1 && arg3>0 && 4+arg3<=arg1P_8 ], cost: 1+arg3 8: f1074_0_imprimer_GE -> f1037_0_imprimer_GE : arg1'=arg1P_9, arg2'=1+arg2, arg3'=arg4, arg4'=arg4P_9, [ arg1P_9<=arg1 && arg4<=arg3 && arg1>2 && arg1P_9>2 && 4+arg4<=arg1 ], cost: 1 10: __init -> f1_0_main_Load : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, [], cost: 1 Eliminated locations (on linear paths): Start location: __init 2: f723_0_init_GE -> f873_0_init_GE : arg1'=arg1P_3, arg3'=0, arg4'=arg3, [ arg1P_3<=arg1 && arg2<3 && arg1>2 && arg1P_3>2 && 4+arg3<=arg1 ], cost: 1 13: f723_0_init_GE -> f873_0_init_GE : arg1'=arg1P_3, arg3'=3, arg4'=arg3, [ arg1P_3<=arg1 && arg2<3 && arg1>2 && arg1P_3>2 && 4+arg3<=arg1 && arg3>arg2 && 4+arg3<=arg1P_3 ], cost: 4 17: f723_0_init_GE -> f1037_0_imprimer_GE : arg1'=arg1P_7, arg2'=0, arg4'=arg4P_7, [ arg3>1 && arg2>2 && arg1>2 && 4+arg3<=arg1 && arg3>x58_1 && arg1P_7<=arg1 && arg1P_7>2 && arg3-2*x57_1>=0 && arg3-2*x57_1<2 && -2*x58_1+arg3<2 && -2*x58_1+arg3>=0 ], cost: 2 3: f873_0_init_GE -> f723_0_init_GE : arg1'=arg1P_4, arg2'=1+arg2, arg3'=arg4, arg4'=arg4P_4, [ arg1>=arg1P_4 && arg3>2 && arg1>2 && arg1P_4>2 && arg1>=4+arg4 ], cost: 1 7: f1037_0_imprimer_GE -> f1074_0_imprimer_GE : arg1'=arg1P_8, arg3'=0, arg4'=arg3, [ arg1P_8<=arg1 && arg3>arg2 && arg1>2 && arg1P_8>2 && 4+arg3<=arg1 ], cost: 1 14: f1037_0_imprimer_GE -> f1074_0_imprimer_GE : arg1'=arg1P_8, arg4'=arg3, [ arg1P_8<=arg1 && arg3>arg2 && arg1>2 && arg1P_8>2 && 4+arg3<=arg1 && arg3>0 && 4+arg3<=arg1P_8 ], cost: 1+arg3 8: f1074_0_imprimer_GE -> f1037_0_imprimer_GE : arg1'=arg1P_9, arg2'=1+arg2, arg3'=arg4, arg4'=arg4P_9, [ arg1P_9<=arg1 && arg4<=arg3 && arg1>2 && arg1P_9>2 && 4+arg4<=arg1 ], cost: 1 16: __init -> f723_0_init_GE : arg1'=arg1P_2, arg2'=0, arg3'=1+2*x45_1, arg4'=arg4P_2, [ 2*x39_1>0 && arg2P_11>0 && arg1P_11>0 && 2*x45_1>0 && arg1P_2>2 ], cost: 3 Eliminated locations (on tree-shaped paths): Start location: __init 17: f723_0_init_GE -> f1037_0_imprimer_GE : arg1'=arg1P_7, arg2'=0, arg4'=arg4P_7, [ arg3>1 && arg2>2 && arg1>2 && 4+arg3<=arg1 && arg3>x58_1 && arg1P_7<=arg1 && arg1P_7>2 && arg3-2*x57_1>=0 && arg3-2*x57_1<2 && -2*x58_1+arg3<2 && -2*x58_1+arg3>=0 ], cost: 2 18: f723_0_init_GE -> f723_0_init_GE : arg1'=arg1P_4, arg2'=1+arg2, arg3'=arg3, arg4'=arg4P_4, [ arg1P_3<=arg1 && arg2<3 && arg1>2 && arg1P_3>2 && 4+arg3<=arg1 && arg3>arg2 && 4+arg3<=arg1P_3 && arg1P_3>=arg1P_4 && arg1P_4>2 ], cost: 5 19: f1037_0_imprimer_GE -> f1037_0_imprimer_GE : arg1'=arg1P_9, arg2'=1+arg2, arg3'=arg3, arg4'=arg4P_9, [ arg1P_8<=arg1 && arg3>arg2 && arg1>2 && arg1P_8>2 && 4+arg3<=arg1 && arg1P_9<=arg1P_8 && arg3<=0 && arg1P_9>2 && 4+arg3<=arg1P_8 ], cost: 2 20: f1037_0_imprimer_GE -> f1037_0_imprimer_GE : arg1'=arg1P_9, arg2'=1+arg2, arg3'=arg3, arg4'=arg4P_9, [ arg1P_8<=arg1 && arg3>arg2 && arg1>2 && arg1P_8>2 && 4+arg3<=arg1 && arg3>0 && 4+arg3<=arg1P_8 && arg1P_9<=arg1P_8 && arg1P_9>2 ], cost: 2+arg3 16: __init -> f723_0_init_GE : arg1'=arg1P_2, arg2'=0, arg3'=1+2*x45_1, arg4'=arg4P_2, [ 2*x39_1>0 && arg2P_11>0 && arg1P_11>0 && 2*x45_1>0 && arg1P_2>2 ], cost: 3 Accelerating simple loops of location 2. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 18: f723_0_init_GE -> f723_0_init_GE : arg1'=arg1P_4, arg2'=1+arg2, arg4'=arg4P_4, [ arg2<3 && arg1>2 && 4+arg3<=arg1 && arg3>arg2 && arg1P_4>2 && arg1P_4<=arg1 ], cost: 5 Found no metering function for rule 18. Removing the simple loops:. Accelerating simple loops of location 5. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 19: f1037_0_imprimer_GE -> f1037_0_imprimer_GE : arg1'=arg1P_9, arg2'=1+arg2, arg4'=arg4P_9, [ arg3>arg2 && arg1>2 && 4+arg3<=arg1 && arg3<=0 && arg1P_9>2 && arg1P_9<=arg1 ], cost: 2 20: f1037_0_imprimer_GE -> f1037_0_imprimer_GE : arg1'=arg1P_9, arg2'=1+arg2, arg4'=arg4P_9, [ arg3>arg2 && arg1>2 && 4+arg3<=arg1 && arg3>0 && arg1P_9>2 && arg1P_9<=arg1 ], cost: 2+arg3 During metering: Instantiating temporary variables by {arg1P_9==arg1} Accelerated rule 19 with metering function arg3-arg2, yielding the new rule 21. During metering: Instantiating temporary variables by {arg1P_9==arg1} Accelerated rule 20 with metering function arg3-arg2, yielding the new rule 22. Removing the simple loops: 19 20. Accelerated all simple loops using metering functions (where possible): Start location: __init 17: f723_0_init_GE -> f1037_0_imprimer_GE : arg1'=arg1P_7, arg2'=0, arg4'=arg4P_7, [ arg3>1 && arg2>2 && arg1>2 && 4+arg3<=arg1 && arg3>x58_1 && arg1P_7<=arg1 && arg1P_7>2 && arg3-2*x57_1>=0 && arg3-2*x57_1<2 && -2*x58_1+arg3<2 && -2*x58_1+arg3>=0 ], cost: 2 18: f723_0_init_GE -> f723_0_init_GE : arg1'=arg1P_4, arg2'=1+arg2, arg4'=arg4P_4, [ arg2<3 && arg1>2 && 4+arg3<=arg1 && arg3>arg2 && arg1P_4>2 && arg1P_4<=arg1 ], cost: 5 21: f1037_0_imprimer_GE -> f1037_0_imprimer_GE : arg1'=arg1, arg2'=arg3, arg4'=arg4P_9, [ arg3>arg2 && arg1>2 && 4+arg3<=arg1 && arg3<=0 ], cost: 2*arg3-2*arg2 22: f1037_0_imprimer_GE -> f1037_0_imprimer_GE : arg1'=arg1, arg2'=arg3, arg4'=arg4P_9, [ arg3>arg2 && arg1>2 && 4+arg3<=arg1 && arg3>0 ], cost: 2*arg3-2*arg2+arg3*(arg3-arg2) 16: __init -> f723_0_init_GE : arg1'=arg1P_2, arg2'=0, arg3'=1+2*x45_1, arg4'=arg4P_2, [ 2*x39_1>0 && arg2P_11>0 && arg1P_11>0 && 2*x45_1>0 && arg1P_2>2 ], cost: 3 Chained accelerated rules (with incoming rules): Start location: __init 17: f723_0_init_GE -> f1037_0_imprimer_GE : arg1'=arg1P_7, arg2'=0, arg4'=arg4P_7, [ arg3>1 && arg2>2 && arg1>2 && 4+arg3<=arg1 && arg3>x58_1 && arg1P_7<=arg1 && arg1P_7>2 && arg3-2*x57_1>=0 && arg3-2*x57_1<2 && -2*x58_1+arg3<2 && -2*x58_1+arg3>=0 ], cost: 2 24: f723_0_init_GE -> f1037_0_imprimer_GE : arg1'=arg1P_7, arg2'=arg3, arg4'=arg4P_9, [ arg3>1 && arg2>2 && arg1>2 && 4+arg3<=arg1 && arg3>x58_1 && arg1P_7<=arg1 && arg1P_7>2 && arg3-2*x57_1>=0 && arg3-2*x57_1<2 && -2*x58_1+arg3<2 && -2*x58_1+arg3>=0 && 4+arg3<=arg1P_7 ], cost: 2+2*arg3+arg3^2 16: __init -> f723_0_init_GE : arg1'=arg1P_2, arg2'=0, arg3'=1+2*x45_1, arg4'=arg4P_2, [ 2*x39_1>0 && arg2P_11>0 && arg1P_11>0 && 2*x45_1>0 && arg1P_2>2 ], cost: 3 23: __init -> f723_0_init_GE : arg1'=arg1P_4, arg2'=1, arg3'=1+2*x45_1, arg4'=arg4P_4, [ 2*x39_1>0 && 2*x45_1>0 && arg1P_4>2 ], cost: 8 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 24: f723_0_init_GE -> f1037_0_imprimer_GE : arg1'=arg1P_7, arg2'=arg3, arg4'=arg4P_9, [ arg3>1 && arg2>2 && arg1>2 && 4+arg3<=arg1 && arg3>x58_1 && arg1P_7<=arg1 && arg1P_7>2 && arg3-2*x57_1>=0 && arg3-2*x57_1<2 && -2*x58_1+arg3<2 && -2*x58_1+arg3>=0 && 4+arg3<=arg1P_7 ], cost: 2+2*arg3+arg3^2 16: __init -> f723_0_init_GE : arg1'=arg1P_2, arg2'=0, arg3'=1+2*x45_1, arg4'=arg4P_2, [ 2*x39_1>0 && arg2P_11>0 && arg1P_11>0 && 2*x45_1>0 && arg1P_2>2 ], cost: 3 23: __init -> f723_0_init_GE : arg1'=arg1P_4, arg2'=1, arg3'=1+2*x45_1, arg4'=arg4P_4, [ 2*x39_1>0 && 2*x45_1>0 && arg1P_4>2 ], cost: 8 Eliminated locations (on tree-shaped paths): Start location: __init Applied pruning (of leafs and parallel rules): Start location: __init ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Constant Cpx degree: 0 Solved cost: 1 Rule cost: 1 Rule guard: [] WORST_CASE(Omega(1),?)