WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_ConstantStackPush -> f500_0_main_GE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, arg5'=arg5P_1, [ arg1P_1<=arg1 && arg2>-1 && arg1>0 && arg1P_1>0 && 0==arg2P_1 && arg2==arg3P_1 ], cost: 1 1: f500_0_main_GE -> f500_0_main_GE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, arg5'=arg5P_2, [ arg3>arg2 && arg3>0 && arg1P_2<=arg1 && arg1>0 && arg1P_2>0 && 1+arg2==arg2P_2 && arg3==arg3P_2 ], cost: 1 2: f500_0_main_GE -> f323_0_rec0_GT : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, [ arg3>arg2 && arg3>0 && arg1>0 && 0==arg1P_3 && arg3==arg2P_3 ], cost: 1 3: f323_0_rec0_GT -> f323_0_rec0_GT : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, arg5'=arg5P_4, [ arg2>=arg1 && arg1>-1 && arg2>0 && 1+arg1==arg1P_4 && arg2==arg2P_4 ], cost: 1 4: f323_0_rec0_GT -> f376_0_rec1_GT : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, arg5'=arg5P_5, [ arg2>0 && arg2>=arg1 && arg1==arg1P_5 && 0==arg2P_5 && 2*arg1==arg3P_5 ], cost: 1 5: f376_0_rec1_GT -> f376_0_rec1_GT : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, arg5'=arg5P_6, [ arg1>-1 && arg3>=arg2 && arg2>-1 && arg1==arg1P_6 && 1+arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1 6: f376_0_rec1_GT -> f319_0_rec2_LT : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, arg5'=arg5P_7, [ arg1>-1 && arg3>=arg2 && arg2>-1 && arg1==arg1P_7 && arg2==arg2P_7 && arg2+arg1==arg3P_7 ], cost: 1 7: f319_0_rec2_LT -> f319_0_rec2_LT : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, arg5'=arg5P_8, [ 3*arg2>=0 && arg3>-1 && 2*arg1>=0 && 3*arg2+2*arg1>=0 && 4*arg3>=0 && arg1==arg1P_8 && arg2==arg2P_8 && -1+arg3==arg3P_8 ], cost: 1 8: f319_0_rec2_LT -> f541_0_rec3_GT : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, arg5'=arg5P_9, [ 3*arg2>=0 && arg3>-1 && 2*arg1>=0 && 3*arg2+2*arg1>=0 && 4*arg3>=0 && arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 && 0==arg4P_9 && 3*arg2+4*arg3+2*arg1==arg5P_9 ], cost: 1 9: f541_0_rec3_GT -> f541_0_rec3_GT : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, arg5'=arg5P_10, [ 100*arg2>=0 && arg5>=arg4 && 1000*arg1>=0 && 10*arg3>=0 && 100*arg2+1000*arg1>=0 && arg3>-1 && 100*arg2+10*arg3+1000*arg1>=0 && arg4>-1 && arg1==arg1P_10 && arg2==arg2P_10 && arg3==arg3P_10 && 1+arg4==arg4P_10 && arg5==arg5P_10 ], cost: 1 10: f541_0_rec3_GT -> f493_0_rec4_LT : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, arg5'=arg5P_11, [ 100*arg2>=0 && arg5>=arg4 && 1000*arg1>=0 && 10*arg3>=0 && 100*arg2+1000*arg1>=0 && arg3>-1 && arg4>-1 && 100*arg2+10*arg3+1000*arg1>=0 && 100*arg2+10*arg3+arg4+1000*arg1==arg1P_11 ], cost: 1 11: f493_0_rec4_LT -> f493_0_rec4_LT : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, arg5'=arg5P_12, [ arg1>-1 && -1+arg1==arg1P_12 ], cost: 1 12: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, arg5'=arg5P_13, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 12: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, arg5'=arg5P_13, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_ConstantStackPush -> f500_0_main_GE : arg1'=arg1P_1, arg2'=0, arg3'=arg2, arg4'=arg4P_1, arg5'=arg5P_1, [ arg1P_1<=arg1 && arg2>-1 && arg1>0 && arg1P_1>0 ], cost: 1 1: f500_0_main_GE -> f500_0_main_GE : arg1'=arg1P_2, arg2'=1+arg2, arg4'=arg4P_2, arg5'=arg5P_2, [ arg3>arg2 && arg3>0 && arg1P_2<=arg1 && arg1>0 && arg1P_2>0 ], cost: 1 2: f500_0_main_GE -> f323_0_rec0_GT : arg1'=0, arg2'=arg3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, [ arg3>arg2 && arg3>0 && arg1>0 ], cost: 1 3: f323_0_rec0_GT -> f323_0_rec0_GT : arg1'=1+arg1, arg3'=arg3P_4, arg4'=arg4P_4, arg5'=arg5P_4, [ arg2>=arg1 && arg1>-1 && arg2>0 ], cost: 1 4: f323_0_rec0_GT -> f376_0_rec1_GT : arg2'=0, arg3'=2*arg1, arg4'=arg4P_5, arg5'=arg5P_5, [ arg2>0 && arg2>=arg1 ], cost: 1 5: f376_0_rec1_GT -> f376_0_rec1_GT : arg2'=1+arg2, arg4'=arg4P_6, arg5'=arg5P_6, [ arg1>-1 && arg3>=arg2 && arg2>-1 ], cost: 1 6: f376_0_rec1_GT -> f319_0_rec2_LT : arg3'=arg2+arg1, arg4'=arg4P_7, arg5'=arg5P_7, [ arg1>-1 && arg3>=arg2 && arg2>-1 ], cost: 1 7: f319_0_rec2_LT -> f319_0_rec2_LT : arg3'=-1+arg3, arg4'=arg4P_8, arg5'=arg5P_8, [ 3*arg2>=0 && arg3>-1 && 2*arg1>=0 ], cost: 1 8: f319_0_rec2_LT -> f541_0_rec3_GT : arg4'=0, arg5'=3*arg2+4*arg3+2*arg1, [ 3*arg2>=0 && arg3>-1 && 2*arg1>=0 ], cost: 1 9: f541_0_rec3_GT -> f541_0_rec3_GT : arg4'=1+arg4, [ 100*arg2>=0 && arg5>=arg4 && 1000*arg1>=0 && 10*arg3>=0 && arg4>-1 ], cost: 1 10: f541_0_rec3_GT -> f493_0_rec4_LT : arg1'=100*arg2+10*arg3+arg4+1000*arg1, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, arg5'=arg5P_11, [ 100*arg2>=0 && arg5>=arg4 && 1000*arg1>=0 && 10*arg3>=0 && arg4>-1 ], cost: 1 11: f493_0_rec4_LT -> f493_0_rec4_LT : arg1'=-1+arg1, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, arg5'=arg5P_12, [ arg1>-1 ], cost: 1 12: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, arg5'=arg5P_13, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 1: f500_0_main_GE -> f500_0_main_GE : arg1'=arg1P_2, arg2'=1+arg2, arg4'=arg4P_2, arg5'=arg5P_2, [ arg3>arg2 && arg3>0 && arg1P_2<=arg1 && arg1>0 && arg1P_2>0 ], cost: 1 Accelerated rule 1 with backward acceleration, yielding the new rule 13. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 1. Accelerating simple loops of location 2. Accelerating the following rules: 3: f323_0_rec0_GT -> f323_0_rec0_GT : arg1'=1+arg1, arg3'=arg3P_4, arg4'=arg4P_4, arg5'=arg5P_4, [ arg2>=arg1 && arg1>-1 && arg2>0 ], cost: 1 Accelerated rule 3 with backward acceleration, yielding the new rule 14. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 3. Accelerating simple loops of location 3. Accelerating the following rules: 5: f376_0_rec1_GT -> f376_0_rec1_GT : arg2'=1+arg2, arg4'=arg4P_6, arg5'=arg5P_6, [ arg1>-1 && arg3>=arg2 && arg2>-1 ], cost: 1 Accelerated rule 5 with backward acceleration, yielding the new rule 15. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 5. Accelerating simple loops of location 4. Accelerating the following rules: 7: f319_0_rec2_LT -> f319_0_rec2_LT : arg3'=-1+arg3, arg4'=arg4P_8, arg5'=arg5P_8, [ 3*arg2>=0 && arg3>-1 && 2*arg1>=0 ], cost: 1 Accelerated rule 7 with backward acceleration, yielding the new rule 16. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 7. Accelerating simple loops of location 5. Accelerating the following rules: 9: f541_0_rec3_GT -> f541_0_rec3_GT : arg4'=1+arg4, [ 100*arg2>=0 && arg5>=arg4 && 1000*arg1>=0 && 10*arg3>=0 && arg4>-1 ], cost: 1 Accelerated rule 9 with backward acceleration, yielding the new rule 17. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 9. Accelerating simple loops of location 6. Accelerating the following rules: 11: f493_0_rec4_LT -> f493_0_rec4_LT : arg1'=-1+arg1, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, arg5'=arg5P_12, [ arg1>-1 ], cost: 1 Accelerated rule 11 with backward acceleration, yielding the new rule 18. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 11. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_ConstantStackPush -> f500_0_main_GE : arg1'=arg1P_1, arg2'=0, arg3'=arg2, arg4'=arg4P_1, arg5'=arg5P_1, [ arg1P_1<=arg1 && arg2>-1 && arg1>0 && arg1P_1>0 ], cost: 1 2: f500_0_main_GE -> f323_0_rec0_GT : arg1'=0, arg2'=arg3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, [ arg3>arg2 && arg3>0 && arg1>0 ], cost: 1 13: f500_0_main_GE -> f500_0_main_GE : arg1'=arg1P_2, arg2'=arg3, arg4'=arg4P_2, arg5'=arg5P_2, [ arg3>0 && arg1P_2<=arg1 && arg1>0 && arg1P_2>0 && -arg2+arg3>=1 ], cost: -arg2+arg3 4: f323_0_rec0_GT -> f376_0_rec1_GT : arg2'=0, arg3'=2*arg1, arg4'=arg4P_5, arg5'=arg5P_5, [ arg2>0 && arg2>=arg1 ], cost: 1 14: f323_0_rec0_GT -> f323_0_rec0_GT : arg1'=1+arg2, arg3'=arg3P_4, arg4'=arg4P_4, arg5'=arg5P_4, [ arg1>-1 && arg2>0 && 1+arg2-arg1>=1 ], cost: 1+arg2-arg1 6: f376_0_rec1_GT -> f319_0_rec2_LT : arg3'=arg2+arg1, arg4'=arg4P_7, arg5'=arg5P_7, [ arg1>-1 && arg3>=arg2 && arg2>-1 ], cost: 1 15: f376_0_rec1_GT -> f376_0_rec1_GT : arg2'=1+arg3, arg4'=arg4P_6, arg5'=arg5P_6, [ arg1>-1 && arg2>-1 && 1-arg2+arg3>=1 ], cost: 1-arg2+arg3 8: f319_0_rec2_LT -> f541_0_rec3_GT : arg4'=0, arg5'=3*arg2+4*arg3+2*arg1, [ 3*arg2>=0 && arg3>-1 && 2*arg1>=0 ], cost: 1 16: f319_0_rec2_LT -> f319_0_rec2_LT : arg3'=-1, arg4'=arg4P_8, arg5'=arg5P_8, [ 3*arg2>=0 && 2*arg1>=0 && 1+arg3>=1 ], cost: 1+arg3 10: f541_0_rec3_GT -> f493_0_rec4_LT : arg1'=100*arg2+10*arg3+arg4+1000*arg1, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, arg5'=arg5P_11, [ 100*arg2>=0 && arg5>=arg4 && 1000*arg1>=0 && 10*arg3>=0 && arg4>-1 ], cost: 1 17: f541_0_rec3_GT -> f541_0_rec3_GT : arg4'=1+arg5, [ 100*arg2>=0 && 1000*arg1>=0 && 10*arg3>=0 && arg4>-1 && 1+arg5-arg4>=0 ], cost: 1+arg5-arg4 18: f493_0_rec4_LT -> f493_0_rec4_LT : arg1'=-1, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, arg5'=arg5P_12, [ 1+arg1>=1 ], cost: 1+arg1 12: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, arg5'=arg5P_13, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_ConstantStackPush -> f500_0_main_GE : arg1'=arg1P_1, arg2'=0, arg3'=arg2, arg4'=arg4P_1, arg5'=arg5P_1, [ arg1P_1<=arg1 && arg2>-1 && arg1>0 && arg1P_1>0 ], cost: 1 19: f1_0_main_ConstantStackPush -> f500_0_main_GE : arg1'=arg1P_2, arg3'=arg2, arg4'=arg4P_2, arg5'=arg5P_2, [ arg1>0 && arg2>0 && arg1P_2>0 && arg1P_2<=arg1 ], cost: 1+arg2 2: f500_0_main_GE -> f323_0_rec0_GT : arg1'=0, arg2'=arg3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, [ arg3>arg2 && arg3>0 && arg1>0 ], cost: 1 20: f500_0_main_GE -> f323_0_rec0_GT : arg1'=1+arg3, arg2'=arg3, arg3'=arg3P_4, arg4'=arg4P_4, arg5'=arg5P_4, [ arg3>arg2 && arg3>0 && arg1>0 ], cost: 2+arg3 4: f323_0_rec0_GT -> f376_0_rec1_GT : arg2'=0, arg3'=2*arg1, arg4'=arg4P_5, arg5'=arg5P_5, [ arg2>0 && arg2>=arg1 ], cost: 1 21: f323_0_rec0_GT -> f376_0_rec1_GT : arg2'=1+2*arg1, arg3'=2*arg1, arg4'=arg4P_6, arg5'=arg5P_6, [ arg2>0 && arg2>=arg1 && arg1>-1 && 1+2*arg1>=1 ], cost: 2+2*arg1 6: f376_0_rec1_GT -> f319_0_rec2_LT : arg3'=arg2+arg1, arg4'=arg4P_7, arg5'=arg5P_7, [ arg1>-1 && arg3>=arg2 && arg2>-1 ], cost: 1 22: f376_0_rec1_GT -> f319_0_rec2_LT : arg3'=-1, arg4'=arg4P_8, arg5'=arg5P_8, [ arg1>-1 && arg3>=arg2 && arg2>-1 && 3*arg2>=0 && 2*arg1>=0 && 1+arg2+arg1>=1 ], cost: 2+arg2+arg1 8: f319_0_rec2_LT -> f541_0_rec3_GT : arg4'=0, arg5'=3*arg2+4*arg3+2*arg1, [ 3*arg2>=0 && arg3>-1 && 2*arg1>=0 ], cost: 1 23: f319_0_rec2_LT -> f541_0_rec3_GT : arg4'=1+3*arg2+4*arg3+2*arg1, arg5'=3*arg2+4*arg3+2*arg1, [ 3*arg2>=0 && arg3>-1 && 2*arg1>=0 && 100*arg2>=0 && 1000*arg1>=0 && 10*arg3>=0 && 1+3*arg2+4*arg3+2*arg1>=0 ], cost: 2+3*arg2+4*arg3+2*arg1 10: f541_0_rec3_GT -> f493_0_rec4_LT : arg1'=100*arg2+10*arg3+arg4+1000*arg1, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, arg5'=arg5P_11, [ 100*arg2>=0 && arg5>=arg4 && 1000*arg1>=0 && 10*arg3>=0 && arg4>-1 ], cost: 1 24: f541_0_rec3_GT -> f493_0_rec4_LT : arg1'=-1, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, arg5'=arg5P_12, [ 100*arg2>=0 && arg5>=arg4 && 1000*arg1>=0 && 10*arg3>=0 && arg4>-1 && 1+100*arg2+10*arg3+arg4+1000*arg1>=1 ], cost: 2+100*arg2+10*arg3+arg4+1000*arg1 12: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, arg5'=arg5P_13, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 0: f1_0_main_ConstantStackPush -> f500_0_main_GE : arg1'=arg1P_1, arg2'=0, arg3'=arg2, arg4'=arg4P_1, arg5'=arg5P_1, [ arg1P_1<=arg1 && arg2>-1 && arg1>0 && arg1P_1>0 ], cost: 1 19: f1_0_main_ConstantStackPush -> f500_0_main_GE : arg1'=arg1P_2, arg3'=arg2, arg4'=arg4P_2, arg5'=arg5P_2, [ arg1>0 && arg2>0 && arg1P_2>0 && arg1P_2<=arg1 ], cost: 1+arg2 2: f500_0_main_GE -> f323_0_rec0_GT : arg1'=0, arg2'=arg3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, [ arg3>arg2 && arg3>0 && arg1>0 ], cost: 1 20: f500_0_main_GE -> f323_0_rec0_GT : arg1'=1+arg3, arg2'=arg3, arg3'=arg3P_4, arg4'=arg4P_4, arg5'=arg5P_4, [ arg3>arg2 && arg3>0 && arg1>0 ], cost: 2+arg3 4: f323_0_rec0_GT -> f376_0_rec1_GT : arg2'=0, arg3'=2*arg1, arg4'=arg4P_5, arg5'=arg5P_5, [ arg2>0 && arg2>=arg1 ], cost: 1 21: f323_0_rec0_GT -> f376_0_rec1_GT : arg2'=1+2*arg1, arg3'=2*arg1, arg4'=arg4P_6, arg5'=arg5P_6, [ arg2>0 && arg2>=arg1 && arg1>-1 && 1+2*arg1>=1 ], cost: 2+2*arg1 6: f376_0_rec1_GT -> f319_0_rec2_LT : arg3'=arg2+arg1, arg4'=arg4P_7, arg5'=arg5P_7, [ arg1>-1 && arg3>=arg2 && arg2>-1 ], cost: 1 22: f376_0_rec1_GT -> f319_0_rec2_LT : arg3'=-1, arg4'=arg4P_8, arg5'=arg5P_8, [ arg1>-1 && arg3>=arg2 && arg2>-1 && 3*arg2>=0 && 2*arg1>=0 && 1+arg2+arg1>=1 ], cost: 2+arg2+arg1 8: f319_0_rec2_LT -> f541_0_rec3_GT : arg4'=0, arg5'=3*arg2+4*arg3+2*arg1, [ 3*arg2>=0 && arg3>-1 && 2*arg1>=0 ], cost: 1 23: f319_0_rec2_LT -> f541_0_rec3_GT : arg4'=1+3*arg2+4*arg3+2*arg1, arg5'=3*arg2+4*arg3+2*arg1, [ 3*arg2>=0 && arg3>-1 && 2*arg1>=0 && 100*arg2>=0 && 1000*arg1>=0 && 10*arg3>=0 && 1+3*arg2+4*arg3+2*arg1>=0 ], cost: 2+3*arg2+4*arg3+2*arg1 24: f541_0_rec3_GT -> f493_0_rec4_LT : arg1'=-1, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, arg5'=arg5P_12, [ 100*arg2>=0 && arg5>=arg4 && 1000*arg1>=0 && 10*arg3>=0 && arg4>-1 && 1+100*arg2+10*arg3+arg4+1000*arg1>=1 ], cost: 2+100*arg2+10*arg3+arg4+1000*arg1 12: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, arg5'=arg5P_13, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: __init 27: f500_0_main_GE -> f376_0_rec1_GT : arg1'=0, arg2'=0, arg3'=0, arg4'=arg4P_5, arg5'=arg5P_5, [ arg3>arg2 && arg3>0 && arg1>0 ], cost: 2 28: f500_0_main_GE -> f376_0_rec1_GT : arg1'=0, arg2'=1, arg3'=0, arg4'=arg4P_6, arg5'=arg5P_6, [ arg3>arg2 && arg3>0 && arg1>0 ], cost: 3 29: f500_0_main_GE -> [14] : [ arg3>arg2 && arg3>0 && arg1>0 ], cost: 2+arg3 30: f376_0_rec1_GT -> f541_0_rec3_GT : arg3'=arg2+arg1, arg4'=0, arg5'=7*arg2+6*arg1, [ arg1>-1 && arg3>=arg2 && arg2>-1 && 3*arg2>=0 && arg2+arg1>-1 && 2*arg1>=0 ], cost: 2 31: f376_0_rec1_GT -> f541_0_rec3_GT : arg3'=arg2+arg1, arg4'=1+7*arg2+6*arg1, arg5'=7*arg2+6*arg1, [ arg1>-1 && arg3>=arg2 && arg2>-1 && 3*arg2>=0 && arg2+arg1>-1 && 2*arg1>=0 && 100*arg2>=0 && 1000*arg1>=0 && 10*arg2+10*arg1>=0 && 1+7*arg2+6*arg1>=0 ], cost: 3+7*arg2+6*arg1 32: f376_0_rec1_GT -> [15] : [ arg1>-1 && arg3>=arg2 && arg2>-1 && 3*arg2>=0 && 2*arg1>=0 && 1+arg2+arg1>=1 ], cost: 2+arg2+arg1 24: f541_0_rec3_GT -> f493_0_rec4_LT : arg1'=-1, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, arg5'=arg5P_12, [ 100*arg2>=0 && arg5>=arg4 && 1000*arg1>=0 && 10*arg3>=0 && arg4>-1 && 1+100*arg2+10*arg3+arg4+1000*arg1>=1 ], cost: 2+100*arg2+10*arg3+arg4+1000*arg1 25: __init -> f500_0_main_GE : arg1'=arg1P_1, arg2'=0, arg3'=arg2P_13, arg4'=arg4P_1, arg5'=arg5P_1, [ arg1P_1<=arg1P_13 && arg2P_13>-1 && arg1P_13>0 && arg1P_1>0 ], cost: 2 26: __init -> f500_0_main_GE : arg1'=arg1P_2, arg2'=arg2P_13, arg3'=arg2P_13, arg4'=arg4P_2, arg5'=arg5P_2, [ arg1P_13>0 && arg2P_13>0 && arg1P_2>0 && arg1P_2<=arg1P_13 ], cost: 2+arg2P_13 Eliminated locations (on tree-shaped paths): Start location: __init 32: f376_0_rec1_GT -> [15] : [ arg1>-1 && arg3>=arg2 && arg2>-1 && 3*arg2>=0 && 2*arg1>=0 && 1+arg2+arg1>=1 ], cost: 2+arg2+arg1 37: f376_0_rec1_GT -> f493_0_rec4_LT : arg1'=-1, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, arg5'=arg5P_12, [ arg1>-1 && arg3>=arg2 && arg2>-1 && 3*arg2>=0 && arg2+arg1>-1 && 2*arg1>=0 && 100*arg2>=0 && 7*arg2+6*arg1>=0 && 1000*arg1>=0 && 10*arg2+10*arg1>=0 && 1+110*arg2+1010*arg1>=1 ], cost: 4+110*arg2+1010*arg1 38: f376_0_rec1_GT -> [17] : [ arg1>-1 && arg3>=arg2 && arg2>-1 && 3*arg2>=0 && arg2+arg1>-1 && 2*arg1>=0 && 100*arg2>=0 && 1000*arg1>=0 && 10*arg2+10*arg1>=0 && 1+7*arg2+6*arg1>=0 ], cost: 3+7*arg2+6*arg1 33: __init -> f376_0_rec1_GT : arg1'=0, arg2'=0, arg3'=0, arg4'=arg4P_5, arg5'=arg5P_5, [ arg1P_1<=arg1P_13 && arg1P_13>0 && arg1P_1>0 && arg2P_13>0 ], cost: 4 34: __init -> f376_0_rec1_GT : arg1'=0, arg2'=1, arg3'=0, arg4'=arg4P_6, arg5'=arg5P_6, [ arg1P_1<=arg1P_13 && arg1P_13>0 && arg1P_1>0 && arg2P_13>0 ], cost: 5 35: __init -> [14] : arg1'=arg1P_1, arg2'=0, arg3'=arg2P_13, arg4'=arg4P_1, arg5'=arg5P_1, [ arg1P_1<=arg1P_13 && arg1P_13>0 && arg1P_1>0 && arg2P_13>0 ], cost: 4+arg2P_13 36: __init -> [16] : [ arg1P_13>0 && arg2P_13>0 && arg1P_2>0 && arg1P_2<=arg1P_13 ], cost: 2+arg2P_13 Eliminated locations (on tree-shaped paths): Start location: __init 35: __init -> [14] : arg1'=arg1P_1, arg2'=0, arg3'=arg2P_13, arg4'=arg4P_1, arg5'=arg5P_1, [ arg1P_1<=arg1P_13 && arg1P_13>0 && arg1P_1>0 && arg2P_13>0 ], cost: 4+arg2P_13 36: __init -> [16] : [ arg1P_13>0 && arg2P_13>0 && arg1P_2>0 && arg1P_2<=arg1P_13 ], cost: 2+arg2P_13 39: __init -> [15] : arg1'=0, arg2'=0, arg3'=0, arg4'=arg4P_5, arg5'=arg5P_5, [ arg1P_1<=arg1P_13 && arg1P_13>0 && arg1P_1>0 && arg2P_13>0 ], cost: 6 40: __init -> f493_0_rec4_LT : arg1'=-1, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, arg5'=arg5P_12, [ arg1P_1<=arg1P_13 && arg1P_13>0 && arg1P_1>0 && arg2P_13>0 ], cost: 8 41: __init -> [17] : arg1'=0, arg2'=0, arg3'=0, arg4'=arg4P_5, arg5'=arg5P_5, [ arg1P_1<=arg1P_13 && arg1P_13>0 && arg1P_1>0 && arg2P_13>0 ], cost: 7 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 35: __init -> [14] : arg1'=arg1P_1, arg2'=0, arg3'=arg2P_13, arg4'=arg4P_1, arg5'=arg5P_1, [ arg1P_1<=arg1P_13 && arg1P_13>0 && arg1P_1>0 && arg2P_13>0 ], cost: 4+arg2P_13 36: __init -> [16] : [ arg1P_13>0 && arg2P_13>0 && arg1P_2>0 && arg1P_2<=arg1P_13 ], cost: 2+arg2P_13 40: __init -> f493_0_rec4_LT : arg1'=-1, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, arg5'=arg5P_12, [ arg1P_1<=arg1P_13 && arg1P_13>0 && arg1P_1>0 && arg2P_13>0 ], cost: 8 Computing asymptotic complexity for rule 35 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 36 Simplified the guard: 36: __init -> [16] : [ arg2P_13>0 && arg1P_2>0 && arg1P_2<=arg1P_13 ], cost: 2+arg2P_13 Resulting cost 0 has complexity: Unknown 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),?)