WORST_CASE(INF,?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f93_0_mk_Return -> f148_0_main_InvokeMethod : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1P_1<=arg1 && arg2>-1 && arg1>0 && arg1P_1>0 && arg2==arg2P_1 ], cost: 1 2: f148_0_main_InvokeMethod -> f341_0_main_GE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg1>0 && arg2>-1 && 0==arg1P_3 ], cost: 1 7: f148_0_main_InvokeMethod -> f165_0_mk_LE : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg1>0 && -1+arg2==arg1P_8 && arg2==arg2P_8 ], cost: 1 8: f148_0_main_InvokeMethod -> f165_0_mk_LE : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ arg1>0 && arg2>-1 && -1+arg2==arg1P_9 && arg2==arg2P_9 ], cost: 1 1: f1_0_main_ConstantStackPush -> f148_0_main_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1P_2<=arg1 && arg2>-1 && arg1>0 && arg1P_2>0 && arg2==arg2P_2 ], cost: 1 6: f1_0_main_ConstantStackPush -> f165_0_mk_LE : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg1>0 && arg2>-1 && -1+arg2==arg1P_7 && arg2==arg2P_7 ], cost: 1 3: f341_0_main_GE -> f475_0_main_GE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1<3 && arg1==arg1P_4 && 0==arg2P_4 ], cost: 1 10: f341_0_main_GE -> f291_0_length_NULL : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ arg1P_11>-1 && arg2P_11>-1 && arg1<3 ], cost: 1 4: f475_0_main_GE -> f341_0_main_GE : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg3<=arg2 && 1+arg1==arg1P_5 ], cost: 1 5: f475_0_main_GE -> f475_0_main_GE : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg3>0 && arg1<3 && arg3>arg2 && arg1==arg1P_6 && 1+arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1 12: f475_0_main_GE -> f541_0_bubble_NULL : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ arg3>0 && arg3>arg2 && arg1<3 && arg2P_13>-1 && arg1P_13>-1 ], cost: 1 9: f165_0_mk_LE -> f165_0_mk_LE : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ arg2>0 && -1+arg1==arg1P_10 && arg1==arg2P_10 ], cost: 1 11: f291_0_length_NULL -> f291_0_length_NULL : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [ 1+arg1P_12<=arg1 && 1+arg1P_12<=arg2 && 1+arg2P_12<=arg1 && 1+arg2P_12<=arg2 && arg1>0 && arg2>0 && arg1P_12>-1 && arg2P_12>-1 ], cost: 1 13: f541_0_bubble_NULL -> f541_0_bubble_NULL : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, [ 2+arg1P_14<=arg1 && x41_1>=x40_1 && 2+arg1P_14<=arg2 && 2+arg2P_14<=arg1 && 2+arg2P_14<=arg2 && arg1>2 && arg2>2 && arg1P_14>0 && arg2P_14>0 ], cost: 1 14: f541_0_bubble_NULL -> f541_0_bubble_NULL : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, [ arg1P_15<=arg1 && x47_12 && arg2>2 && arg1P_15>0 && arg2P_15>0 ], cost: 1 15: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 15: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, [], cost: 1 Removed unreachable and leaf rules: Start location: __init 2: f148_0_main_InvokeMethod -> f341_0_main_GE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg1>0 && arg2>-1 && 0==arg1P_3 ], cost: 1 7: f148_0_main_InvokeMethod -> f165_0_mk_LE : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg1>0 && -1+arg2==arg1P_8 && arg2==arg2P_8 ], cost: 1 8: f148_0_main_InvokeMethod -> f165_0_mk_LE : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ arg1>0 && arg2>-1 && -1+arg2==arg1P_9 && arg2==arg2P_9 ], cost: 1 1: f1_0_main_ConstantStackPush -> f148_0_main_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1P_2<=arg1 && arg2>-1 && arg1>0 && arg1P_2>0 && arg2==arg2P_2 ], cost: 1 6: f1_0_main_ConstantStackPush -> f165_0_mk_LE : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg1>0 && arg2>-1 && -1+arg2==arg1P_7 && arg2==arg2P_7 ], cost: 1 3: f341_0_main_GE -> f475_0_main_GE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1<3 && arg1==arg1P_4 && 0==arg2P_4 ], cost: 1 10: f341_0_main_GE -> f291_0_length_NULL : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ arg1P_11>-1 && arg2P_11>-1 && arg1<3 ], cost: 1 4: f475_0_main_GE -> f341_0_main_GE : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg3<=arg2 && 1+arg1==arg1P_5 ], cost: 1 5: f475_0_main_GE -> f475_0_main_GE : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg3>0 && arg1<3 && arg3>arg2 && arg1==arg1P_6 && 1+arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1 12: f475_0_main_GE -> f541_0_bubble_NULL : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ arg3>0 && arg3>arg2 && arg1<3 && arg2P_13>-1 && arg1P_13>-1 ], cost: 1 9: f165_0_mk_LE -> f165_0_mk_LE : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ arg2>0 && -1+arg1==arg1P_10 && arg1==arg2P_10 ], cost: 1 11: f291_0_length_NULL -> f291_0_length_NULL : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [ 1+arg1P_12<=arg1 && 1+arg1P_12<=arg2 && 1+arg2P_12<=arg1 && 1+arg2P_12<=arg2 && arg1>0 && arg2>0 && arg1P_12>-1 && arg2P_12>-1 ], cost: 1 13: f541_0_bubble_NULL -> f541_0_bubble_NULL : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, [ 2+arg1P_14<=arg1 && x41_1>=x40_1 && 2+arg1P_14<=arg2 && 2+arg2P_14<=arg1 && 2+arg2P_14<=arg2 && arg1>2 && arg2>2 && arg1P_14>0 && arg2P_14>0 ], cost: 1 14: f541_0_bubble_NULL -> f541_0_bubble_NULL : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, [ arg1P_15<=arg1 && x47_12 && arg2>2 && arg1P_15>0 && arg2P_15>0 ], cost: 1 15: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, [], cost: 1 Simplified all rules, resulting in: Start location: __init 2: f148_0_main_InvokeMethod -> f341_0_main_GE : arg1'=0, arg2'=arg2P_3, arg3'=arg3P_3, [ arg1>0 && arg2>-1 ], cost: 1 7: f148_0_main_InvokeMethod -> f165_0_mk_LE : arg1'=-1+arg2, arg3'=arg3P_8, [ arg1>0 ], cost: 1 8: f148_0_main_InvokeMethod -> f165_0_mk_LE : arg1'=-1+arg2, arg3'=arg3P_9, [ arg1>0 && arg2>-1 ], cost: 1 1: f1_0_main_ConstantStackPush -> f148_0_main_InvokeMethod : arg1'=arg1P_2, arg3'=arg3P_2, [ arg1P_2<=arg1 && arg2>-1 && arg1>0 && arg1P_2>0 ], cost: 1 6: f1_0_main_ConstantStackPush -> f165_0_mk_LE : arg1'=-1+arg2, arg3'=arg3P_7, [ arg1>0 && arg2>-1 ], cost: 1 3: f341_0_main_GE -> f475_0_main_GE : arg2'=0, arg3'=arg3P_4, [ arg1<3 ], cost: 1 10: f341_0_main_GE -> f291_0_length_NULL : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ arg1P_11>-1 && arg2P_11>-1 && arg1<3 ], cost: 1 4: f475_0_main_GE -> f341_0_main_GE : arg1'=1+arg1, arg2'=arg2P_5, arg3'=arg3P_5, [ arg3<=arg2 ], cost: 1 5: f475_0_main_GE -> f475_0_main_GE : arg2'=1+arg2, [ arg3>0 && arg1<3 && arg3>arg2 ], cost: 1 12: f475_0_main_GE -> f541_0_bubble_NULL : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ arg3>0 && arg3>arg2 && arg1<3 && arg2P_13>-1 && arg1P_13>-1 ], cost: 1 9: f165_0_mk_LE -> f165_0_mk_LE : arg1'=-1+arg1, arg2'=arg1, arg3'=arg3P_10, [ arg2>0 ], cost: 1 11: f291_0_length_NULL -> f291_0_length_NULL : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [ 1+arg1P_12<=arg1 && 1+arg1P_12<=arg2 && 1+arg2P_12<=arg1 && 1+arg2P_12<=arg2 && arg1>0 && arg2>0 && arg1P_12>-1 && arg2P_12>-1 ], cost: 1 13: f541_0_bubble_NULL -> f541_0_bubble_NULL : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, [ 2+arg1P_14<=arg1 && 2+arg1P_14<=arg2 && 2+arg2P_14<=arg1 && 2+arg2P_14<=arg2 && arg1>2 && arg2>2 && arg1P_14>0 && arg2P_14>0 ], cost: 1 14: f541_0_bubble_NULL -> f541_0_bubble_NULL : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, [ arg1P_15<=arg1 && arg1P_15<=arg2 && arg2P_15<=arg1 && arg2P_15<=arg2 && arg1>2 && arg2>2 && arg1P_15>0 && arg2P_15>0 ], cost: 1 15: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 4. Accelerating the following rules: 5: f475_0_main_GE -> f475_0_main_GE : arg2'=1+arg2, [ arg3>0 && arg1<3 && arg3>arg2 ], cost: 1 Accelerated rule 5 with metering function arg3-arg2, yielding the new rule 16. Removing the simple loops: 5. Accelerating simple loops of location 5. Accelerating the following rules: 9: f165_0_mk_LE -> f165_0_mk_LE : arg1'=-1+arg1, arg2'=arg1, arg3'=arg3P_10, [ arg2>0 ], cost: 1 Found no metering function for rule 9. Removing the simple loops:. Accelerating simple loops of location 6. Accelerating the following rules: 11: f291_0_length_NULL -> f291_0_length_NULL : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [ 1+arg1P_12<=arg1 && 1+arg1P_12<=arg2 && 1+arg2P_12<=arg1 && 1+arg2P_12<=arg2 && arg1>0 && arg2>0 && arg1P_12>-1 && arg2P_12>-1 ], cost: 1 During metering: Instantiating temporary variables by {arg2P_12==-1+arg1,arg1P_12==-1+arg2} Accelerated rule 11 with metering function 2*arg1-arg2, yielding the new rule 17. Removing the simple loops: 11. Accelerating simple loops of location 7. Accelerating the following rules: 13: f541_0_bubble_NULL -> f541_0_bubble_NULL : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, [ 2+arg1P_14<=arg1 && 2+arg1P_14<=arg2 && 2+arg2P_14<=arg1 && 2+arg2P_14<=arg2 && arg1>2 && arg2>2 && arg1P_14>0 && arg2P_14>0 ], cost: 1 14: f541_0_bubble_NULL -> f541_0_bubble_NULL : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, [ arg1P_15<=arg1 && arg1P_15<=arg2 && arg2P_15<=arg1 && arg2P_15<=arg2 && arg1>2 && arg2>2 && arg1P_15>0 && arg2P_15>0 ], cost: 1 During metering: Instantiating temporary variables by {arg2P_14==-2+arg2,arg1P_14==-2+arg1} Accelerated rule 13 with metering function arg1-arg2, yielding the new rule 18. Accelerated rule 14 with NONTERM (after strengthening guard), yielding the new rule 19. Removing the simple loops: 13. Accelerated all simple loops using metering functions (where possible): Start location: __init 2: f148_0_main_InvokeMethod -> f341_0_main_GE : arg1'=0, arg2'=arg2P_3, arg3'=arg3P_3, [ arg1>0 && arg2>-1 ], cost: 1 7: f148_0_main_InvokeMethod -> f165_0_mk_LE : arg1'=-1+arg2, arg3'=arg3P_8, [ arg1>0 ], cost: 1 8: f148_0_main_InvokeMethod -> f165_0_mk_LE : arg1'=-1+arg2, arg3'=arg3P_9, [ arg1>0 && arg2>-1 ], cost: 1 1: f1_0_main_ConstantStackPush -> f148_0_main_InvokeMethod : arg1'=arg1P_2, arg3'=arg3P_2, [ arg1P_2<=arg1 && arg2>-1 && arg1>0 && arg1P_2>0 ], cost: 1 6: f1_0_main_ConstantStackPush -> f165_0_mk_LE : arg1'=-1+arg2, arg3'=arg3P_7, [ arg1>0 && arg2>-1 ], cost: 1 3: f341_0_main_GE -> f475_0_main_GE : arg2'=0, arg3'=arg3P_4, [ arg1<3 ], cost: 1 10: f341_0_main_GE -> f291_0_length_NULL : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ arg1P_11>-1 && arg2P_11>-1 && arg1<3 ], cost: 1 4: f475_0_main_GE -> f341_0_main_GE : arg1'=1+arg1, arg2'=arg2P_5, arg3'=arg3P_5, [ arg3<=arg2 ], cost: 1 12: f475_0_main_GE -> f541_0_bubble_NULL : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ arg3>0 && arg3>arg2 && arg1<3 && arg2P_13>-1 && arg1P_13>-1 ], cost: 1 16: f475_0_main_GE -> f475_0_main_GE : arg2'=arg3, [ arg3>0 && arg1<3 && arg3>arg2 ], cost: arg3-arg2 9: f165_0_mk_LE -> f165_0_mk_LE : arg1'=-1+arg1, arg2'=arg1, arg3'=arg3P_10, [ arg2>0 ], cost: 1 17: f291_0_length_NULL -> f291_0_length_NULL : arg1'=-arg1+arg2, arg2'=-arg1+arg2, arg3'=arg3P_12, [ arg1>0 && arg2>0 && arg2==arg1 && 2*arg1-arg2>=1 ], cost: 2*arg1-arg2 14: f541_0_bubble_NULL -> f541_0_bubble_NULL : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, [ arg1P_15<=arg1 && arg1P_15<=arg2 && arg2P_15<=arg1 && arg2P_15<=arg2 && arg1>2 && arg2>2 && arg1P_15>0 && arg2P_15>0 ], cost: 1 18: f541_0_bubble_NULL -> f541_0_bubble_NULL : arg1'=-arg1+2*arg2, arg2'=-2*arg1+3*arg2, arg3'=arg3P_14, [ arg1<=arg2 && arg1>2 && arg2>2 && arg1-arg2>=1 ], cost: arg1-arg2 19: f541_0_bubble_NULL -> [12] : [ arg1P_15<=arg1 && arg1P_15<=arg2 && arg2P_15<=arg1 && arg2P_15<=arg2 && arg1>2 && arg2>2 && arg2P_15<=arg1P_15 && arg1P_15>2 && arg1P_15<=arg2P_15 && arg2P_15>2 ], cost: NONTERM 15: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 2: f148_0_main_InvokeMethod -> f341_0_main_GE : arg1'=0, arg2'=arg2P_3, arg3'=arg3P_3, [ arg1>0 && arg2>-1 ], cost: 1 7: f148_0_main_InvokeMethod -> f165_0_mk_LE : arg1'=-1+arg2, arg3'=arg3P_8, [ arg1>0 ], cost: 1 8: f148_0_main_InvokeMethod -> f165_0_mk_LE : arg1'=-1+arg2, arg3'=arg3P_9, [ arg1>0 && arg2>-1 ], cost: 1 22: f148_0_main_InvokeMethod -> f165_0_mk_LE : arg1'=-2+arg2, arg2'=-1+arg2, arg3'=arg3P_10, [ arg1>0 && arg2>0 ], cost: 2 23: f148_0_main_InvokeMethod -> f165_0_mk_LE : arg1'=-2+arg2, arg2'=-1+arg2, arg3'=arg3P_10, [ arg1>0 && arg2>0 ], cost: 2 1: f1_0_main_ConstantStackPush -> f148_0_main_InvokeMethod : arg1'=arg1P_2, arg3'=arg3P_2, [ arg1P_2<=arg1 && arg2>-1 && arg1>0 && arg1P_2>0 ], cost: 1 6: f1_0_main_ConstantStackPush -> f165_0_mk_LE : arg1'=-1+arg2, arg3'=arg3P_7, [ arg1>0 && arg2>-1 ], cost: 1 21: f1_0_main_ConstantStackPush -> f165_0_mk_LE : arg1'=-2+arg2, arg2'=-1+arg2, arg3'=arg3P_10, [ arg1>0 && arg2>0 ], cost: 2 3: f341_0_main_GE -> f475_0_main_GE : arg2'=0, arg3'=arg3P_4, [ arg1<3 ], cost: 1 10: f341_0_main_GE -> f291_0_length_NULL : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ arg1P_11>-1 && arg2P_11>-1 && arg1<3 ], cost: 1 20: f341_0_main_GE -> f475_0_main_GE : arg2'=arg3P_4, arg3'=arg3P_4, [ arg1<3 && arg3P_4>0 ], cost: 1+arg3P_4 24: f341_0_main_GE -> f291_0_length_NULL : arg1'=0, arg2'=0, arg3'=arg3P_12, [ arg1<3 && arg1P_11>0 ], cost: 1+arg1P_11 4: f475_0_main_GE -> f341_0_main_GE : arg1'=1+arg1, arg2'=arg2P_5, arg3'=arg3P_5, [ arg3<=arg2 ], cost: 1 12: f475_0_main_GE -> f541_0_bubble_NULL : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ arg3>0 && arg3>arg2 && arg1<3 && arg2P_13>-1 && arg1P_13>-1 ], cost: 1 25: f475_0_main_GE -> f541_0_bubble_NULL : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, [ arg3>0 && arg3>arg2 && arg1<3 && arg1P_15>0 && arg2P_15>0 ], cost: 2 26: f475_0_main_GE -> [12] : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ arg3>0 && arg3>arg2 && arg1<3 && arg1P_13>2 && arg2P_13>2 ], cost: NONTERM 15: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 2: f148_0_main_InvokeMethod -> f341_0_main_GE : arg1'=0, arg2'=arg2P_3, arg3'=arg3P_3, [ arg1>0 && arg2>-1 ], cost: 1 1: f1_0_main_ConstantStackPush -> f148_0_main_InvokeMethod : arg1'=arg1P_2, arg3'=arg3P_2, [ arg1P_2<=arg1 && arg2>-1 && arg1>0 && arg1P_2>0 ], cost: 1 3: f341_0_main_GE -> f475_0_main_GE : arg2'=0, arg3'=arg3P_4, [ arg1<3 ], cost: 1 20: f341_0_main_GE -> f475_0_main_GE : arg2'=arg3P_4, arg3'=arg3P_4, [ arg1<3 && arg3P_4>0 ], cost: 1+arg3P_4 24: f341_0_main_GE -> f291_0_length_NULL : arg1'=0, arg2'=0, arg3'=arg3P_12, [ arg1<3 && arg1P_11>0 ], cost: 1+arg1P_11 4: f475_0_main_GE -> f341_0_main_GE : arg1'=1+arg1, arg2'=arg2P_5, arg3'=arg3P_5, [ arg3<=arg2 ], cost: 1 26: f475_0_main_GE -> [12] : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ arg3>0 && arg3>arg2 && arg1<3 && arg1P_13>2 && arg2P_13>2 ], cost: NONTERM 15: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, [], cost: 1 Eliminated locations (on linear paths): Start location: __init 3: f341_0_main_GE -> f475_0_main_GE : arg2'=0, arg3'=arg3P_4, [ arg1<3 ], cost: 1 20: f341_0_main_GE -> f475_0_main_GE : arg2'=arg3P_4, arg3'=arg3P_4, [ arg1<3 && arg3P_4>0 ], cost: 1+arg3P_4 24: f341_0_main_GE -> f291_0_length_NULL : arg1'=0, arg2'=0, arg3'=arg3P_12, [ arg1<3 && arg1P_11>0 ], cost: 1+arg1P_11 4: f475_0_main_GE -> f341_0_main_GE : arg1'=1+arg1, arg2'=arg2P_5, arg3'=arg3P_5, [ arg3<=arg2 ], cost: 1 26: f475_0_main_GE -> [12] : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ arg3>0 && arg3>arg2 && arg1<3 && arg1P_13>2 && arg2P_13>2 ], cost: NONTERM 28: __init -> f341_0_main_GE : arg1'=0, arg2'=arg2P_3, arg3'=arg3P_3, [ arg1P_2<=arg1P_16 && arg2P_16>-1 && arg1P_16>0 && arg1P_2>0 ], cost: 3 Eliminated locations (on tree-shaped paths): Start location: __init 24: f341_0_main_GE -> f291_0_length_NULL : arg1'=0, arg2'=0, arg3'=arg3P_12, [ arg1<3 && arg1P_11>0 ], cost: 1+arg1P_11 29: f341_0_main_GE -> f341_0_main_GE : arg1'=1+arg1, arg2'=arg2P_5, arg3'=arg3P_5, [ arg1<3 && arg3P_4<=0 ], cost: 2 30: f341_0_main_GE -> [12] : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ arg1<3 && arg3P_4>0 && arg1P_13>2 && arg2P_13>2 ], cost: NONTERM 31: f341_0_main_GE -> f341_0_main_GE : arg1'=1+arg1, arg2'=arg2P_5, arg3'=arg3P_5, [ arg1<3 && arg3P_4>0 ], cost: 2+arg3P_4 32: f341_0_main_GE -> [13] : [ arg1<3 && arg3P_4>0 ], cost: 1+arg3P_4 28: __init -> f341_0_main_GE : arg1'=0, arg2'=arg2P_3, arg3'=arg3P_3, [ arg1P_2<=arg1P_16 && arg2P_16>-1 && arg1P_16>0 && arg1P_2>0 ], cost: 3 Accelerating simple loops of location 3. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 29: f341_0_main_GE -> f341_0_main_GE : arg1'=1+arg1, arg2'=arg2P_5, arg3'=arg3P_5, [ arg1<3 ], cost: 2 31: f341_0_main_GE -> f341_0_main_GE : arg1'=1+arg1, arg2'=arg2P_5, arg3'=arg3P_5, [ arg1<3 && arg3P_4>0 ], cost: 2+arg3P_4 Accelerated rule 29 with metering function 3-arg1, yielding the new rule 33. Accelerated rule 31 with metering function 3-arg1, yielding the new rule 34. Removing the simple loops: 29 31. Accelerated all simple loops using metering functions (where possible): Start location: __init 24: f341_0_main_GE -> f291_0_length_NULL : arg1'=0, arg2'=0, arg3'=arg3P_12, [ arg1<3 && arg1P_11>0 ], cost: 1+arg1P_11 30: f341_0_main_GE -> [12] : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ arg1<3 && arg3P_4>0 && arg1P_13>2 && arg2P_13>2 ], cost: NONTERM 32: f341_0_main_GE -> [13] : [ arg1<3 && arg3P_4>0 ], cost: 1+arg3P_4 33: f341_0_main_GE -> f341_0_main_GE : arg1'=3, arg2'=arg2P_5, arg3'=arg3P_5, [ arg1<3 ], cost: 6-2*arg1 34: f341_0_main_GE -> f341_0_main_GE : arg1'=3, arg2'=arg2P_5, arg3'=arg3P_5, [ arg1<3 && arg3P_4>0 ], cost: 6-2*arg1-arg3P_4*(-3+arg1) 28: __init -> f341_0_main_GE : arg1'=0, arg2'=arg2P_3, arg3'=arg3P_3, [ arg1P_2<=arg1P_16 && arg2P_16>-1 && arg1P_16>0 && arg1P_2>0 ], cost: 3 Chained accelerated rules (with incoming rules): Start location: __init 24: f341_0_main_GE -> f291_0_length_NULL : arg1'=0, arg2'=0, arg3'=arg3P_12, [ arg1<3 && arg1P_11>0 ], cost: 1+arg1P_11 30: f341_0_main_GE -> [12] : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ arg1<3 && arg3P_4>0 && arg1P_13>2 && arg2P_13>2 ], cost: NONTERM 32: f341_0_main_GE -> [13] : [ arg1<3 && arg3P_4>0 ], cost: 1+arg3P_4 28: __init -> f341_0_main_GE : arg1'=0, arg2'=arg2P_3, arg3'=arg3P_3, [ arg1P_2<=arg1P_16 && arg2P_16>-1 && arg1P_16>0 && arg1P_2>0 ], cost: 3 35: __init -> f341_0_main_GE : arg1'=3, arg2'=arg2P_5, arg3'=arg3P_5, [], cost: 9 36: __init -> f341_0_main_GE : arg1'=3, arg2'=arg2P_5, arg3'=arg3P_5, [ arg3P_4>0 ], cost: 9+3*arg3P_4 Eliminated locations (on tree-shaped paths): Start location: __init 37: __init -> f291_0_length_NULL : arg1'=0, arg2'=0, arg3'=arg3P_12, [ arg1P_2<=arg1P_16 && arg2P_16>-1 && arg1P_16>0 && arg1P_2>0 && arg1P_11>0 ], cost: 4+arg1P_11 38: __init -> [12] : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ arg1P_2<=arg1P_16 && arg2P_16>-1 && arg1P_16>0 && arg1P_2>0 && arg3P_4>0 && arg1P_13>2 && arg2P_13>2 ], cost: NONTERM 39: __init -> [13] : arg1'=0, arg2'=arg2P_3, arg3'=arg3P_3, [ arg1P_2<=arg1P_16 && arg2P_16>-1 && arg1P_16>0 && arg1P_2>0 && arg3P_4>0 ], cost: 4+arg3P_4 40: __init -> [15] : [ arg3P_4>0 ], cost: 9+3*arg3P_4 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 37: __init -> f291_0_length_NULL : arg1'=0, arg2'=0, arg3'=arg3P_12, [ arg1P_2<=arg1P_16 && arg2P_16>-1 && arg1P_16>0 && arg1P_2>0 && arg1P_11>0 ], cost: 4+arg1P_11 38: __init -> [12] : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ arg1P_2<=arg1P_16 && arg2P_16>-1 && arg1P_16>0 && arg1P_2>0 && arg3P_4>0 && arg1P_13>2 && arg2P_13>2 ], cost: NONTERM 39: __init -> [13] : arg1'=0, arg2'=arg2P_3, arg3'=arg3P_3, [ arg1P_2<=arg1P_16 && arg2P_16>-1 && arg1P_16>0 && arg1P_2>0 && arg3P_4>0 ], cost: 4+arg3P_4 40: __init -> [15] : [ arg3P_4>0 ], cost: 9+3*arg3P_4 Computing asymptotic complexity for rule 37 Solved the limit problem by the following transformations: Created initial limit problem: 4+arg1P_11 (+), arg1P_16 (+/+!), 1+arg1P_16-arg1P_2 (+/+!), arg1P_2 (+/+!), arg1P_11 (+/+!), 1+arg2P_16 (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {arg1P_16==1,arg2P_16==n,arg1P_2==1,arg1P_11==n} resulting limit problem: [solved] Solution: arg1P_16 / 1 arg2P_16 / n arg1P_2 / 1 arg1P_11 / n Resulting cost 4+n has complexity: Unbounded Found new complexity Unbounded. Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Unbounded Cpx degree: Unbounded Solved cost: 4+n Rule cost: 4+arg1P_11 Rule guard: [ arg1P_2<=arg1P_16 && arg2P_16>-1 && arg1P_16>0 && arg1P_2>0 && arg1P_11>0 ] WORST_CASE(INF,?)