WORST_CASE(INF,?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f2097_0_flatten_NULL : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ 1+arg1P_1<=arg1 && arg2>0 && arg1>0 && arg1P_1>-1 ], cost: 1 1: f1_0_main_Load -> f1795_0_main_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1P_2<=arg1 && arg1>0 && arg1P_2>0 && arg2P_2>2 ], cost: 1 4: f1_0_main_Load -> f1759_0_createTree_LE : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg3P_5>0 && arg2>-1 && -2+arg1P_5<=arg1 && -2+arg2P_5<=arg1 && arg1>0 && arg1P_5>2 && arg2P_5>2 && 1==arg4P_5 ], cost: 1 11: f2097_0_flatten_NULL -> f2097_0_flatten_NULL : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [ 2+arg1P_12<=arg1 && arg1>1 && arg1P_12>-1 ], cost: 1 12: f2097_0_flatten_NULL -> f2097_0_flatten_NULL : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, [ -2+arg1P_13<=arg1 && arg1>2 && arg1P_13>2 ], cost: 1 3: f1795_0_main_InvokeMethod -> f2097_0_flatten_NULL : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg1P_4<=arg2 && x14_1>0 && arg1>0 && arg2>2 && arg1P_4>2 && 2+arg3<=arg2 ], cost: 1 2: f456_0_createTree_Return -> f1795_0_main_InvokeMethod : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ arg1>=arg1P_3 && 2+arg1P_3<=arg2 && arg2P_3<=arg2 && arg1>0 && arg2>2 && arg1P_3>0 && arg2P_3>2 && 2+arg3<=arg2 && arg3==arg3P_3 ], cost: 1 5: f1759_0_createTree_LE -> f1759_0_createTree_LE : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, [ arg4>-1 && arg3>0 && arg1P_6<=arg1 && 2+arg2P_6<=arg2 && arg1>2 && arg2>2 && arg1P_6>2 && arg2P_6>0 && -1+arg3==arg3P_6 && 1+arg4==arg4P_6 ], cost: 1 6: f1759_0_createTree_LE -> f1759_0_createTree_LE : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [ arg3>0 && x36_1>0 && arg4>-1 && arg1P_7<=arg1 && 2+arg2P_7<=arg2 && arg1>2 && arg2>2 && arg1P_7>2 && arg2P_7>0 && -1+arg3==arg3P_7 && 1+arg4==arg4P_7 ], cost: 1 7: f1759_0_createTree_LE -> f1759_0_createTree_LE : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, [ arg3>0 && x43_1>0 && arg4>-1 && arg1>2 && arg2>1 && arg1P_8>2 && arg2P_8>2 && -1+arg3==arg3P_8 && 1+arg4==arg4P_8 ], cost: 1 8: f1759_0_createTree_LE -> f1759_0_createTree_LE : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, [ arg4>-1 && arg3>0 && arg1>2 && arg2>1 && arg1P_9>2 && arg2P_9>2 && -1+arg3==arg3P_9 && 1+arg4==arg4P_9 ], cost: 1 9: f1759_0_createTree_LE -> f1759_0_createTree_LE : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, [ arg4>-1 && arg3>0 && -2+arg1P_10<=arg1 && -2+arg1P_10<=arg2 && -2+arg2P_10<=arg1 && -2+arg2P_10<=arg2 && arg1>2 && arg2>2 && arg1P_10>4 && arg2P_10>4 && -1+arg3==arg3P_10 && 1+arg4==arg4P_10 ], cost: 1 10: f1759_0_createTree_LE -> f1759_0_createTree_LE : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, [ arg3>0 && x62_1>0 && arg4>-1 && -2+arg1P_11<=arg1 && -2+arg1P_11<=arg2 && -2+arg2P_11<=arg1 && -2+arg2P_11<=arg2 && arg1>2 && arg2>2 && arg1P_11>4 && arg2P_11>4 && -1+arg3==arg3P_11 && 1+arg4==arg4P_11 ], cost: 1 13: __init -> f1_0_main_Load : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, arg4'=arg4P_14, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 13: __init -> f1_0_main_Load : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, arg4'=arg4P_14, [], cost: 1 Removed unreachable and leaf rules: Start location: __init 0: f1_0_main_Load -> f2097_0_flatten_NULL : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ 1+arg1P_1<=arg1 && arg2>0 && arg1>0 && arg1P_1>-1 ], cost: 1 1: f1_0_main_Load -> f1795_0_main_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1P_2<=arg1 && arg1>0 && arg1P_2>0 && arg2P_2>2 ], cost: 1 4: f1_0_main_Load -> f1759_0_createTree_LE : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg3P_5>0 && arg2>-1 && -2+arg1P_5<=arg1 && -2+arg2P_5<=arg1 && arg1>0 && arg1P_5>2 && arg2P_5>2 && 1==arg4P_5 ], cost: 1 11: f2097_0_flatten_NULL -> f2097_0_flatten_NULL : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [ 2+arg1P_12<=arg1 && arg1>1 && arg1P_12>-1 ], cost: 1 12: f2097_0_flatten_NULL -> f2097_0_flatten_NULL : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, [ -2+arg1P_13<=arg1 && arg1>2 && arg1P_13>2 ], cost: 1 3: f1795_0_main_InvokeMethod -> f2097_0_flatten_NULL : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg1P_4<=arg2 && x14_1>0 && arg1>0 && arg2>2 && arg1P_4>2 && 2+arg3<=arg2 ], cost: 1 5: f1759_0_createTree_LE -> f1759_0_createTree_LE : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, [ arg4>-1 && arg3>0 && arg1P_6<=arg1 && 2+arg2P_6<=arg2 && arg1>2 && arg2>2 && arg1P_6>2 && arg2P_6>0 && -1+arg3==arg3P_6 && 1+arg4==arg4P_6 ], cost: 1 6: f1759_0_createTree_LE -> f1759_0_createTree_LE : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [ arg3>0 && x36_1>0 && arg4>-1 && arg1P_7<=arg1 && 2+arg2P_7<=arg2 && arg1>2 && arg2>2 && arg1P_7>2 && arg2P_7>0 && -1+arg3==arg3P_7 && 1+arg4==arg4P_7 ], cost: 1 7: f1759_0_createTree_LE -> f1759_0_createTree_LE : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, [ arg3>0 && x43_1>0 && arg4>-1 && arg1>2 && arg2>1 && arg1P_8>2 && arg2P_8>2 && -1+arg3==arg3P_8 && 1+arg4==arg4P_8 ], cost: 1 8: f1759_0_createTree_LE -> f1759_0_createTree_LE : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, [ arg4>-1 && arg3>0 && arg1>2 && arg2>1 && arg1P_9>2 && arg2P_9>2 && -1+arg3==arg3P_9 && 1+arg4==arg4P_9 ], cost: 1 9: f1759_0_createTree_LE -> f1759_0_createTree_LE : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, [ arg4>-1 && arg3>0 && -2+arg1P_10<=arg1 && -2+arg1P_10<=arg2 && -2+arg2P_10<=arg1 && -2+arg2P_10<=arg2 && arg1>2 && arg2>2 && arg1P_10>4 && arg2P_10>4 && -1+arg3==arg3P_10 && 1+arg4==arg4P_10 ], cost: 1 10: f1759_0_createTree_LE -> f1759_0_createTree_LE : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, [ arg3>0 && x62_1>0 && arg4>-1 && -2+arg1P_11<=arg1 && -2+arg1P_11<=arg2 && -2+arg2P_11<=arg1 && -2+arg2P_11<=arg2 && arg1>2 && arg2>2 && arg1P_11>4 && arg2P_11>4 && -1+arg3==arg3P_11 && 1+arg4==arg4P_11 ], cost: 1 13: __init -> f1_0_main_Load : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, arg4'=arg4P_14, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f2097_0_flatten_NULL : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ 1+arg1P_1<=arg1 && arg2>0 && arg1>0 && arg1P_1>-1 ], cost: 1 1: f1_0_main_Load -> f1795_0_main_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1P_2<=arg1 && arg1>0 && arg1P_2>0 && arg2P_2>2 ], cost: 1 4: f1_0_main_Load -> f1759_0_createTree_LE : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=1, [ arg3P_5>0 && arg2>-1 && -2+arg1P_5<=arg1 && -2+arg2P_5<=arg1 && arg1>0 && arg1P_5>2 && arg2P_5>2 ], cost: 1 11: f2097_0_flatten_NULL -> f2097_0_flatten_NULL : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [ 2+arg1P_12<=arg1 && arg1>1 && arg1P_12>-1 ], cost: 1 12: f2097_0_flatten_NULL -> f2097_0_flatten_NULL : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, [ -2+arg1P_13<=arg1 && arg1>2 && arg1P_13>2 ], cost: 1 3: f1795_0_main_InvokeMethod -> f2097_0_flatten_NULL : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg1P_4<=arg2 && arg1>0 && arg2>2 && arg1P_4>2 && 2+arg3<=arg2 ], cost: 1 5: f1759_0_createTree_LE -> f1759_0_createTree_LE : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=-1+arg3, arg4'=1+arg4, [ arg4>-1 && arg3>0 && arg1P_6<=arg1 && 2+arg2P_6<=arg2 && arg1>2 && arg2>2 && arg1P_6>2 && arg2P_6>0 ], cost: 1 6: f1759_0_createTree_LE -> f1759_0_createTree_LE : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=-1+arg3, arg4'=1+arg4, [ arg3>0 && arg4>-1 && arg1P_7<=arg1 && 2+arg2P_7<=arg2 && arg1>2 && arg2>2 && arg1P_7>2 && arg2P_7>0 ], cost: 1 7: f1759_0_createTree_LE -> f1759_0_createTree_LE : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=-1+arg3, arg4'=1+arg4, [ arg3>0 && arg4>-1 && arg1>2 && arg2>1 && arg1P_8>2 && arg2P_8>2 ], cost: 1 8: f1759_0_createTree_LE -> f1759_0_createTree_LE : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=-1+arg3, arg4'=1+arg4, [ arg4>-1 && arg3>0 && arg1>2 && arg2>1 && arg1P_9>2 && arg2P_9>2 ], cost: 1 9: f1759_0_createTree_LE -> f1759_0_createTree_LE : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=-1+arg3, arg4'=1+arg4, [ arg4>-1 && arg3>0 && -2+arg1P_10<=arg1 && -2+arg1P_10<=arg2 && -2+arg2P_10<=arg1 && -2+arg2P_10<=arg2 && arg1>2 && arg2>2 && arg1P_10>4 && arg2P_10>4 ], cost: 1 10: f1759_0_createTree_LE -> f1759_0_createTree_LE : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=-1+arg3, arg4'=1+arg4, [ arg3>0 && arg4>-1 && -2+arg1P_11<=arg1 && -2+arg1P_11<=arg2 && -2+arg2P_11<=arg1 && -2+arg2P_11<=arg2 && arg1>2 && arg2>2 && arg1P_11>4 && arg2P_11>4 ], cost: 1 13: __init -> f1_0_main_Load : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, arg4'=arg4P_14, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 11: f2097_0_flatten_NULL -> f2097_0_flatten_NULL : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [ 2+arg1P_12<=arg1 && arg1>1 && arg1P_12>-1 ], cost: 1 12: f2097_0_flatten_NULL -> f2097_0_flatten_NULL : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, [ -2+arg1P_13<=arg1 && arg1>2 && arg1P_13>2 ], cost: 1 During metering: Instantiating temporary variables by {arg1P_12==-2+arg1} Accelerated rule 11 with metering function meter (where 2*meter==-1+arg1), yielding the new rule 14. Accelerated rule 12 with NONTERM, yielding the new rule 15. Removing the simple loops: 11 12. Accelerating simple loops of location 4. Accelerating the following rules: 5: f1759_0_createTree_LE -> f1759_0_createTree_LE : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=-1+arg3, arg4'=1+arg4, [ arg4>-1 && arg3>0 && arg1P_6<=arg1 && 2+arg2P_6<=arg2 && arg1>2 && arg2>2 && arg1P_6>2 && arg2P_6>0 ], cost: 1 6: f1759_0_createTree_LE -> f1759_0_createTree_LE : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=-1+arg3, arg4'=1+arg4, [ arg3>0 && arg4>-1 && arg1P_7<=arg1 && 2+arg2P_7<=arg2 && arg1>2 && arg2>2 && arg1P_7>2 && arg2P_7>0 ], cost: 1 7: f1759_0_createTree_LE -> f1759_0_createTree_LE : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=-1+arg3, arg4'=1+arg4, [ arg3>0 && arg4>-1 && arg1>2 && arg2>1 && arg1P_8>2 && arg2P_8>2 ], cost: 1 8: f1759_0_createTree_LE -> f1759_0_createTree_LE : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=-1+arg3, arg4'=1+arg4, [ arg4>-1 && arg3>0 && arg1>2 && arg2>1 && arg1P_9>2 && arg2P_9>2 ], cost: 1 9: f1759_0_createTree_LE -> f1759_0_createTree_LE : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=-1+arg3, arg4'=1+arg4, [ arg4>-1 && arg3>0 && -2+arg1P_10<=arg1 && -2+arg1P_10<=arg2 && -2+arg2P_10<=arg1 && -2+arg2P_10<=arg2 && arg1>2 && arg2>2 && arg1P_10>4 && arg2P_10>4 ], cost: 1 10: f1759_0_createTree_LE -> f1759_0_createTree_LE : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=-1+arg3, arg4'=1+arg4, [ arg3>0 && arg4>-1 && -2+arg1P_11<=arg1 && -2+arg1P_11<=arg2 && -2+arg2P_11<=arg1 && -2+arg2P_11<=arg2 && arg1>2 && arg2>2 && arg1P_11>4 && arg2P_11>4 ], cost: 1 Found no metering function for rule 5. Found no metering function for rule 6. Accelerated rule 7 with metering function arg3, yielding the new rule 16. Accelerated rule 8 with metering function arg3, yielding the new rule 17. During metering: Instantiating temporary variables by {arg1P_10==2+arg1,arg2P_10==2+arg2} Accelerated rule 9 with metering function arg3, yielding the new rule 18. During metering: Instantiating temporary variables by {arg2P_11==2+arg2,arg1P_11==2+arg1} Accelerated rule 10 with metering function arg3, yielding the new rule 19. Removing the simple loops: 7 8 9 10. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f2097_0_flatten_NULL : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ 1+arg1P_1<=arg1 && arg2>0 && arg1>0 && arg1P_1>-1 ], cost: 1 1: f1_0_main_Load -> f1795_0_main_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1P_2<=arg1 && arg1>0 && arg1P_2>0 && arg2P_2>2 ], cost: 1 4: f1_0_main_Load -> f1759_0_createTree_LE : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=1, [ arg3P_5>0 && arg2>-1 && -2+arg1P_5<=arg1 && -2+arg2P_5<=arg1 && arg1>0 && arg1P_5>2 && arg2P_5>2 ], cost: 1 14: f2097_0_flatten_NULL -> f2097_0_flatten_NULL : arg1'=arg1-2*meter, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [ arg1>1 && 2*meter==-1+arg1 && meter>=1 ], cost: meter 15: f2097_0_flatten_NULL -> [6] : [ -2+arg1P_13<=arg1 && arg1>2 && arg1P_13>2 ], cost: NONTERM 3: f1795_0_main_InvokeMethod -> f2097_0_flatten_NULL : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg1P_4<=arg2 && arg1>0 && arg2>2 && arg1P_4>2 && 2+arg3<=arg2 ], cost: 1 5: f1759_0_createTree_LE -> f1759_0_createTree_LE : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=-1+arg3, arg4'=1+arg4, [ arg4>-1 && arg3>0 && arg1P_6<=arg1 && 2+arg2P_6<=arg2 && arg1>2 && arg2>2 && arg1P_6>2 && arg2P_6>0 ], cost: 1 6: f1759_0_createTree_LE -> f1759_0_createTree_LE : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=-1+arg3, arg4'=1+arg4, [ arg3>0 && arg4>-1 && arg1P_7<=arg1 && 2+arg2P_7<=arg2 && arg1>2 && arg2>2 && arg1P_7>2 && arg2P_7>0 ], cost: 1 16: f1759_0_createTree_LE -> f1759_0_createTree_LE : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=0, arg4'=arg3+arg4, [ arg3>0 && arg4>-1 && arg1>2 && arg2>1 && arg1P_8>2 && arg2P_8>2 ], cost: arg3 17: f1759_0_createTree_LE -> f1759_0_createTree_LE : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=0, arg4'=arg3+arg4, [ arg4>-1 && arg3>0 && arg1>2 && arg2>1 && arg1P_9>2 && arg2P_9>2 ], cost: arg3 18: f1759_0_createTree_LE -> f1759_0_createTree_LE : arg1'=2*arg3+arg1, arg2'=2*arg3+arg2, arg3'=0, arg4'=arg3+arg4, [ arg4>-1 && arg3>0 && arg1<=arg2 && arg2<=arg1 && arg1>2 && arg2>2 ], cost: arg3 19: f1759_0_createTree_LE -> f1759_0_createTree_LE : arg1'=2*arg3+arg1, arg2'=2*arg3+arg2, arg3'=0, arg4'=arg3+arg4, [ arg3>0 && arg4>-1 && arg1<=arg2 && arg2<=arg1 && arg1>2 && arg2>2 ], cost: arg3 13: __init -> f1_0_main_Load : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, arg4'=arg4P_14, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f2097_0_flatten_NULL : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ 1+arg1P_1<=arg1 && arg2>0 && arg1>0 && arg1P_1>-1 ], cost: 1 1: f1_0_main_Load -> f1795_0_main_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1P_2<=arg1 && arg1>0 && arg1P_2>0 && arg2P_2>2 ], cost: 1 4: f1_0_main_Load -> f1759_0_createTree_LE : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=1, [ arg3P_5>0 && arg2>-1 && -2+arg1P_5<=arg1 && -2+arg2P_5<=arg1 && arg1>0 && arg1P_5>2 && arg2P_5>2 ], cost: 1 20: f1_0_main_Load -> f2097_0_flatten_NULL : arg1'=1, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [ 2+2*meter<=arg1 && arg2>0 && arg1>0 && 1+2*meter>1 && meter>=1 ], cost: 1+meter 22: f1_0_main_Load -> [6] : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ 1+arg1P_1<=arg1 && arg2>0 && arg1>0 && arg1P_1>2 ], cost: NONTERM 24: f1_0_main_Load -> f1759_0_createTree_LE : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=-1+arg3P_5, arg4'=2, [ arg3P_5>0 && arg2>-1 && arg1>0 && arg1P_6>2 && arg2P_6>0 && arg1P_6<=2+arg1 && 2+arg2P_6<=2+arg1 ], cost: 2 25: f1_0_main_Load -> f1759_0_createTree_LE : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=-1+arg3P_5, arg4'=2, [ arg3P_5>0 && arg2>-1 && arg1>0 && arg1P_7>2 && arg2P_7>0 && arg1P_7<=2+arg1 && 2+arg2P_7<=2+arg1 ], cost: 2 26: f1_0_main_Load -> f1759_0_createTree_LE : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=0, arg4'=1+arg3P_5, [ arg3P_5>0 && arg2>-1 && arg1>0 && arg1P_8>2 && arg2P_8>2 ], cost: 1+arg3P_5 27: f1_0_main_Load -> f1759_0_createTree_LE : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=0, arg4'=1+arg3P_5, [ arg3P_5>0 && arg2>-1 && arg1>0 && arg1P_9>2 && arg2P_9>2 ], cost: 1+arg3P_5 28: f1_0_main_Load -> f1759_0_createTree_LE : arg1'=arg2P_5+2*arg3P_5, arg2'=arg2P_5+2*arg3P_5, arg3'=0, arg4'=1+arg3P_5, [ arg3P_5>0 && arg2>-1 && -2+arg2P_5<=arg1 && arg1>0 && arg2P_5>2 ], cost: 1+arg3P_5 29: f1_0_main_Load -> f1759_0_createTree_LE : arg1'=arg2P_5+2*arg3P_5, arg2'=arg2P_5+2*arg3P_5, arg3'=0, arg4'=1+arg3P_5, [ arg3P_5>0 && arg2>-1 && -2+arg2P_5<=arg1 && arg1>0 && arg2P_5>2 ], cost: 1+arg3P_5 3: f1795_0_main_InvokeMethod -> f2097_0_flatten_NULL : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg1P_4<=arg2 && arg1>0 && arg2>2 && arg1P_4>2 && 2+arg3<=arg2 ], cost: 1 21: f1795_0_main_InvokeMethod -> f2097_0_flatten_NULL : arg1'=1, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [ 1+2*meter<=arg2 && arg1>0 && arg2>2 && 1+2*meter>2 && 2+arg3<=arg2 && meter>=1 ], cost: 1+meter 23: f1795_0_main_InvokeMethod -> [6] : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg1P_4<=arg2 && arg1>0 && arg2>2 && arg1P_4>2 && 2+arg3<=arg2 ], cost: NONTERM 13: __init -> f1_0_main_Load : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, arg4'=arg4P_14, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 1: f1_0_main_Load -> f1795_0_main_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1P_2<=arg1 && arg1>0 && arg1P_2>0 && arg2P_2>2 ], cost: 1 20: f1_0_main_Load -> f2097_0_flatten_NULL : arg1'=1, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [ 2+2*meter<=arg1 && arg2>0 && arg1>0 && 1+2*meter>1 && meter>=1 ], cost: 1+meter 22: f1_0_main_Load -> [6] : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ 1+arg1P_1<=arg1 && arg2>0 && arg1>0 && arg1P_1>2 ], cost: NONTERM 26: f1_0_main_Load -> f1759_0_createTree_LE : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=0, arg4'=1+arg3P_5, [ arg3P_5>0 && arg2>-1 && arg1>0 && arg1P_8>2 && arg2P_8>2 ], cost: 1+arg3P_5 27: f1_0_main_Load -> f1759_0_createTree_LE : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=0, arg4'=1+arg3P_5, [ arg3P_5>0 && arg2>-1 && arg1>0 && arg1P_9>2 && arg2P_9>2 ], cost: 1+arg3P_5 28: f1_0_main_Load -> f1759_0_createTree_LE : arg1'=arg2P_5+2*arg3P_5, arg2'=arg2P_5+2*arg3P_5, arg3'=0, arg4'=1+arg3P_5, [ arg3P_5>0 && arg2>-1 && -2+arg2P_5<=arg1 && arg1>0 && arg2P_5>2 ], cost: 1+arg3P_5 29: f1_0_main_Load -> f1759_0_createTree_LE : arg1'=arg2P_5+2*arg3P_5, arg2'=arg2P_5+2*arg3P_5, arg3'=0, arg4'=1+arg3P_5, [ arg3P_5>0 && arg2>-1 && -2+arg2P_5<=arg1 && arg1>0 && arg2P_5>2 ], cost: 1+arg3P_5 21: f1795_0_main_InvokeMethod -> f2097_0_flatten_NULL : arg1'=1, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [ 1+2*meter<=arg2 && arg1>0 && arg2>2 && 1+2*meter>2 && 2+arg3<=arg2 && meter>=1 ], cost: 1+meter 23: f1795_0_main_InvokeMethod -> [6] : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg1P_4<=arg2 && arg1>0 && arg2>2 && arg1P_4>2 && 2+arg3<=arg2 ], cost: NONTERM 13: __init -> f1_0_main_Load : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, arg4'=arg4P_14, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: __init 21: f1795_0_main_InvokeMethod -> f2097_0_flatten_NULL : arg1'=1, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [ 1+2*meter<=arg2 && arg1>0 && arg2>2 && 1+2*meter>2 && 2+arg3<=arg2 && meter>=1 ], cost: 1+meter 23: f1795_0_main_InvokeMethod -> [6] : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg1P_4<=arg2 && arg1>0 && arg2>2 && arg1P_4>2 && 2+arg3<=arg2 ], cost: NONTERM 30: __init -> f1795_0_main_InvokeMethod : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1P_2<=arg1P_14 && arg1P_14>0 && arg1P_2>0 && arg2P_2>2 ], cost: 2 31: __init -> f2097_0_flatten_NULL : arg1'=1, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [ 2+2*meter<=arg1P_14 && arg2P_14>0 && arg1P_14>0 && 1+2*meter>1 && meter>=1 ], cost: 2+meter 32: __init -> [6] : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ 1+arg1P_1<=arg1P_14 && arg2P_14>0 && arg1P_14>0 && arg1P_1>2 ], cost: NONTERM 33: __init -> f1759_0_createTree_LE : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=0, arg4'=1+arg3P_5, [ arg3P_5>0 && arg2P_14>-1 && arg1P_14>0 && arg1P_8>2 && arg2P_8>2 ], cost: 2+arg3P_5 34: __init -> f1759_0_createTree_LE : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=0, arg4'=1+arg3P_5, [ arg3P_5>0 && arg2P_14>-1 && arg1P_14>0 && arg1P_9>2 && arg2P_9>2 ], cost: 2+arg3P_5 35: __init -> f1759_0_createTree_LE : arg1'=arg2P_5+2*arg3P_5, arg2'=arg2P_5+2*arg3P_5, arg3'=0, arg4'=1+arg3P_5, [ arg3P_5>0 && arg2P_14>-1 && -2+arg2P_5<=arg1P_14 && arg1P_14>0 && arg2P_5>2 ], cost: 2+arg3P_5 36: __init -> f1759_0_createTree_LE : arg1'=arg2P_5+2*arg3P_5, arg2'=arg2P_5+2*arg3P_5, arg3'=0, arg4'=1+arg3P_5, [ arg3P_5>0 && arg2P_14>-1 && -2+arg2P_5<=arg1P_14 && arg1P_14>0 && arg2P_5>2 ], cost: 2+arg3P_5 Eliminated locations (on tree-shaped paths): Start location: __init 31: __init -> f2097_0_flatten_NULL : arg1'=1, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [ 2+2*meter<=arg1P_14 && arg2P_14>0 && arg1P_14>0 && 1+2*meter>1 && meter>=1 ], cost: 2+meter 32: __init -> [6] : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ 1+arg1P_1<=arg1P_14 && arg2P_14>0 && arg1P_14>0 && arg1P_1>2 ], cost: NONTERM 33: __init -> f1759_0_createTree_LE : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=0, arg4'=1+arg3P_5, [ arg3P_5>0 && arg2P_14>-1 && arg1P_14>0 && arg1P_8>2 && arg2P_8>2 ], cost: 2+arg3P_5 34: __init -> f1759_0_createTree_LE : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=0, arg4'=1+arg3P_5, [ arg3P_5>0 && arg2P_14>-1 && arg1P_14>0 && arg1P_9>2 && arg2P_9>2 ], cost: 2+arg3P_5 36: __init -> f1759_0_createTree_LE : arg1'=arg2P_5+2*arg3P_5, arg2'=arg2P_5+2*arg3P_5, arg3'=0, arg4'=1+arg3P_5, [ arg3P_5>0 && arg2P_14>-1 && -2+arg2P_5<=arg1P_14 && arg1P_14>0 && arg2P_5>2 ], cost: 2+arg3P_5 37: __init -> f2097_0_flatten_NULL : arg1'=1, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [ arg1P_2<=arg1P_14 && arg1P_14>0 && arg1P_2>0 && arg2P_2>2 && 1+2*meter<=arg2P_2 && 1+2*meter>2 && 2+arg3P_2<=arg2P_2 && meter>=1 ], cost: 3+meter 38: __init -> [6] : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg1P_2<=arg1P_14 && arg1P_14>0 && arg1P_2>0 && arg2P_2>2 && arg1P_4<=arg2P_2 && arg1P_4>2 && 2+arg3P_2<=arg2P_2 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 31: __init -> f2097_0_flatten_NULL : arg1'=1, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [ 2+2*meter<=arg1P_14 && arg2P_14>0 && arg1P_14>0 && 1+2*meter>1 && meter>=1 ], cost: 2+meter 32: __init -> [6] : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ 1+arg1P_1<=arg1P_14 && arg2P_14>0 && arg1P_14>0 && arg1P_1>2 ], cost: NONTERM 33: __init -> f1759_0_createTree_LE : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=0, arg4'=1+arg3P_5, [ arg3P_5>0 && arg2P_14>-1 && arg1P_14>0 && arg1P_8>2 && arg2P_8>2 ], cost: 2+arg3P_5 34: __init -> f1759_0_createTree_LE : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=0, arg4'=1+arg3P_5, [ arg3P_5>0 && arg2P_14>-1 && arg1P_14>0 && arg1P_9>2 && arg2P_9>2 ], cost: 2+arg3P_5 36: __init -> f1759_0_createTree_LE : arg1'=arg2P_5+2*arg3P_5, arg2'=arg2P_5+2*arg3P_5, arg3'=0, arg4'=1+arg3P_5, [ arg3P_5>0 && arg2P_14>-1 && -2+arg2P_5<=arg1P_14 && arg1P_14>0 && arg2P_5>2 ], cost: 2+arg3P_5 37: __init -> f2097_0_flatten_NULL : arg1'=1, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [ arg1P_2<=arg1P_14 && arg1P_14>0 && arg1P_2>0 && arg2P_2>2 && 1+2*meter<=arg2P_2 && 1+2*meter>2 && 2+arg3P_2<=arg2P_2 && meter>=1 ], cost: 3+meter 38: __init -> [6] : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg1P_2<=arg1P_14 && arg1P_14>0 && arg1P_2>0 && arg2P_2>2 && arg1P_4<=arg2P_2 && arg1P_4>2 && 2+arg3P_2<=arg2P_2 ], cost: NONTERM Computing asymptotic complexity for rule 31 Solved the limit problem by the following transformations: Created initial limit problem: -1+arg1P_14-2*meter (+/+!), 2*meter (+/+!), arg1P_14 (+/+!), arg2P_14 (+/+!), 2+meter (+) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {arg1P_14==2*n,arg2P_14==n,meter==-1+n} resulting limit problem: [solved] Solution: arg1P_14 / 2*n arg2P_14 / n meter / -1+n Resulting cost 1+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: 1+n Rule cost: 2+meter Rule guard: [ 2+2*meter<=arg1P_14 && arg2P_14>0 && arg1P_14>0 && 1+2*meter>1 ] WORST_CASE(INF,?)