WORST_CASE(INF,?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f289_0_createIntList_Return -> f491_0_random_ArrayAccess : arg1'=arg1P_1, arg2'=arg2P_1, [ arg1P_1<=arg1 && arg1>-1 && arg1P_1>-1 ], cost: 1 2: f491_0_random_ArrayAccess -> f815_0_main_NULL : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1P_3<=arg1 && x7_1>0 && arg1>-1 && arg1P_3>-1 ], cost: 1 1: f1_0_main_Load -> f491_0_random_ArrayAccess : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1>0 && arg1P_2>-1 ], cost: 1 6: f1_0_main_Load -> f639_0_createIntList_LE : arg1'=arg1P_7, arg2'=arg2P_7, [ arg2>-1 && arg1P_7>-1 && arg1>0 && 1==arg2P_7 ], cost: 1 3: f815_0_main_NULL -> f815_0_main_NULL : arg1'=arg1P_4, arg2'=arg2P_4, [ 2+arg1P_4<=arg1 && x12_1<1 && arg1>1 && arg1P_4>-1 ], cost: 1 4: f815_0_main_NULL -> f815_0_main_NULL : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1P_5<=arg1 && x15_1>0 && arg1>0 && arg1P_5>0 ], cost: 1 5: f815_0_main_NULL -> f815_0_main_NULL : arg1'=arg1P_6, arg2'=arg2P_6, [ 2+arg1P_6<=arg1 && x18_1<1 && arg1>2 && arg1P_6>0 ], cost: 1 7: f639_0_createIntList_LE -> f639_0_createIntList_LE : arg1'=arg1P_8, arg2'=arg2P_8, [ arg1>0 && arg2>0 && -1+arg1==arg1P_8 && 1+arg2==arg2P_8 ], cost: 1 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, [], cost: 1 Removed unreachable and leaf rules: Start location: __init 2: f491_0_random_ArrayAccess -> f815_0_main_NULL : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1P_3<=arg1 && x7_1>0 && arg1>-1 && arg1P_3>-1 ], cost: 1 1: f1_0_main_Load -> f491_0_random_ArrayAccess : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1>0 && arg1P_2>-1 ], cost: 1 6: f1_0_main_Load -> f639_0_createIntList_LE : arg1'=arg1P_7, arg2'=arg2P_7, [ arg2>-1 && arg1P_7>-1 && arg1>0 && 1==arg2P_7 ], cost: 1 3: f815_0_main_NULL -> f815_0_main_NULL : arg1'=arg1P_4, arg2'=arg2P_4, [ 2+arg1P_4<=arg1 && x12_1<1 && arg1>1 && arg1P_4>-1 ], cost: 1 4: f815_0_main_NULL -> f815_0_main_NULL : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1P_5<=arg1 && x15_1>0 && arg1>0 && arg1P_5>0 ], cost: 1 5: f815_0_main_NULL -> f815_0_main_NULL : arg1'=arg1P_6, arg2'=arg2P_6, [ 2+arg1P_6<=arg1 && x18_1<1 && arg1>2 && arg1P_6>0 ], cost: 1 7: f639_0_createIntList_LE -> f639_0_createIntList_LE : arg1'=arg1P_8, arg2'=arg2P_8, [ arg1>0 && arg2>0 && -1+arg1==arg1P_8 && 1+arg2==arg2P_8 ], cost: 1 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, [], cost: 1 Simplified all rules, resulting in: Start location: __init 2: f491_0_random_ArrayAccess -> f815_0_main_NULL : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1P_3<=arg1 && arg1>-1 && arg1P_3>-1 ], cost: 1 1: f1_0_main_Load -> f491_0_random_ArrayAccess : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1>0 && arg1P_2>-1 ], cost: 1 6: f1_0_main_Load -> f639_0_createIntList_LE : arg1'=arg1P_7, arg2'=1, [ arg2>-1 && arg1P_7>-1 && arg1>0 ], cost: 1 3: f815_0_main_NULL -> f815_0_main_NULL : arg1'=arg1P_4, arg2'=arg2P_4, [ 2+arg1P_4<=arg1 && arg1>1 && arg1P_4>-1 ], cost: 1 4: f815_0_main_NULL -> f815_0_main_NULL : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1P_5<=arg1 && arg1>0 && arg1P_5>0 ], cost: 1 5: f815_0_main_NULL -> f815_0_main_NULL : arg1'=arg1P_6, arg2'=arg2P_6, [ 2+arg1P_6<=arg1 && arg1>2 && arg1P_6>0 ], cost: 1 7: f639_0_createIntList_LE -> f639_0_createIntList_LE : arg1'=-1+arg1, arg2'=1+arg2, [ arg1>0 && arg2>0 ], cost: 1 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 3. Accelerating the following rules: 3: f815_0_main_NULL -> f815_0_main_NULL : arg1'=arg1P_4, arg2'=arg2P_4, [ 2+arg1P_4<=arg1 && arg1>1 && arg1P_4>-1 ], cost: 1 4: f815_0_main_NULL -> f815_0_main_NULL : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1P_5<=arg1 && arg1>0 && arg1P_5>0 ], cost: 1 5: f815_0_main_NULL -> f815_0_main_NULL : arg1'=arg1P_6, arg2'=arg2P_6, [ 2+arg1P_6<=arg1 && arg1>2 && arg1P_6>0 ], cost: 1 During metering: Instantiating temporary variables by {arg1P_4==-2+arg1} Accelerated rule 3 with metering function meter (where 2*meter==-1+arg1), yielding the new rule 9. Accelerated rule 4 with NONTERM, yielding the new rule 10. During metering: Instantiating temporary variables by {arg1P_6==-2+arg1} Accelerated rule 5 with metering function meter_1 (where 2*meter_1==-2+arg1), yielding the new rule 11. Nested simple loops 3 (outer loop) and 11 (inner loop) with metering function -arg1P_4, resulting in the new rules: 12. Removing the simple loops: 3 4 5. Accelerating simple loops of location 4. Accelerating the following rules: 7: f639_0_createIntList_LE -> f639_0_createIntList_LE : arg1'=-1+arg1, arg2'=1+arg2, [ arg1>0 && arg2>0 ], cost: 1 Accelerated rule 7 with metering function arg1, yielding the new rule 13. Removing the simple loops: 7. Accelerated all simple loops using metering functions (where possible): Start location: __init 2: f491_0_random_ArrayAccess -> f815_0_main_NULL : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1P_3<=arg1 && arg1>-1 && arg1P_3>-1 ], cost: 1 1: f1_0_main_Load -> f491_0_random_ArrayAccess : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1>0 && arg1P_2>-1 ], cost: 1 6: f1_0_main_Load -> f639_0_createIntList_LE : arg1'=arg1P_7, arg2'=1, [ arg2>-1 && arg1P_7>-1 && arg1>0 ], cost: 1 9: f815_0_main_NULL -> f815_0_main_NULL : arg1'=-2*meter+arg1, arg2'=arg2P_4, [ arg1>1 && 2*meter==-1+arg1 && meter>=1 ], cost: meter 10: f815_0_main_NULL -> [6] : [ arg1P_5<=arg1 && arg1>0 && arg1P_5>0 ], cost: NONTERM 11: f815_0_main_NULL -> f815_0_main_NULL : arg1'=-2*meter_1+arg1, arg2'=arg2P_6, [ arg1>2 && 2*meter_1==-2+arg1 && meter_1>=1 ], cost: meter_1 12: f815_0_main_NULL -> f815_0_main_NULL : arg1'=arg1P_4, arg2'=arg2P_4, [ arg1>2 && 2*meter_1==-2+arg1 && meter_1>=1 && 2+arg1P_4<=-2*meter_1+arg1 && arg1P_4>-1 && -arg1P_4>=1 ], cost: -arg1P_4-meter_1*arg1P_4 13: f639_0_createIntList_LE -> f639_0_createIntList_LE : arg1'=0, arg2'=arg1+arg2, [ arg1>0 && arg2>0 ], cost: arg1 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 2: f491_0_random_ArrayAccess -> f815_0_main_NULL : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1P_3<=arg1 && arg1>-1 && arg1P_3>-1 ], cost: 1 14: f491_0_random_ArrayAccess -> f815_0_main_NULL : arg1'=1, arg2'=arg2P_4, [ 1+2*meter<=arg1 && arg1>-1 && 1+2*meter>1 && meter>=1 ], cost: 1+meter 15: f491_0_random_ArrayAccess -> [6] : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1P_3<=arg1 && arg1>-1 && arg1P_3>0 ], cost: NONTERM 16: f491_0_random_ArrayAccess -> f815_0_main_NULL : arg1'=2, arg2'=arg2P_6, [ 2+2*meter_1<=arg1 && arg1>-1 && 2+2*meter_1>2 && meter_1>=1 ], cost: 1+meter_1 1: f1_0_main_Load -> f491_0_random_ArrayAccess : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1>0 && arg1P_2>-1 ], cost: 1 6: f1_0_main_Load -> f639_0_createIntList_LE : arg1'=arg1P_7, arg2'=1, [ arg2>-1 && arg1P_7>-1 && arg1>0 ], cost: 1 17: f1_0_main_Load -> f639_0_createIntList_LE : arg1'=0, arg2'=1+arg1P_7, [ arg2>-1 && arg1>0 && arg1P_7>0 ], cost: 1+arg1P_7 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 14: f491_0_random_ArrayAccess -> f815_0_main_NULL : arg1'=1, arg2'=arg2P_4, [ 1+2*meter<=arg1 && arg1>-1 && 1+2*meter>1 && meter>=1 ], cost: 1+meter 15: f491_0_random_ArrayAccess -> [6] : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1P_3<=arg1 && arg1>-1 && arg1P_3>0 ], cost: NONTERM 16: f491_0_random_ArrayAccess -> f815_0_main_NULL : arg1'=2, arg2'=arg2P_6, [ 2+2*meter_1<=arg1 && arg1>-1 && 2+2*meter_1>2 && meter_1>=1 ], cost: 1+meter_1 1: f1_0_main_Load -> f491_0_random_ArrayAccess : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1>0 && arg1P_2>-1 ], cost: 1 17: f1_0_main_Load -> f639_0_createIntList_LE : arg1'=0, arg2'=1+arg1P_7, [ arg2>-1 && arg1>0 && arg1P_7>0 ], cost: 1+arg1P_7 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: __init 14: f491_0_random_ArrayAccess -> f815_0_main_NULL : arg1'=1, arg2'=arg2P_4, [ 1+2*meter<=arg1 && arg1>-1 && 1+2*meter>1 && meter>=1 ], cost: 1+meter 15: f491_0_random_ArrayAccess -> [6] : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1P_3<=arg1 && arg1>-1 && arg1P_3>0 ], cost: NONTERM 16: f491_0_random_ArrayAccess -> f815_0_main_NULL : arg1'=2, arg2'=arg2P_6, [ 2+2*meter_1<=arg1 && arg1>-1 && 2+2*meter_1>2 && meter_1>=1 ], cost: 1+meter_1 18: __init -> f491_0_random_ArrayAccess : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1P_9>0 && arg1P_2>-1 ], cost: 2 19: __init -> f639_0_createIntList_LE : arg1'=0, arg2'=1+arg1P_7, [ arg2P_9>-1 && arg1P_9>0 && arg1P_7>0 ], cost: 2+arg1P_7 Eliminated locations (on tree-shaped paths): Start location: __init 19: __init -> f639_0_createIntList_LE : arg1'=0, arg2'=1+arg1P_7, [ arg2P_9>-1 && arg1P_9>0 && arg1P_7>0 ], cost: 2+arg1P_7 20: __init -> f815_0_main_NULL : arg1'=1, arg2'=arg2P_4, [ arg1P_9>0 && arg1P_2>-1 && 1+2*meter<=arg1P_2 && 1+2*meter>1 && meter>=1 ], cost: 3+meter 21: __init -> [6] : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1P_9>0 && arg1P_2>-1 && arg1P_3<=arg1P_2 && arg1P_3>0 ], cost: NONTERM 22: __init -> f815_0_main_NULL : arg1'=2, arg2'=arg2P_6, [ arg1P_9>0 && arg1P_2>-1 && 2+2*meter_1<=arg1P_2 && 2+2*meter_1>2 && meter_1>=1 ], cost: 3+meter_1 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 19: __init -> f639_0_createIntList_LE : arg1'=0, arg2'=1+arg1P_7, [ arg2P_9>-1 && arg1P_9>0 && arg1P_7>0 ], cost: 2+arg1P_7 20: __init -> f815_0_main_NULL : arg1'=1, arg2'=arg2P_4, [ arg1P_9>0 && arg1P_2>-1 && 1+2*meter<=arg1P_2 && 1+2*meter>1 && meter>=1 ], cost: 3+meter 21: __init -> [6] : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1P_9>0 && arg1P_2>-1 && arg1P_3<=arg1P_2 && arg1P_3>0 ], cost: NONTERM 22: __init -> f815_0_main_NULL : arg1'=2, arg2'=arg2P_6, [ arg1P_9>0 && arg1P_2>-1 && 2+2*meter_1<=arg1P_2 && 2+2*meter_1>2 && meter_1>=1 ], cost: 3+meter_1 Computing asymptotic complexity for rule 19 Solved the limit problem by the following transformations: Created initial limit problem: arg1P_9 (+/+!), 1+arg2P_9 (+/+!), 2+arg1P_7 (+), arg1P_7 (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {arg1P_9==n,arg2P_9==n,arg1P_7==n} resulting limit problem: [solved] Solution: arg1P_9 / n arg2P_9 / n arg1P_7 / n Resulting cost 2+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: 2+n Rule cost: 2+arg1P_7 Rule guard: [ arg2P_9>-1 && arg1P_9>0 && arg1P_7>0 ] WORST_CASE(INF,?)