WORST_CASE(INF,?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f169_0_createList_Return -> f229_0_random_ArrayAccess : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1P_1<=arg2 && arg1>0 && arg2>-1 && arg1P_1>-1 ], cost: 1 4: f229_0_random_ArrayAccess -> f298_0_appE_NONNULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg2P_5>-1 && arg2>1 && arg1P_5<=arg1 && 1+arg3P_5<=arg1 && arg1>0 && arg1P_5>0 && arg3P_5>-1 ], cost: 1 1: f1_0_main_Load -> f229_0_random_ArrayAccess : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1>0 && arg1P_2>-1 && arg2==arg2P_2 ], cost: 1 2: f1_0_main_Load -> f194_0_createList_LE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg2>-1 && arg1P_3>-1 && arg1>0 ], cost: 1 3: f194_0_createList_LE -> f194_0_createList_LE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1>0 && -1+arg1==arg1P_4 ], cost: 1 5: f298_0_appE_NONNULL -> f298_0_appE_NONNULL : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ 2+arg1P_6<=arg1 && arg1P_6<=arg3 && 3+arg3P_6<=arg1 && 1+arg3P_6<=arg3 && arg1>2 && arg3>0 && arg1P_6>0 && arg3P_6>-1 && arg2==arg2P_6 ], cost: 1 6: f298_0_appE_NONNULL -> f298_0_appE_NONNULL : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg1P_7<=arg1 && arg2>0 && -2+arg1P_7<=arg3 && 2+arg3P_7<=arg1 && arg3P_7<=arg3 && arg1>1 && arg3>-1 && arg1P_7>1 && arg3P_7>-1 && -1+arg2==arg2P_7 ], cost: 1 7: __init -> f1_0_main_Load : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 7: __init -> f1_0_main_Load : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [], cost: 1 Removed unreachable and leaf rules: Start location: __init 4: f229_0_random_ArrayAccess -> f298_0_appE_NONNULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg2P_5>-1 && arg2>1 && arg1P_5<=arg1 && 1+arg3P_5<=arg1 && arg1>0 && arg1P_5>0 && arg3P_5>-1 ], cost: 1 1: f1_0_main_Load -> f229_0_random_ArrayAccess : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1>0 && arg1P_2>-1 && arg2==arg2P_2 ], cost: 1 2: f1_0_main_Load -> f194_0_createList_LE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg2>-1 && arg1P_3>-1 && arg1>0 ], cost: 1 3: f194_0_createList_LE -> f194_0_createList_LE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1>0 && -1+arg1==arg1P_4 ], cost: 1 5: f298_0_appE_NONNULL -> f298_0_appE_NONNULL : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ 2+arg1P_6<=arg1 && arg1P_6<=arg3 && 3+arg3P_6<=arg1 && 1+arg3P_6<=arg3 && arg1>2 && arg3>0 && arg1P_6>0 && arg3P_6>-1 && arg2==arg2P_6 ], cost: 1 6: f298_0_appE_NONNULL -> f298_0_appE_NONNULL : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg1P_7<=arg1 && arg2>0 && -2+arg1P_7<=arg3 && 2+arg3P_7<=arg1 && arg3P_7<=arg3 && arg1>1 && arg3>-1 && arg1P_7>1 && arg3P_7>-1 && -1+arg2==arg2P_7 ], cost: 1 7: __init -> f1_0_main_Load : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [], cost: 1 Simplified all rules, resulting in: Start location: __init 4: f229_0_random_ArrayAccess -> f298_0_appE_NONNULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg2P_5>-1 && arg2>1 && arg1P_5<=arg1 && 1+arg3P_5<=arg1 && arg1>0 && arg1P_5>0 && arg3P_5>-1 ], cost: 1 1: f1_0_main_Load -> f229_0_random_ArrayAccess : arg1'=arg1P_2, arg3'=arg3P_2, [ arg1>0 && arg1P_2>-1 ], cost: 1 2: f1_0_main_Load -> f194_0_createList_LE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg2>-1 && arg1P_3>-1 && arg1>0 ], cost: 1 3: f194_0_createList_LE -> f194_0_createList_LE : arg1'=-1+arg1, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1>0 ], cost: 1 5: f298_0_appE_NONNULL -> f298_0_appE_NONNULL : arg1'=arg1P_6, arg3'=arg3P_6, [ 2+arg1P_6<=arg1 && arg1P_6<=arg3 && 3+arg3P_6<=arg1 && 1+arg3P_6<=arg3 && arg1>2 && arg3>0 && arg1P_6>0 && arg3P_6>-1 ], cost: 1 6: f298_0_appE_NONNULL -> f298_0_appE_NONNULL : arg1'=arg1P_7, arg2'=-1+arg2, arg3'=arg3P_7, [ arg1P_7<=arg1 && arg2>0 && -2+arg1P_7<=arg3 && 2+arg3P_7<=arg1 && arg3P_7<=arg3 && arg1>1 && arg3>-1 && arg1P_7>1 && arg3P_7>-1 ], cost: 1 7: __init -> f1_0_main_Load : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 3. Accelerating the following rules: 3: f194_0_createList_LE -> f194_0_createList_LE : arg1'=-1+arg1, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1>0 ], cost: 1 Accelerated rule 3 with metering function arg1, yielding the new rule 8. Removing the simple loops: 3. Accelerating simple loops of location 4. Accelerating the following rules: 5: f298_0_appE_NONNULL -> f298_0_appE_NONNULL : arg1'=arg1P_6, arg3'=arg3P_6, [ 2+arg1P_6<=arg1 && arg1P_6<=arg3 && 3+arg3P_6<=arg1 && 1+arg3P_6<=arg3 && arg1>2 && arg3>0 && arg1P_6>0 && arg3P_6>-1 ], cost: 1 6: f298_0_appE_NONNULL -> f298_0_appE_NONNULL : arg1'=arg1P_7, arg2'=-1+arg2, arg3'=arg3P_7, [ arg1P_7<=arg1 && arg2>0 && -2+arg1P_7<=arg3 && 2+arg3P_7<=arg1 && arg3P_7<=arg3 && arg1>1 && arg3>-1 && arg1P_7>1 && arg3P_7>-1 ], cost: 1 During metering: Instantiating temporary variables by {arg3P_6==-3+arg1,arg1P_6==-2+arg1} Accelerated rule 5 with metering function meter (where 2*meter==-2+arg1), yielding the new rule 9. During metering: Instantiating temporary variables by {arg1P_7==arg1,arg3P_7==arg3} Accelerated rule 6 with metering function arg2, yielding the new rule 10. Nested simple loops 6 (outer loop) and 9 (inner loop) with metering function 2-arg1P_7-arg3P_7, resulting in the new rules: 11. During metering: Instantiating temporary variables by {arg3P_6==-3+arg1,arg1P_6==-2+arg1} Removing the simple loops: 5 6. Accelerated all simple loops using metering functions (where possible): Start location: __init 4: f229_0_random_ArrayAccess -> f298_0_appE_NONNULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg2P_5>-1 && arg2>1 && arg1P_5<=arg1 && 1+arg3P_5<=arg1 && arg1>0 && arg1P_5>0 && arg3P_5>-1 ], cost: 1 1: f1_0_main_Load -> f229_0_random_ArrayAccess : arg1'=arg1P_2, arg3'=arg3P_2, [ arg1>0 && arg1P_2>-1 ], cost: 1 2: f1_0_main_Load -> f194_0_createList_LE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg2>-1 && arg1P_3>-1 && arg1>0 ], cost: 1 8: f194_0_createList_LE -> f194_0_createList_LE : arg1'=0, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1>0 ], cost: arg1 9: f298_0_appE_NONNULL -> f298_0_appE_NONNULL : arg1'=arg1-2*meter, arg3'=-1+arg1-2*meter, [ -2+arg1<=arg3 && arg1>2 && arg3>0 && 2*meter==-2+arg1 && meter>=1 ], cost: meter 10: f298_0_appE_NONNULL -> f298_0_appE_NONNULL : arg1'=arg1, arg2'=0, arg3'=arg3, [ arg2>0 && -2+arg1<=arg3 && 2+arg3<=arg1 && arg1>1 && arg3>-1 ], cost: arg2 11: f298_0_appE_NONNULL -> f298_0_appE_NONNULL : arg1'=arg1P_7, arg2'=-2+arg1P_7+arg2+arg3P_7, arg3'=arg3P_7, [ -2+arg1<=arg3 && arg1>2 && arg3>0 && 2*meter==-2+arg1 && meter>=1 && arg1P_7<=arg1-2*meter && arg2>0 && 2+arg3P_7<=arg1-2*meter && arg1P_7>1 && arg3P_7>-1 && 2-arg1P_7-arg3P_7>=1 ], cost: 2-arg1P_7-meter*(-2+arg1P_7+arg3P_7)-arg3P_7 7: __init -> f1_0_main_Load : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 4: f229_0_random_ArrayAccess -> f298_0_appE_NONNULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg2P_5>-1 && arg2>1 && arg1P_5<=arg1 && 1+arg3P_5<=arg1 && arg1>0 && arg1P_5>0 && arg3P_5>-1 ], cost: 1 13: f229_0_random_ArrayAccess -> f298_0_appE_NONNULL : arg1'=2, arg2'=arg2P_5, arg3'=1, [ arg2P_5>-1 && arg2>1 && 2+2*meter<=arg1 && 2+2*meter>2 && meter>=1 && 1<=-1+arg1 ], cost: 1+meter 14: f229_0_random_ArrayAccess -> f298_0_appE_NONNULL : arg1'=arg1P_5, arg2'=0, arg3'=-2+arg1P_5, [ arg2>1 && arg1P_5<=arg1 && arg1>0 && -2+arg1P_5>-1 && arg2P_5>0 ], cost: 1+arg2P_5 1: f1_0_main_Load -> f229_0_random_ArrayAccess : arg1'=arg1P_2, arg3'=arg3P_2, [ arg1>0 && arg1P_2>-1 ], cost: 1 2: f1_0_main_Load -> f194_0_createList_LE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg2>-1 && arg1P_3>-1 && arg1>0 ], cost: 1 12: f1_0_main_Load -> f194_0_createList_LE : arg1'=0, arg2'=arg2P_4, arg3'=arg3P_4, [ arg2>-1 && arg1>0 && arg1P_3>0 ], cost: 1+arg1P_3 7: __init -> f1_0_main_Load : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 13: f229_0_random_ArrayAccess -> f298_0_appE_NONNULL : arg1'=2, arg2'=arg2P_5, arg3'=1, [ arg2P_5>-1 && arg2>1 && 2+2*meter<=arg1 && 2+2*meter>2 && meter>=1 && 1<=-1+arg1 ], cost: 1+meter 14: f229_0_random_ArrayAccess -> f298_0_appE_NONNULL : arg1'=arg1P_5, arg2'=0, arg3'=-2+arg1P_5, [ arg2>1 && arg1P_5<=arg1 && arg1>0 && -2+arg1P_5>-1 && arg2P_5>0 ], cost: 1+arg2P_5 1: f1_0_main_Load -> f229_0_random_ArrayAccess : arg1'=arg1P_2, arg3'=arg3P_2, [ arg1>0 && arg1P_2>-1 ], cost: 1 12: f1_0_main_Load -> f194_0_createList_LE : arg1'=0, arg2'=arg2P_4, arg3'=arg3P_4, [ arg2>-1 && arg1>0 && arg1P_3>0 ], cost: 1+arg1P_3 7: __init -> f1_0_main_Load : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: __init 13: f229_0_random_ArrayAccess -> f298_0_appE_NONNULL : arg1'=2, arg2'=arg2P_5, arg3'=1, [ arg2P_5>-1 && arg2>1 && 2+2*meter<=arg1 && 2+2*meter>2 && meter>=1 && 1<=-1+arg1 ], cost: 1+meter 14: f229_0_random_ArrayAccess -> f298_0_appE_NONNULL : arg1'=arg1P_5, arg2'=0, arg3'=-2+arg1P_5, [ arg2>1 && arg1P_5<=arg1 && arg1>0 && -2+arg1P_5>-1 && arg2P_5>0 ], cost: 1+arg2P_5 15: __init -> f229_0_random_ArrayAccess : arg1'=arg1P_2, arg2'=arg2P_8, arg3'=arg3P_2, [ arg1P_8>0 && arg1P_2>-1 ], cost: 2 16: __init -> f194_0_createList_LE : arg1'=0, arg2'=arg2P_4, arg3'=arg3P_4, [ arg2P_8>-1 && arg1P_8>0 && arg1P_3>0 ], cost: 2+arg1P_3 Eliminated locations (on tree-shaped paths): Start location: __init 16: __init -> f194_0_createList_LE : arg1'=0, arg2'=arg2P_4, arg3'=arg3P_4, [ arg2P_8>-1 && arg1P_8>0 && arg1P_3>0 ], cost: 2+arg1P_3 17: __init -> f298_0_appE_NONNULL : arg1'=2, arg2'=arg2P_5, arg3'=1, [ arg1P_8>0 && arg2P_5>-1 && arg2P_8>1 && 2+2*meter<=arg1P_2 && 2+2*meter>2 && meter>=1 && 1<=-1+arg1P_2 ], cost: 3+meter 18: __init -> f298_0_appE_NONNULL : arg1'=arg1P_5, arg2'=0, arg3'=-2+arg1P_5, [ arg1P_8>0 && arg2P_8>1 && arg1P_5<=arg1P_2 && arg1P_2>0 && -2+arg1P_5>-1 && arg2P_5>0 ], cost: 3+arg2P_5 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 16: __init -> f194_0_createList_LE : arg1'=0, arg2'=arg2P_4, arg3'=arg3P_4, [ arg2P_8>-1 && arg1P_8>0 && arg1P_3>0 ], cost: 2+arg1P_3 17: __init -> f298_0_appE_NONNULL : arg1'=2, arg2'=arg2P_5, arg3'=1, [ arg1P_8>0 && arg2P_5>-1 && arg2P_8>1 && 2+2*meter<=arg1P_2 && 2+2*meter>2 && meter>=1 && 1<=-1+arg1P_2 ], cost: 3+meter 18: __init -> f298_0_appE_NONNULL : arg1'=arg1P_5, arg2'=0, arg3'=-2+arg1P_5, [ arg1P_8>0 && arg2P_8>1 && arg1P_5<=arg1P_2 && arg1P_2>0 && -2+arg1P_5>-1 && arg2P_5>0 ], cost: 3+arg2P_5 Computing asymptotic complexity for rule 16 Solved the limit problem by the following transformations: Created initial limit problem: arg1P_8 (+/+!), 2+arg1P_3 (+), arg1P_3 (+/+!), 1+arg2P_8 (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {arg1P_8==n,arg2P_8==n,arg1P_3==n} resulting limit problem: [solved] Solution: arg1P_8 / n arg2P_8 / n arg1P_3 / 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_3 Rule guard: [ arg2P_8>-1 && arg1P_8>0 && arg1P_3>0 ] WORST_CASE(INF,?)