WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f303_0_createIntList_Return -> f517_0_random_ArrayAccess : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ arg1P_1<=arg1 && arg1>-1 && arg1P_1>-1 ], cost: 1 2: f517_0_random_ArrayAccess -> f704_0_nth_LE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ x7_1>0 && arg3P_3>-1 && arg1P_3<=arg1 && arg1>=arg2P_3 && arg1>-1 && arg1P_3>-1 && arg2P_3>-1 && 1+x7_1==arg4P_3 ], cost: 1 1: f1_0_main_Load -> f517_0_random_ArrayAccess : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1>0 && arg1P_2>-1 ], cost: 1 10: f1_0_main_Load -> f673_0_createIntList_LE : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, [ arg2>-1 && arg1P_11>-1 && arg1>0 && 1==arg2P_11 ], cost: 1 3: f704_0_nth_LE -> f754_0_main_LE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg1P_4<=arg1 && arg3<2 && arg1>-1 && arg2>0 && arg1P_4>-1 && 2+arg2P_4<=arg2 && arg4==arg3P_4 ], cost: 1 4: f704_0_nth_LE -> f704_0_nth_LE : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg1P_5<=arg1 && arg3>1 && 1+arg2P_5<=arg2 && arg1>-1 && arg2>0 && arg1P_5>-1 && arg2P_5>-1 && -1+arg3==arg3P_5 && arg4==arg4P_5 ], cost: 1 5: f754_0_main_LE -> f964_0_nth_LE : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, [ arg3P_6>-1 && arg3>0 && arg2>0 && 1+arg1P_6<=arg1 && 1+arg2P_6<=arg1 && arg1>0 && arg1P_6>-1 && arg2P_6>-1 && 1+arg3==arg4P_6 ], cost: 1 6: f964_0_nth_LE -> f754_0_main_LE : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [ arg1P_7<=arg1 && arg3<2 && arg1>-1 && arg2>0 && arg1P_7>-1 && 2+arg2P_7<=arg2 && arg4==arg3P_7 ], cost: 1 7: f964_0_nth_LE -> f964_0_nth_LE : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, [ arg1P_8<=arg1 && arg3>1 && 1+arg2P_8<=arg2 && arg1>-1 && arg2>0 && arg1P_8>-1 && arg2P_8>-1 && -1+arg3==arg3P_8 && arg4==arg4P_8 ], cost: 1 8: f964_0_nth_LE -> f754_0_main_LE : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, [ arg1P_9<=arg1 && arg3<2 && arg1>-1 && arg2>-1 && arg1P_9>-1 && 0==arg2P_9 && arg4==arg3P_9 ], cost: 1 9: f964_0_nth_LE -> f754_0_main_LE : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, [ arg1P_10<=arg1 && arg3>1 && arg1>-1 && arg2>-1 && arg1P_10>-1 && 0==arg2P_10 && arg4==arg3P_10 ], cost: 1 11: f673_0_createIntList_LE -> f673_0_createIntList_LE : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [ arg1>0 && arg2>0 && -1+arg1==arg1P_12 && 1+arg2==arg2P_12 ], cost: 1 12: __init -> f1_0_main_Load : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 12: __init -> f1_0_main_Load : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, [], cost: 1 Removed unreachable and leaf rules: Start location: __init 2: f517_0_random_ArrayAccess -> f704_0_nth_LE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ x7_1>0 && arg3P_3>-1 && arg1P_3<=arg1 && arg1>=arg2P_3 && arg1>-1 && arg1P_3>-1 && arg2P_3>-1 && 1+x7_1==arg4P_3 ], cost: 1 1: f1_0_main_Load -> f517_0_random_ArrayAccess : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1>0 && arg1P_2>-1 ], cost: 1 10: f1_0_main_Load -> f673_0_createIntList_LE : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, [ arg2>-1 && arg1P_11>-1 && arg1>0 && 1==arg2P_11 ], cost: 1 3: f704_0_nth_LE -> f754_0_main_LE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg1P_4<=arg1 && arg3<2 && arg1>-1 && arg2>0 && arg1P_4>-1 && 2+arg2P_4<=arg2 && arg4==arg3P_4 ], cost: 1 4: f704_0_nth_LE -> f704_0_nth_LE : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg1P_5<=arg1 && arg3>1 && 1+arg2P_5<=arg2 && arg1>-1 && arg2>0 && arg1P_5>-1 && arg2P_5>-1 && -1+arg3==arg3P_5 && arg4==arg4P_5 ], cost: 1 5: f754_0_main_LE -> f964_0_nth_LE : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, [ arg3P_6>-1 && arg3>0 && arg2>0 && 1+arg1P_6<=arg1 && 1+arg2P_6<=arg1 && arg1>0 && arg1P_6>-1 && arg2P_6>-1 && 1+arg3==arg4P_6 ], cost: 1 6: f964_0_nth_LE -> f754_0_main_LE : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [ arg1P_7<=arg1 && arg3<2 && arg1>-1 && arg2>0 && arg1P_7>-1 && 2+arg2P_7<=arg2 && arg4==arg3P_7 ], cost: 1 7: f964_0_nth_LE -> f964_0_nth_LE : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, [ arg1P_8<=arg1 && arg3>1 && 1+arg2P_8<=arg2 && arg1>-1 && arg2>0 && arg1P_8>-1 && arg2P_8>-1 && -1+arg3==arg3P_8 && arg4==arg4P_8 ], cost: 1 8: f964_0_nth_LE -> f754_0_main_LE : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, [ arg1P_9<=arg1 && arg3<2 && arg1>-1 && arg2>-1 && arg1P_9>-1 && 0==arg2P_9 && arg4==arg3P_9 ], cost: 1 9: f964_0_nth_LE -> f754_0_main_LE : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, [ arg1P_10<=arg1 && arg3>1 && arg1>-1 && arg2>-1 && arg1P_10>-1 && 0==arg2P_10 && arg4==arg3P_10 ], cost: 1 11: f673_0_createIntList_LE -> f673_0_createIntList_LE : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [ arg1>0 && arg2>0 && -1+arg1==arg1P_12 && 1+arg2==arg2P_12 ], cost: 1 12: __init -> f1_0_main_Load : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, [], cost: 1 Simplified all rules, resulting in: Start location: __init 2: f517_0_random_ArrayAccess -> f704_0_nth_LE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=1+x7_1, [ x7_1>0 && arg3P_3>-1 && arg1P_3<=arg1 && arg1>=arg2P_3 && arg1>-1 && arg1P_3>-1 && arg2P_3>-1 ], cost: 1 1: f1_0_main_Load -> f517_0_random_ArrayAccess : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1>0 && arg1P_2>-1 ], cost: 1 10: f1_0_main_Load -> f673_0_createIntList_LE : arg1'=arg1P_11, arg2'=1, arg3'=arg3P_11, arg4'=arg4P_11, [ arg2>-1 && arg1P_11>-1 && arg1>0 ], cost: 1 3: f704_0_nth_LE -> f754_0_main_LE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg4, arg4'=arg4P_4, [ arg1P_4<=arg1 && arg3<2 && arg1>-1 && arg2>0 && arg1P_4>-1 && 2+arg2P_4<=arg2 ], cost: 1 4: f704_0_nth_LE -> f704_0_nth_LE : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=-1+arg3, [ arg1P_5<=arg1 && arg3>1 && 1+arg2P_5<=arg2 && arg1>-1 && arg2>0 && arg1P_5>-1 && arg2P_5>-1 ], cost: 1 5: f754_0_main_LE -> f964_0_nth_LE : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=1+arg3, [ arg3P_6>-1 && arg3>0 && arg2>0 && 1+arg1P_6<=arg1 && 1+arg2P_6<=arg1 && arg1>0 && arg1P_6>-1 && arg2P_6>-1 ], cost: 1 6: f964_0_nth_LE -> f754_0_main_LE : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg4, arg4'=arg4P_7, [ arg1P_7<=arg1 && arg3<2 && arg1>-1 && arg2>0 && arg1P_7>-1 && 2+arg2P_7<=arg2 ], cost: 1 7: f964_0_nth_LE -> f964_0_nth_LE : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=-1+arg3, [ arg1P_8<=arg1 && arg3>1 && 1+arg2P_8<=arg2 && arg1>-1 && arg2>0 && arg1P_8>-1 && arg2P_8>-1 ], cost: 1 8: f964_0_nth_LE -> f754_0_main_LE : arg1'=arg1P_9, arg2'=0, arg3'=arg4, arg4'=arg4P_9, [ arg1P_9<=arg1 && arg3<2 && arg1>-1 && arg2>-1 && arg1P_9>-1 ], cost: 1 9: f964_0_nth_LE -> f754_0_main_LE : arg1'=arg1P_10, arg2'=0, arg3'=arg4, arg4'=arg4P_10, [ arg1P_10<=arg1 && arg3>1 && arg1>-1 && arg2>-1 && arg1P_10>-1 ], cost: 1 11: f673_0_createIntList_LE -> f673_0_createIntList_LE : arg1'=-1+arg1, arg2'=1+arg2, arg3'=arg3P_12, arg4'=arg4P_12, [ arg1>0 && arg2>0 ], cost: 1 12: __init -> f1_0_main_Load : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 3. Accelerating the following rules: 4: f704_0_nth_LE -> f704_0_nth_LE : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=-1+arg3, [ arg1P_5<=arg1 && arg3>1 && 1+arg2P_5<=arg2 && arg1>-1 && arg2>0 && arg1P_5>-1 && arg2P_5>-1 ], cost: 1 Failed to prove monotonicity of the guard of rule 4. [accelerate] Nesting with 1 inner and 1 outer candidates Accelerating simple loops of location 5. Accelerating the following rules: 7: f964_0_nth_LE -> f964_0_nth_LE : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=-1+arg3, [ arg1P_8<=arg1 && arg3>1 && 1+arg2P_8<=arg2 && arg1>-1 && arg2>0 && arg1P_8>-1 && arg2P_8>-1 ], cost: 1 Failed to prove monotonicity of the guard of rule 7. [accelerate] Nesting with 1 inner and 1 outer candidates Accelerating simple loops of location 6. Accelerating the following rules: 11: f673_0_createIntList_LE -> f673_0_createIntList_LE : arg1'=-1+arg1, arg2'=1+arg2, arg3'=arg3P_12, arg4'=arg4P_12, [ arg1>0 && arg2>0 ], cost: 1 Accelerated rule 11 with backward acceleration, yielding the new rule 13. [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 2: f517_0_random_ArrayAccess -> f704_0_nth_LE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=1+x7_1, [ x7_1>0 && arg3P_3>-1 && arg1P_3<=arg1 && arg1>=arg2P_3 && arg1>-1 && arg1P_3>-1 && arg2P_3>-1 ], cost: 1 1: f1_0_main_Load -> f517_0_random_ArrayAccess : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1>0 && arg1P_2>-1 ], cost: 1 10: f1_0_main_Load -> f673_0_createIntList_LE : arg1'=arg1P_11, arg2'=1, arg3'=arg3P_11, arg4'=arg4P_11, [ arg2>-1 && arg1P_11>-1 && arg1>0 ], cost: 1 3: f704_0_nth_LE -> f754_0_main_LE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg4, arg4'=arg4P_4, [ arg1P_4<=arg1 && arg3<2 && arg1>-1 && arg2>0 && arg1P_4>-1 && 2+arg2P_4<=arg2 ], cost: 1 4: f704_0_nth_LE -> f704_0_nth_LE : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=-1+arg3, [ arg1P_5<=arg1 && arg3>1 && 1+arg2P_5<=arg2 && arg1>-1 && arg2>0 && arg1P_5>-1 && arg2P_5>-1 ], cost: 1 5: f754_0_main_LE -> f964_0_nth_LE : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=1+arg3, [ arg3P_6>-1 && arg3>0 && arg2>0 && 1+arg1P_6<=arg1 && 1+arg2P_6<=arg1 && arg1>0 && arg1P_6>-1 && arg2P_6>-1 ], cost: 1 6: f964_0_nth_LE -> f754_0_main_LE : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg4, arg4'=arg4P_7, [ arg1P_7<=arg1 && arg3<2 && arg1>-1 && arg2>0 && arg1P_7>-1 && 2+arg2P_7<=arg2 ], cost: 1 7: f964_0_nth_LE -> f964_0_nth_LE : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=-1+arg3, [ arg1P_8<=arg1 && arg3>1 && 1+arg2P_8<=arg2 && arg1>-1 && arg2>0 && arg1P_8>-1 && arg2P_8>-1 ], cost: 1 8: f964_0_nth_LE -> f754_0_main_LE : arg1'=arg1P_9, arg2'=0, arg3'=arg4, arg4'=arg4P_9, [ arg1P_9<=arg1 && arg3<2 && arg1>-1 && arg2>-1 && arg1P_9>-1 ], cost: 1 9: f964_0_nth_LE -> f754_0_main_LE : arg1'=arg1P_10, arg2'=0, arg3'=arg4, arg4'=arg4P_10, [ arg1P_10<=arg1 && arg3>1 && arg1>-1 && arg2>-1 && arg1P_10>-1 ], cost: 1 13: f673_0_createIntList_LE -> f673_0_createIntList_LE : arg1'=0, arg2'=arg2+arg1, arg3'=arg3P_12, arg4'=arg4P_12, [ arg2>0 && arg1>=1 ], cost: arg1 12: __init -> f1_0_main_Load : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 2: f517_0_random_ArrayAccess -> f704_0_nth_LE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=1+x7_1, [ x7_1>0 && arg3P_3>-1 && arg1P_3<=arg1 && arg1>=arg2P_3 && arg1>-1 && arg1P_3>-1 && arg2P_3>-1 ], cost: 1 14: f517_0_random_ArrayAccess -> f704_0_nth_LE : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=-1+arg3P_3, arg4'=1+x7_1, [ x7_1>0 && arg3P_3>1 && arg1P_5>-1 && arg2P_5>-1 && arg1P_5<=arg1 && 1+arg2P_5<=arg1 && 1<=arg1 ], cost: 2 1: f1_0_main_Load -> f517_0_random_ArrayAccess : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1>0 && arg1P_2>-1 ], cost: 1 10: f1_0_main_Load -> f673_0_createIntList_LE : arg1'=arg1P_11, arg2'=1, arg3'=arg3P_11, arg4'=arg4P_11, [ arg2>-1 && arg1P_11>-1 && arg1>0 ], cost: 1 16: f1_0_main_Load -> f673_0_createIntList_LE : arg1'=0, arg2'=1+arg1P_11, arg3'=arg3P_12, arg4'=arg4P_12, [ arg2>-1 && arg1>0 && arg1P_11>=1 ], cost: 1+arg1P_11 3: f704_0_nth_LE -> f754_0_main_LE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg4, arg4'=arg4P_4, [ arg1P_4<=arg1 && arg3<2 && arg1>-1 && arg2>0 && arg1P_4>-1 && 2+arg2P_4<=arg2 ], cost: 1 5: f754_0_main_LE -> f964_0_nth_LE : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=1+arg3, [ arg3P_6>-1 && arg3>0 && arg2>0 && 1+arg1P_6<=arg1 && 1+arg2P_6<=arg1 && arg1>0 && arg1P_6>-1 && arg2P_6>-1 ], cost: 1 15: f754_0_main_LE -> f964_0_nth_LE : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=-1+arg3P_6, arg4'=1+arg3, [ arg3>0 && arg2>0 && arg3P_6>1 && arg1P_8>-1 && arg2P_8>-1 && 1+arg2P_8<=-1+arg1 && 1<=-1+arg1 && arg1P_8<=-1+arg1 ], cost: 2 6: f964_0_nth_LE -> f754_0_main_LE : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg4, arg4'=arg4P_7, [ arg1P_7<=arg1 && arg3<2 && arg1>-1 && arg2>0 && arg1P_7>-1 && 2+arg2P_7<=arg2 ], cost: 1 8: f964_0_nth_LE -> f754_0_main_LE : arg1'=arg1P_9, arg2'=0, arg3'=arg4, arg4'=arg4P_9, [ arg1P_9<=arg1 && arg3<2 && arg1>-1 && arg2>-1 && arg1P_9>-1 ], cost: 1 9: f964_0_nth_LE -> f754_0_main_LE : arg1'=arg1P_10, arg2'=0, arg3'=arg4, arg4'=arg4P_10, [ arg1P_10<=arg1 && arg3>1 && arg1>-1 && arg2>-1 && arg1P_10>-1 ], cost: 1 12: __init -> f1_0_main_Load : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 2: f517_0_random_ArrayAccess -> f704_0_nth_LE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=1+x7_1, [ x7_1>0 && arg3P_3>-1 && arg1P_3<=arg1 && arg1>=arg2P_3 && arg1>-1 && arg1P_3>-1 && arg2P_3>-1 ], cost: 1 14: f517_0_random_ArrayAccess -> f704_0_nth_LE : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=-1+arg3P_3, arg4'=1+x7_1, [ x7_1>0 && arg3P_3>1 && arg1P_5>-1 && arg2P_5>-1 && arg1P_5<=arg1 && 1+arg2P_5<=arg1 && 1<=arg1 ], cost: 2 1: f1_0_main_Load -> f517_0_random_ArrayAccess : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1>0 && arg1P_2>-1 ], cost: 1 16: f1_0_main_Load -> f673_0_createIntList_LE : arg1'=0, arg2'=1+arg1P_11, arg3'=arg3P_12, arg4'=arg4P_12, [ arg2>-1 && arg1>0 && arg1P_11>=1 ], cost: 1+arg1P_11 3: f704_0_nth_LE -> f754_0_main_LE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg4, arg4'=arg4P_4, [ arg1P_4<=arg1 && arg3<2 && arg1>-1 && arg2>0 && arg1P_4>-1 && 2+arg2P_4<=arg2 ], cost: 1 5: f754_0_main_LE -> f964_0_nth_LE : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=1+arg3, [ arg3P_6>-1 && arg3>0 && arg2>0 && 1+arg1P_6<=arg1 && 1+arg2P_6<=arg1 && arg1>0 && arg1P_6>-1 && arg2P_6>-1 ], cost: 1 15: f754_0_main_LE -> f964_0_nth_LE : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=-1+arg3P_6, arg4'=1+arg3, [ arg3>0 && arg2>0 && arg3P_6>1 && arg1P_8>-1 && arg2P_8>-1 && 1+arg2P_8<=-1+arg1 && 1<=-1+arg1 && arg1P_8<=-1+arg1 ], cost: 2 6: f964_0_nth_LE -> f754_0_main_LE : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg4, arg4'=arg4P_7, [ arg1P_7<=arg1 && arg3<2 && arg1>-1 && arg2>0 && arg1P_7>-1 && 2+arg2P_7<=arg2 ], cost: 1 8: f964_0_nth_LE -> f754_0_main_LE : arg1'=arg1P_9, arg2'=0, arg3'=arg4, arg4'=arg4P_9, [ arg1P_9<=arg1 && arg3<2 && arg1>-1 && arg2>-1 && arg1P_9>-1 ], cost: 1 9: f964_0_nth_LE -> f754_0_main_LE : arg1'=arg1P_10, arg2'=0, arg3'=arg4, arg4'=arg4P_10, [ arg1P_10<=arg1 && arg3>1 && arg1>-1 && arg2>-1 && arg1P_10>-1 ], cost: 1 12: __init -> f1_0_main_Load : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: __init 19: f517_0_random_ArrayAccess -> f754_0_main_LE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=1+x7_1, arg4'=arg4P_4, [ x7_1>0 && arg3P_3>-1 && arg1P_3<=arg1 && arg1>=arg2P_3 && arg1>-1 && arg1P_3>-1 && arg1P_4<=arg1P_3 && arg3P_3<2 && arg2P_3>0 && arg1P_4>-1 && 2+arg2P_4<=arg2P_3 ], cost: 2 20: f517_0_random_ArrayAccess -> f754_0_main_LE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=1+x7_1, arg4'=arg4P_4, [ x7_1>0 && arg3P_3>1 && arg1P_5>-1 && arg1P_5<=arg1 && 1+arg2P_5<=arg1 && 1<=arg1 && arg1P_4<=arg1P_5 && -1+arg3P_3<2 && arg2P_5>0 && arg1P_4>-1 && 2+arg2P_4<=arg2P_5 ], cost: 3 21: f754_0_main_LE -> f754_0_main_LE : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=1+arg3, arg4'=arg4P_7, [ arg3P_6>-1 && arg3>0 && arg2>0 && 1+arg1P_6<=arg1 && 1+arg2P_6<=arg1 && arg1>0 && arg1P_6>-1 && arg1P_7<=arg1P_6 && arg3P_6<2 && arg2P_6>0 && arg1P_7>-1 && 2+arg2P_7<=arg2P_6 ], cost: 2 22: f754_0_main_LE -> f754_0_main_LE : arg1'=arg1P_9, arg2'=0, arg3'=1+arg3, arg4'=arg4P_9, [ arg3P_6>-1 && arg3>0 && arg2>0 && 1+arg1P_6<=arg1 && 1+arg2P_6<=arg1 && arg1>0 && arg1P_6>-1 && arg2P_6>-1 && arg1P_9<=arg1P_6 && arg3P_6<2 && arg1P_9>-1 ], cost: 2 23: f754_0_main_LE -> f754_0_main_LE : arg1'=arg1P_10, arg2'=0, arg3'=1+arg3, arg4'=arg4P_10, [ arg3>0 && arg2>0 && 1+arg1P_6<=arg1 && 1+arg2P_6<=arg1 && arg1>0 && arg1P_6>-1 && arg2P_6>-1 && arg1P_10<=arg1P_6 && arg3P_6>1 && arg1P_10>-1 ], cost: 2 24: f754_0_main_LE -> f754_0_main_LE : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=1+arg3, arg4'=arg4P_7, [ arg3>0 && arg2>0 && arg3P_6>1 && arg1P_8>-1 && 1+arg2P_8<=-1+arg1 && 1<=-1+arg1 && arg1P_8<=-1+arg1 && arg1P_7<=arg1P_8 && -1+arg3P_6<2 && arg2P_8>0 && arg1P_7>-1 && 2+arg2P_7<=arg2P_8 ], cost: 3 25: f754_0_main_LE -> f754_0_main_LE : arg1'=arg1P_9, arg2'=0, arg3'=1+arg3, arg4'=arg4P_9, [ arg3>0 && arg2>0 && arg3P_6>1 && arg1P_8>-1 && arg2P_8>-1 && 1+arg2P_8<=-1+arg1 && 1<=-1+arg1 && arg1P_8<=-1+arg1 && arg1P_9<=arg1P_8 && -1+arg3P_6<2 && arg1P_9>-1 ], cost: 3 26: f754_0_main_LE -> f754_0_main_LE : arg1'=arg1P_10, arg2'=0, arg3'=1+arg3, arg4'=arg4P_10, [ arg3>0 && arg2>0 && arg1P_8>-1 && arg2P_8>-1 && 1+arg2P_8<=-1+arg1 && 1<=-1+arg1 && arg1P_8<=-1+arg1 && arg1P_10<=arg1P_8 && -1+arg3P_6>1 && arg1P_10>-1 ], cost: 3 17: __init -> f517_0_random_ArrayAccess : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1P_13>0 && arg1P_2>-1 ], cost: 2 18: __init -> f673_0_createIntList_LE : arg1'=0, arg2'=1+arg1P_11, arg3'=arg3P_12, arg4'=arg4P_12, [ arg2P_13>-1 && arg1P_13>0 && arg1P_11>=1 ], cost: 2+arg1P_11 Applied pruning (of leafs and parallel rules): Start location: __init 19: f517_0_random_ArrayAccess -> f754_0_main_LE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=1+x7_1, arg4'=arg4P_4, [ x7_1>0 && arg3P_3>-1 && arg1P_3<=arg1 && arg1>=arg2P_3 && arg1>-1 && arg1P_3>-1 && arg1P_4<=arg1P_3 && arg3P_3<2 && arg2P_3>0 && arg1P_4>-1 && 2+arg2P_4<=arg2P_3 ], cost: 2 20: f517_0_random_ArrayAccess -> f754_0_main_LE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=1+x7_1, arg4'=arg4P_4, [ x7_1>0 && arg3P_3>1 && arg1P_5>-1 && arg1P_5<=arg1 && 1+arg2P_5<=arg1 && 1<=arg1 && arg1P_4<=arg1P_5 && -1+arg3P_3<2 && arg2P_5>0 && arg1P_4>-1 && 2+arg2P_4<=arg2P_5 ], cost: 3 21: f754_0_main_LE -> f754_0_main_LE : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=1+arg3, arg4'=arg4P_7, [ arg3P_6>-1 && arg3>0 && arg2>0 && 1+arg1P_6<=arg1 && 1+arg2P_6<=arg1 && arg1>0 && arg1P_6>-1 && arg1P_7<=arg1P_6 && arg3P_6<2 && arg2P_6>0 && arg1P_7>-1 && 2+arg2P_7<=arg2P_6 ], cost: 2 22: f754_0_main_LE -> f754_0_main_LE : arg1'=arg1P_9, arg2'=0, arg3'=1+arg3, arg4'=arg4P_9, [ arg3P_6>-1 && arg3>0 && arg2>0 && 1+arg1P_6<=arg1 && 1+arg2P_6<=arg1 && arg1>0 && arg1P_6>-1 && arg2P_6>-1 && arg1P_9<=arg1P_6 && arg3P_6<2 && arg1P_9>-1 ], cost: 2 23: f754_0_main_LE -> f754_0_main_LE : arg1'=arg1P_10, arg2'=0, arg3'=1+arg3, arg4'=arg4P_10, [ arg3>0 && arg2>0 && 1+arg1P_6<=arg1 && 1+arg2P_6<=arg1 && arg1>0 && arg1P_6>-1 && arg2P_6>-1 && arg1P_10<=arg1P_6 && arg3P_6>1 && arg1P_10>-1 ], cost: 2 24: f754_0_main_LE -> f754_0_main_LE : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=1+arg3, arg4'=arg4P_7, [ arg3>0 && arg2>0 && arg3P_6>1 && arg1P_8>-1 && 1+arg2P_8<=-1+arg1 && 1<=-1+arg1 && arg1P_8<=-1+arg1 && arg1P_7<=arg1P_8 && -1+arg3P_6<2 && arg2P_8>0 && arg1P_7>-1 && 2+arg2P_7<=arg2P_8 ], cost: 3 26: f754_0_main_LE -> f754_0_main_LE : arg1'=arg1P_10, arg2'=0, arg3'=1+arg3, arg4'=arg4P_10, [ arg3>0 && arg2>0 && arg1P_8>-1 && arg2P_8>-1 && 1+arg2P_8<=-1+arg1 && 1<=-1+arg1 && arg1P_8<=-1+arg1 && arg1P_10<=arg1P_8 && -1+arg3P_6>1 && arg1P_10>-1 ], cost: 3 17: __init -> f517_0_random_ArrayAccess : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1P_13>0 && arg1P_2>-1 ], cost: 2 18: __init -> f673_0_createIntList_LE : arg1'=0, arg2'=1+arg1P_11, arg3'=arg3P_12, arg4'=arg4P_12, [ arg2P_13>-1 && arg1P_13>0 && arg1P_11>=1 ], cost: 2+arg1P_11 Accelerating simple loops of location 4. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 21: f754_0_main_LE -> f754_0_main_LE : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=1+arg3, arg4'=arg4P_7, [ arg3>0 && arg2>0 && arg1P_7>-1 && 1<=-1+arg1 && 2+arg2P_7<=-1+arg1 && arg1P_7<=-1+arg1 ], cost: 2 22: f754_0_main_LE -> f754_0_main_LE : arg1'=arg1P_9, arg2'=0, arg3'=1+arg3, arg4'=arg4P_9, [ arg3>0 && arg2>0 && arg1>0 && arg1P_9>-1 && arg1P_9<=-1+arg1 ], cost: 2 23: f754_0_main_LE -> f754_0_main_LE : arg1'=arg1P_10, arg2'=0, arg3'=1+arg3, arg4'=arg4P_10, [ arg3>0 && arg2>0 && arg1>0 && arg1P_10>-1 && arg1P_10<=-1+arg1 ], cost: 2 24: f754_0_main_LE -> f754_0_main_LE : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=1+arg3, arg4'=arg4P_7, [ arg3>0 && arg2>0 && arg1P_7>-1 && arg1P_7<=-1+arg1 && 1<=-2+arg1 && 2+arg2P_7<=-2+arg1 ], cost: 3 26: f754_0_main_LE -> f754_0_main_LE : arg1'=arg1P_10, arg2'=0, arg3'=1+arg3, arg4'=arg4P_10, [ arg3>0 && arg2>0 && 1<=-1+arg1 && arg1P_10>-1 && arg1P_10<=-1+arg1 ], cost: 3 Failed to prove monotonicity of the guard of rule 21. Failed to prove monotonicity of the guard of rule 22. Failed to prove monotonicity of the guard of rule 23. Failed to prove monotonicity of the guard of rule 24. Failed to prove monotonicity of the guard of rule 26. [accelerate] Nesting with 5 inner and 5 outer candidates Accelerated all simple loops using metering functions (where possible): Start location: __init 19: f517_0_random_ArrayAccess -> f754_0_main_LE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=1+x7_1, arg4'=arg4P_4, [ x7_1>0 && arg3P_3>-1 && arg1P_3<=arg1 && arg1>=arg2P_3 && arg1>-1 && arg1P_3>-1 && arg1P_4<=arg1P_3 && arg3P_3<2 && arg2P_3>0 && arg1P_4>-1 && 2+arg2P_4<=arg2P_3 ], cost: 2 20: f517_0_random_ArrayAccess -> f754_0_main_LE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=1+x7_1, arg4'=arg4P_4, [ x7_1>0 && arg3P_3>1 && arg1P_5>-1 && arg1P_5<=arg1 && 1+arg2P_5<=arg1 && 1<=arg1 && arg1P_4<=arg1P_5 && -1+arg3P_3<2 && arg2P_5>0 && arg1P_4>-1 && 2+arg2P_4<=arg2P_5 ], cost: 3 21: f754_0_main_LE -> f754_0_main_LE : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=1+arg3, arg4'=arg4P_7, [ arg3>0 && arg2>0 && arg1P_7>-1 && 1<=-1+arg1 && 2+arg2P_7<=-1+arg1 && arg1P_7<=-1+arg1 ], cost: 2 22: f754_0_main_LE -> f754_0_main_LE : arg1'=arg1P_9, arg2'=0, arg3'=1+arg3, arg4'=arg4P_9, [ arg3>0 && arg2>0 && arg1>0 && arg1P_9>-1 && arg1P_9<=-1+arg1 ], cost: 2 23: f754_0_main_LE -> f754_0_main_LE : arg1'=arg1P_10, arg2'=0, arg3'=1+arg3, arg4'=arg4P_10, [ arg3>0 && arg2>0 && arg1>0 && arg1P_10>-1 && arg1P_10<=-1+arg1 ], cost: 2 24: f754_0_main_LE -> f754_0_main_LE : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=1+arg3, arg4'=arg4P_7, [ arg3>0 && arg2>0 && arg1P_7>-1 && arg1P_7<=-1+arg1 && 1<=-2+arg1 && 2+arg2P_7<=-2+arg1 ], cost: 3 26: f754_0_main_LE -> f754_0_main_LE : arg1'=arg1P_10, arg2'=0, arg3'=1+arg3, arg4'=arg4P_10, [ arg3>0 && arg2>0 && 1<=-1+arg1 && arg1P_10>-1 && arg1P_10<=-1+arg1 ], cost: 3 17: __init -> f517_0_random_ArrayAccess : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1P_13>0 && arg1P_2>-1 ], cost: 2 18: __init -> f673_0_createIntList_LE : arg1'=0, arg2'=1+arg1P_11, arg3'=arg3P_12, arg4'=arg4P_12, [ arg2P_13>-1 && arg1P_13>0 && arg1P_11>=1 ], cost: 2+arg1P_11 Chained accelerated rules (with incoming rules): Start location: __init 19: f517_0_random_ArrayAccess -> f754_0_main_LE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=1+x7_1, arg4'=arg4P_4, [ x7_1>0 && arg3P_3>-1 && arg1P_3<=arg1 && arg1>=arg2P_3 && arg1>-1 && arg1P_3>-1 && arg1P_4<=arg1P_3 && arg3P_3<2 && arg2P_3>0 && arg1P_4>-1 && 2+arg2P_4<=arg2P_3 ], cost: 2 20: f517_0_random_ArrayAccess -> f754_0_main_LE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=1+x7_1, arg4'=arg4P_4, [ x7_1>0 && arg3P_3>1 && arg1P_5>-1 && arg1P_5<=arg1 && 1+arg2P_5<=arg1 && 1<=arg1 && arg1P_4<=arg1P_5 && -1+arg3P_3<2 && arg2P_5>0 && arg1P_4>-1 && 2+arg2P_4<=arg2P_5 ], cost: 3 27: f517_0_random_ArrayAccess -> f754_0_main_LE : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=2+x7_1, arg4'=arg4P_7, [ x7_1>0 && arg1P_7>-1 && 3+arg2P_7<=arg1 && 1+arg1P_7<=arg1 && 3<=arg1 ], cost: 4 28: f517_0_random_ArrayAccess -> f754_0_main_LE : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=2+x7_1, arg4'=arg4P_7, [ x7_1>0 && arg1P_7>-1 && 3+arg2P_7<=arg1 && 1+arg1P_7<=arg1 && 3<=-1+arg1 ], cost: 5 29: f517_0_random_ArrayAccess -> f754_0_main_LE : arg1'=arg1P_9, arg2'=0, arg3'=2+x7_1, arg4'=arg4P_9, [ x7_1>0 && arg1P_9>-1 && 1+arg1P_9<=arg1 && 3<=arg1 ], cost: 4 30: f517_0_random_ArrayAccess -> f754_0_main_LE : arg1'=arg1P_9, arg2'=0, arg3'=2+x7_1, arg4'=arg4P_9, [ x7_1>0 && arg1P_9>-1 && 1+arg1P_9<=arg1 && 3<=-1+arg1 ], cost: 5 31: f517_0_random_ArrayAccess -> f754_0_main_LE : arg1'=arg1P_10, arg2'=0, arg3'=2+x7_1, arg4'=arg4P_10, [ x7_1>0 && arg1P_10>-1 && 1+arg1P_10<=arg1 && 3<=arg1 ], cost: 4 32: f517_0_random_ArrayAccess -> f754_0_main_LE : arg1'=arg1P_10, arg2'=0, arg3'=2+x7_1, arg4'=arg4P_10, [ x7_1>0 && arg1P_10>-1 && 1+arg1P_10<=arg1 && 3<=-1+arg1 ], cost: 5 33: f517_0_random_ArrayAccess -> f754_0_main_LE : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=2+x7_1, arg4'=arg4P_7, [ x7_1>0 && arg1P_7>-1 && 1+arg1P_7<=arg1 && 3<=arg1 && 4+arg2P_7<=arg1 ], cost: 5 34: f517_0_random_ArrayAccess -> f754_0_main_LE : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=2+x7_1, arg4'=arg4P_7, [ x7_1>0 && arg1P_7>-1 && 1+arg1P_7<=arg1 && 4+arg2P_7<=arg1 && 3<=-1+arg1 ], cost: 6 35: f517_0_random_ArrayAccess -> f754_0_main_LE : arg1'=arg1P_10, arg2'=0, arg3'=2+x7_1, arg4'=arg4P_10, [ x7_1>0 && arg1P_10>-1 && 1+arg1P_10<=arg1 && 3<=arg1 ], cost: 5 36: f517_0_random_ArrayAccess -> f754_0_main_LE : arg1'=arg1P_10, arg2'=0, arg3'=2+x7_1, arg4'=arg4P_10, [ x7_1>0 && arg1P_10>-1 && 1+arg1P_10<=arg1 && 3<=-1+arg1 ], cost: 6 17: __init -> f517_0_random_ArrayAccess : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1P_13>0 && arg1P_2>-1 ], cost: 2 18: __init -> f673_0_createIntList_LE : arg1'=0, arg2'=1+arg1P_11, arg3'=arg3P_12, arg4'=arg4P_12, [ arg2P_13>-1 && arg1P_13>0 && arg1P_11>=1 ], cost: 2+arg1P_11 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 18: __init -> f673_0_createIntList_LE : arg1'=0, arg2'=1+arg1P_11, arg3'=arg3P_12, arg4'=arg4P_12, [ arg2P_13>-1 && arg1P_13>0 && arg1P_11>=1 ], cost: 2+arg1P_11 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 18: __init -> f673_0_createIntList_LE : arg1'=0, arg2'=1+arg1P_11, arg3'=arg3P_12, arg4'=arg4P_12, [ arg2P_13>-1 && arg1P_13>0 && arg1P_11>=1 ], cost: 2+arg1P_11 Computing asymptotic complexity for rule 18 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),?)