WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f234_0_slide93_FieldAccess : arg1'=arg1P_1, arg2'=arg2P_1, [ x4_1>-1 && arg2>1 && arg1P_1>-1 && x5_1>arg2P_1 && x5_1>-1 && arg1>0 ], cost: 1 1: f1_0_main_Load -> f234_0_slide93_FieldAccess : arg1'=arg1P_2, arg2'=arg2P_2, [ x10_1>-1 && arg2>1 && arg2P_2<1 && arg1P_2>-1 && arg1>0 ], cost: 1 12: f1_0_main_Load -> f196_0_create_LE : arg1'=arg1P_13, arg2'=arg2P_13, [ x34_1>-1 && arg2>1 && x33_1>-1 && arg1>0 && -1+x33_1==arg1P_13 ], cost: 1 2: f234_0_slide93_FieldAccess -> f951_0_slide93_EQ : arg1'=arg1P_3, arg2'=arg2P_3, [ arg2>0 && arg1==arg1P_3 && 0==arg2P_3 ], cost: 1 3: f234_0_slide93_FieldAccess -> f951_0_slide93_EQ : arg1'=arg1P_4, arg2'=arg2P_4, [ arg1==arg1P_4 && 1==arg2P_4 ], cost: 1 4: f951_0_slide93_EQ -> f951_0_slide93_EQ\' : arg1'=arg1P_5, arg2'=arg2P_5, [ -2*x25_1+arg1==0 && arg2>0 && x29_10 && arg1>=x36_1 && arg1==arg1P_5 && arg2==arg2P_5 ], cost: 1 6: f951_0_slide93_EQ -> f951_0_slide93_EQ\' : arg1'=arg1P_7, arg2'=arg2P_7, [ -2*x44_1+arg1==1 && arg2>0 && x45_10 && arg1>=x46_1 && arg1==arg1P_7 && arg2==arg2P_7 ], cost: 1 8: f951_0_slide93_EQ -> f951_0_slide93_EQ\' : arg1'=arg1P_9, arg2'=arg2P_9, [ -2*x54_1+arg1==1 && arg2>0 && x55_1=x56_1 && arg1==arg1P_9 && arg2==arg2P_9 ], cost: 1 10: f951_0_slide93_EQ -> f951_0_slide93_EQ\' : arg1'=arg1P_11, arg2'=arg2P_11, [ -2*x64_1+arg1==0 && arg2>0 && x65_1=x66_1 && arg1==arg1P_11 && arg2==arg2P_11 ], cost: 1 5: f951_0_slide93_EQ\' -> f951_0_slide93_EQ : arg1'=arg1P_6, arg2'=arg2P_6, [ -2*x40_1+arg1==0 && arg2>0 && x41_1=arg1P_6 && x41_1>0 && -2*x40_1+arg1>=0 && -2*x40_1+arg1<2 && -2*arg1P_6+arg1<2 && -2*arg1P_6+arg1>=0 && 0==arg2P_6 ], cost: 1 7: f951_0_slide93_EQ\' -> f951_0_slide93_EQ : arg1'=arg1P_8, arg2'=arg2P_8, [ -2*x50_1+arg1==1 && arg2>0 && x51_1=arg1P_8 && x51_1>0 && -2*x50_1+arg1>=0 && -2*x50_1+arg1<2 && -2*arg1P_8+arg1<2 && -2*arg1P_8+arg1>=0 && 1==arg2P_8 ], cost: 1 9: f951_0_slide93_EQ\' -> f951_0_slide93_EQ : arg1'=arg1P_10, arg2'=arg2P_10, [ -2*x60_1+arg1==1 && arg2>0 && arg1>=arg1P_10 && x61_1=0 && -2*x60_1+arg1<2 && -2*arg1P_10+arg1<2 && -2*arg1P_10+arg1>=0 && 1==arg2P_10 ], cost: 1 11: f951_0_slide93_EQ\' -> f951_0_slide93_EQ : arg1'=arg1P_12, arg2'=arg2P_12, [ -2*x70_1+arg1==0 && arg2>0 && arg1>=arg1P_12 && x71_1=0 && -2*x70_1+arg1<2 && -2*arg1P_12+arg1<2 && -2*arg1P_12+arg1>=0 && 1==arg2P_12 ], cost: 1 13: f196_0_create_LE -> f196_0_create_LE : arg1'=arg1P_14, arg2'=arg2P_14, [ arg1>0 && -1+arg1==arg1P_14 ], cost: 1 14: __init -> f1_0_main_Load : arg1'=arg1P_15, arg2'=arg2P_15, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 14: __init -> f1_0_main_Load : arg1'=arg1P_15, arg2'=arg2P_15, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f234_0_slide93_FieldAccess : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2>1 && arg1P_1>-1 && arg1>0 ], cost: 1 1: f1_0_main_Load -> f234_0_slide93_FieldAccess : arg1'=arg1P_2, arg2'=arg2P_2, [ arg2>1 && arg2P_2<1 && arg1P_2>-1 && arg1>0 ], cost: 1 12: f1_0_main_Load -> f196_0_create_LE : arg1'=-1+x33_1, arg2'=arg2P_13, [ arg2>1 && x33_1>-1 && arg1>0 ], cost: 1 2: f234_0_slide93_FieldAccess -> f951_0_slide93_EQ : arg2'=0, [ arg2>0 ], cost: 1 3: f234_0_slide93_FieldAccess -> f951_0_slide93_EQ : arg2'=1, [], cost: 1 4: f951_0_slide93_EQ -> f951_0_slide93_EQ\' : [ -2*x25_1+arg1==0 && 1<=-1+arg2 ], cost: 1 6: f951_0_slide93_EQ -> f951_0_slide93_EQ\' : [ -2*x44_1+arg1==1 && 1<=-1+arg2 ], cost: 1 8: f951_0_slide93_EQ -> f951_0_slide93_EQ\' : [ -2*x54_1+arg1==1 && arg2>0 ], cost: 1 10: f951_0_slide93_EQ -> f951_0_slide93_EQ\' : [ -2*x64_1+arg1==0 && arg2>0 ], cost: 1 5: f951_0_slide93_EQ\' -> f951_0_slide93_EQ : arg1'=arg1P_6, arg2'=0, [ -2*x40_1+arg1==0 && arg1>=arg1P_6 && -2*arg1P_6+arg1<2 && -2*arg1P_6+arg1>=0 && 1<=-1+arg2 ], cost: 1 7: f951_0_slide93_EQ\' -> f951_0_slide93_EQ : arg1'=arg1P_8, arg2'=1, [ -2*x50_1+arg1==1 && arg1>=arg1P_8 && -2*arg1P_8+arg1<2 && -2*arg1P_8+arg1>=0 && 1<=-1+arg2 ], cost: 1 9: f951_0_slide93_EQ\' -> f951_0_slide93_EQ : arg1'=arg1P_10, arg2'=1, [ -2*x60_1+arg1==1 && arg2>0 && arg1>=arg1P_10 && -2*arg1P_10+arg1<2 && -2*arg1P_10+arg1>=0 ], cost: 1 11: f951_0_slide93_EQ\' -> f951_0_slide93_EQ : arg1'=arg1P_12, arg2'=1, [ -2*x70_1+arg1==0 && arg2>0 && arg1>=arg1P_12 && -2*arg1P_12+arg1<2 && -2*arg1P_12+arg1>=0 ], cost: 1 13: f196_0_create_LE -> f196_0_create_LE : arg1'=-1+arg1, arg2'=arg2P_14, [ arg1>0 ], cost: 1 14: __init -> f1_0_main_Load : arg1'=arg1P_15, arg2'=arg2P_15, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 4. Accelerating the following rules: 13: f196_0_create_LE -> f196_0_create_LE : arg1'=-1+arg1, arg2'=arg2P_14, [ arg1>0 ], cost: 1 Accelerated rule 13 with backward acceleration, yielding the new rule 15. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 13. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f234_0_slide93_FieldAccess : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2>1 && arg1P_1>-1 && arg1>0 ], cost: 1 1: f1_0_main_Load -> f234_0_slide93_FieldAccess : arg1'=arg1P_2, arg2'=arg2P_2, [ arg2>1 && arg2P_2<1 && arg1P_2>-1 && arg1>0 ], cost: 1 12: f1_0_main_Load -> f196_0_create_LE : arg1'=-1+x33_1, arg2'=arg2P_13, [ arg2>1 && x33_1>-1 && arg1>0 ], cost: 1 2: f234_0_slide93_FieldAccess -> f951_0_slide93_EQ : arg2'=0, [ arg2>0 ], cost: 1 3: f234_0_slide93_FieldAccess -> f951_0_slide93_EQ : arg2'=1, [], cost: 1 4: f951_0_slide93_EQ -> f951_0_slide93_EQ\' : [ -2*x25_1+arg1==0 && 1<=-1+arg2 ], cost: 1 6: f951_0_slide93_EQ -> f951_0_slide93_EQ\' : [ -2*x44_1+arg1==1 && 1<=-1+arg2 ], cost: 1 8: f951_0_slide93_EQ -> f951_0_slide93_EQ\' : [ -2*x54_1+arg1==1 && arg2>0 ], cost: 1 10: f951_0_slide93_EQ -> f951_0_slide93_EQ\' : [ -2*x64_1+arg1==0 && arg2>0 ], cost: 1 5: f951_0_slide93_EQ\' -> f951_0_slide93_EQ : arg1'=arg1P_6, arg2'=0, [ -2*x40_1+arg1==0 && arg1>=arg1P_6 && -2*arg1P_6+arg1<2 && -2*arg1P_6+arg1>=0 && 1<=-1+arg2 ], cost: 1 7: f951_0_slide93_EQ\' -> f951_0_slide93_EQ : arg1'=arg1P_8, arg2'=1, [ -2*x50_1+arg1==1 && arg1>=arg1P_8 && -2*arg1P_8+arg1<2 && -2*arg1P_8+arg1>=0 && 1<=-1+arg2 ], cost: 1 9: f951_0_slide93_EQ\' -> f951_0_slide93_EQ : arg1'=arg1P_10, arg2'=1, [ -2*x60_1+arg1==1 && arg2>0 && arg1>=arg1P_10 && -2*arg1P_10+arg1<2 && -2*arg1P_10+arg1>=0 ], cost: 1 11: f951_0_slide93_EQ\' -> f951_0_slide93_EQ : arg1'=arg1P_12, arg2'=1, [ -2*x70_1+arg1==0 && arg2>0 && arg1>=arg1P_12 && -2*arg1P_12+arg1<2 && -2*arg1P_12+arg1>=0 ], cost: 1 15: f196_0_create_LE -> f196_0_create_LE : arg1'=0, arg2'=arg2P_14, [ arg1>=1 ], cost: arg1 14: __init -> f1_0_main_Load : arg1'=arg1P_15, arg2'=arg2P_15, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f234_0_slide93_FieldAccess : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2>1 && arg1P_1>-1 && arg1>0 ], cost: 1 1: f1_0_main_Load -> f234_0_slide93_FieldAccess : arg1'=arg1P_2, arg2'=arg2P_2, [ arg2>1 && arg2P_2<1 && arg1P_2>-1 && arg1>0 ], cost: 1 12: f1_0_main_Load -> f196_0_create_LE : arg1'=-1+x33_1, arg2'=arg2P_13, [ arg2>1 && x33_1>-1 && arg1>0 ], cost: 1 16: f1_0_main_Load -> f196_0_create_LE : arg1'=0, arg2'=arg2P_14, [ arg2>1 && arg1>0 && -1+x33_1>=1 ], cost: x33_1 2: f234_0_slide93_FieldAccess -> f951_0_slide93_EQ : arg2'=0, [ arg2>0 ], cost: 1 3: f234_0_slide93_FieldAccess -> f951_0_slide93_EQ : arg2'=1, [], cost: 1 4: f951_0_slide93_EQ -> f951_0_slide93_EQ\' : [ -2*x25_1+arg1==0 && 1<=-1+arg2 ], cost: 1 6: f951_0_slide93_EQ -> f951_0_slide93_EQ\' : [ -2*x44_1+arg1==1 && 1<=-1+arg2 ], cost: 1 8: f951_0_slide93_EQ -> f951_0_slide93_EQ\' : [ -2*x54_1+arg1==1 && arg2>0 ], cost: 1 10: f951_0_slide93_EQ -> f951_0_slide93_EQ\' : [ -2*x64_1+arg1==0 && arg2>0 ], cost: 1 5: f951_0_slide93_EQ\' -> f951_0_slide93_EQ : arg1'=arg1P_6, arg2'=0, [ -2*x40_1+arg1==0 && arg1>=arg1P_6 && -2*arg1P_6+arg1<2 && -2*arg1P_6+arg1>=0 && 1<=-1+arg2 ], cost: 1 7: f951_0_slide93_EQ\' -> f951_0_slide93_EQ : arg1'=arg1P_8, arg2'=1, [ -2*x50_1+arg1==1 && arg1>=arg1P_8 && -2*arg1P_8+arg1<2 && -2*arg1P_8+arg1>=0 && 1<=-1+arg2 ], cost: 1 9: f951_0_slide93_EQ\' -> f951_0_slide93_EQ : arg1'=arg1P_10, arg2'=1, [ -2*x60_1+arg1==1 && arg2>0 && arg1>=arg1P_10 && -2*arg1P_10+arg1<2 && -2*arg1P_10+arg1>=0 ], cost: 1 11: f951_0_slide93_EQ\' -> f951_0_slide93_EQ : arg1'=arg1P_12, arg2'=1, [ -2*x70_1+arg1==0 && arg2>0 && arg1>=arg1P_12 && -2*arg1P_12+arg1<2 && -2*arg1P_12+arg1>=0 ], cost: 1 14: __init -> f1_0_main_Load : arg1'=arg1P_15, arg2'=arg2P_15, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 0: f1_0_main_Load -> f234_0_slide93_FieldAccess : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2>1 && arg1P_1>-1 && arg1>0 ], cost: 1 1: f1_0_main_Load -> f234_0_slide93_FieldAccess : arg1'=arg1P_2, arg2'=arg2P_2, [ arg2>1 && arg2P_2<1 && arg1P_2>-1 && arg1>0 ], cost: 1 16: f1_0_main_Load -> f196_0_create_LE : arg1'=0, arg2'=arg2P_14, [ arg2>1 && arg1>0 && -1+x33_1>=1 ], cost: x33_1 2: f234_0_slide93_FieldAccess -> f951_0_slide93_EQ : arg2'=0, [ arg2>0 ], cost: 1 3: f234_0_slide93_FieldAccess -> f951_0_slide93_EQ : arg2'=1, [], cost: 1 4: f951_0_slide93_EQ -> f951_0_slide93_EQ\' : [ -2*x25_1+arg1==0 && 1<=-1+arg2 ], cost: 1 6: f951_0_slide93_EQ -> f951_0_slide93_EQ\' : [ -2*x44_1+arg1==1 && 1<=-1+arg2 ], cost: 1 8: f951_0_slide93_EQ -> f951_0_slide93_EQ\' : [ -2*x54_1+arg1==1 && arg2>0 ], cost: 1 10: f951_0_slide93_EQ -> f951_0_slide93_EQ\' : [ -2*x64_1+arg1==0 && arg2>0 ], cost: 1 5: f951_0_slide93_EQ\' -> f951_0_slide93_EQ : arg1'=arg1P_6, arg2'=0, [ -2*x40_1+arg1==0 && arg1>=arg1P_6 && -2*arg1P_6+arg1<2 && -2*arg1P_6+arg1>=0 && 1<=-1+arg2 ], cost: 1 7: f951_0_slide93_EQ\' -> f951_0_slide93_EQ : arg1'=arg1P_8, arg2'=1, [ -2*x50_1+arg1==1 && arg1>=arg1P_8 && -2*arg1P_8+arg1<2 && -2*arg1P_8+arg1>=0 && 1<=-1+arg2 ], cost: 1 9: f951_0_slide93_EQ\' -> f951_0_slide93_EQ : arg1'=arg1P_10, arg2'=1, [ -2*x60_1+arg1==1 && arg2>0 && arg1>=arg1P_10 && -2*arg1P_10+arg1<2 && -2*arg1P_10+arg1>=0 ], cost: 1 11: f951_0_slide93_EQ\' -> f951_0_slide93_EQ : arg1'=arg1P_12, arg2'=1, [ -2*x70_1+arg1==0 && arg2>0 && arg1>=arg1P_12 && -2*arg1P_12+arg1<2 && -2*arg1P_12+arg1>=0 ], cost: 1 14: __init -> f1_0_main_Load : arg1'=arg1P_15, arg2'=arg2P_15, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: __init 2: f234_0_slide93_FieldAccess -> f951_0_slide93_EQ : arg2'=0, [ arg2>0 ], cost: 1 3: f234_0_slide93_FieldAccess -> f951_0_slide93_EQ : arg2'=1, [], cost: 1 20: f951_0_slide93_EQ -> f951_0_slide93_EQ : arg1'=arg1P_6, arg2'=0, [ -2*x25_1+arg1==0 && 1<=-1+arg2 && -2*x40_1+arg1==0 && arg1>=arg1P_6 && -2*arg1P_6+arg1<2 && -2*arg1P_6+arg1>=0 ], cost: 2 21: f951_0_slide93_EQ -> f951_0_slide93_EQ : arg1'=arg1P_12, arg2'=1, [ -2*x25_1+arg1==0 && 1<=-1+arg2 && -2*x70_1+arg1==0 && arg1>=arg1P_12 && -2*arg1P_12+arg1<2 && -2*arg1P_12+arg1>=0 ], cost: 2 22: f951_0_slide93_EQ -> f951_0_slide93_EQ : arg1'=arg1P_8, arg2'=1, [ -2*x44_1+arg1==1 && 1<=-1+arg2 && -2*x50_1+arg1==1 && arg1>=arg1P_8 && -2*arg1P_8+arg1<2 && -2*arg1P_8+arg1>=0 ], cost: 2 23: f951_0_slide93_EQ -> f951_0_slide93_EQ : arg1'=arg1P_10, arg2'=1, [ -2*x44_1+arg1==1 && 1<=-1+arg2 && -2*x60_1+arg1==1 && arg1>=arg1P_10 && -2*arg1P_10+arg1<2 && -2*arg1P_10+arg1>=0 ], cost: 2 24: f951_0_slide93_EQ -> f951_0_slide93_EQ : arg1'=arg1P_8, arg2'=1, [ -2*x54_1+arg1==1 && -2*x50_1+arg1==1 && arg1>=arg1P_8 && -2*arg1P_8+arg1<2 && -2*arg1P_8+arg1>=0 && 1<=-1+arg2 ], cost: 2 25: f951_0_slide93_EQ -> f951_0_slide93_EQ : arg1'=arg1P_10, arg2'=1, [ -2*x54_1+arg1==1 && arg2>0 && -2*x60_1+arg1==1 && arg1>=arg1P_10 && -2*arg1P_10+arg1<2 && -2*arg1P_10+arg1>=0 ], cost: 2 26: f951_0_slide93_EQ -> f951_0_slide93_EQ : arg1'=arg1P_6, arg2'=0, [ -2*x64_1+arg1==0 && -2*x40_1+arg1==0 && arg1>=arg1P_6 && -2*arg1P_6+arg1<2 && -2*arg1P_6+arg1>=0 && 1<=-1+arg2 ], cost: 2 27: f951_0_slide93_EQ -> f951_0_slide93_EQ : arg1'=arg1P_12, arg2'=1, [ -2*x64_1+arg1==0 && arg2>0 && -2*x70_1+arg1==0 && arg1>=arg1P_12 && -2*arg1P_12+arg1<2 && -2*arg1P_12+arg1>=0 ], cost: 2 17: __init -> f234_0_slide93_FieldAccess : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2P_15>1 && arg1P_1>-1 && arg1P_15>0 ], cost: 2 18: __init -> f234_0_slide93_FieldAccess : arg1'=arg1P_2, arg2'=arg2P_2, [ arg2P_15>1 && arg2P_2<1 && arg1P_2>-1 && arg1P_15>0 ], cost: 2 19: __init -> f196_0_create_LE : arg1'=0, arg2'=arg2P_14, [ arg2P_15>1 && arg1P_15>0 && -1+x33_1>=1 ], cost: 1+x33_1 Applied pruning (of leafs and parallel rules): Start location: __init 2: f234_0_slide93_FieldAccess -> f951_0_slide93_EQ : arg2'=0, [ arg2>0 ], cost: 1 3: f234_0_slide93_FieldAccess -> f951_0_slide93_EQ : arg2'=1, [], cost: 1 20: f951_0_slide93_EQ -> f951_0_slide93_EQ : arg1'=arg1P_6, arg2'=0, [ -2*x25_1+arg1==0 && 1<=-1+arg2 && -2*x40_1+arg1==0 && arg1>=arg1P_6 && -2*arg1P_6+arg1<2 && -2*arg1P_6+arg1>=0 ], cost: 2 21: f951_0_slide93_EQ -> f951_0_slide93_EQ : arg1'=arg1P_12, arg2'=1, [ -2*x25_1+arg1==0 && 1<=-1+arg2 && -2*x70_1+arg1==0 && arg1>=arg1P_12 && -2*arg1P_12+arg1<2 && -2*arg1P_12+arg1>=0 ], cost: 2 23: f951_0_slide93_EQ -> f951_0_slide93_EQ : arg1'=arg1P_10, arg2'=1, [ -2*x44_1+arg1==1 && 1<=-1+arg2 && -2*x60_1+arg1==1 && arg1>=arg1P_10 && -2*arg1P_10+arg1<2 && -2*arg1P_10+arg1>=0 ], cost: 2 24: f951_0_slide93_EQ -> f951_0_slide93_EQ : arg1'=arg1P_8, arg2'=1, [ -2*x54_1+arg1==1 && -2*x50_1+arg1==1 && arg1>=arg1P_8 && -2*arg1P_8+arg1<2 && -2*arg1P_8+arg1>=0 && 1<=-1+arg2 ], cost: 2 25: f951_0_slide93_EQ -> f951_0_slide93_EQ : arg1'=arg1P_10, arg2'=1, [ -2*x54_1+arg1==1 && arg2>0 && -2*x60_1+arg1==1 && arg1>=arg1P_10 && -2*arg1P_10+arg1<2 && -2*arg1P_10+arg1>=0 ], cost: 2 17: __init -> f234_0_slide93_FieldAccess : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2P_15>1 && arg1P_1>-1 && arg1P_15>0 ], cost: 2 18: __init -> f234_0_slide93_FieldAccess : arg1'=arg1P_2, arg2'=arg2P_2, [ arg2P_15>1 && arg2P_2<1 && arg1P_2>-1 && arg1P_15>0 ], cost: 2 19: __init -> f196_0_create_LE : arg1'=0, arg2'=arg2P_14, [ arg2P_15>1 && arg1P_15>0 && -1+x33_1>=1 ], cost: 1+x33_1 Accelerating simple loops of location 2. Accelerating the following rules: 20: f951_0_slide93_EQ -> f951_0_slide93_EQ : arg1'=arg1P_6, arg2'=0, [ -2*x25_1+arg1==0 && 1<=-1+arg2 && -2*x40_1+arg1==0 && arg1>=arg1P_6 && -2*arg1P_6+arg1<2 && -2*arg1P_6+arg1>=0 ], cost: 2 21: f951_0_slide93_EQ -> f951_0_slide93_EQ : arg1'=arg1P_12, arg2'=1, [ -2*x25_1+arg1==0 && 1<=-1+arg2 && -2*x70_1+arg1==0 && arg1>=arg1P_12 && -2*arg1P_12+arg1<2 && -2*arg1P_12+arg1>=0 ], cost: 2 23: f951_0_slide93_EQ -> f951_0_slide93_EQ : arg1'=arg1P_10, arg2'=1, [ -2*x44_1+arg1==1 && 1<=-1+arg2 && -2*x60_1+arg1==1 && arg1>=arg1P_10 && -2*arg1P_10+arg1<2 && -2*arg1P_10+arg1>=0 ], cost: 2 24: f951_0_slide93_EQ -> f951_0_slide93_EQ : arg1'=arg1P_8, arg2'=1, [ -2*x54_1+arg1==1 && -2*x50_1+arg1==1 && arg1>=arg1P_8 && -2*arg1P_8+arg1<2 && -2*arg1P_8+arg1>=0 && 1<=-1+arg2 ], cost: 2 25: f951_0_slide93_EQ -> f951_0_slide93_EQ : arg1'=arg1P_10, arg2'=1, [ -2*x54_1+arg1==1 && arg2>0 && -2*x60_1+arg1==1 && arg1>=arg1P_10 && -2*arg1P_10+arg1<2 && -2*arg1P_10+arg1>=0 ], cost: 2 Failed to prove monotonicity of the guard of rule 20. Failed to prove monotonicity of the guard of rule 21. Failed to prove monotonicity of the guard of rule 23. Failed to prove monotonicity of the guard of rule 24. Accelerated rule 25 with non-termination, yielding the new rule 28. Accelerated rule 25 with backward acceleration, yielding the new rule 29. [accelerate] Nesting with 5 inner and 4 outer candidates Removing the simple loops: 25. Accelerated all simple loops using metering functions (where possible): Start location: __init 2: f234_0_slide93_FieldAccess -> f951_0_slide93_EQ : arg2'=0, [ arg2>0 ], cost: 1 3: f234_0_slide93_FieldAccess -> f951_0_slide93_EQ : arg2'=1, [], cost: 1 20: f951_0_slide93_EQ -> f951_0_slide93_EQ : arg1'=arg1P_6, arg2'=0, [ -2*x25_1+arg1==0 && 1<=-1+arg2 && -2*x40_1+arg1==0 && arg1>=arg1P_6 && -2*arg1P_6+arg1<2 && -2*arg1P_6+arg1>=0 ], cost: 2 21: f951_0_slide93_EQ -> f951_0_slide93_EQ : arg1'=arg1P_12, arg2'=1, [ -2*x25_1+arg1==0 && 1<=-1+arg2 && -2*x70_1+arg1==0 && arg1>=arg1P_12 && -2*arg1P_12+arg1<2 && -2*arg1P_12+arg1>=0 ], cost: 2 23: f951_0_slide93_EQ -> f951_0_slide93_EQ : arg1'=arg1P_10, arg2'=1, [ -2*x44_1+arg1==1 && 1<=-1+arg2 && -2*x60_1+arg1==1 && arg1>=arg1P_10 && -2*arg1P_10+arg1<2 && -2*arg1P_10+arg1>=0 ], cost: 2 24: f951_0_slide93_EQ -> f951_0_slide93_EQ : arg1'=arg1P_8, arg2'=1, [ -2*x54_1+arg1==1 && -2*x50_1+arg1==1 && arg1>=arg1P_8 && -2*arg1P_8+arg1<2 && -2*arg1P_8+arg1>=0 && 1<=-1+arg2 ], cost: 2 28: f951_0_slide93_EQ -> [7] : [ -2*x54_1+arg1==1 && arg2>0 && -2*x60_1+arg1==1 && arg1>=arg1P_10 && -2*arg1P_10+arg1<2 && -2*arg1P_10+arg1>=0 && -2*x54_1+arg1P_10==1 && -2*x60_1+arg1P_10==1 && -arg1P_10<2 && -arg1P_10>=0 ], cost: NONTERM 29: f951_0_slide93_EQ -> f951_0_slide93_EQ : arg1'=arg1P_10, arg2'=1, [ arg2>0 && arg1>=arg1P_10 && -2*arg1P_10+arg1<2 && k_5>=1 && -2*x54_1+arg1P_10==1 && -2*x60_1+arg1P_10==1 && -arg1P_10>=0 ], cost: 2*k_5 17: __init -> f234_0_slide93_FieldAccess : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2P_15>1 && arg1P_1>-1 && arg1P_15>0 ], cost: 2 18: __init -> f234_0_slide93_FieldAccess : arg1'=arg1P_2, arg2'=arg2P_2, [ arg2P_15>1 && arg2P_2<1 && arg1P_2>-1 && arg1P_15>0 ], cost: 2 19: __init -> f196_0_create_LE : arg1'=0, arg2'=arg2P_14, [ arg2P_15>1 && arg1P_15>0 && -1+x33_1>=1 ], cost: 1+x33_1 Chained accelerated rules (with incoming rules): Start location: __init 2: f234_0_slide93_FieldAccess -> f951_0_slide93_EQ : arg2'=0, [ arg2>0 ], cost: 1 3: f234_0_slide93_FieldAccess -> f951_0_slide93_EQ : arg2'=1, [], cost: 1 30: f234_0_slide93_FieldAccess -> [7] : [ -2*x54_1+arg1==1 && -2-4*x54_1+arg1<2 && -2-4*x54_1+arg1>=0 && -1-2*x54_1<2 && -1-2*x54_1>=0 ], cost: NONTERM 31: f234_0_slide93_FieldAccess -> f951_0_slide93_EQ : arg1'=1+2*x54_1, arg2'=1, [ arg1>=1+2*x54_1 && -2-4*x54_1+arg1<2 && k_5>=1 && -1-2*x54_1>=0 ], cost: 1+2*k_5 17: __init -> f234_0_slide93_FieldAccess : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2P_15>1 && arg1P_1>-1 && arg1P_15>0 ], cost: 2 18: __init -> f234_0_slide93_FieldAccess : arg1'=arg1P_2, arg2'=arg2P_2, [ arg2P_15>1 && arg2P_2<1 && arg1P_2>-1 && arg1P_15>0 ], cost: 2 19: __init -> f196_0_create_LE : arg1'=0, arg2'=arg2P_14, [ arg2P_15>1 && arg1P_15>0 && -1+x33_1>=1 ], cost: 1+x33_1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 30: f234_0_slide93_FieldAccess -> [7] : [ -2*x54_1+arg1==1 && -2-4*x54_1+arg1<2 && -2-4*x54_1+arg1>=0 && -1-2*x54_1<2 && -1-2*x54_1>=0 ], cost: NONTERM 31: f234_0_slide93_FieldAccess -> f951_0_slide93_EQ : arg1'=1+2*x54_1, arg2'=1, [ arg1>=1+2*x54_1 && -2-4*x54_1+arg1<2 && k_5>=1 && -1-2*x54_1>=0 ], cost: 1+2*k_5 17: __init -> f234_0_slide93_FieldAccess : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2P_15>1 && arg1P_1>-1 && arg1P_15>0 ], cost: 2 18: __init -> f234_0_slide93_FieldAccess : arg1'=arg1P_2, arg2'=arg2P_2, [ arg2P_15>1 && arg2P_2<1 && arg1P_2>-1 && arg1P_15>0 ], cost: 2 19: __init -> f196_0_create_LE : arg1'=0, arg2'=arg2P_14, [ arg2P_15>1 && arg1P_15>0 && -1+x33_1>=1 ], cost: 1+x33_1 Eliminated locations (on tree-shaped paths): Start location: __init 19: __init -> f196_0_create_LE : arg1'=0, arg2'=arg2P_14, [ arg2P_15>1 && arg1P_15>0 && -1+x33_1>=1 ], cost: 1+x33_1 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 19: __init -> f196_0_create_LE : arg1'=0, arg2'=arg2P_14, [ arg2P_15>1 && arg1P_15>0 && -1+x33_1>=1 ], cost: 1+x33_1 Computing asymptotic complexity for rule 19 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),?)