WORST_CASE(INF,?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f234_0_slide95_FieldAccess : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_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_slide95_FieldAccess : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ x10_1>-1 && arg2>1 && arg2P_2<1 && arg1P_2>-1 && arg1>0 ], cost: 1 9: f1_0_main_Load -> f196_0_create_LE : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ x37_1>-1 && arg2>1 && x36_1>-1 && arg1>0 && -1+x36_1==arg1P_10 ], cost: 1 2: f234_0_slide95_FieldAccess -> f411_0_slide95_EQ : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg2>0 && arg1==arg1P_3 && arg2==arg2P_3 && arg2==arg3P_3 ], cost: 1 3: f411_0_slide95_EQ -> f411_0_slide95_EQ\' : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ x39_1>-1 && arg2>0 && x39_1-1 && x39_1x39_1 && x42_1x39_1 && arg1>=x44_1 && arg1-2*x45_1==0 && arg1==arg1P_4 && arg2==arg2P_4 && arg3==arg3P_4 ], cost: 1 5: f411_0_slide95_EQ -> f411_0_slide95_EQ\' : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg3>-1 && arg2>0 && x59_1=x62_1 && x60_1>-1 && x60_1>=x63_1 && x59_1>0 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1 7: f411_0_slide95_EQ -> f411_0_slide95_EQ\' : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg3>-1 && arg2>0 && x75_10 && arg1>=x77_1 && arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 ], cost: 1 4: f411_0_slide95_EQ\' -> f411_0_slide95_EQ : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ x52_1>-1 && arg2>0 && x52_1-1 && x52_1x52_1 && arg2P_5x52_1 && -2*x55_1+arg1==0 && arg1>=arg1P_5 && -2*x55_1+arg1>=0 && -2*x55_1+arg1<2 && -2*arg1P_5+arg1<2 && -2*arg1P_5+arg1>=0 ], cost: 1 6: f411_0_slide95_EQ\' -> f411_0_slide95_EQ : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg3>-1 && arg2>0 && arg3P_7=arg1P_7 && x70_1>-1 && arg3P_7>0 && x70_1>=arg2P_7 && arg1-2*x71_1>=0 && arg1-2*x71_1<2 && arg1-2*arg1P_7<2 && arg1-2*arg1P_7>=0 ], cost: 1 8: f411_0_slide95_EQ\' -> f411_0_slide95_EQ : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ arg3>-1 && arg2>0 && arg2P_9=arg1P_9 && arg2P_9>0 && arg1-2*x83_1>=0 && arg1-2*x83_1<2 && -2*arg1P_9+arg1<2 && -2*arg1P_9+arg1>=0 && arg2P_9==arg3P_9 ], cost: 1 10: f196_0_create_LE -> f196_0_create_LE : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ arg1>0 && -1+arg1==arg1P_11 ], cost: 1 11: __init -> f1_0_main_Load : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 11: __init -> f1_0_main_Load : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f234_0_slide95_FieldAccess : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg2>1 && arg1P_1>-1 && arg1>0 ], cost: 1 1: f1_0_main_Load -> f234_0_slide95_FieldAccess : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg2>1 && arg2P_2<1 && arg1P_2>-1 && arg1>0 ], cost: 1 9: f1_0_main_Load -> f196_0_create_LE : arg1'=-1+x36_1, arg2'=arg2P_10, arg3'=arg3P_10, [ arg2>1 && x36_1>-1 && arg1>0 ], cost: 1 2: f234_0_slide95_FieldAccess -> f411_0_slide95_EQ : arg3'=arg2, [ arg2>0 ], cost: 1 3: f411_0_slide95_EQ -> f411_0_slide95_EQ\' : [ arg1-2*x45_1==0 && 0<=-1+arg3 && 0<=-2+arg2 ], cost: 1 5: f411_0_slide95_EQ -> f411_0_slide95_EQ\' : [ -2*x61_1+arg1==1 && 1<=-1+arg3 && 0<=-1+arg2 ], cost: 1 7: f411_0_slide95_EQ -> f411_0_slide95_EQ\' : [ -2*x76_1+arg1==1 && 1<=-1+arg3 && 1<=-1+arg2 ], cost: 1 4: f411_0_slide95_EQ\' -> f411_0_slide95_EQ : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg2>0 && arg2P_5=arg1P_5 && -2*arg1P_5+arg1<2 && -2*arg1P_5+arg1>=0 && 0<=-1+arg3P_5 && 0<=-1+arg3 && 0<=-1+arg2P_5 ], cost: 1 6: f411_0_slide95_EQ\' -> f411_0_slide95_EQ : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg3P_7=arg1P_7 && arg3P_7>0 && arg1-2*arg1P_7<2 && arg1-2*arg1P_7>=0 && 0<=-1+arg2 && arg2P_7<=-1+arg2 ], cost: 1 8: f411_0_slide95_EQ\' -> f411_0_slide95_EQ : arg1'=arg1P_9, arg2'=arg3P_9, arg3'=arg3P_9, [ arg3P_9=arg1P_9 && arg3P_9>0 && -2*arg1P_9+arg1<2 && -2*arg1P_9+arg1>=0 ], cost: 1 10: f196_0_create_LE -> f196_0_create_LE : arg1'=-1+arg1, arg2'=arg2P_11, arg3'=arg3P_11, [ arg1>0 ], cost: 1 11: __init -> f1_0_main_Load : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 4. Accelerating the following rules: 10: f196_0_create_LE -> f196_0_create_LE : arg1'=-1+arg1, arg2'=arg2P_11, arg3'=arg3P_11, [ arg1>0 ], cost: 1 Accelerated rule 10 with metering function arg1, yielding the new rule 12. Removing the simple loops: 10. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f234_0_slide95_FieldAccess : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg2>1 && arg1P_1>-1 && arg1>0 ], cost: 1 1: f1_0_main_Load -> f234_0_slide95_FieldAccess : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg2>1 && arg2P_2<1 && arg1P_2>-1 && arg1>0 ], cost: 1 9: f1_0_main_Load -> f196_0_create_LE : arg1'=-1+x36_1, arg2'=arg2P_10, arg3'=arg3P_10, [ arg2>1 && x36_1>-1 && arg1>0 ], cost: 1 2: f234_0_slide95_FieldAccess -> f411_0_slide95_EQ : arg3'=arg2, [ arg2>0 ], cost: 1 3: f411_0_slide95_EQ -> f411_0_slide95_EQ\' : [ arg1-2*x45_1==0 && 0<=-1+arg3 && 0<=-2+arg2 ], cost: 1 5: f411_0_slide95_EQ -> f411_0_slide95_EQ\' : [ -2*x61_1+arg1==1 && 1<=-1+arg3 && 0<=-1+arg2 ], cost: 1 7: f411_0_slide95_EQ -> f411_0_slide95_EQ\' : [ -2*x76_1+arg1==1 && 1<=-1+arg3 && 1<=-1+arg2 ], cost: 1 4: f411_0_slide95_EQ\' -> f411_0_slide95_EQ : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg2>0 && arg2P_5=arg1P_5 && -2*arg1P_5+arg1<2 && -2*arg1P_5+arg1>=0 && 0<=-1+arg3P_5 && 0<=-1+arg3 && 0<=-1+arg2P_5 ], cost: 1 6: f411_0_slide95_EQ\' -> f411_0_slide95_EQ : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg3P_7=arg1P_7 && arg3P_7>0 && arg1-2*arg1P_7<2 && arg1-2*arg1P_7>=0 && 0<=-1+arg2 && arg2P_7<=-1+arg2 ], cost: 1 8: f411_0_slide95_EQ\' -> f411_0_slide95_EQ : arg1'=arg1P_9, arg2'=arg3P_9, arg3'=arg3P_9, [ arg3P_9=arg1P_9 && arg3P_9>0 && -2*arg1P_9+arg1<2 && -2*arg1P_9+arg1>=0 ], cost: 1 12: f196_0_create_LE -> f196_0_create_LE : arg1'=0, arg2'=arg2P_11, arg3'=arg3P_11, [ arg1>0 ], cost: arg1 11: __init -> f1_0_main_Load : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f234_0_slide95_FieldAccess : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg2>1 && arg1P_1>-1 && arg1>0 ], cost: 1 1: f1_0_main_Load -> f234_0_slide95_FieldAccess : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg2>1 && arg2P_2<1 && arg1P_2>-1 && arg1>0 ], cost: 1 9: f1_0_main_Load -> f196_0_create_LE : arg1'=-1+x36_1, arg2'=arg2P_10, arg3'=arg3P_10, [ arg2>1 && x36_1>-1 && arg1>0 ], cost: 1 13: f1_0_main_Load -> f196_0_create_LE : arg1'=0, arg2'=arg2P_11, arg3'=arg3P_11, [ arg2>1 && arg1>0 && -1+x36_1>0 ], cost: x36_1 2: f234_0_slide95_FieldAccess -> f411_0_slide95_EQ : arg3'=arg2, [ arg2>0 ], cost: 1 3: f411_0_slide95_EQ -> f411_0_slide95_EQ\' : [ arg1-2*x45_1==0 && 0<=-1+arg3 && 0<=-2+arg2 ], cost: 1 5: f411_0_slide95_EQ -> f411_0_slide95_EQ\' : [ -2*x61_1+arg1==1 && 1<=-1+arg3 && 0<=-1+arg2 ], cost: 1 7: f411_0_slide95_EQ -> f411_0_slide95_EQ\' : [ -2*x76_1+arg1==1 && 1<=-1+arg3 && 1<=-1+arg2 ], cost: 1 4: f411_0_slide95_EQ\' -> f411_0_slide95_EQ : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg2>0 && arg2P_5=arg1P_5 && -2*arg1P_5+arg1<2 && -2*arg1P_5+arg1>=0 && 0<=-1+arg3P_5 && 0<=-1+arg3 && 0<=-1+arg2P_5 ], cost: 1 6: f411_0_slide95_EQ\' -> f411_0_slide95_EQ : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg3P_7=arg1P_7 && arg3P_7>0 && arg1-2*arg1P_7<2 && arg1-2*arg1P_7>=0 && 0<=-1+arg2 && arg2P_7<=-1+arg2 ], cost: 1 8: f411_0_slide95_EQ\' -> f411_0_slide95_EQ : arg1'=arg1P_9, arg2'=arg3P_9, arg3'=arg3P_9, [ arg3P_9=arg1P_9 && arg3P_9>0 && -2*arg1P_9+arg1<2 && -2*arg1P_9+arg1>=0 ], cost: 1 11: __init -> f1_0_main_Load : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 0: f1_0_main_Load -> f234_0_slide95_FieldAccess : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg2>1 && arg1P_1>-1 && arg1>0 ], cost: 1 1: f1_0_main_Load -> f234_0_slide95_FieldAccess : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg2>1 && arg2P_2<1 && arg1P_2>-1 && arg1>0 ], cost: 1 13: f1_0_main_Load -> f196_0_create_LE : arg1'=0, arg2'=arg2P_11, arg3'=arg3P_11, [ arg2>1 && arg1>0 && -1+x36_1>0 ], cost: x36_1 2: f234_0_slide95_FieldAccess -> f411_0_slide95_EQ : arg3'=arg2, [ arg2>0 ], cost: 1 3: f411_0_slide95_EQ -> f411_0_slide95_EQ\' : [ arg1-2*x45_1==0 && 0<=-1+arg3 && 0<=-2+arg2 ], cost: 1 5: f411_0_slide95_EQ -> f411_0_slide95_EQ\' : [ -2*x61_1+arg1==1 && 1<=-1+arg3 && 0<=-1+arg2 ], cost: 1 7: f411_0_slide95_EQ -> f411_0_slide95_EQ\' : [ -2*x76_1+arg1==1 && 1<=-1+arg3 && 1<=-1+arg2 ], cost: 1 4: f411_0_slide95_EQ\' -> f411_0_slide95_EQ : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg2>0 && arg2P_5=arg1P_5 && -2*arg1P_5+arg1<2 && -2*arg1P_5+arg1>=0 && 0<=-1+arg3P_5 && 0<=-1+arg3 && 0<=-1+arg2P_5 ], cost: 1 6: f411_0_slide95_EQ\' -> f411_0_slide95_EQ : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg3P_7=arg1P_7 && arg3P_7>0 && arg1-2*arg1P_7<2 && arg1-2*arg1P_7>=0 && 0<=-1+arg2 && arg2P_7<=-1+arg2 ], cost: 1 8: f411_0_slide95_EQ\' -> f411_0_slide95_EQ : arg1'=arg1P_9, arg2'=arg3P_9, arg3'=arg3P_9, [ arg3P_9=arg1P_9 && arg3P_9>0 && -2*arg1P_9+arg1<2 && -2*arg1P_9+arg1>=0 ], cost: 1 11: __init -> f1_0_main_Load : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: __init 2: f234_0_slide95_FieldAccess -> f411_0_slide95_EQ : arg3'=arg2, [ arg2>0 ], cost: 1 17: f411_0_slide95_EQ -> f411_0_slide95_EQ : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg1-2*x45_1==0 && 0<=-1+arg3 && 0<=-2+arg2 && arg2P_5=arg1P_5 && -2*arg1P_5+arg1<2 && -2*arg1P_5+arg1>=0 && 0<=-1+arg3P_5 && 0<=-1+arg2P_5 ], cost: 2 18: f411_0_slide95_EQ -> f411_0_slide95_EQ : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ -2*x61_1+arg1==1 && 1<=-1+arg3 && 0<=-1+arg2 && arg3P_7=arg1P_7 && arg3P_7>0 && arg1-2*arg1P_7<2 && arg1-2*arg1P_7>=0 && arg2P_7<=-1+arg2 ], cost: 2 19: f411_0_slide95_EQ -> f411_0_slide95_EQ : arg1'=arg1P_9, arg2'=arg3P_9, arg3'=arg3P_9, [ -2*x61_1+arg1==1 && 1<=-1+arg3 && 0<=-1+arg2 && arg3P_9=arg1P_9 && arg3P_9>0 && -2*arg1P_9+arg1<2 && -2*arg1P_9+arg1>=0 ], cost: 2 20: f411_0_slide95_EQ -> f411_0_slide95_EQ : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ -2*x76_1+arg1==1 && 1<=-1+arg3 && 1<=-1+arg2 && arg3P_7=arg1P_7 && arg3P_7>0 && arg1-2*arg1P_7<2 && arg1-2*arg1P_7>=0 && arg2P_7<=-1+arg2 ], cost: 2 21: f411_0_slide95_EQ -> f411_0_slide95_EQ : arg1'=arg1P_9, arg2'=arg3P_9, arg3'=arg3P_9, [ -2*x76_1+arg1==1 && 1<=-1+arg3 && 1<=-1+arg2 && arg3P_9=arg1P_9 && arg3P_9>0 && -2*arg1P_9+arg1<2 && -2*arg1P_9+arg1>=0 ], cost: 2 14: __init -> f234_0_slide95_FieldAccess : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg2P_12>1 && arg1P_1>-1 && arg1P_12>0 ], cost: 2 15: __init -> f234_0_slide95_FieldAccess : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg2P_12>1 && arg2P_2<1 && arg1P_2>-1 && arg1P_12>0 ], cost: 2 16: __init -> f196_0_create_LE : arg1'=0, arg2'=arg2P_11, arg3'=arg3P_11, [ arg2P_12>1 && arg1P_12>0 && -1+x36_1>0 ], cost: 1+x36_1 Accelerating simple loops of location 2. Accelerating the following rules: 17: f411_0_slide95_EQ -> f411_0_slide95_EQ : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg1-2*x45_1==0 && 0<=-1+arg3 && 0<=-2+arg2 && arg2P_5=arg1P_5 && -2*arg1P_5+arg1<2 && -2*arg1P_5+arg1>=0 && 0<=-1+arg3P_5 && 0<=-1+arg2P_5 ], cost: 2 18: f411_0_slide95_EQ -> f411_0_slide95_EQ : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ -2*x61_1+arg1==1 && 1<=-1+arg3 && 0<=-1+arg2 && arg3P_7=arg1P_7 && arg3P_7>0 && arg1-2*arg1P_7<2 && arg1-2*arg1P_7>=0 && arg2P_7<=-1+arg2 ], cost: 2 19: f411_0_slide95_EQ -> f411_0_slide95_EQ : arg1'=arg1P_9, arg2'=arg3P_9, arg3'=arg3P_9, [ -2*x61_1+arg1==1 && 1<=-1+arg3 && 0<=-1+arg2 && arg3P_9=arg1P_9 && arg3P_9>0 && -2*arg1P_9+arg1<2 && -2*arg1P_9+arg1>=0 ], cost: 2 20: f411_0_slide95_EQ -> f411_0_slide95_EQ : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ -2*x76_1+arg1==1 && 1<=-1+arg3 && 1<=-1+arg2 && arg3P_7=arg1P_7 && arg3P_7>0 && arg1-2*arg1P_7<2 && arg1-2*arg1P_7>=0 && arg2P_7<=-1+arg2 ], cost: 2 21: f411_0_slide95_EQ -> f411_0_slide95_EQ : arg1'=arg1P_9, arg2'=arg3P_9, arg3'=arg3P_9, [ -2*x76_1+arg1==1 && 1<=-1+arg3 && 1<=-1+arg2 && arg3P_9=arg1P_9 && arg3P_9>0 && -2*arg1P_9+arg1<2 && -2*arg1P_9+arg1>=0 ], cost: 2 During metering: Instantiating temporary variables by {arg2P_5==-1+arg2,arg1P_5==arg1} Accelerated rule 17 with metering function -1+arg2, yielding the new rule 22. Found no metering function for rule 18. During metering: Instantiating temporary variables by {arg1P_9==arg1,arg3P_9==-1+arg2} Accelerated rule 19 with metering function -1+arg2, yielding the new rule 23. Found no metering function for rule 20. During metering: Instantiating temporary variables by {arg1P_9==arg1,arg3P_9==-1+arg2} Accelerated rule 21 with metering function -1+arg2, yielding the new rule 24. Nested simple loops 18 (outer loop) and 22 (inner loop) with metering function -1-x61_1+arg1-x71_1, resulting in the new rules: 25. Nested simple loops 19 (outer loop) and 22 (inner loop) with metering function -1-x61_1+arg1-x83_1, resulting in the new rules: 26. Nested simple loops 20 (outer loop) and 22 (inner loop) with metering function -1-x76_1+arg1-x71_1, resulting in the new rules: 27. Nested simple loops 21 (outer loop) and 22 (inner loop) with metering function -1-x76_1+arg1-x83_1, resulting in the new rules: 28. Removing the simple loops: 17 18 19 20 21. Accelerated all simple loops using metering functions (where possible): Start location: __init 2: f234_0_slide95_FieldAccess -> f411_0_slide95_EQ : arg3'=arg2, [ arg2>0 ], cost: 1 22: f411_0_slide95_EQ -> f411_0_slide95_EQ : arg1'=arg1, arg2'=1, arg3'=arg3P_5, [ arg1-2*x45_1==0 && 0<=-1+arg3 && 0<=-2+arg2 && -2*x55_1+arg1==0 && -arg1<2 && -arg1>=0 && 0<=-1+arg3P_5 ], cost: -2+2*arg2 23: f411_0_slide95_EQ -> f411_0_slide95_EQ : arg1'=arg1, arg2'=1, arg3'=1, [ -2*x61_1+arg1==1 && 1<=-1+arg3 && -1+arg20 && -arg1<2 && -arg1>=0 ], cost: -2+2*arg2 24: f411_0_slide95_EQ -> f411_0_slide95_EQ : arg1'=arg1, arg2'=1, arg3'=1, [ -2*x76_1+arg1==1 && 1<=-1+arg3 && 1<=-1+arg2 && -1+arg2=0 ], cost: -2+2*arg2 25: f411_0_slide95_EQ -> f411_0_slide95_EQ : arg1'=2*x45_1, arg2'=1, arg3'=arg3P_5, [ -2*x61_1+arg1==1 && 1<=-1+arg3 && 0<=-1+arg2 && arg1-2*x71_1==1 && arg1>=2*x45_1 && arg1-4*x45_1<2 && arg1-4*x45_1>=0 && arg2P_7<=-1+arg2 && 0<=-2+arg2P_7 && -2*x45_1<2 && -2*x45_1>=0 && 0<=-1+arg3P_5 && -1-x61_1+arg1-x71_1>=1 ], cost: -2*arg2P_7*(1+x61_1-arg1+x71_1) 26: f411_0_slide95_EQ -> f411_0_slide95_EQ : arg1'=2*x45_1, arg2'=1, arg3'=arg3P_5, [ -2*x61_1+arg1==1 && 1<=-1+arg3 && 0<=-1+arg2 && arg3P_9=2*x45_1 && arg1-4*x45_1<2 && arg1-4*x45_1>=0 && 0<=-2+arg3P_9 && -2*x45_1<2 && -2*x45_1>=0 && 0<=-1+arg3P_5 && -1-x61_1+arg1-x83_1>=1 ], cost: -2*(1+x61_1-arg1+x83_1)*arg3P_9 27: f411_0_slide95_EQ -> f411_0_slide95_EQ : arg1'=2*x45_1, arg2'=1, arg3'=arg3P_5, [ -2*x76_1+arg1==1 && 1<=-1+arg3 && 1<=-1+arg2 && arg1-2*x71_1==1 && arg1>=2*x45_1 && arg1-4*x45_1<2 && arg1-4*x45_1>=0 && arg2P_7<=-1+arg2 && 0<=-2+arg2P_7 && -2*x45_1<2 && -2*x45_1>=0 && 0<=-1+arg3P_5 && -1-x76_1+arg1-x71_1>=1 ], cost: -2*arg2P_7*(1+x76_1-arg1+x71_1) 28: f411_0_slide95_EQ -> f411_0_slide95_EQ : arg1'=2*x45_1, arg2'=1, arg3'=arg3P_5, [ -2*x76_1+arg1==1 && 1<=-1+arg3 && 1<=-1+arg2 && arg3P_9=2*x45_1 && arg1-4*x45_1<2 && arg1-4*x45_1>=0 && 0<=-2+arg3P_9 && -2*x45_1<2 && -2*x45_1>=0 && 0<=-1+arg3P_5 && -1-x76_1+arg1-x83_1>=1 ], cost: -2*(1+x76_1-arg1+x83_1)*arg3P_9 14: __init -> f234_0_slide95_FieldAccess : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg2P_12>1 && arg1P_1>-1 && arg1P_12>0 ], cost: 2 15: __init -> f234_0_slide95_FieldAccess : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg2P_12>1 && arg2P_2<1 && arg1P_2>-1 && arg1P_12>0 ], cost: 2 16: __init -> f196_0_create_LE : arg1'=0, arg2'=arg2P_11, arg3'=arg3P_11, [ arg2P_12>1 && arg1P_12>0 && -1+x36_1>0 ], cost: 1+x36_1 Chained accelerated rules (with incoming rules): Start location: __init 2: f234_0_slide95_FieldAccess -> f411_0_slide95_EQ : arg3'=arg2, [ arg2>0 ], cost: 1 29: f234_0_slide95_FieldAccess -> f411_0_slide95_EQ : arg2'=1, arg3'=arg3P_5, [ arg1-2*x45_1==0 && 0<=-2+arg2 && -2*x55_1+arg1==0 && -arg1<2 && -arg1>=0 && 0<=-1+arg3P_5 ], cost: -1+2*arg2 30: f234_0_slide95_FieldAccess -> f411_0_slide95_EQ : arg2'=1, arg3'=1, [ -2*x61_1+arg1==1 && 1<=-1+arg2 && arg1-2*x83_1==1 && -arg1<2 && -arg1>=0 ], cost: -1+2*arg2 31: f234_0_slide95_FieldAccess -> f411_0_slide95_EQ : arg2'=1, arg3'=1, [ -2*x76_1+arg1==1 && 1<=-1+arg2 && arg1-2*x83_1==1 && -arg1<2 && -arg1>=0 ], cost: -1+2*arg2 14: __init -> f234_0_slide95_FieldAccess : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg2P_12>1 && arg1P_1>-1 && arg1P_12>0 ], cost: 2 15: __init -> f234_0_slide95_FieldAccess : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg2P_12>1 && arg2P_2<1 && arg1P_2>-1 && arg1P_12>0 ], cost: 2 16: __init -> f196_0_create_LE : arg1'=0, arg2'=arg2P_11, arg3'=arg3P_11, [ arg2P_12>1 && arg1P_12>0 && -1+x36_1>0 ], cost: 1+x36_1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 29: f234_0_slide95_FieldAccess -> f411_0_slide95_EQ : arg2'=1, arg3'=arg3P_5, [ arg1-2*x45_1==0 && 0<=-2+arg2 && -2*x55_1+arg1==0 && -arg1<2 && -arg1>=0 && 0<=-1+arg3P_5 ], cost: -1+2*arg2 30: f234_0_slide95_FieldAccess -> f411_0_slide95_EQ : arg2'=1, arg3'=1, [ -2*x61_1+arg1==1 && 1<=-1+arg2 && arg1-2*x83_1==1 && -arg1<2 && -arg1>=0 ], cost: -1+2*arg2 31: f234_0_slide95_FieldAccess -> f411_0_slide95_EQ : arg2'=1, arg3'=1, [ -2*x76_1+arg1==1 && 1<=-1+arg2 && arg1-2*x83_1==1 && -arg1<2 && -arg1>=0 ], cost: -1+2*arg2 14: __init -> f234_0_slide95_FieldAccess : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg2P_12>1 && arg1P_1>-1 && arg1P_12>0 ], cost: 2 15: __init -> f234_0_slide95_FieldAccess : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg2P_12>1 && arg2P_2<1 && arg1P_2>-1 && arg1P_12>0 ], cost: 2 16: __init -> f196_0_create_LE : arg1'=0, arg2'=arg2P_11, arg3'=arg3P_11, [ arg2P_12>1 && arg1P_12>0 && -1+x36_1>0 ], cost: 1+x36_1 Eliminated locations (on tree-shaped paths): Start location: __init 16: __init -> f196_0_create_LE : arg1'=0, arg2'=arg2P_11, arg3'=arg3P_11, [ arg2P_12>1 && arg1P_12>0 && -1+x36_1>0 ], cost: 1+x36_1 32: __init -> f411_0_slide95_EQ : arg1'=arg1P_1, arg2'=1, arg3'=arg3P_5, [ arg2P_12>1 && arg1P_1>-1 && arg1P_12>0 && arg1P_1-2*x45_1==0 && 0<=-2+arg2P_1 && -2*x55_1+arg1P_1==0 && -arg1P_1>=0 && 0<=-1+arg3P_5 ], cost: 1+2*arg2P_1 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 16: __init -> f196_0_create_LE : arg1'=0, arg2'=arg2P_11, arg3'=arg3P_11, [ arg2P_12>1 && arg1P_12>0 && -1+x36_1>0 ], cost: 1+x36_1 32: __init -> f411_0_slide95_EQ : arg1'=arg1P_1, arg2'=1, arg3'=arg3P_5, [ arg2P_12>1 && arg1P_1>-1 && arg1P_12>0 && arg1P_1-2*x45_1==0 && 0<=-2+arg2P_1 && -2*x55_1+arg1P_1==0 && -arg1P_1>=0 && 0<=-1+arg3P_5 ], cost: 1+2*arg2P_1 Computing asymptotic complexity for rule 16 Solved the limit problem by the following transformations: Created initial limit problem: -1+arg2P_12 (+/+!), 1+x36_1 (+), arg1P_12 (+/+!), -1+x36_1 (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {x36_1==n,arg1P_12==n,arg2P_12==n} resulting limit problem: [solved] Solution: x36_1 / n arg1P_12 / n arg2P_12 / 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: 1+x36_1 Rule guard: [ arg2P_12>1 && arg1P_12>0 && -1+x36_1>0 ] WORST_CASE(INF,?)