WORST_CASE(INF,?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f254_0_main_GE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ arg1P_1<=arg1 && arg2>-1 && arg1>0 && arg1P_1>0 && 0==arg2P_1 && -1+arg2==arg3P_1 && arg2==arg4P_1 ], cost: 1 1: f254_0_main_GE -> f254_0_main_GE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg3>arg2 && arg2-1 && arg1P_2<=arg1 && arg1>0 && arg1P_2>0 && 1+arg2==arg2P_2 && -1+arg4==arg3P_2 && arg4==arg4P_2 ], cost: 1 2: f254_0_main_GE -> f494_0_main_GE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ arg3<=arg2 && arg4>-1 && arg1>=arg1P_3 && arg1>0 && arg1P_3>0 && 0==arg2P_3 && -1+arg4==arg3P_3 && arg4==arg4P_3 ], cost: 1 3: f494_0_main_GE -> f510_0_main_GE : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg2>-1 && arg3>arg2 && arg2P_4<=arg1 && arg1>0 && arg2P_4>0 && arg2==arg1P_4 && 1+arg2==arg3P_4 && arg4==arg4P_4 ], cost: 1 5: f494_0_main_GE -> f609_0_main_GE : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, [ arg3<=arg2 && arg4>-1 && arg1P_6<=arg1 && arg1>0 && arg1P_6>0 && 0==arg2P_6 && -1+arg4==arg3P_6 && arg4==arg4P_6 ], cost: 1 4: f510_0_main_GE -> f494_0_main_GE : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg4>-1 && arg4<=arg3 && arg1P_5<=arg2 && arg2>0 && arg1P_5>0 && 1+arg1==arg2P_5 && -1+arg4==arg3P_5 && arg4==arg4P_5 ], cost: 1 7: f510_0_main_GE -> f510_0_main_GE : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, [ arg4>arg3 && arg4>arg1 && x39_1>=x38_1 && arg2P_8<=arg2 && arg2>0 && arg2P_8>0 && arg1==arg1P_8 && 1+arg3==arg3P_8 && arg4==arg4P_8 ], cost: 1 8: f510_0_main_GE -> f510_0_main_GE : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, [ arg4>arg3 && arg4>arg1 && x46_10 && arg2P_9>0 && arg1==arg1P_9 && 1+arg3==arg3P_9 && arg4==arg4P_9 ], cost: 1 6: f609_0_main_GE -> f609_0_main_GE : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [ arg4>-1 && arg3>arg2 && arg1P_7<=arg1 && arg1>0 && arg1P_7>0 && 1+arg2==arg2P_7 && -1+arg4==arg3P_7 && arg4==arg4P_7 ], cost: 1 9: __init -> f1_0_main_Load : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 9: __init -> f1_0_main_Load : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f254_0_main_GE : arg1'=arg1P_1, arg2'=0, arg3'=-1+arg2, arg4'=arg2, [ arg1P_1<=arg1 && arg2>-1 && arg1>0 && arg1P_1>0 ], cost: 1 1: f254_0_main_GE -> f254_0_main_GE : arg1'=arg1P_2, arg2'=1+arg2, arg3'=-1+arg4, [ arg3>arg2 && arg2-1 && arg1P_2<=arg1 && arg1>0 && arg1P_2>0 ], cost: 1 2: f254_0_main_GE -> f494_0_main_GE : arg1'=arg1P_3, arg2'=0, arg3'=-1+arg4, [ arg3<=arg2 && arg4>-1 && arg1>=arg1P_3 && arg1>0 && arg1P_3>0 ], cost: 1 3: f494_0_main_GE -> f510_0_main_GE : arg1'=arg2, arg2'=arg2P_4, arg3'=1+arg2, [ arg2>-1 && arg3>arg2 && arg2P_4<=arg1 && arg1>0 && arg2P_4>0 ], cost: 1 5: f494_0_main_GE -> f609_0_main_GE : arg1'=arg1P_6, arg2'=0, arg3'=-1+arg4, [ arg3<=arg2 && arg4>-1 && arg1P_6<=arg1 && arg1>0 && arg1P_6>0 ], cost: 1 4: f510_0_main_GE -> f494_0_main_GE : arg1'=arg1P_5, arg2'=1+arg1, arg3'=-1+arg4, [ arg4>-1 && arg4<=arg3 && arg1P_5<=arg2 && arg2>0 && arg1P_5>0 ], cost: 1 7: f510_0_main_GE -> f510_0_main_GE : arg2'=arg2P_8, arg3'=1+arg3, [ arg4>arg3 && arg4>arg1 && arg2P_8<=arg2 && arg2>0 && arg2P_8>0 ], cost: 1 8: f510_0_main_GE -> f510_0_main_GE : arg2'=arg2P_9, arg3'=1+arg3, [ arg4>arg3 && arg4>arg1 && arg2P_9<=arg2 && arg2>0 && arg2P_9>0 ], cost: 1 6: f609_0_main_GE -> f609_0_main_GE : arg1'=arg1P_7, arg2'=1+arg2, arg3'=-1+arg4, [ arg4>-1 && arg3>arg2 && arg1P_7<=arg1 && arg1>0 && arg1P_7>0 ], cost: 1 9: __init -> f1_0_main_Load : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 1: f254_0_main_GE -> f254_0_main_GE : arg1'=arg1P_2, arg2'=1+arg2, arg3'=-1+arg4, [ arg3>arg2 && arg2-1 && arg1P_2<=arg1 && arg1>0 && arg1P_2>0 ], cost: 1 Accelerated rule 1 with metering function -2+arg4-arg2 (after strengthening guard), yielding the new rule 10. Removing the simple loops:. Accelerating simple loops of location 3. Accelerating the following rules: 7: f510_0_main_GE -> f510_0_main_GE : arg2'=arg2P_8, arg3'=1+arg3, [ arg4>arg3 && arg4>arg1 && arg2P_8<=arg2 && arg2>0 && arg2P_8>0 ], cost: 1 8: f510_0_main_GE -> f510_0_main_GE : arg2'=arg2P_9, arg3'=1+arg3, [ arg4>arg3 && arg4>arg1 && arg2P_9<=arg2 && arg2>0 && arg2P_9>0 ], cost: 1 Accelerated rule 7 with metering function -arg3+arg4, yielding the new rule 11. Accelerated rule 8 with metering function -arg3+arg4, yielding the new rule 12. Removing the simple loops: 7 8. Accelerating simple loops of location 4. Accelerating the following rules: 6: f609_0_main_GE -> f609_0_main_GE : arg1'=arg1P_7, arg2'=1+arg2, arg3'=-1+arg4, [ arg4>-1 && arg3>arg2 && arg1P_7<=arg1 && arg1>0 && arg1P_7>0 ], cost: 1 Accelerated rule 6 with metering function -2+arg4-arg2 (after strengthening guard), yielding the new rule 13. Removing the simple loops:. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f254_0_main_GE : arg1'=arg1P_1, arg2'=0, arg3'=-1+arg2, arg4'=arg2, [ arg1P_1<=arg1 && arg2>-1 && arg1>0 && arg1P_1>0 ], cost: 1 1: f254_0_main_GE -> f254_0_main_GE : arg1'=arg1P_2, arg2'=1+arg2, arg3'=-1+arg4, [ arg3>arg2 && arg2-1 && arg1P_2<=arg1 && arg1>0 && arg1P_2>0 ], cost: 1 2: f254_0_main_GE -> f494_0_main_GE : arg1'=arg1P_3, arg2'=0, arg3'=-1+arg4, [ arg3<=arg2 && arg4>-1 && arg1>=arg1P_3 && arg1>0 && arg1P_3>0 ], cost: 1 10: f254_0_main_GE -> f254_0_main_GE : arg1'=arg1P_2, arg2'=-2+arg4, arg3'=-1+arg4, [ arg3>arg2 && arg4>-1 && arg1P_2<=arg1 && arg1>0 && arg1P_2>0 && -1+arg4>1+arg2 ], cost: -2+arg4-arg2 3: f494_0_main_GE -> f510_0_main_GE : arg1'=arg2, arg2'=arg2P_4, arg3'=1+arg2, [ arg2>-1 && arg3>arg2 && arg2P_4<=arg1 && arg1>0 && arg2P_4>0 ], cost: 1 5: f494_0_main_GE -> f609_0_main_GE : arg1'=arg1P_6, arg2'=0, arg3'=-1+arg4, [ arg3<=arg2 && arg4>-1 && arg1P_6<=arg1 && arg1>0 && arg1P_6>0 ], cost: 1 4: f510_0_main_GE -> f494_0_main_GE : arg1'=arg1P_5, arg2'=1+arg1, arg3'=-1+arg4, [ arg4>-1 && arg4<=arg3 && arg1P_5<=arg2 && arg2>0 && arg1P_5>0 ], cost: 1 11: f510_0_main_GE -> f510_0_main_GE : arg2'=arg2P_8, arg3'=arg4, [ arg4>arg3 && arg4>arg1 && arg2P_8<=arg2 && arg2>0 && arg2P_8>0 ], cost: -arg3+arg4 12: f510_0_main_GE -> f510_0_main_GE : arg2'=arg2P_9, arg3'=arg4, [ arg4>arg3 && arg4>arg1 && arg2P_9<=arg2 && arg2>0 && arg2P_9>0 ], cost: -arg3+arg4 6: f609_0_main_GE -> f609_0_main_GE : arg1'=arg1P_7, arg2'=1+arg2, arg3'=-1+arg4, [ arg4>-1 && arg3>arg2 && arg1P_7<=arg1 && arg1>0 && arg1P_7>0 ], cost: 1 13: f609_0_main_GE -> f609_0_main_GE : arg1'=arg1P_7, arg2'=-2+arg4, arg3'=-1+arg4, [ arg4>-1 && arg3>arg2 && arg1P_7<=arg1 && arg1>0 && arg1P_7>0 && -1+arg4>1+arg2 ], cost: -2+arg4-arg2 9: __init -> f1_0_main_Load : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f254_0_main_GE : arg1'=arg1P_1, arg2'=0, arg3'=-1+arg2, arg4'=arg2, [ arg1P_1<=arg1 && arg2>-1 && arg1>0 && arg1P_1>0 ], cost: 1 14: f1_0_main_Load -> f254_0_main_GE : arg1'=arg1P_2, arg2'=1, arg3'=-1+arg2, arg4'=arg2, [ arg1>0 && -1+arg2>0 && arg1P_2>0 && arg1P_2<=arg1 ], cost: 2 15: f1_0_main_Load -> f254_0_main_GE : arg1'=arg1P_2, arg2'=-2+arg2, arg3'=-1+arg2, arg4'=arg2, [ arg1>0 && arg1P_2>0 && -1+arg2>1 && arg1P_2<=arg1 ], cost: -1+arg2 2: f254_0_main_GE -> f494_0_main_GE : arg1'=arg1P_3, arg2'=0, arg3'=-1+arg4, [ arg3<=arg2 && arg4>-1 && arg1>=arg1P_3 && arg1>0 && arg1P_3>0 ], cost: 1 3: f494_0_main_GE -> f510_0_main_GE : arg1'=arg2, arg2'=arg2P_4, arg3'=1+arg2, [ arg2>-1 && arg3>arg2 && arg2P_4<=arg1 && arg1>0 && arg2P_4>0 ], cost: 1 5: f494_0_main_GE -> f609_0_main_GE : arg1'=arg1P_6, arg2'=0, arg3'=-1+arg4, [ arg3<=arg2 && arg4>-1 && arg1P_6<=arg1 && arg1>0 && arg1P_6>0 ], cost: 1 16: f494_0_main_GE -> f510_0_main_GE : arg1'=arg2, arg2'=arg2P_8, arg3'=arg4, [ arg2>-1 && arg3>arg2 && arg1>0 && arg4>1+arg2 && arg2P_8>0 && arg2P_8<=arg1 ], cost: arg4-arg2 17: f494_0_main_GE -> f510_0_main_GE : arg1'=arg2, arg2'=arg2P_9, arg3'=arg4, [ arg2>-1 && arg3>arg2 && arg1>0 && arg4>1+arg2 && arg2P_9>0 && arg2P_9<=arg1 ], cost: arg4-arg2 18: f494_0_main_GE -> f609_0_main_GE : arg1'=arg1P_7, arg2'=1, arg3'=-1+arg4, [ arg3<=arg2 && arg1>0 && -1+arg4>0 && arg1P_7>0 && arg1P_7<=arg1 ], cost: 2 19: f494_0_main_GE -> f609_0_main_GE : arg1'=arg1P_7, arg2'=-2+arg4, arg3'=-1+arg4, [ arg3<=arg2 && arg1>0 && arg1P_7>0 && -1+arg4>1 && arg1P_7<=arg1 ], cost: -1+arg4 4: f510_0_main_GE -> f494_0_main_GE : arg1'=arg1P_5, arg2'=1+arg1, arg3'=-1+arg4, [ arg4>-1 && arg4<=arg3 && arg1P_5<=arg2 && arg2>0 && arg1P_5>0 ], cost: 1 9: __init -> f1_0_main_Load : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 0: f1_0_main_Load -> f254_0_main_GE : arg1'=arg1P_1, arg2'=0, arg3'=-1+arg2, arg4'=arg2, [ arg1P_1<=arg1 && arg2>-1 && arg1>0 && arg1P_1>0 ], cost: 1 14: f1_0_main_Load -> f254_0_main_GE : arg1'=arg1P_2, arg2'=1, arg3'=-1+arg2, arg4'=arg2, [ arg1>0 && -1+arg2>0 && arg1P_2>0 && arg1P_2<=arg1 ], cost: 2 15: f1_0_main_Load -> f254_0_main_GE : arg1'=arg1P_2, arg2'=-2+arg2, arg3'=-1+arg2, arg4'=arg2, [ arg1>0 && arg1P_2>0 && -1+arg2>1 && arg1P_2<=arg1 ], cost: -1+arg2 2: f254_0_main_GE -> f494_0_main_GE : arg1'=arg1P_3, arg2'=0, arg3'=-1+arg4, [ arg3<=arg2 && arg4>-1 && arg1>=arg1P_3 && arg1>0 && arg1P_3>0 ], cost: 1 3: f494_0_main_GE -> f510_0_main_GE : arg1'=arg2, arg2'=arg2P_4, arg3'=1+arg2, [ arg2>-1 && arg3>arg2 && arg2P_4<=arg1 && arg1>0 && arg2P_4>0 ], cost: 1 16: f494_0_main_GE -> f510_0_main_GE : arg1'=arg2, arg2'=arg2P_8, arg3'=arg4, [ arg2>-1 && arg3>arg2 && arg1>0 && arg4>1+arg2 && arg2P_8>0 && arg2P_8<=arg1 ], cost: arg4-arg2 17: f494_0_main_GE -> f510_0_main_GE : arg1'=arg2, arg2'=arg2P_9, arg3'=arg4, [ arg2>-1 && arg3>arg2 && arg1>0 && arg4>1+arg2 && arg2P_9>0 && arg2P_9<=arg1 ], cost: arg4-arg2 19: f494_0_main_GE -> f609_0_main_GE : arg1'=arg1P_7, arg2'=-2+arg4, arg3'=-1+arg4, [ arg3<=arg2 && arg1>0 && arg1P_7>0 && -1+arg4>1 && arg1P_7<=arg1 ], cost: -1+arg4 4: f510_0_main_GE -> f494_0_main_GE : arg1'=arg1P_5, arg2'=1+arg1, arg3'=-1+arg4, [ arg4>-1 && arg4<=arg3 && arg1P_5<=arg2 && arg2>0 && arg1P_5>0 ], cost: 1 9: __init -> f1_0_main_Load : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: __init 2: f254_0_main_GE -> f494_0_main_GE : arg1'=arg1P_3, arg2'=0, arg3'=-1+arg4, [ arg3<=arg2 && arg4>-1 && arg1>=arg1P_3 && arg1>0 && arg1P_3>0 ], cost: 1 19: f494_0_main_GE -> f609_0_main_GE : arg1'=arg1P_7, arg2'=-2+arg4, arg3'=-1+arg4, [ arg3<=arg2 && arg1>0 && arg1P_7>0 && -1+arg4>1 && arg1P_7<=arg1 ], cost: -1+arg4 23: f494_0_main_GE -> f494_0_main_GE : arg1'=arg1P_5, arg2'=1+arg2, arg3'=-1+arg4, [ arg2>-1 && arg3>arg2 && arg2P_4<=arg1 && arg1>0 && arg2P_4>0 && arg4>-1 && arg4<=1+arg2 && arg1P_5<=arg2P_4 && arg1P_5>0 ], cost: 2 24: f494_0_main_GE -> f494_0_main_GE : arg1'=arg1P_5, arg2'=1+arg2, arg3'=-1+arg4, [ arg2>-1 && arg3>arg2 && arg1>0 && arg4>1+arg2 && arg2P_8>0 && arg2P_8<=arg1 && arg4>-1 && arg1P_5<=arg2P_8 && arg1P_5>0 ], cost: 1+arg4-arg2 25: f494_0_main_GE -> f494_0_main_GE : arg1'=arg1P_5, arg2'=1+arg2, arg3'=-1+arg4, [ arg2>-1 && arg3>arg2 && arg1>0 && arg4>1+arg2 && arg2P_9>0 && arg2P_9<=arg1 && arg4>-1 && arg1P_5<=arg2P_9 && arg1P_5>0 ], cost: 1+arg4-arg2 20: __init -> f254_0_main_GE : arg1'=arg1P_1, arg2'=0, arg3'=-1+arg2P_10, arg4'=arg2P_10, [ arg1P_1<=arg1P_10 && arg2P_10>-1 && arg1P_10>0 && arg1P_1>0 ], cost: 2 21: __init -> f254_0_main_GE : arg1'=arg1P_2, arg2'=1, arg3'=-1+arg2P_10, arg4'=arg2P_10, [ arg1P_10>0 && -1+arg2P_10>0 && arg1P_2>0 && arg1P_2<=arg1P_10 ], cost: 3 22: __init -> f254_0_main_GE : arg1'=arg1P_2, arg2'=-2+arg2P_10, arg3'=-1+arg2P_10, arg4'=arg2P_10, [ arg1P_10>0 && arg1P_2>0 && -1+arg2P_10>1 && arg1P_2<=arg1P_10 ], cost: arg2P_10 Accelerating simple loops of location 2. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 23: f494_0_main_GE -> f494_0_main_GE : arg1'=arg1P_5, arg2'=1+arg2, arg3'=-1+arg4, [ arg2>-1 && arg3>arg2 && arg1>0 && arg4>-1 && arg4<=1+arg2 && arg1P_5>0 && arg1P_5<=arg1 ], cost: 2 25: f494_0_main_GE -> f494_0_main_GE : arg1'=arg1P_5, arg2'=1+arg2, arg3'=-1+arg4, [ arg2>-1 && arg3>arg2 && arg1>0 && arg4>1+arg2 && arg4>-1 && arg1P_5>0 && arg1P_5<=arg1 ], cost: 1+arg4-arg2 Accelerated rule 23 with NONTERM (after strengthening guard), yielding the new rule 26. Accelerated rule 25 with metering function -2+arg4-arg2 (after strengthening guard), yielding the new rule 27. Removing the simple loops:. Accelerated all simple loops using metering functions (where possible): Start location: __init 2: f254_0_main_GE -> f494_0_main_GE : arg1'=arg1P_3, arg2'=0, arg3'=-1+arg4, [ arg3<=arg2 && arg4>-1 && arg1>=arg1P_3 && arg1>0 && arg1P_3>0 ], cost: 1 19: f494_0_main_GE -> f609_0_main_GE : arg1'=arg1P_7, arg2'=-2+arg4, arg3'=-1+arg4, [ arg3<=arg2 && arg1>0 && arg1P_7>0 && -1+arg4>1 && arg1P_7<=arg1 ], cost: -1+arg4 23: f494_0_main_GE -> f494_0_main_GE : arg1'=arg1P_5, arg2'=1+arg2, arg3'=-1+arg4, [ arg2>-1 && arg3>arg2 && arg1>0 && arg4>-1 && arg4<=1+arg2 && arg1P_5>0 && arg1P_5<=arg1 ], cost: 2 25: f494_0_main_GE -> f494_0_main_GE : arg1'=arg1P_5, arg2'=1+arg2, arg3'=-1+arg4, [ arg2>-1 && arg3>arg2 && arg1>0 && arg4>1+arg2 && arg4>-1 && arg1P_5>0 && arg1P_5<=arg1 ], cost: 1+arg4-arg2 26: f494_0_main_GE -> [9] : [ arg2>-1 && arg3>arg2 && arg1>0 && arg4>-1 && arg4<=1+arg2 && arg1P_5>0 && arg1P_5<=arg1 && -1+arg4>1+arg2 ], cost: NONTERM 27: f494_0_main_GE -> f494_0_main_GE : arg1'=arg1P_5, arg2'=-2+arg4, arg3'=-1+arg4, [ arg2>-1 && arg3>arg2 && arg1>0 && arg4>-1 && arg1P_5>0 && arg1P_5<=arg1 && -1+arg4>1+arg2 ], cost: -3+3/2*arg4-(-2+arg4-arg2)*arg2-1/2*(-2+arg4-arg2)^2+(-2+arg4-arg2)*arg4-3/2*arg2 20: __init -> f254_0_main_GE : arg1'=arg1P_1, arg2'=0, arg3'=-1+arg2P_10, arg4'=arg2P_10, [ arg1P_1<=arg1P_10 && arg2P_10>-1 && arg1P_10>0 && arg1P_1>0 ], cost: 2 21: __init -> f254_0_main_GE : arg1'=arg1P_2, arg2'=1, arg3'=-1+arg2P_10, arg4'=arg2P_10, [ arg1P_10>0 && -1+arg2P_10>0 && arg1P_2>0 && arg1P_2<=arg1P_10 ], cost: 3 22: __init -> f254_0_main_GE : arg1'=arg1P_2, arg2'=-2+arg2P_10, arg3'=-1+arg2P_10, arg4'=arg2P_10, [ arg1P_10>0 && arg1P_2>0 && -1+arg2P_10>1 && arg1P_2<=arg1P_10 ], cost: arg2P_10 Chained accelerated rules (with incoming rules): Start location: __init 2: f254_0_main_GE -> f494_0_main_GE : arg1'=arg1P_3, arg2'=0, arg3'=-1+arg4, [ arg3<=arg2 && arg4>-1 && arg1>=arg1P_3 && arg1>0 && arg1P_3>0 ], cost: 1 28: f254_0_main_GE -> f494_0_main_GE : arg1'=arg1P_5, arg2'=1, arg3'=-1+arg4, [ arg3<=arg2 && arg1>0 && -1+arg4>0 && arg1P_5>0 && arg1P_5<=arg1 ], cost: 2+arg4 29: f254_0_main_GE -> f494_0_main_GE : arg1'=arg1P_5, arg2'=-2+arg4, arg3'=-1+arg4, [ arg3<=arg2 && arg1>0 && arg1P_5>0 && -1+arg4>1 && arg1P_5<=arg1 ], cost: -2+arg4*(-2+arg4)+3/2*arg4-1/2*(-2+arg4)^2 19: f494_0_main_GE -> f609_0_main_GE : arg1'=arg1P_7, arg2'=-2+arg4, arg3'=-1+arg4, [ arg3<=arg2 && arg1>0 && arg1P_7>0 && -1+arg4>1 && arg1P_7<=arg1 ], cost: -1+arg4 20: __init -> f254_0_main_GE : arg1'=arg1P_1, arg2'=0, arg3'=-1+arg2P_10, arg4'=arg2P_10, [ arg1P_1<=arg1P_10 && arg2P_10>-1 && arg1P_10>0 && arg1P_1>0 ], cost: 2 21: __init -> f254_0_main_GE : arg1'=arg1P_2, arg2'=1, arg3'=-1+arg2P_10, arg4'=arg2P_10, [ arg1P_10>0 && -1+arg2P_10>0 && arg1P_2>0 && arg1P_2<=arg1P_10 ], cost: 3 22: __init -> f254_0_main_GE : arg1'=arg1P_2, arg2'=-2+arg2P_10, arg3'=-1+arg2P_10, arg4'=arg2P_10, [ arg1P_10>0 && arg1P_2>0 && -1+arg2P_10>1 && arg1P_2<=arg1P_10 ], cost: arg2P_10 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 2: f254_0_main_GE -> f494_0_main_GE : arg1'=arg1P_3, arg2'=0, arg3'=-1+arg4, [ arg3<=arg2 && arg4>-1 && arg1>=arg1P_3 && arg1>0 && arg1P_3>0 ], cost: 1 28: f254_0_main_GE -> f494_0_main_GE : arg1'=arg1P_5, arg2'=1, arg3'=-1+arg4, [ arg3<=arg2 && arg1>0 && -1+arg4>0 && arg1P_5>0 && arg1P_5<=arg1 ], cost: 2+arg4 29: f254_0_main_GE -> f494_0_main_GE : arg1'=arg1P_5, arg2'=-2+arg4, arg3'=-1+arg4, [ arg3<=arg2 && arg1>0 && arg1P_5>0 && -1+arg4>1 && arg1P_5<=arg1 ], cost: -2+arg4*(-2+arg4)+3/2*arg4-1/2*(-2+arg4)^2 19: f494_0_main_GE -> f609_0_main_GE : arg1'=arg1P_7, arg2'=-2+arg4, arg3'=-1+arg4, [ arg3<=arg2 && arg1>0 && arg1P_7>0 && -1+arg4>1 && arg1P_7<=arg1 ], cost: -1+arg4 20: __init -> f254_0_main_GE : arg1'=arg1P_1, arg2'=0, arg3'=-1+arg2P_10, arg4'=arg2P_10, [ arg1P_1<=arg1P_10 && arg2P_10>-1 && arg1P_10>0 && arg1P_1>0 ], cost: 2 21: __init -> f254_0_main_GE : arg1'=arg1P_2, arg2'=1, arg3'=-1+arg2P_10, arg4'=arg2P_10, [ arg1P_10>0 && -1+arg2P_10>0 && arg1P_2>0 && arg1P_2<=arg1P_10 ], cost: 3 22: __init -> f254_0_main_GE : arg1'=arg1P_2, arg2'=-2+arg2P_10, arg3'=-1+arg2P_10, arg4'=arg2P_10, [ arg1P_10>0 && arg1P_2>0 && -1+arg2P_10>1 && arg1P_2<=arg1P_10 ], cost: arg2P_10 Eliminated locations (on tree-shaped paths): Start location: __init 19: f494_0_main_GE -> f609_0_main_GE : arg1'=arg1P_7, arg2'=-2+arg4, arg3'=-1+arg4, [ arg3<=arg2 && arg1>0 && arg1P_7>0 && -1+arg4>1 && arg1P_7<=arg1 ], cost: -1+arg4 30: __init -> f494_0_main_GE : arg1'=arg1P_3, arg2'=0, arg3'=-1+arg2P_10, arg4'=arg2P_10, [ arg1P_1<=arg1P_10 && arg2P_10>-1 && arg1P_10>0 && arg1P_1>0 && -1+arg2P_10<=0 && arg1P_1>=arg1P_3 && arg1P_3>0 ], cost: 3 31: __init -> f494_0_main_GE : arg1'=arg1P_3, arg2'=0, arg3'=-1+arg2P_10, arg4'=arg2P_10, [ arg1P_10>0 && -1+arg2P_10>0 && arg1P_2>0 && arg1P_2<=arg1P_10 && -1+arg2P_10<=1 && arg1P_2>=arg1P_3 && arg1P_3>0 ], cost: 4 32: __init -> f494_0_main_GE : arg1'=arg1P_5, arg2'=1, arg3'=-1+arg2P_10, arg4'=arg2P_10, [ arg1P_10>0 && -1+arg2P_10>0 && arg1P_2>0 && arg1P_2<=arg1P_10 && -1+arg2P_10<=1 && arg1P_5>0 && arg1P_5<=arg1P_2 ], cost: 5+arg2P_10 33: __init -> [10] : [ arg1P_10>0 && arg1P_2>0 && -1+arg2P_10>1 && arg1P_2<=arg1P_10 ], cost: arg2P_10 Eliminated locations (on tree-shaped paths): Start location: __init 33: __init -> [10] : [ arg1P_10>0 && arg1P_2>0 && -1+arg2P_10>1 && arg1P_2<=arg1P_10 ], cost: arg2P_10 34: __init -> [11] : [ arg1P_10>0 && -1+arg2P_10>0 && arg1P_2>0 && arg1P_2<=arg1P_10 && -1+arg2P_10<=1 && arg1P_5>0 && arg1P_5<=arg1P_2 ], cost: 5+arg2P_10 Applied pruning (of leafs and parallel rules): Start location: __init 33: __init -> [10] : [ arg1P_10>0 && arg1P_2>0 && -1+arg2P_10>1 && arg1P_2<=arg1P_10 ], cost: arg2P_10 34: __init -> [11] : [ arg1P_10>0 && -1+arg2P_10>0 && arg1P_2>0 && arg1P_2<=arg1P_10 && -1+arg2P_10<=1 && arg1P_5>0 && arg1P_5<=arg1P_2 ], cost: 5+arg2P_10 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 33: __init -> [10] : [ arg1P_10>0 && arg1P_2>0 && -1+arg2P_10>1 && arg1P_2<=arg1P_10 ], cost: arg2P_10 34: __init -> [11] : [ arg1P_10>0 && -1+arg2P_10>0 && arg1P_2>0 && arg1P_2<=arg1P_10 && -1+arg2P_10<=1 && arg1P_5>0 && arg1P_5<=arg1P_2 ], cost: 5+arg2P_10 Computing asymptotic complexity for rule 33 Simplified the guard: 33: __init -> [10] : [ arg1P_2>0 && -1+arg2P_10>1 && arg1P_2<=arg1P_10 ], cost: arg2P_10 Solved the limit problem by the following transformations: Created initial limit problem: arg1P_2 (+/+!), -2+arg2P_10 (+/+!), arg2P_10 (+), 1-arg1P_2+arg1P_10 (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {arg1P_2==1,arg1P_10==1,arg2P_10==n} resulting limit problem: [solved] Solution: arg1P_2 / 1 arg1P_10 / 1 arg2P_10 / n Resulting cost 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: n Rule cost: arg2P_10 Rule guard: [ arg1P_2>0 && -1+arg2P_10>1 && arg1P_2<=arg1P_10 ] WORST_CASE(INF,?)