WORST_CASE(Omega(1),?) ### 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 Failed to prove monotonicity of the guard of rule 1. [accelerate] Nesting with 1 inner and 1 outer candidates 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 backward acceleration, yielding the new rule 10. Accelerated rule 8 with backward acceleration, yielding the new rule 11. [accelerate] Nesting with 2 inner and 2 outer candidates 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 Failed to prove monotonicity of the guard of rule 6. [accelerate] Nesting with 1 inner and 1 outer candidates 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 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 10: f510_0_main_GE -> f510_0_main_GE : arg2'=arg2P_8, arg3'=arg4, [ arg4>arg1 && arg2P_8<=arg2 && arg2>0 && arg2P_8>0 && -arg3+arg4>=1 ], cost: -arg3+arg4 11: f510_0_main_GE -> f510_0_main_GE : arg2'=arg2P_9, arg3'=arg4, [ arg4>arg1 && arg2P_9<=arg2 && arg2>0 && arg2P_9>0 && -arg3+arg4>=1 ], 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 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 12: 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 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 13: f494_0_main_GE -> f510_0_main_GE : arg1'=arg2, arg2'=arg2P_8, arg3'=arg4, [ arg2>-1 && arg3>arg2 && arg1>0 && arg2P_8>0 && -1-arg2+arg4>=1 && arg2P_8<=arg1 ], cost: -arg2+arg4 14: f494_0_main_GE -> f510_0_main_GE : arg1'=arg2, arg2'=arg2P_9, arg3'=arg4, [ arg2>-1 && arg3>arg2 && arg1>0 && arg2P_9>0 && -1-arg2+arg4>=1 && arg2P_9<=arg1 ], cost: -arg2+arg4 15: 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 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 12: 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 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 13: f494_0_main_GE -> f510_0_main_GE : arg1'=arg2, arg2'=arg2P_8, arg3'=arg4, [ arg2>-1 && arg3>arg2 && arg1>0 && arg2P_8>0 && -1-arg2+arg4>=1 && arg2P_8<=arg1 ], cost: -arg2+arg4 14: f494_0_main_GE -> f510_0_main_GE : arg1'=arg2, arg2'=arg2P_9, arg3'=arg4, [ arg2>-1 && arg3>arg2 && arg1>0 && arg2P_9>0 && -1-arg2+arg4>=1 && arg2P_9<=arg1 ], cost: -arg2+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 18: 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 19: f494_0_main_GE -> f494_0_main_GE : arg1'=arg1P_5, arg2'=1+arg2, arg3'=-1+arg4, [ arg2>-1 && arg3>arg2 && arg1>0 && arg2P_8>0 && -1-arg2+arg4>=1 && arg2P_8<=arg1 && arg4>-1 && arg1P_5<=arg2P_8 && arg1P_5>0 ], cost: 1-arg2+arg4 20: f494_0_main_GE -> f494_0_main_GE : arg1'=arg1P_5, arg2'=1+arg2, arg3'=-1+arg4, [ arg2>-1 && arg3>arg2 && arg1>0 && arg2P_9>0 && -1-arg2+arg4>=1 && arg2P_9<=arg1 && arg4>-1 && arg1P_5<=arg2P_9 && arg1P_5>0 ], cost: 1-arg2+arg4 16: __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 17: __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 Accelerating simple loops of location 2. [accelerate] Removed some duplicate simple loops Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 18: 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 20: f494_0_main_GE -> f494_0_main_GE : arg1'=arg1P_5, arg2'=1+arg2, arg3'=-1+arg4, [ arg2>-1 && arg3>arg2 && arg1>0 && -1-arg2+arg4>=1 && arg4>-1 && arg1P_5>0 && arg1P_5<=arg1 ], cost: 1-arg2+arg4 Failed to prove monotonicity of the guard of rule 18. Failed to prove monotonicity of the guard of rule 20. [accelerate] Nesting with 2 inner and 2 outer candidates 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 18: 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 20: f494_0_main_GE -> f494_0_main_GE : arg1'=arg1P_5, arg2'=1+arg2, arg3'=-1+arg4, [ arg2>-1 && arg3>arg2 && arg1>0 && -1-arg2+arg4>=1 && arg4>-1 && arg1P_5>0 && arg1P_5<=arg1 ], cost: 1-arg2+arg4 16: __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 17: __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 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 21: 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 16: __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 17: __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 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 21: 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 16: __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 17: __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 Eliminated locations (on tree-shaped paths): Start location: __init 22: __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 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 22: __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 Computing asymptotic complexity for rule 22 Simplified the guard: 22: __init -> f494_0_main_GE : arg1'=arg1P_5, arg2'=1, arg3'=-1+arg2P_10, arg4'=arg2P_10, [ -1+arg2P_10>0 && arg1P_2<=arg1P_10 && -1+arg2P_10<=1 && arg1P_5>0 && arg1P_5<=arg1P_2 ], cost: 5+arg2P_10 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),?)