NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f1_0_main_Load\' : arg1'=arg1P_1, arg2'=arg2P_1, [ x12_1>-1 && arg2>1 && x13_1-2*x14_1==1 && x13_1>-1 && arg1>0 && arg1==arg1P_1 && arg2==arg2P_1 ], cost: 1 2: f1_0_main_Load -> f1_0_main_Load\' : arg1'=arg1P_3, arg2'=arg2P_3, [ x22_1>-1 && arg2>1 && x23_1>-1 && -2*x24_1+x23_1==0 && arg1>0 && arg1==arg1P_3 && arg2==arg2P_3 ], cost: 1 1: f1_0_main_Load\' -> f119_0_loop_LE : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1P_2>-1 && arg2>1 && x18_1-2*x19_1==1 && x18_1>-1 && arg1>0 && x18_1-2*x19_1<2 && x18_1-2*x19_1>=0 ], cost: 1 3: f1_0_main_Load\' -> f137_0_loop_GE : arg1'=arg1P_4, arg2'=arg2P_4, [ x27_1>-1 && arg2>1 && x28_1>-1 && -2*x29_1+x28_1==0 && arg1>0 && -2*x29_1+x28_1<2 && -2*x29_1+x28_1>=0 && -x27_1==arg1P_4 ], cost: 1 4: f119_0_loop_LE -> f119_0_loop_LE : arg1'=arg1P_5, arg2'=arg2P_5, [ 0==arg1 && 0==arg1P_5 ], cost: 1 5: f119_0_loop_LE -> f119_0_loop_LE : arg1'=arg1P_6, arg2'=arg2P_6, [ arg1>0 && -1+arg1==arg1P_6 ], cost: 1 6: f137_0_loop_GE -> f119_0_loop_LE : arg1'=arg1P_7, arg2'=arg2P_7, [ 0==arg1 && 0==arg1P_7 ], cost: 1 7: f137_0_loop_GE -> f137_0_loop_GE : arg1'=arg1P_8, arg2'=arg2P_8, [ arg1<0 && 1+arg1==arg1P_8 ], cost: 1 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f1_0_main_Load\' : [ arg2>1 && 1+2*x14_1>-1 && arg1>0 ], cost: 1 2: f1_0_main_Load -> f1_0_main_Load\' : [ arg2>1 && 2*x24_1>-1 && arg1>0 ], cost: 1 1: f1_0_main_Load\' -> f119_0_loop_LE : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1P_2>-1 && arg2>1 && 1+2*x19_1>-1 && arg1>0 ], cost: 1 3: f1_0_main_Load\' -> f137_0_loop_GE : arg1'=-x27_1, arg2'=arg2P_4, [ x27_1>-1 && arg2>1 && 2*x29_1>-1 && arg1>0 ], cost: 1 4: f119_0_loop_LE -> f119_0_loop_LE : arg1'=0, arg2'=arg2P_5, [ 0==arg1 ], cost: 1 5: f119_0_loop_LE -> f119_0_loop_LE : arg1'=-1+arg1, arg2'=arg2P_6, [ arg1>0 ], cost: 1 6: f137_0_loop_GE -> f119_0_loop_LE : arg1'=0, arg2'=arg2P_7, [ 0==arg1 ], cost: 1 7: f137_0_loop_GE -> f137_0_loop_GE : arg1'=1+arg1, arg2'=arg2P_8, [ arg1<0 ], cost: 1 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 2. Accelerating the following rules: 4: f119_0_loop_LE -> f119_0_loop_LE : arg1'=0, arg2'=arg2P_5, [ 0==arg1 ], cost: 1 5: f119_0_loop_LE -> f119_0_loop_LE : arg1'=-1+arg1, arg2'=arg2P_6, [ arg1>0 ], cost: 1 Accelerated rule 4 with non-termination, yielding the new rule 9. Accelerated rule 5 with backward acceleration, yielding the new rule 10. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 4 5. Accelerating simple loops of location 3. Accelerating the following rules: 7: f137_0_loop_GE -> f137_0_loop_GE : arg1'=1+arg1, arg2'=arg2P_8, [ arg1<0 ], cost: 1 Accelerated rule 7 with backward acceleration, yielding the new rule 11. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 7. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f1_0_main_Load\' : [ arg2>1 && 1+2*x14_1>-1 && arg1>0 ], cost: 1 2: f1_0_main_Load -> f1_0_main_Load\' : [ arg2>1 && 2*x24_1>-1 && arg1>0 ], cost: 1 1: f1_0_main_Load\' -> f119_0_loop_LE : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1P_2>-1 && arg2>1 && 1+2*x19_1>-1 && arg1>0 ], cost: 1 3: f1_0_main_Load\' -> f137_0_loop_GE : arg1'=-x27_1, arg2'=arg2P_4, [ x27_1>-1 && arg2>1 && 2*x29_1>-1 && arg1>0 ], cost: 1 9: f119_0_loop_LE -> [5] : [ 0==arg1 ], cost: NONTERM 10: f119_0_loop_LE -> f119_0_loop_LE : arg1'=0, arg2'=arg2P_6, [ arg1>=1 ], cost: arg1 6: f137_0_loop_GE -> f119_0_loop_LE : arg1'=0, arg2'=arg2P_7, [ 0==arg1 ], cost: 1 11: f137_0_loop_GE -> f137_0_loop_GE : arg1'=0, arg2'=arg2P_8, [ -arg1>=1 ], cost: -arg1 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f1_0_main_Load\' : [ arg2>1 && 1+2*x14_1>-1 && arg1>0 ], cost: 1 2: f1_0_main_Load -> f1_0_main_Load\' : [ arg2>1 && 2*x24_1>-1 && arg1>0 ], cost: 1 1: f1_0_main_Load\' -> f119_0_loop_LE : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1P_2>-1 && arg2>1 && 1+2*x19_1>-1 && arg1>0 ], cost: 1 3: f1_0_main_Load\' -> f137_0_loop_GE : arg1'=-x27_1, arg2'=arg2P_4, [ x27_1>-1 && arg2>1 && 2*x29_1>-1 && arg1>0 ], cost: 1 12: f1_0_main_Load\' -> [5] : [ arg2>1 && 1+2*x19_1>-1 && arg1>0 ], cost: NONTERM 14: f1_0_main_Load\' -> f119_0_loop_LE : arg1'=0, arg2'=arg2P_6, [ arg2>1 && 1+2*x19_1>-1 && arg1>0 && arg1P_2>=1 ], cost: 1+arg1P_2 15: f1_0_main_Load\' -> f137_0_loop_GE : arg1'=0, arg2'=arg2P_8, [ arg2>1 && 2*x29_1>-1 && arg1>0 && x27_1>=1 ], cost: 1+x27_1 6: f137_0_loop_GE -> f119_0_loop_LE : arg1'=0, arg2'=arg2P_7, [ 0==arg1 ], cost: 1 13: f137_0_loop_GE -> [5] : [ 0==arg1 ], cost: NONTERM 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 0: f1_0_main_Load -> f1_0_main_Load\' : [ arg2>1 && 1+2*x14_1>-1 && arg1>0 ], cost: 1 2: f1_0_main_Load -> f1_0_main_Load\' : [ arg2>1 && 2*x24_1>-1 && arg1>0 ], cost: 1 3: f1_0_main_Load\' -> f137_0_loop_GE : arg1'=-x27_1, arg2'=arg2P_4, [ x27_1>-1 && arg2>1 && 2*x29_1>-1 && arg1>0 ], cost: 1 12: f1_0_main_Load\' -> [5] : [ arg2>1 && 1+2*x19_1>-1 && arg1>0 ], cost: NONTERM 14: f1_0_main_Load\' -> f119_0_loop_LE : arg1'=0, arg2'=arg2P_6, [ arg2>1 && 1+2*x19_1>-1 && arg1>0 && arg1P_2>=1 ], cost: 1+arg1P_2 15: f1_0_main_Load\' -> f137_0_loop_GE : arg1'=0, arg2'=arg2P_8, [ arg2>1 && 2*x29_1>-1 && arg1>0 && x27_1>=1 ], cost: 1+x27_1 13: f137_0_loop_GE -> [5] : [ 0==arg1 ], cost: NONTERM 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: __init 12: f1_0_main_Load\' -> [5] : [ arg2>1 && 1+2*x19_1>-1 && arg1>0 ], cost: NONTERM 14: f1_0_main_Load\' -> f119_0_loop_LE : arg1'=0, arg2'=arg2P_6, [ arg2>1 && 1+2*x19_1>-1 && arg1>0 && arg1P_2>=1 ], cost: 1+arg1P_2 18: f1_0_main_Load\' -> [5] : [ arg2>1 && 2*x29_1>-1 && arg1>0 && 0==-x27_1 ], cost: NONTERM 19: f1_0_main_Load\' -> [5] : [ arg2>1 && 2*x29_1>-1 && arg1>0 && x27_1>=1 ], cost: NONTERM 16: __init -> f1_0_main_Load\' : arg1'=arg1P_9, arg2'=arg2P_9, [ arg2P_9>1 && 1+2*x14_1>-1 && arg1P_9>0 ], cost: 2 17: __init -> f1_0_main_Load\' : arg1'=arg1P_9, arg2'=arg2P_9, [ arg2P_9>1 && 2*x24_1>-1 && arg1P_9>0 ], cost: 2 Eliminated locations (on tree-shaped paths): Start location: __init 20: __init -> [5] : [ arg2P_9>1 && 1+2*x14_1>-1 && arg1P_9>0 && 1+2*x19_1>-1 ], cost: NONTERM 21: __init -> f119_0_loop_LE : arg1'=0, arg2'=arg2P_6, [ arg2P_9>1 && 1+2*x14_1>-1 && arg1P_9>0 && 1+2*x19_1>-1 && arg1P_2>=1 ], cost: 3+arg1P_2 22: __init -> [5] : [ arg2P_9>1 && 1+2*x14_1>-1 && arg1P_9>0 && 2*x29_1>-1 && 0==-x27_1 ], cost: NONTERM 23: __init -> [5] : [ arg2P_9>1 && 1+2*x14_1>-1 && arg1P_9>0 && 2*x29_1>-1 && x27_1>=1 ], cost: NONTERM 24: __init -> [5] : [ arg2P_9>1 && 2*x24_1>-1 && arg1P_9>0 && 1+2*x19_1>-1 ], cost: NONTERM 25: __init -> f119_0_loop_LE : arg1'=0, arg2'=arg2P_6, [ arg2P_9>1 && 2*x24_1>-1 && arg1P_9>0 && 1+2*x19_1>-1 && arg1P_2>=1 ], cost: 3+arg1P_2 26: __init -> [5] : [ arg2P_9>1 && 2*x24_1>-1 && arg1P_9>0 && 2*x29_1>-1 && 0==-x27_1 ], cost: NONTERM 27: __init -> [5] : [ arg2P_9>1 && 2*x24_1>-1 && arg1P_9>0 && 2*x29_1>-1 && x27_1>=1 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 20: __init -> [5] : [ arg2P_9>1 && 1+2*x14_1>-1 && arg1P_9>0 && 1+2*x19_1>-1 ], cost: NONTERM 21: __init -> f119_0_loop_LE : arg1'=0, arg2'=arg2P_6, [ arg2P_9>1 && 1+2*x14_1>-1 && arg1P_9>0 && 1+2*x19_1>-1 && arg1P_2>=1 ], cost: 3+arg1P_2 22: __init -> [5] : [ arg2P_9>1 && 1+2*x14_1>-1 && arg1P_9>0 && 2*x29_1>-1 && 0==-x27_1 ], cost: NONTERM 23: __init -> [5] : [ arg2P_9>1 && 1+2*x14_1>-1 && arg1P_9>0 && 2*x29_1>-1 && x27_1>=1 ], cost: NONTERM 24: __init -> [5] : [ arg2P_9>1 && 2*x24_1>-1 && arg1P_9>0 && 1+2*x19_1>-1 ], cost: NONTERM 25: __init -> f119_0_loop_LE : arg1'=0, arg2'=arg2P_6, [ arg2P_9>1 && 2*x24_1>-1 && arg1P_9>0 && 1+2*x19_1>-1 && arg1P_2>=1 ], cost: 3+arg1P_2 26: __init -> [5] : [ arg2P_9>1 && 2*x24_1>-1 && arg1P_9>0 && 2*x29_1>-1 && 0==-x27_1 ], cost: NONTERM 27: __init -> [5] : [ arg2P_9>1 && 2*x24_1>-1 && arg1P_9>0 && 2*x29_1>-1 && x27_1>=1 ], cost: NONTERM Computing asymptotic complexity for rule 20 Guard is satisfiable, yielding nontermination Resulting cost NONTERM has complexity: Nonterm Found new complexity Nonterm. Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: [ arg2P_9>1 && 1+2*x14_1>-1 && arg1P_9>0 && 1+2*x19_1>-1 ] NO