NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_Load -> f221_0_generate_GE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, arg5'=arg5P_1, [ arg1P_1<=arg1 && arg2>-1 && arg1>0 && arg1P_1>0 && 0==arg2P_1 && -1+arg2==arg3P_1 && 0==arg4P_1 && arg2==arg5P_1 ], cost: 1 1: f221_0_generate_GE -> f221_0_generate_GE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, arg5'=arg5P_2, [ arg5>-1 && arg3>arg2 && arg1P_2<=arg1 && arg1>0 && arg1P_2>0 && 1+arg2==arg2P_2 && -1+arg5==arg3P_2 && arg5==arg5P_2 ], cost: 1 2: f221_0_generate_GE -> f348_0_duplicate_EQ : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, [ arg3<=arg2 && arg4>0 && arg2P_3>arg4 && arg1>0 && 1==arg1P_3 ], cost: 1 3: f221_0_generate_GE -> f348_0_duplicate_EQ : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, arg5'=arg5P_4, [ arg1>0 && arg3<=arg2 && 1==arg1P_4 && 1==arg2P_4 ], cost: 1 4: f348_0_duplicate_EQ -> f348_0_duplicate_EQ : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, arg5'=arg5P_5, [ arg2>-1 && x23_1>0 && x23_1 f348_0_duplicate_EQ : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, arg5'=arg5P_6, [ x34_1-1 && 0==arg1 && 1==arg1P_6 && 1==arg2P_6 ], cost: 1 6: f348_0_duplicate_EQ -> f348_0_duplicate_EQ : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, arg5'=arg5P_7, [ arg2>-1 && x27_1>0 && x27_1x27_1 && x28_1>x27_1 && 1==arg1 && 0==arg1P_7 && 0==arg2P_7 ], cost: 1 7: f348_0_duplicate_EQ -> f348_0_duplicate_EQ : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, arg5'=arg5P_8, [ x37_1-1 && 1==arg1 && 0==arg1P_8 && 2==arg2P_8 ], cost: 1 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, arg5'=arg5P_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, arg3'=arg3P_9, arg4'=arg4P_9, arg5'=arg5P_9, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f221_0_generate_GE : arg1'=arg1P_1, arg2'=0, arg3'=-1+arg2, arg4'=0, arg5'=arg2, [ arg1P_1<=arg1 && arg2>-1 && arg1>0 && arg1P_1>0 ], cost: 1 1: f221_0_generate_GE -> f221_0_generate_GE : arg1'=arg1P_2, arg2'=1+arg2, arg3'=-1+arg5, arg4'=arg4P_2, [ arg5>-1 && arg3>arg2 && arg1P_2<=arg1 && arg1>0 && arg1P_2>0 ], cost: 1 2: f221_0_generate_GE -> f348_0_duplicate_EQ : arg1'=1, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, [ arg3<=arg2 && arg4>0 && arg2P_3>arg4 && arg1>0 ], cost: 1 3: f221_0_generate_GE -> f348_0_duplicate_EQ : arg1'=1, arg2'=1, arg3'=arg3P_4, arg4'=arg4P_4, arg5'=arg5P_4, [ arg1>0 && arg3<=arg2 ], cost: 1 4: f348_0_duplicate_EQ -> f348_0_duplicate_EQ : arg1'=1, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, arg5'=arg5P_5, [ 0==arg1 && 1<=-1+arg2 && 1<=-1+arg2P_5 ], cost: 1 5: f348_0_duplicate_EQ -> f348_0_duplicate_EQ : arg1'=1, arg2'=1, arg3'=arg3P_6, arg4'=arg4P_6, arg5'=arg5P_6, [ arg2>-1 && 0==arg1 ], cost: 1 6: f348_0_duplicate_EQ -> f348_0_duplicate_EQ : arg1'=0, arg2'=0, arg3'=arg3P_7, arg4'=arg4P_7, arg5'=arg5P_7, [ 1==arg1 && 1<=-1+arg2 ], cost: 1 7: f348_0_duplicate_EQ -> f348_0_duplicate_EQ : arg1'=0, arg2'=2, arg3'=arg3P_8, arg4'=arg4P_8, arg5'=arg5P_8, [ arg2>-1 && 1==arg1 ], cost: 1 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, arg5'=arg5P_9, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 1: f221_0_generate_GE -> f221_0_generate_GE : arg1'=arg1P_2, arg2'=1+arg2, arg3'=-1+arg5, arg4'=arg4P_2, [ arg5>-1 && arg3>arg2 && arg1P_2<=arg1 && arg1>0 && arg1P_2>0 ], cost: 1 [test] deduced pseudo-invariant -2+arg5-arg3<=0, also trying 2-arg5+arg3<=-1 Accelerated rule 1 with backward acceleration, yielding the new rule 9. [accelerate] Nesting with 1 inner and 1 outer candidates Accelerating simple loops of location 2. Accelerating the following rules: 4: f348_0_duplicate_EQ -> f348_0_duplicate_EQ : arg1'=1, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, arg5'=arg5P_5, [ 0==arg1 && 1<=-1+arg2 && 1<=-1+arg2P_5 ], cost: 1 5: f348_0_duplicate_EQ -> f348_0_duplicate_EQ : arg1'=1, arg2'=1, arg3'=arg3P_6, arg4'=arg4P_6, arg5'=arg5P_6, [ arg2>-1 && 0==arg1 ], cost: 1 6: f348_0_duplicate_EQ -> f348_0_duplicate_EQ : arg1'=0, arg2'=0, arg3'=arg3P_7, arg4'=arg4P_7, arg5'=arg5P_7, [ 1==arg1 && 1<=-1+arg2 ], cost: 1 7: f348_0_duplicate_EQ -> f348_0_duplicate_EQ : arg1'=0, arg2'=2, arg3'=arg3P_8, arg4'=arg4P_8, arg5'=arg5P_8, [ arg2>-1 && 1==arg1 ], cost: 1 Failed to prove monotonicity of the guard of rule 4. Failed to prove monotonicity of the guard of rule 5. Failed to prove monotonicity of the guard of rule 6. Failed to prove monotonicity of the guard of rule 7. [accelerate] Nesting with 4 inner and 4 outer candidates Nested simple loops 7 (outer loop) and 4 (inner loop) with Rule(2 | 0==arg1, 1<=-1+arg2, | NONTERM || 5 | ), resulting in the new rules: 10, 11. Nested simple loops 7 (outer loop) and 5 (inner loop) with Rule(2 | arg2>-1, 0==arg1, | NONTERM || 5 | ), resulting in the new rules: 12, 13. Nested simple loops 4 (outer loop) and 7 (inner loop) with Rule(2 | arg2>-1, 1==arg1, 1<=-1+arg2P_5, | NONTERM || 5 | ), resulting in the new rules: 14, 15. Nested simple loops 5 (outer loop) and 7 (inner loop) with Rule(2 | arg2>-1, 1==arg1, | NONTERM || 5 | ), resulting in the new rules: 16, 17. Removing the simple loops: 4 5 7. Also removing duplicate rules: 11 12 13. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f221_0_generate_GE : arg1'=arg1P_1, arg2'=0, arg3'=-1+arg2, arg4'=0, arg5'=arg2, [ arg1P_1<=arg1 && arg2>-1 && arg1>0 && arg1P_1>0 ], cost: 1 1: f221_0_generate_GE -> f221_0_generate_GE : arg1'=arg1P_2, arg2'=1+arg2, arg3'=-1+arg5, arg4'=arg4P_2, [ arg5>-1 && arg3>arg2 && arg1P_2<=arg1 && arg1>0 && arg1P_2>0 ], cost: 1 2: f221_0_generate_GE -> f348_0_duplicate_EQ : arg1'=1, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, [ arg3<=arg2 && arg4>0 && arg2P_3>arg4 && arg1>0 ], cost: 1 3: f221_0_generate_GE -> f348_0_duplicate_EQ : arg1'=1, arg2'=1, arg3'=arg3P_4, arg4'=arg4P_4, arg5'=arg5P_4, [ arg1>0 && arg3<=arg2 ], cost: 1 9: f221_0_generate_GE -> f221_0_generate_GE : arg1'=arg1P_2, arg2'=-1+arg5, arg3'=-1+arg5, arg4'=arg4P_2, [ arg5>-1 && arg1P_2<=arg1 && arg1>0 && arg1P_2>0 && -2+arg5-arg3<=0 && -1+arg5-arg2>=1 ], cost: -1+arg5-arg2 6: f348_0_duplicate_EQ -> f348_0_duplicate_EQ : arg1'=0, arg2'=0, arg3'=arg3P_7, arg4'=arg4P_7, arg5'=arg5P_7, [ 1==arg1 && 1<=-1+arg2 ], cost: 1 10: f348_0_duplicate_EQ -> [5] : [ 0==arg1 && 1<=-1+arg2 ], cost: NONTERM 14: f348_0_duplicate_EQ -> [5] : [ arg2>-1 && 1==arg1 && 1<=-1+arg2P_5 ], cost: NONTERM 15: f348_0_duplicate_EQ -> [5] : [ 0==arg1 && 1<=-1+arg2 && 1<=-1+arg2P_5 ], cost: NONTERM 16: f348_0_duplicate_EQ -> [5] : [ arg2>-1 && 1==arg1 ], cost: NONTERM 17: f348_0_duplicate_EQ -> [5] : [ arg2>-1 && 0==arg1 ], cost: NONTERM 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, arg5'=arg5P_9, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f221_0_generate_GE : arg1'=arg1P_1, arg2'=0, arg3'=-1+arg2, arg4'=0, arg5'=arg2, [ arg1P_1<=arg1 && arg2>-1 && arg1>0 && arg1P_1>0 ], cost: 1 18: f1_0_main_Load -> f221_0_generate_GE : arg1'=arg1P_2, arg2'=1, arg3'=-1+arg2, arg4'=arg4P_2, arg5'=arg2, [ arg1>0 && -1+arg2>0 && arg1P_2>0 && arg1P_2<=arg1 ], cost: 2 19: f1_0_main_Load -> f221_0_generate_GE : arg1'=arg1P_2, arg2'=-1+arg2, arg3'=-1+arg2, arg4'=arg4P_2, arg5'=arg2, [ arg1>0 && arg1P_2>0 && -1+arg2>=1 && arg1P_2<=arg1 ], cost: arg2 2: f221_0_generate_GE -> f348_0_duplicate_EQ : arg1'=1, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, [ arg3<=arg2 && arg4>0 && arg2P_3>arg4 && arg1>0 ], cost: 1 3: f221_0_generate_GE -> f348_0_duplicate_EQ : arg1'=1, arg2'=1, arg3'=arg3P_4, arg4'=arg4P_4, arg5'=arg5P_4, [ arg1>0 && arg3<=arg2 ], cost: 1 20: f221_0_generate_GE -> f348_0_duplicate_EQ : arg1'=0, arg2'=0, arg3'=arg3P_7, arg4'=arg4P_7, arg5'=arg5P_7, [ arg3<=arg2 && arg4>0 && arg1>0 ], cost: 2 21: f221_0_generate_GE -> [5] : [ arg3<=arg2 && arg4>0 && arg1>0 ], cost: NONTERM 22: f221_0_generate_GE -> [5] : [ arg1>0 && arg3<=arg2 ], cost: NONTERM 23: f221_0_generate_GE -> [5] : [ arg3<=arg2 && arg4>0 && arg1>0 ], cost: NONTERM 24: f221_0_generate_GE -> [5] : [ arg1>0 && arg3<=arg2 ], cost: NONTERM 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, arg5'=arg5P_9, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 0: f1_0_main_Load -> f221_0_generate_GE : arg1'=arg1P_1, arg2'=0, arg3'=-1+arg2, arg4'=0, arg5'=arg2, [ arg1P_1<=arg1 && arg2>-1 && arg1>0 && arg1P_1>0 ], cost: 1 18: f1_0_main_Load -> f221_0_generate_GE : arg1'=arg1P_2, arg2'=1, arg3'=-1+arg2, arg4'=arg4P_2, arg5'=arg2, [ arg1>0 && -1+arg2>0 && arg1P_2>0 && arg1P_2<=arg1 ], cost: 2 19: f1_0_main_Load -> f221_0_generate_GE : arg1'=arg1P_2, arg2'=-1+arg2, arg3'=-1+arg2, arg4'=arg4P_2, arg5'=arg2, [ arg1>0 && arg1P_2>0 && -1+arg2>=1 && arg1P_2<=arg1 ], cost: arg2 21: f221_0_generate_GE -> [5] : [ arg3<=arg2 && arg4>0 && arg1>0 ], cost: NONTERM 22: f221_0_generate_GE -> [5] : [ arg1>0 && arg3<=arg2 ], cost: NONTERM 23: f221_0_generate_GE -> [5] : [ arg3<=arg2 && arg4>0 && arg1>0 ], cost: NONTERM 24: f221_0_generate_GE -> [5] : [ arg1>0 && arg3<=arg2 ], cost: NONTERM 8: __init -> f1_0_main_Load : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, arg5'=arg5P_9, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: __init 21: f221_0_generate_GE -> [5] : [ arg3<=arg2 && arg4>0 && arg1>0 ], cost: NONTERM 22: f221_0_generate_GE -> [5] : [ arg1>0 && arg3<=arg2 ], cost: NONTERM 23: f221_0_generate_GE -> [5] : [ arg3<=arg2 && arg4>0 && arg1>0 ], cost: NONTERM 24: f221_0_generate_GE -> [5] : [ arg1>0 && arg3<=arg2 ], cost: NONTERM 25: __init -> f221_0_generate_GE : arg1'=arg1P_1, arg2'=0, arg3'=-1+arg2P_9, arg4'=0, arg5'=arg2P_9, [ arg1P_1<=arg1P_9 && arg2P_9>-1 && arg1P_9>0 && arg1P_1>0 ], cost: 2 26: __init -> f221_0_generate_GE : arg1'=arg1P_2, arg2'=1, arg3'=-1+arg2P_9, arg4'=arg4P_2, arg5'=arg2P_9, [ arg1P_9>0 && -1+arg2P_9>0 && arg1P_2>0 && arg1P_2<=arg1P_9 ], cost: 3 27: __init -> f221_0_generate_GE : arg1'=arg1P_2, arg2'=-1+arg2P_9, arg3'=-1+arg2P_9, arg4'=arg4P_2, arg5'=arg2P_9, [ arg1P_9>0 && arg1P_2>0 && -1+arg2P_9>=1 && arg1P_2<=arg1P_9 ], cost: 1+arg2P_9 Merged rules: Start location: __init 30: f221_0_generate_GE -> [5] : [ arg1>0 && arg3<=arg2 ], cost: NONTERM 25: __init -> f221_0_generate_GE : arg1'=arg1P_1, arg2'=0, arg3'=-1+arg2P_9, arg4'=0, arg5'=arg2P_9, [ arg1P_1<=arg1P_9 && arg2P_9>-1 && arg1P_9>0 && arg1P_1>0 ], cost: 2 26: __init -> f221_0_generate_GE : arg1'=arg1P_2, arg2'=1, arg3'=-1+arg2P_9, arg4'=arg4P_2, arg5'=arg2P_9, [ arg1P_9>0 && -1+arg2P_9>0 && arg1P_2>0 && arg1P_2<=arg1P_9 ], cost: 3 27: __init -> f221_0_generate_GE : arg1'=arg1P_2, arg2'=-1+arg2P_9, arg3'=-1+arg2P_9, arg4'=arg4P_2, arg5'=arg2P_9, [ arg1P_9>0 && arg1P_2>0 && -1+arg2P_9>=1 && arg1P_2<=arg1P_9 ], cost: 1+arg2P_9 Eliminated locations (on tree-shaped paths): Start location: __init 31: __init -> [5] : [ arg1P_1<=arg1P_9 && arg2P_9>-1 && arg1P_9>0 && arg1P_1>0 && -1+arg2P_9<=0 ], cost: NONTERM 32: __init -> [5] : [ arg1P_9>0 && -1+arg2P_9>0 && arg1P_2>0 && arg1P_2<=arg1P_9 && -1+arg2P_9<=1 ], cost: NONTERM 33: __init -> [5] : [ arg1P_9>0 && arg1P_2>0 && -1+arg2P_9>=1 && arg1P_2<=arg1P_9 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 31: __init -> [5] : [ arg1P_1<=arg1P_9 && arg2P_9>-1 && arg1P_9>0 && arg1P_1>0 && -1+arg2P_9<=0 ], cost: NONTERM 32: __init -> [5] : [ arg1P_9>0 && -1+arg2P_9>0 && arg1P_2>0 && arg1P_2<=arg1P_9 && -1+arg2P_9<=1 ], cost: NONTERM 33: __init -> [5] : [ arg1P_9>0 && arg1P_2>0 && -1+arg2P_9>=1 && arg1P_2<=arg1P_9 ], cost: NONTERM Computing asymptotic complexity for rule 33 Simplified the guard: 33: __init -> [5] : [ arg1P_2>0 && -1+arg2P_9>=1 && arg1P_2<=arg1P_9 ], cost: NONTERM 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: [ arg1P_2>0 && -1+arg2P_9>=1 && arg1P_2<=arg1P_9 ] NO