NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f265_0_createMetaList_Return -> f724_0_countMetaList_NULL : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ arg1P_1<=arg1 && arg1>-1 && arg1P_1>-1 ], cost: 1 2: f724_0_countMetaList_NULL -> f724_0_countMetaList_NULL : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ 2+arg1P_3<=arg1 && arg1>2 && arg1P_3>-1 ], cost: 1 3: f724_0_countMetaList_NULL -> f724_0_countMetaList_NULL : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ 2+arg1P_4<=arg1 && arg1>1 && arg1P_4>-1 ], cost: 1 4: f724_0_countMetaList_NULL -> f724_0_countMetaList_NULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg1>=arg1P_5 && arg1>2 && arg1P_5>0 ], cost: 1 1: f1_0_main_Load -> f724_0_countMetaList_NULL : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1>0 && arg1P_2>-1 ], cost: 1 5: f1_0_main_Load -> f693_0_createMetaList_GE : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, [ arg2>-1 && arg2P_6>-1 && arg1>0 && 0==arg1P_6 && 1==arg3P_6 ], cost: 1 6: f693_0_createMetaList_GE -> f932_0_createMetaList_LE : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [ arg3P_7>-1 && arg2>arg1 && arg3>0 && arg2==arg1P_7 && arg1==arg2P_7 && 1+arg3==arg4P_7 ], cost: 1 7: f932_0_createMetaList_LE -> f693_0_createMetaList_GE : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, [ 0==arg3 && 1+arg2==arg1P_8 && arg1==arg2P_8 && arg4==arg3P_8 ], cost: 1 8: f932_0_createMetaList_LE -> f932_0_createMetaList_LE : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, [ arg3>0 && arg1==arg1P_9 && arg2==arg2P_9 && -1+arg3==arg3P_9 && arg4==arg4P_9 ], 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 Removed unreachable and leaf rules: Start location: __init 2: f724_0_countMetaList_NULL -> f724_0_countMetaList_NULL : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ 2+arg1P_3<=arg1 && arg1>2 && arg1P_3>-1 ], cost: 1 3: f724_0_countMetaList_NULL -> f724_0_countMetaList_NULL : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ 2+arg1P_4<=arg1 && arg1>1 && arg1P_4>-1 ], cost: 1 4: f724_0_countMetaList_NULL -> f724_0_countMetaList_NULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg1>=arg1P_5 && arg1>2 && arg1P_5>0 ], cost: 1 1: f1_0_main_Load -> f724_0_countMetaList_NULL : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1>0 && arg1P_2>-1 ], cost: 1 5: f1_0_main_Load -> f693_0_createMetaList_GE : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, [ arg2>-1 && arg2P_6>-1 && arg1>0 && 0==arg1P_6 && 1==arg3P_6 ], cost: 1 6: f693_0_createMetaList_GE -> f932_0_createMetaList_LE : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [ arg3P_7>-1 && arg2>arg1 && arg3>0 && arg2==arg1P_7 && arg1==arg2P_7 && 1+arg3==arg4P_7 ], cost: 1 7: f932_0_createMetaList_LE -> f693_0_createMetaList_GE : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, [ 0==arg3 && 1+arg2==arg1P_8 && arg1==arg2P_8 && arg4==arg3P_8 ], cost: 1 8: f932_0_createMetaList_LE -> f932_0_createMetaList_LE : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, [ arg3>0 && arg1==arg1P_9 && arg2==arg2P_9 && -1+arg3==arg3P_9 && arg4==arg4P_9 ], cost: 1 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 2: f724_0_countMetaList_NULL -> f724_0_countMetaList_NULL : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ 2+arg1P_3<=arg1 && arg1>2 && arg1P_3>-1 ], cost: 1 3: f724_0_countMetaList_NULL -> f724_0_countMetaList_NULL : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ 2+arg1P_4<=arg1 && arg1>1 && arg1P_4>-1 ], cost: 1 4: f724_0_countMetaList_NULL -> f724_0_countMetaList_NULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg1>=arg1P_5 && arg1>2 && arg1P_5>0 ], cost: 1 1: f1_0_main_Load -> f724_0_countMetaList_NULL : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1>0 && arg1P_2>-1 ], cost: 1 5: f1_0_main_Load -> f693_0_createMetaList_GE : arg1'=0, arg2'=arg2P_6, arg3'=1, arg4'=arg4P_6, [ arg2>-1 && arg2P_6>-1 && arg1>0 ], cost: 1 6: f693_0_createMetaList_GE -> f932_0_createMetaList_LE : arg1'=arg2, arg2'=arg1, arg3'=arg3P_7, arg4'=1+arg3, [ arg3P_7>-1 && arg2>arg1 && arg3>0 ], cost: 1 7: f932_0_createMetaList_LE -> f693_0_createMetaList_GE : arg1'=1+arg2, arg2'=arg1, arg3'=arg4, arg4'=arg4P_8, [ 0==arg3 ], cost: 1 8: f932_0_createMetaList_LE -> f932_0_createMetaList_LE : arg3'=-1+arg3, [ arg3>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: 2: f724_0_countMetaList_NULL -> f724_0_countMetaList_NULL : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ 2+arg1P_3<=arg1 && arg1>2 && arg1P_3>-1 ], cost: 1 3: f724_0_countMetaList_NULL -> f724_0_countMetaList_NULL : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ 2+arg1P_4<=arg1 && arg1>1 && arg1P_4>-1 ], cost: 1 4: f724_0_countMetaList_NULL -> f724_0_countMetaList_NULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg1>=arg1P_5 && arg1>2 && arg1P_5>0 ], cost: 1 Failed to prove monotonicity of the guard of rule 2. Failed to prove monotonicity of the guard of rule 3. Accelerated rule 4 with non-termination, yielding the new rule 10. Accelerated rule 4 with backward acceleration, yielding the new rule 11. [accelerate] Nesting with 3 inner and 2 outer candidates Removing the simple loops: 4. Accelerating simple loops of location 4. Accelerating the following rules: 8: f932_0_createMetaList_LE -> f932_0_createMetaList_LE : arg3'=-1+arg3, [ arg3>0 ], cost: 1 Accelerated rule 8 with backward acceleration, yielding the new rule 12. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 8. Accelerated all simple loops using metering functions (where possible): Start location: __init 2: f724_0_countMetaList_NULL -> f724_0_countMetaList_NULL : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ 2+arg1P_3<=arg1 && arg1>2 && arg1P_3>-1 ], cost: 1 3: f724_0_countMetaList_NULL -> f724_0_countMetaList_NULL : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ 2+arg1P_4<=arg1 && arg1>1 && arg1P_4>-1 ], cost: 1 10: f724_0_countMetaList_NULL -> [6] : [ arg1>=arg1P_5 && arg1>2 && arg1P_5>2 ], cost: NONTERM 11: f724_0_countMetaList_NULL -> f724_0_countMetaList_NULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg1>=arg1P_5 && k>=1 && arg1P_5>2 ], cost: k 1: f1_0_main_Load -> f724_0_countMetaList_NULL : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1>0 && arg1P_2>-1 ], cost: 1 5: f1_0_main_Load -> f693_0_createMetaList_GE : arg1'=0, arg2'=arg2P_6, arg3'=1, arg4'=arg4P_6, [ arg2>-1 && arg2P_6>-1 && arg1>0 ], cost: 1 6: f693_0_createMetaList_GE -> f932_0_createMetaList_LE : arg1'=arg2, arg2'=arg1, arg3'=arg3P_7, arg4'=1+arg3, [ arg3P_7>-1 && arg2>arg1 && arg3>0 ], cost: 1 7: f932_0_createMetaList_LE -> f693_0_createMetaList_GE : arg1'=1+arg2, arg2'=arg1, arg3'=arg4, arg4'=arg4P_8, [ 0==arg3 ], cost: 1 12: f932_0_createMetaList_LE -> f932_0_createMetaList_LE : arg3'=0, [ arg3>=0 ], cost: arg3 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 1: f1_0_main_Load -> f724_0_countMetaList_NULL : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1>0 && arg1P_2>-1 ], cost: 1 5: f1_0_main_Load -> f693_0_createMetaList_GE : arg1'=0, arg2'=arg2P_6, arg3'=1, arg4'=arg4P_6, [ arg2>-1 && arg2P_6>-1 && arg1>0 ], cost: 1 13: f1_0_main_Load -> f724_0_countMetaList_NULL : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ arg1>0 && arg1P_3>-1 ], cost: 2 14: f1_0_main_Load -> f724_0_countMetaList_NULL : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg1>0 && arg1P_4>-1 ], cost: 2 15: f1_0_main_Load -> [6] : [ arg1>0 ], cost: NONTERM 16: f1_0_main_Load -> f724_0_countMetaList_NULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg1>0 && k>=1 && arg1P_5>2 ], cost: 1+k 6: f693_0_createMetaList_GE -> f932_0_createMetaList_LE : arg1'=arg2, arg2'=arg1, arg3'=arg3P_7, arg4'=1+arg3, [ arg3P_7>-1 && arg2>arg1 && arg3>0 ], cost: 1 17: f693_0_createMetaList_GE -> f932_0_createMetaList_LE : arg1'=arg2, arg2'=arg1, arg3'=0, arg4'=1+arg3, [ arg3P_7>-1 && arg2>arg1 && arg3>0 ], cost: 1+arg3P_7 7: f932_0_createMetaList_LE -> f693_0_createMetaList_GE : arg1'=1+arg2, arg2'=arg1, arg3'=arg4, arg4'=arg4P_8, [ 0==arg3 ], 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 5: f1_0_main_Load -> f693_0_createMetaList_GE : arg1'=0, arg2'=arg2P_6, arg3'=1, arg4'=arg4P_6, [ arg2>-1 && arg2P_6>-1 && arg1>0 ], cost: 1 15: f1_0_main_Load -> [6] : [ arg1>0 ], cost: NONTERM 16: f1_0_main_Load -> f724_0_countMetaList_NULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg1>0 && k>=1 && arg1P_5>2 ], cost: 1+k 6: f693_0_createMetaList_GE -> f932_0_createMetaList_LE : arg1'=arg2, arg2'=arg1, arg3'=arg3P_7, arg4'=1+arg3, [ arg3P_7>-1 && arg2>arg1 && arg3>0 ], cost: 1 17: f693_0_createMetaList_GE -> f932_0_createMetaList_LE : arg1'=arg2, arg2'=arg1, arg3'=0, arg4'=1+arg3, [ arg3P_7>-1 && arg2>arg1 && arg3>0 ], cost: 1+arg3P_7 7: f932_0_createMetaList_LE -> f693_0_createMetaList_GE : arg1'=1+arg2, arg2'=arg1, arg3'=arg4, arg4'=arg4P_8, [ 0==arg3 ], 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 21: f693_0_createMetaList_GE -> f693_0_createMetaList_GE : arg1'=1+arg1, arg2'=arg2, arg3'=1+arg3, arg4'=arg4P_8, [ arg2>arg1 && arg3>0 && 0==arg3P_7 ], cost: 2 22: f693_0_createMetaList_GE -> f693_0_createMetaList_GE : arg1'=1+arg1, arg2'=arg2, arg3'=1+arg3, arg4'=arg4P_8, [ arg3P_7>-1 && arg2>arg1 && arg3>0 ], cost: 2+arg3P_7 18: __init -> f693_0_createMetaList_GE : arg1'=0, arg2'=arg2P_6, arg3'=1, arg4'=arg4P_6, [ arg2P_10>-1 && arg2P_6>-1 && arg1P_10>0 ], cost: 2 19: __init -> [6] : [ arg1P_10>0 ], cost: NONTERM 20: __init -> f724_0_countMetaList_NULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg1P_10>0 && k>=1 && arg1P_5>2 ], cost: 2+k Accelerating simple loops of location 3. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 21: f693_0_createMetaList_GE -> f693_0_createMetaList_GE : arg1'=1+arg1, arg3'=1+arg3, arg4'=arg4P_8, [ arg2>arg1 && arg3>0 ], cost: 2 22: f693_0_createMetaList_GE -> f693_0_createMetaList_GE : arg1'=1+arg1, arg3'=1+arg3, arg4'=arg4P_8, [ arg3P_7>-1 && arg2>arg1 && arg3>0 ], cost: 2+arg3P_7 Accelerated rule 21 with backward acceleration, yielding the new rule 23. Accelerated rule 22 with backward acceleration, yielding the new rule 24. [accelerate] Nesting with 2 inner and 2 outer candidates Removing the simple loops: 21 22. Accelerated all simple loops using metering functions (where possible): Start location: __init 23: f693_0_createMetaList_GE -> f693_0_createMetaList_GE : arg1'=arg2, arg3'=arg2+arg3-arg1, arg4'=arg4P_8, [ arg3>0 && arg2-arg1>=1 ], cost: 2*arg2-2*arg1 24: f693_0_createMetaList_GE -> f693_0_createMetaList_GE : arg1'=arg2, arg3'=arg2+arg3-arg1, arg4'=arg4P_8, [ arg3P_7>-1 && arg3>0 && arg2-arg1>=1 ], cost: 2*arg2+(arg2-arg1)*arg3P_7-2*arg1 18: __init -> f693_0_createMetaList_GE : arg1'=0, arg2'=arg2P_6, arg3'=1, arg4'=arg4P_6, [ arg2P_10>-1 && arg2P_6>-1 && arg1P_10>0 ], cost: 2 19: __init -> [6] : [ arg1P_10>0 ], cost: NONTERM 20: __init -> f724_0_countMetaList_NULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg1P_10>0 && k>=1 && arg1P_5>2 ], cost: 2+k Chained accelerated rules (with incoming rules): Start location: __init 18: __init -> f693_0_createMetaList_GE : arg1'=0, arg2'=arg2P_6, arg3'=1, arg4'=arg4P_6, [ arg2P_10>-1 && arg2P_6>-1 && arg1P_10>0 ], cost: 2 19: __init -> [6] : [ arg1P_10>0 ], cost: NONTERM 20: __init -> f724_0_countMetaList_NULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg1P_10>0 && k>=1 && arg1P_5>2 ], cost: 2+k 25: __init -> f693_0_createMetaList_GE : arg1'=arg2P_6, arg2'=arg2P_6, arg3'=1+arg2P_6, arg4'=arg4P_8, [ arg2P_6>=1 ], cost: 2+2*arg2P_6 26: __init -> f693_0_createMetaList_GE : arg1'=arg2P_6, arg2'=arg2P_6, arg3'=1+arg2P_6, arg4'=arg4P_8, [ arg3P_7>-1 && arg2P_6>=1 ], cost: 2+2*arg2P_6+arg2P_6*arg3P_7 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 19: __init -> [6] : [ arg1P_10>0 ], cost: NONTERM 20: __init -> f724_0_countMetaList_NULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg1P_10>0 && k>=1 && arg1P_5>2 ], cost: 2+k 25: __init -> f693_0_createMetaList_GE : arg1'=arg2P_6, arg2'=arg2P_6, arg3'=1+arg2P_6, arg4'=arg4P_8, [ arg2P_6>=1 ], cost: 2+2*arg2P_6 26: __init -> f693_0_createMetaList_GE : arg1'=arg2P_6, arg2'=arg2P_6, arg3'=1+arg2P_6, arg4'=arg4P_8, [ arg3P_7>-1 && arg2P_6>=1 ], cost: 2+2*arg2P_6+arg2P_6*arg3P_7 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 19: __init -> [6] : [ arg1P_10>0 ], cost: NONTERM 20: __init -> f724_0_countMetaList_NULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg1P_10>0 && k>=1 && arg1P_5>2 ], cost: 2+k 25: __init -> f693_0_createMetaList_GE : arg1'=arg2P_6, arg2'=arg2P_6, arg3'=1+arg2P_6, arg4'=arg4P_8, [ arg2P_6>=1 ], cost: 2+2*arg2P_6 26: __init -> f693_0_createMetaList_GE : arg1'=arg2P_6, arg2'=arg2P_6, arg3'=1+arg2P_6, arg4'=arg4P_8, [ arg3P_7>-1 && arg2P_6>=1 ], cost: 2+2*arg2P_6+arg2P_6*arg3P_7 Computing asymptotic complexity for rule 19 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_10>0 ] NO