NO ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: __init 0: f1_0_main_New -> f216_0_main_GE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, arg5'=arg5P_1, arg6'=arg6P_1, [ arg1P_1<=arg1 && arg2>-1 && -1+arg2P_1<=arg1 && arg1>0 && arg1P_1>0 && arg2P_1>1 && 0==arg3P_1 && 1+arg2==arg4P_1 && 0==arg5P_1 && arg2==arg6P_1 ], cost: 1 1: f216_0_main_GE -> f216_0_main_GE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, arg5'=arg5P_2, arg6'=arg6P_2, [ arg4>arg3 && arg5>0 && arg6>-1 && arg5=arg1P_2 && arg2>=arg1P_2 && arg1>0 && arg2>0 && arg1P_2>0 && arg2P_2>0 && 1+arg3==arg3P_2 && 1+arg6==arg4P_2 && arg6==arg6P_2 ], cost: 1 2: f216_0_main_GE -> f216_0_main_GE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, arg6'=arg6P_3, [ arg6>-1 && arg4>arg3 && arg1P_3<=arg1 && 1+arg1P_3<=arg2 && -3+arg2P_3<=arg1 && -2+arg2P_3<=arg2 && arg1>0 && arg2>1 && arg1P_3>0 && arg2P_3>3 && 1+arg3==arg3P_3 && 1+arg6==arg4P_3 && 1==arg5P_3 && arg6==arg6P_3 ], cost: 1 4: f216_0_main_GE -> f339_0_length_Load : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, arg5'=arg5P_5, arg6'=arg6P_5, [ arg1P_5<=arg1 && arg4<=arg3 && 1+arg1P_5<=arg2 && arg1>0 && arg2>1 && arg1P_5>0 && 1==arg2P_5 && arg6==arg3P_5 ], cost: 1 5: f216_0_main_GE -> f340_0_length_FieldAccess : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, arg5'=arg5P_6, arg6'=arg6P_6, [ arg5>0 && arg4<=arg3 && arg1>0 && arg2>0 && arg1P_6>0 && arg5==arg2P_6 && 0==arg3P_6 && 0==arg4P_6 && 0==arg5P_6 && arg5==arg6P_6 ], cost: 1 3: f339_0_length_Load -> f339_0_length_Load : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, arg5'=arg5P_4, arg6'=arg6P_4, [ arg1P_4<=arg1 && arg1>0 && arg1P_4>0 && 1+arg2==arg2P_4 && arg3==arg3P_4 ], cost: 1 6: f340_0_length_FieldAccess -> f340_0_length_FieldAccess : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, arg5'=arg5P_7, arg6'=arg6P_7, [ arg5>0 && arg4>0 && arg5P_7>arg5 && arg50 && arg4P_72 && arg1P_7>0 && arg2==arg2P_7 && arg3==arg3P_7 ], cost: 1 7: f340_0_length_FieldAccess -> f340_0_length_FieldAccess : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, arg5'=arg5P_8, arg6'=arg6P_8, [ arg6P_8-1 && arg3>-1 && arg4P_82 && arg1P_8>0 && arg1>=3+x54_1 && arg2==arg6 && 0==arg3P_8 && 1==arg5P_8 ], cost: 1 8: __init -> f1_0_main_New : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, arg5'=arg5P_9, arg6'=arg6P_9, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 8: __init -> f1_0_main_New : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, arg5'=arg5P_9, arg6'=arg6P_9, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_New -> f216_0_main_GE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=0, arg4'=1+arg2, arg5'=0, arg6'=arg2, [ arg1P_1<=arg1 && arg2>-1 && -1+arg2P_1<=arg1 && arg1>0 && arg1P_1>0 && arg2P_1>1 ], cost: 1 1: f216_0_main_GE -> f216_0_main_GE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=1+arg3, arg4'=1+arg6, arg5'=arg5P_2, [ arg4>arg3 && arg5>0 && arg6>-1 && arg5=arg1P_2 && arg2>=arg1P_2 && arg1>0 && arg2>0 && arg1P_2>0 && arg2P_2>0 ], cost: 1 2: f216_0_main_GE -> f216_0_main_GE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=1+arg3, arg4'=1+arg6, arg5'=1, [ arg6>-1 && arg4>arg3 && arg1P_3<=arg1 && 1+arg1P_3<=arg2 && -3+arg2P_3<=arg1 && -2+arg2P_3<=arg2 && arg1>0 && arg2>1 && arg1P_3>0 && arg2P_3>3 ], cost: 1 4: f216_0_main_GE -> f339_0_length_Load : arg1'=arg1P_5, arg2'=1, arg3'=arg6, arg4'=arg4P_5, arg5'=arg5P_5, arg6'=arg6P_5, [ arg1P_5<=arg1 && arg4<=arg3 && 1+arg1P_5<=arg2 && arg1>0 && arg2>1 && arg1P_5>0 ], cost: 1 5: f216_0_main_GE -> f340_0_length_FieldAccess : arg1'=arg1P_6, arg2'=arg5, arg3'=0, arg4'=0, arg5'=0, arg6'=arg5, [ arg5>0 && arg4<=arg3 && arg1>0 && arg2>0 && arg1P_6>0 ], cost: 1 3: f339_0_length_Load -> f339_0_length_Load : arg1'=arg1P_4, arg2'=1+arg2, arg4'=arg4P_4, arg5'=arg5P_4, arg6'=arg6P_4, [ arg1P_4<=arg1 && arg1>0 && arg1P_4>0 ], cost: 1 6: f340_0_length_FieldAccess -> f340_0_length_FieldAccess : arg1'=arg1P_7, arg4'=arg4P_7, arg5'=arg5P_7, arg6'=arg6P_7, [ arg5>0 && arg4>0 && arg5P_7>arg5 && arg52 && arg1P_7>0 ], cost: 1 7: f340_0_length_FieldAccess -> f340_0_length_FieldAccess : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=0, arg4'=arg4P_8, arg5'=1, arg6'=arg6P_8, [ arg6P_8-1 && arg3>-1 && arg4P_82 && arg1P_8>0 && arg2==arg6 ], cost: 1 8: __init -> f1_0_main_New : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, arg5'=arg5P_9, arg6'=arg6P_9, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 1: f216_0_main_GE -> f216_0_main_GE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=1+arg3, arg4'=1+arg6, arg5'=arg5P_2, [ arg4>arg3 && arg5>0 && arg6>-1 && arg5=arg1P_2 && arg2>=arg1P_2 && arg1>0 && arg2>0 && arg1P_2>0 && arg2P_2>0 ], cost: 1 2: f216_0_main_GE -> f216_0_main_GE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=1+arg3, arg4'=1+arg6, arg5'=1, [ arg6>-1 && arg4>arg3 && arg1P_3<=arg1 && 1+arg1P_3<=arg2 && -3+arg2P_3<=arg1 && -2+arg2P_3<=arg2 && arg1>0 && arg2>1 && arg1P_3>0 && arg2P_3>3 ], cost: 1 Found no metering function for rule 1. During metering: Instantiating temporary variables by {arg1P_3==-1+arg2,arg2P_3==3+arg1} Found no metering function for rule 2 (rule is too complicated). Removing the simple loops:. Accelerating simple loops of location 2. Accelerating the following rules: 3: f339_0_length_Load -> f339_0_length_Load : arg1'=arg1P_4, arg2'=1+arg2, arg4'=arg4P_4, arg5'=arg5P_4, arg6'=arg6P_4, [ arg1P_4<=arg1 && arg1>0 && arg1P_4>0 ], cost: 1 Accelerated rule 3 with NONTERM, yielding the new rule 9. Removing the simple loops: 3. Accelerating simple loops of location 3. Accelerating the following rules: 6: f340_0_length_FieldAccess -> f340_0_length_FieldAccess : arg1'=arg1P_7, arg4'=arg4P_7, arg5'=arg5P_7, arg6'=arg6P_7, [ arg5>0 && arg4>0 && arg5P_7>arg5 && arg52 && arg1P_7>0 ], cost: 1 7: f340_0_length_FieldAccess -> f340_0_length_FieldAccess : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=0, arg4'=arg4P_8, arg5'=1, arg6'=arg6P_8, [ arg6P_8-1 && arg3>-1 && arg4P_82 && arg1P_8>0 && arg2==arg6 ], cost: 1 Found no metering function for rule 6. Accelerated rule 7 with NONTERM (after strengthening guard), yielding the new rule 10. Removing the simple loops:. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_New -> f216_0_main_GE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=0, arg4'=1+arg2, arg5'=0, arg6'=arg2, [ arg1P_1<=arg1 && arg2>-1 && -1+arg2P_1<=arg1 && arg1>0 && arg1P_1>0 && arg2P_1>1 ], cost: 1 1: f216_0_main_GE -> f216_0_main_GE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=1+arg3, arg4'=1+arg6, arg5'=arg5P_2, [ arg4>arg3 && arg5>0 && arg6>-1 && arg5=arg1P_2 && arg2>=arg1P_2 && arg1>0 && arg2>0 && arg1P_2>0 && arg2P_2>0 ], cost: 1 2: f216_0_main_GE -> f216_0_main_GE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=1+arg3, arg4'=1+arg6, arg5'=1, [ arg6>-1 && arg4>arg3 && arg1P_3<=arg1 && 1+arg1P_3<=arg2 && -3+arg2P_3<=arg1 && -2+arg2P_3<=arg2 && arg1>0 && arg2>1 && arg1P_3>0 && arg2P_3>3 ], cost: 1 4: f216_0_main_GE -> f339_0_length_Load : arg1'=arg1P_5, arg2'=1, arg3'=arg6, arg4'=arg4P_5, arg5'=arg5P_5, arg6'=arg6P_5, [ arg1P_5<=arg1 && arg4<=arg3 && 1+arg1P_5<=arg2 && arg1>0 && arg2>1 && arg1P_5>0 ], cost: 1 5: f216_0_main_GE -> f340_0_length_FieldAccess : arg1'=arg1P_6, arg2'=arg5, arg3'=0, arg4'=0, arg5'=0, arg6'=arg5, [ arg5>0 && arg4<=arg3 && arg1>0 && arg2>0 && arg1P_6>0 ], cost: 1 9: f339_0_length_Load -> [6] : [ arg1P_4<=arg1 && arg1>0 && arg1P_4>0 ], cost: NONTERM 6: f340_0_length_FieldAccess -> f340_0_length_FieldAccess : arg1'=arg1P_7, arg4'=arg4P_7, arg5'=arg5P_7, arg6'=arg6P_7, [ arg5>0 && arg4>0 && arg5P_7>arg5 && arg52 && arg1P_7>0 ], cost: 1 7: f340_0_length_FieldAccess -> f340_0_length_FieldAccess : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=0, arg4'=arg4P_8, arg5'=1, arg6'=arg6P_8, [ arg6P_8-1 && arg3>-1 && arg4P_82 && arg1P_8>0 && arg2==arg6 ], cost: 1 10: f340_0_length_FieldAccess -> [7] : [ arg6P_8-1 && arg3>-1 && arg4P_82 && arg2==arg6 && arg1P_8>2 && arg6P_8-1 && arg2P_8==arg6P_8 && arg4P_8<0 ], cost: NONTERM 8: __init -> f1_0_main_New : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, arg5'=arg5P_9, arg6'=arg6P_9, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_New -> f216_0_main_GE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=0, arg4'=1+arg2, arg5'=0, arg6'=arg2, [ arg1P_1<=arg1 && arg2>-1 && -1+arg2P_1<=arg1 && arg1>0 && arg1P_1>0 && arg2P_1>1 ], cost: 1 11: f1_0_main_New -> f216_0_main_GE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=1, arg4'=1+arg2, arg5'=1, arg6'=arg2, [ arg2>-1 && arg1>0 && arg1P_3>0 && arg2P_3>3 && 1+arg1P_3<=1+arg1 && -2+arg2P_3<=1+arg1 ], cost: 2 4: f216_0_main_GE -> f339_0_length_Load : arg1'=arg1P_5, arg2'=1, arg3'=arg6, arg4'=arg4P_5, arg5'=arg5P_5, arg6'=arg6P_5, [ arg1P_5<=arg1 && arg4<=arg3 && 1+arg1P_5<=arg2 && arg1>0 && arg2>1 && arg1P_5>0 ], cost: 1 5: f216_0_main_GE -> f340_0_length_FieldAccess : arg1'=arg1P_6, arg2'=arg5, arg3'=0, arg4'=0, arg5'=0, arg6'=arg5, [ arg5>0 && arg4<=arg3 && arg1>0 && arg2>0 && arg1P_6>0 ], cost: 1 12: f216_0_main_GE -> [6] : arg1'=arg1P_5, arg2'=1, arg3'=arg6, arg4'=arg4P_5, arg5'=arg5P_5, arg6'=arg6P_5, [ arg1P_5<=arg1 && arg4<=arg3 && 1+arg1P_5<=arg2 && arg1>0 && arg2>1 && arg1P_5>0 ], cost: NONTERM 13: f216_0_main_GE -> f340_0_length_FieldAccess : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=0, arg4'=arg4P_8, arg5'=1, arg6'=arg6P_8, [ arg5>0 && arg4<=arg3 && arg1>0 && arg2>0 && arg6P_80 ], cost: 2 8: __init -> f1_0_main_New : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, arg5'=arg5P_9, arg6'=arg6P_9, [], cost: 1 Removed unreachable locations (and leaf rules with constant cost): Start location: __init 0: f1_0_main_New -> f216_0_main_GE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=0, arg4'=1+arg2, arg5'=0, arg6'=arg2, [ arg1P_1<=arg1 && arg2>-1 && -1+arg2P_1<=arg1 && arg1>0 && arg1P_1>0 && arg2P_1>1 ], cost: 1 11: f1_0_main_New -> f216_0_main_GE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=1, arg4'=1+arg2, arg5'=1, arg6'=arg2, [ arg2>-1 && arg1>0 && arg1P_3>0 && arg2P_3>3 && 1+arg1P_3<=1+arg1 && -2+arg2P_3<=1+arg1 ], cost: 2 12: f216_0_main_GE -> [6] : arg1'=arg1P_5, arg2'=1, arg3'=arg6, arg4'=arg4P_5, arg5'=arg5P_5, arg6'=arg6P_5, [ arg1P_5<=arg1 && arg4<=arg3 && 1+arg1P_5<=arg2 && arg1>0 && arg2>1 && arg1P_5>0 ], cost: NONTERM 8: __init -> f1_0_main_New : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, arg5'=arg5P_9, arg6'=arg6P_9, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: __init 12: f216_0_main_GE -> [6] : arg1'=arg1P_5, arg2'=1, arg3'=arg6, arg4'=arg4P_5, arg5'=arg5P_5, arg6'=arg6P_5, [ arg1P_5<=arg1 && arg4<=arg3 && 1+arg1P_5<=arg2 && arg1>0 && arg2>1 && arg1P_5>0 ], cost: NONTERM 14: __init -> f216_0_main_GE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=0, arg4'=1+arg2P_9, arg5'=0, arg6'=arg2P_9, [ arg1P_1<=arg1P_9 && arg2P_9>-1 && -1+arg2P_1<=arg1P_9 && arg1P_9>0 && arg1P_1>0 && arg2P_1>1 ], cost: 2 15: __init -> f216_0_main_GE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=1, arg4'=1+arg2P_9, arg5'=1, arg6'=arg2P_9, [ arg2P_9>-1 && arg1P_9>0 && arg1P_3>0 && arg2P_3>3 && 1+arg1P_3<=1+arg1P_9 && -2+arg2P_3<=1+arg1P_9 ], cost: 3 Eliminated locations (on tree-shaped paths): Start location: __init 16: __init -> [6] : arg1'=arg1P_5, arg2'=1, arg3'=arg2P_9, arg4'=arg4P_5, arg5'=arg5P_5, arg6'=arg6P_5, [ arg2P_9>-1 && arg1P_9>0 && arg1P_3>0 && arg2P_3>3 && 1+arg1P_3<=1+arg1P_9 && -2+arg2P_3<=1+arg1P_9 && arg1P_5<=arg1P_3 && 1+arg2P_9<=1 && 1+arg1P_5<=arg2P_3 && arg1P_5>0 ], cost: NONTERM ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 16: __init -> [6] : arg1'=arg1P_5, arg2'=1, arg3'=arg2P_9, arg4'=arg4P_5, arg5'=arg5P_5, arg6'=arg6P_5, [ arg2P_9>-1 && arg1P_9>0 && arg1P_3>0 && arg2P_3>3 && 1+arg1P_3<=1+arg1P_9 && -2+arg2P_3<=1+arg1P_9 && arg1P_5<=arg1P_3 && 1+arg2P_9<=1 && 1+arg1P_5<=arg2P_3 && arg1P_5>0 ], cost: NONTERM Computing asymptotic complexity for rule 16 Simplified the guard: 16: __init -> [6] : arg1'=arg1P_5, arg2'=1, arg3'=arg2P_9, arg4'=arg4P_5, arg5'=arg5P_5, arg6'=arg6P_5, [ arg2P_9>-1 && arg2P_3>3 && 1+arg1P_3<=1+arg1P_9 && -2+arg2P_3<=1+arg1P_9 && arg1P_5<=arg1P_3 && 1+arg2P_9<=1 && 1+arg1P_5<=arg2P_3 && arg1P_5>0 ], 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: [ arg2P_9>-1 && arg2P_3>3 && 1+arg1P_3<=1+arg1P_9 && -2+arg2P_3<=1+arg1P_9 && arg1P_5<=arg1P_3 && 1+arg2P_9<=1 && 1+arg1P_5<=arg2P_3 && arg1P_5>0 ] NO