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, [ x8_1>-1 && arg2>1 && x9_1-2*x10_1==0 && x9_1>-1 && arg1>0 && arg1==arg1P_1 && arg2==arg2P_1 ], cost: 1 1: f1_0_main_Load\' -> f128_0_loop_GE : arg1'=arg1P_2, arg2'=arg2P_2, [ x13_1>-1 && arg2>1 && x14_1-2*x15_1==0 && x14_1>-1 && arg1>0 && x14_1-2*x15_1<2 && x14_1-2*x15_1>=0 && -x13_1==arg1P_2 ], cost: 1 2: f128_0_loop_GE -> f128_0_loop_GE : arg1'=arg1P_3, arg2'=arg2P_3, [ -5==arg1 && -5==arg1P_3 ], cost: 1 3: f128_0_loop_GE -> f128_0_loop_GE : arg1'=arg1P_4, arg2'=arg2P_4, [ arg1<0 && arg1<-5 && 1+arg1==arg1P_4 ], cost: 1 4: f128_0_loop_GE -> f128_0_loop_GE : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1<0 && arg1>-5 && 1+arg1==arg1P_5 ], cost: 1 5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, [], cost: 1 Simplified all rules, resulting in: Start location: __init 0: f1_0_main_Load -> f1_0_main_Load\' : [ arg2>1 && 2*x10_1>-1 && arg1>0 ], cost: 1 1: f1_0_main_Load\' -> f128_0_loop_GE : arg1'=-x13_1, arg2'=arg2P_2, [ x13_1>-1 && arg2>1 && 2*x15_1>-1 && arg1>0 ], cost: 1 2: f128_0_loop_GE -> f128_0_loop_GE : arg1'=-5, arg2'=arg2P_3, [ -5==arg1 ], cost: 1 3: f128_0_loop_GE -> f128_0_loop_GE : arg1'=1+arg1, arg2'=arg2P_4, [ arg1<-5 ], cost: 1 4: f128_0_loop_GE -> f128_0_loop_GE : arg1'=1+arg1, arg2'=arg2P_5, [ arg1<0 && arg1>-5 ], cost: 1 5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 2. Accelerating the following rules: 2: f128_0_loop_GE -> f128_0_loop_GE : arg1'=-5, arg2'=arg2P_3, [ -5==arg1 ], cost: 1 3: f128_0_loop_GE -> f128_0_loop_GE : arg1'=1+arg1, arg2'=arg2P_4, [ arg1<-5 ], cost: 1 4: f128_0_loop_GE -> f128_0_loop_GE : arg1'=1+arg1, arg2'=arg2P_5, [ arg1<0 && arg1>-5 ], cost: 1 Accelerated rule 2 with non-termination, yielding the new rule 6. Accelerated rule 3 with backward acceleration, yielding the new rule 7. Accelerated rule 4 with backward acceleration, yielding the new rule 8. [accelerate] Nesting with 2 inner and 2 outer candidates Removing the simple loops: 2 3 4. Accelerated all simple loops using metering functions (where possible): Start location: __init 0: f1_0_main_Load -> f1_0_main_Load\' : [ arg2>1 && 2*x10_1>-1 && arg1>0 ], cost: 1 1: f1_0_main_Load\' -> f128_0_loop_GE : arg1'=-x13_1, arg2'=arg2P_2, [ x13_1>-1 && arg2>1 && 2*x15_1>-1 && arg1>0 ], cost: 1 6: f128_0_loop_GE -> [4] : [ -5==arg1 ], cost: NONTERM 7: f128_0_loop_GE -> f128_0_loop_GE : arg1'=-5, arg2'=arg2P_4, [ -5-arg1>=1 ], cost: -5-arg1 8: f128_0_loop_GE -> f128_0_loop_GE : arg1'=0, arg2'=arg2P_5, [ arg1>-5 && -arg1>=1 ], cost: -arg1 5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: __init 0: f1_0_main_Load -> f1_0_main_Load\' : [ arg2>1 && 2*x10_1>-1 && arg1>0 ], cost: 1 1: f1_0_main_Load\' -> f128_0_loop_GE : arg1'=-x13_1, arg2'=arg2P_2, [ x13_1>-1 && arg2>1 && 2*x15_1>-1 && arg1>0 ], cost: 1 9: f1_0_main_Load\' -> [4] : [ arg2>1 && 2*x15_1>-1 && arg1>0 ], cost: NONTERM 10: f1_0_main_Load\' -> f128_0_loop_GE : arg1'=-5, arg2'=arg2P_4, [ arg2>1 && 2*x15_1>-1 && arg1>0 && -5+x13_1>=1 ], cost: -4+x13_1 11: f1_0_main_Load\' -> f128_0_loop_GE : arg1'=0, arg2'=arg2P_5, [ arg2>1 && 2*x15_1>-1 && arg1>0 && -x13_1>-5 && x13_1>=1 ], cost: 1+x13_1 5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, [], 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 && 2*x10_1>-1 && arg1>0 ], cost: 1 9: f1_0_main_Load\' -> [4] : [ arg2>1 && 2*x15_1>-1 && arg1>0 ], cost: NONTERM 10: f1_0_main_Load\' -> f128_0_loop_GE : arg1'=-5, arg2'=arg2P_4, [ arg2>1 && 2*x15_1>-1 && arg1>0 && -5+x13_1>=1 ], cost: -4+x13_1 11: f1_0_main_Load\' -> f128_0_loop_GE : arg1'=0, arg2'=arg2P_5, [ arg2>1 && 2*x15_1>-1 && arg1>0 && -x13_1>-5 && x13_1>=1 ], cost: 1+x13_1 5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, [], cost: 1 Eliminated locations (on linear paths): Start location: __init 9: f1_0_main_Load\' -> [4] : [ arg2>1 && 2*x15_1>-1 && arg1>0 ], cost: NONTERM 10: f1_0_main_Load\' -> f128_0_loop_GE : arg1'=-5, arg2'=arg2P_4, [ arg2>1 && 2*x15_1>-1 && arg1>0 && -5+x13_1>=1 ], cost: -4+x13_1 11: f1_0_main_Load\' -> f128_0_loop_GE : arg1'=0, arg2'=arg2P_5, [ arg2>1 && 2*x15_1>-1 && arg1>0 && -x13_1>-5 && x13_1>=1 ], cost: 1+x13_1 12: __init -> f1_0_main_Load\' : arg1'=arg1P_6, arg2'=arg2P_6, [ arg2P_6>1 && 2*x10_1>-1 && arg1P_6>0 ], cost: 2 Eliminated locations (on tree-shaped paths): Start location: __init 13: __init -> [4] : [ arg2P_6>1 && 2*x10_1>-1 && arg1P_6>0 && 2*x15_1>-1 ], cost: NONTERM 14: __init -> f128_0_loop_GE : arg1'=-5, arg2'=arg2P_4, [ arg2P_6>1 && 2*x10_1>-1 && arg1P_6>0 && 2*x15_1>-1 && -5+x13_1>=1 ], cost: -2+x13_1 15: __init -> f128_0_loop_GE : arg1'=0, arg2'=arg2P_5, [ arg2P_6>1 && 2*x10_1>-1 && arg1P_6>0 && 2*x15_1>-1 && -x13_1>-5 && x13_1>=1 ], cost: 3+x13_1 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: __init 13: __init -> [4] : [ arg2P_6>1 && 2*x10_1>-1 && arg1P_6>0 && 2*x15_1>-1 ], cost: NONTERM 14: __init -> f128_0_loop_GE : arg1'=-5, arg2'=arg2P_4, [ arg2P_6>1 && 2*x10_1>-1 && arg1P_6>0 && 2*x15_1>-1 && -5+x13_1>=1 ], cost: -2+x13_1 15: __init -> f128_0_loop_GE : arg1'=0, arg2'=arg2P_5, [ arg2P_6>1 && 2*x10_1>-1 && arg1P_6>0 && 2*x15_1>-1 && -x13_1>-5 && x13_1>=1 ], cost: 3+x13_1 Computing asymptotic complexity for rule 13 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_6>1 && 2*x10_1>-1 && arg1P_6>0 && 2*x15_1>-1 ] NO