NO Initial ITS Start location: __init 0: f1_0_main_Load -> f1_0_main_Load\' : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+x70 > 0 /\ 1+x80 > 0 /\ -1+arg2 > 0 /\ arg1-arg1P0 == 0 /\ -arg2P0+arg2 == 0 /\ -2*x90+x80 == 0), cost: 1 1: f1_0_main_Load\' -> f128_0_loop_GE : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ -arg1P1-x120 == 0 /\ -2+x130-2*x140 < 0 /\ x130-2*x140 >= 0 /\ x130-2*x140 == 0 /\ -1+arg2 > 0 /\ 1+x130 > 0 /\ 1+x120 > 0), cost: 1 2: f128_0_loop_GE -> f128_0_loop_GE : arg1'=arg1P2, arg2'=arg2P2, (arg1 < 0 /\ -1+arg1-arg1P2 == 0), cost: 1 3: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_Load -> f1_0_main_Load\' : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+x70 > 0 /\ 1+x80 > 0 /\ -1+arg2 > 0 /\ arg1-arg1P0 == 0 /\ -arg2P0+arg2 == 0 /\ -2*x90+x80 == 0), cost: 1 New rule: f1_0_main_Load -> f1_0_main_Load\' : (arg1 > 0 /\ 1+2*x90 > 0 /\ -1+arg2 > 0), cost: 1 Applied preprocessing Original rule: f1_0_main_Load\' -> f128_0_loop_GE : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ -arg1P1-x120 == 0 /\ -2+x130-2*x140 < 0 /\ x130-2*x140 >= 0 /\ x130-2*x140 == 0 /\ -1+arg2 > 0 /\ 1+x130 > 0 /\ 1+x120 > 0), cost: 1 New rule: f1_0_main_Load\' -> f128_0_loop_GE : arg1'=-x120, arg2'=arg2P1, (arg1 > 0 /\ 1+2*x140 > 0 /\ -1+arg2 > 0 /\ 1+x120 > 0), cost: 1 Applied preprocessing Original rule: f128_0_loop_GE -> f128_0_loop_GE : arg1'=arg1P2, arg2'=arg2P2, (arg1 < 0 /\ -1+arg1-arg1P2 == 0), cost: 1 New rule: f128_0_loop_GE -> f128_0_loop_GE : arg1'=-1+arg1, arg2'=arg2P2, -arg1 > 0, cost: 1 Simplified rules Start location: __init 4: f1_0_main_Load -> f1_0_main_Load\' : (arg1 > 0 /\ 1+2*x90 > 0 /\ -1+arg2 > 0), cost: 1 5: f1_0_main_Load\' -> f128_0_loop_GE : arg1'=-x120, arg2'=arg2P1, (arg1 > 0 /\ 1+2*x140 > 0 /\ -1+arg2 > 0 /\ 1+x120 > 0), cost: 1 6: f128_0_loop_GE -> f128_0_loop_GE : arg1'=-1+arg1, arg2'=arg2P2, -arg1 > 0, cost: 1 3: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Applied nonterm Original rule: f128_0_loop_GE -> f128_0_loop_GE : arg1'=-1+arg1, arg2'=arg2P2, -arg1 > 0, cost: 1 New rule: f128_0_loop_GE -> [4] : -arg1 > 0, cost: NONTERM Applied acceleration Original rule: f128_0_loop_GE -> f128_0_loop_GE : arg1'=-1+arg1, arg2'=arg2P2, -arg1 > 0, cost: 1 New rule: f128_0_loop_GE -> f128_0_loop_GE : arg1'=arg1-n0, arg2'=arg2P2, -arg1 > 0, cost: n0 Applied deletion Removed the following rules: 6 Accelerated simple loops Start location: __init 4: f1_0_main_Load -> f1_0_main_Load\' : (arg1 > 0 /\ 1+2*x90 > 0 /\ -1+arg2 > 0), cost: 1 5: f1_0_main_Load\' -> f128_0_loop_GE : arg1'=-x120, arg2'=arg2P1, (arg1 > 0 /\ 1+2*x140 > 0 /\ -1+arg2 > 0 /\ 1+x120 > 0), cost: 1 7: f128_0_loop_GE -> [4] : -arg1 > 0, cost: NONTERM 8: f128_0_loop_GE -> f128_0_loop_GE : arg1'=arg1-n0, arg2'=arg2P2, -arg1 > 0, cost: n0 3: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Applied chaining First rule: f1_0_main_Load\' -> f128_0_loop_GE : arg1'=-x120, arg2'=arg2P1, (arg1 > 0 /\ 1+2*x140 > 0 /\ -1+arg2 > 0 /\ 1+x120 > 0), cost: 1 Second rule: f128_0_loop_GE -> [4] : -arg1 > 0, cost: NONTERM New rule: f1_0_main_Load\' -> [4] : (arg1 > 0 /\ 1+2*x140 > 0 /\ -1+arg2 > 0), cost: NONTERM Applied chaining First rule: f1_0_main_Load\' -> f128_0_loop_GE : arg1'=-x120, arg2'=arg2P1, (arg1 > 0 /\ 1+2*x140 > 0 /\ -1+arg2 > 0 /\ 1+x120 > 0), cost: 1 Second rule: f128_0_loop_GE -> f128_0_loop_GE : arg1'=arg1-n0, arg2'=arg2P2, -arg1 > 0, cost: n0 New rule: f1_0_main_Load\' -> f128_0_loop_GE : arg1'=-n0-x120, arg2'=arg2P2, (arg1 > 0 /\ 1+2*x140 > 0 /\ -1+arg2 > 0 /\ x120 > 0), cost: 1+n0 Applied deletion Removed the following rules: 7 8 Chained accelerated rules with incoming rules Start location: __init 4: f1_0_main_Load -> f1_0_main_Load\' : (arg1 > 0 /\ 1+2*x90 > 0 /\ -1+arg2 > 0), cost: 1 5: f1_0_main_Load\' -> f128_0_loop_GE : arg1'=-x120, arg2'=arg2P1, (arg1 > 0 /\ 1+2*x140 > 0 /\ -1+arg2 > 0 /\ 1+x120 > 0), cost: 1 9: f1_0_main_Load\' -> [4] : (arg1 > 0 /\ 1+2*x140 > 0 /\ -1+arg2 > 0), cost: NONTERM 10: f1_0_main_Load\' -> f128_0_loop_GE : arg1'=-n0-x120, arg2'=arg2P2, (arg1 > 0 /\ 1+2*x140 > 0 /\ -1+arg2 > 0 /\ x120 > 0), cost: 1+n0 3: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Removed unreachable locations and irrelevant leafs Start location: __init 4: f1_0_main_Load -> f1_0_main_Load\' : (arg1 > 0 /\ 1+2*x90 > 0 /\ -1+arg2 > 0), cost: 1 9: f1_0_main_Load\' -> [4] : (arg1 > 0 /\ 1+2*x140 > 0 /\ -1+arg2 > 0), cost: NONTERM 3: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Eliminating location f1_0_main_Load by chaining: Applied chaining First rule: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Second rule: f1_0_main_Load -> f1_0_main_Load\' : (arg1 > 0 /\ 1+2*x90 > 0 /\ -1+arg2 > 0), cost: 1 New rule: __init -> f1_0_main_Load\' : arg1'=arg1P3, arg2'=arg2P3, (arg1P3 > 0 /\ 1+2*x90 > 0 /\ -1+arg2P3 > 0), cost: 2 Applied deletion Removed the following rules: 3 4 Eliminating location f1_0_main_Load\' by chaining: Applied chaining First rule: __init -> f1_0_main_Load\' : arg1'=arg1P3, arg2'=arg2P3, (arg1P3 > 0 /\ 1+2*x90 > 0 /\ -1+arg2P3 > 0), cost: 2 Second rule: f1_0_main_Load\' -> [4] : (arg1 > 0 /\ 1+2*x140 > 0 /\ -1+arg2 > 0), cost: NONTERM New rule: __init -> [4] : (arg1P3 > 0 /\ 1+2*x140 > 0 /\ 1+2*x90 > 0 /\ -1+arg2P3 > 0), cost: NONTERM Applied deletion Removed the following rules: 9 11 Eliminated locations on linear paths Start location: __init 12: __init -> [4] : (arg1P3 > 0 /\ 1+2*x140 > 0 /\ 1+2*x90 > 0 /\ -1+arg2P3 > 0), cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 12 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: (arg1P3 > 0 /\ 1+2*x140 > 0 /\ 1+2*x90 > 0 /\ -1+arg2P3 > 0)