NO Initial ITS Start location: __init 0: f1_0_main_Load -> f142_0_loop_EQ : arg1'=arg1P0, arg2'=arg2P0, (arg2-arg2P0 == 0 /\ arg1 > 0 /\ 5-arg1P0 == 0 /\ 1+arg2 > 0), cost: 1 1: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=arg1P1, arg2'=arg2P1, (arg1+arg2 < 0 /\ arg2 < 0 /\ 1+arg1-arg1P1 == 0 /\ 1-arg2P1-arg2 == 0), cost: 1 2: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=arg1P2, arg2'=arg2P2, (arg1+arg2 < 0 /\ 1-arg2P2-arg2 == 0 /\ 1+arg1-arg1P2 == 0 /\ arg2 > 0), cost: 1 3: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=arg1P3, arg2'=arg2P3, (arg1+arg2 >= 0 /\ -arg2P3 == 0 /\ 1+arg1-arg1P3 == 0 /\ -arg1+arg2 <= 0 /\ arg2 < 0), cost: 1 4: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=arg1P4, arg2'=arg2P4, (arg1+arg2 >= 0 /\ 1+arg1-arg1P4 == 0 /\ -arg1+arg2 <= 0 /\ arg2 > 0 /\ -arg2P4 == 0), cost: 1 5: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=arg1P5, arg2'=arg2P5, (-1-arg2-arg2P5 == 0 /\ arg1+arg2 >= 0 /\ -arg1+arg2 > 0 /\ arg2 < 0 /\ 1+arg1-arg1P5 == 0), cost: 1 6: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=arg1P6, arg2'=arg2P6, (arg1+arg2 >= 0 /\ -1-arg2P6-arg2 == 0 /\ -arg1+arg2 > 0 /\ arg2 > 0 /\ 1+arg1-arg1P6 == 0), cost: 1 7: __init -> f1_0_main_Load : arg1'=arg1P7, arg2'=arg2P7, TRUE, cost: 1 Removed rules with unsatisfiable guard Start location: __init 0: f1_0_main_Load -> f142_0_loop_EQ : arg1'=arg1P0, arg2'=arg2P0, (arg2-arg2P0 == 0 /\ arg1 > 0 /\ 5-arg1P0 == 0 /\ 1+arg2 > 0), cost: 1 1: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=arg1P1, arg2'=arg2P1, (arg1+arg2 < 0 /\ arg2 < 0 /\ 1+arg1-arg1P1 == 0 /\ 1-arg2P1-arg2 == 0), cost: 1 2: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=arg1P2, arg2'=arg2P2, (arg1+arg2 < 0 /\ 1-arg2P2-arg2 == 0 /\ 1+arg1-arg1P2 == 0 /\ arg2 > 0), cost: 1 3: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=arg1P3, arg2'=arg2P3, (arg1+arg2 >= 0 /\ -arg2P3 == 0 /\ 1+arg1-arg1P3 == 0 /\ -arg1+arg2 <= 0 /\ arg2 < 0), cost: 1 4: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=arg1P4, arg2'=arg2P4, (arg1+arg2 >= 0 /\ 1+arg1-arg1P4 == 0 /\ -arg1+arg2 <= 0 /\ arg2 > 0 /\ -arg2P4 == 0), cost: 1 6: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=arg1P6, arg2'=arg2P6, (arg1+arg2 >= 0 /\ -1-arg2P6-arg2 == 0 /\ -arg1+arg2 > 0 /\ arg2 > 0 /\ 1+arg1-arg1P6 == 0), cost: 1 7: __init -> f1_0_main_Load : arg1'=arg1P7, arg2'=arg2P7, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_Load -> f142_0_loop_EQ : arg1'=arg1P0, arg2'=arg2P0, (arg2-arg2P0 == 0 /\ arg1 > 0 /\ 5-arg1P0 == 0 /\ 1+arg2 > 0), cost: 1 New rule: f1_0_main_Load -> f142_0_loop_EQ : arg1'=5, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Applied preprocessing Original rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=arg1P1, arg2'=arg2P1, (arg1+arg2 < 0 /\ arg2 < 0 /\ 1+arg1-arg1P1 == 0 /\ 1-arg2P1-arg2 == 0), cost: 1 New rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=1-arg2, (-arg1-arg2 > 0 /\ -arg2 > 0), cost: 1 Applied preprocessing Original rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=arg1P2, arg2'=arg2P2, (arg1+arg2 < 0 /\ 1-arg2P2-arg2 == 0 /\ 1+arg1-arg1P2 == 0 /\ arg2 > 0), cost: 1 New rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=1-arg2, (-arg1-arg2 > 0 /\ arg2 > 0), cost: 1 Applied preprocessing Original rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=arg1P3, arg2'=arg2P3, (arg1+arg2 >= 0 /\ -arg2P3 == 0 /\ 1+arg1-arg1P3 == 0 /\ -arg1+arg2 <= 0 /\ arg2 < 0), cost: 1 New rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=0, (arg1+arg2 >= 0 /\ -arg2 > 0), cost: 1 Applied preprocessing Original rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=arg1P4, arg2'=arg2P4, (arg1+arg2 >= 0 /\ 1+arg1-arg1P4 == 0 /\ -arg1+arg2 <= 0 /\ arg2 > 0 /\ -arg2P4 == 0), cost: 1 New rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=0, (-arg1+arg2 <= 0 /\ arg2 > 0), cost: 1 Applied preprocessing Original rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=arg1P6, arg2'=arg2P6, (arg1+arg2 >= 0 /\ -1-arg2P6-arg2 == 0 /\ -arg1+arg2 > 0 /\ arg2 > 0 /\ 1+arg1-arg1P6 == 0), cost: 1 New rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=-1-arg2, (arg1+arg2 >= 0 /\ -arg1+arg2 > 0), cost: 1 Simplified rules Start location: __init 8: f1_0_main_Load -> f142_0_loop_EQ : arg1'=5, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 9: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=1-arg2, (-arg1-arg2 > 0 /\ -arg2 > 0), cost: 1 10: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=1-arg2, (-arg1-arg2 > 0 /\ arg2 > 0), cost: 1 11: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=0, (arg1+arg2 >= 0 /\ -arg2 > 0), cost: 1 12: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=0, (-arg1+arg2 <= 0 /\ arg2 > 0), cost: 1 13: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=-1-arg2, (arg1+arg2 >= 0 /\ -arg1+arg2 > 0), cost: 1 7: __init -> f1_0_main_Load : arg1'=arg1P7, arg2'=arg2P7, TRUE, cost: 1 Applied chaining First rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=1-arg2, (-arg1-arg2 > 0 /\ -arg2 > 0), cost: 1 Second rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=-1-arg2, (arg1+arg2 >= 0 /\ -arg1+arg2 > 0), cost: 1 New rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=2+arg1, arg2'=-2+arg2, (-arg1-arg2 > 0 /\ -arg2 > 0 /\ 2+arg1-arg2 >= 0), cost: 2 Applied nonterm Original rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=2+arg1, arg2'=-2+arg2, (-arg1-arg2 > 0 /\ -arg2 > 0 /\ 2+arg1-arg2 >= 0), cost: 2 New rule: f142_0_loop_EQ -> [3] : (-arg1-arg2 > 0 /\ -arg2 > 0 /\ 2+arg1-arg2 >= 0), cost: NONTERM Applied acceleration Original rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=2+arg1, arg2'=-2+arg2, (-arg1-arg2 > 0 /\ -arg2 > 0 /\ 2+arg1-arg2 >= 0), cost: 2 New rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=arg1+2*n8, arg2'=-2*n8+arg2, (-arg1-arg2 > 0 /\ -arg2 > 0 /\ 2+arg1-arg2 >= 0), cost: 2*n8 Applied chaining First rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=-1-arg2, (arg1+arg2 >= 0 /\ -arg1+arg2 > 0), cost: 1 Second rule: f142_0_loop_EQ -> [3] : (-arg1-arg2 > 0 /\ -arg2 > 0 /\ 2+arg1-arg2 >= 0), cost: NONTERM New rule: f142_0_loop_EQ -> [3] : (arg1+arg2 >= 0 /\ -arg1+arg2 > 0 /\ 4+arg1+arg2 >= 0 /\ 1+arg2 > 0), cost: NONTERM Applied chaining First rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=-1-arg2, (arg1+arg2 >= 0 /\ -arg1+arg2 > 0), cost: 1 Second rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=arg1+2*n8, arg2'=-2*n8+arg2, (-arg1-arg2 > 0 /\ -arg2 > 0 /\ 2+arg1-arg2 >= 0), cost: 2*n8 New rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1+2*n8, arg2'=-1-2*n8-arg2, (arg1+arg2 >= 0 /\ -arg1+arg2 > 0 /\ 4+arg1+arg2 >= 0 /\ 1+arg2 > 0), cost: 1+2*n8 Applied chaining First rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=-1-arg2, (arg1+arg2 >= 0 /\ -arg1+arg2 > 0), cost: 1 Second rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=1-arg2, (-arg1-arg2 > 0 /\ -arg2 > 0), cost: 1 New rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=2+arg1, arg2'=2+arg2, (arg1+arg2 >= 0 /\ -arg1+arg2 > 0), cost: 2 Applied nonterm Original rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=2+arg1, arg2'=2+arg2, (arg1+arg2 >= 0 /\ -arg1+arg2 > 0), cost: 2 New rule: f142_0_loop_EQ -> [3] : (arg1+arg2 >= 0 /\ -arg1+arg2 > 0), cost: NONTERM Applied acceleration Original rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=2+arg1, arg2'=2+arg2, (arg1+arg2 >= 0 /\ -arg1+arg2 > 0), cost: 2 New rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=arg1+2*n12, arg2'=arg2+2*n12, (arg1+arg2 >= 0 /\ -arg1+arg2 > 0), cost: 2*n12 Applied chaining First rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=1-arg2, (-arg1-arg2 > 0 /\ -arg2 > 0), cost: 1 Second rule: f142_0_loop_EQ -> [3] : (arg1+arg2 >= 0 /\ -arg1+arg2 > 0), cost: NONTERM New rule: f142_0_loop_EQ -> [3] : (-arg1-arg2 > 0 /\ -arg2 > 0 /\ 2+arg1-arg2 >= 0), cost: NONTERM Applied chaining First rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=1-arg2, (-arg1-arg2 > 0 /\ -arg2 > 0), cost: 1 Second rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=arg1+2*n12, arg2'=arg2+2*n12, (arg1+arg2 >= 0 /\ -arg1+arg2 > 0), cost: 2*n12 New rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1+2*n12, arg2'=1-arg2+2*n12, (-arg1-arg2 > 0 /\ -arg2 > 0 /\ 2+arg1-arg2 >= 0), cost: 1+2*n12 Applied simplification Original rule: f142_0_loop_EQ -> [3] : (arg1+arg2 >= 0 /\ -arg1+arg2 > 0 /\ 4+arg1+arg2 >= 0 /\ 1+arg2 > 0), cost: NONTERM New rule: f142_0_loop_EQ -> [3] : (arg1+arg2 >= 0 /\ -arg1+arg2 > 0), cost: NONTERM Applied simplification Original rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1+2*n8, arg2'=-1-2*n8-arg2, (arg1+arg2 >= 0 /\ -arg1+arg2 > 0 /\ 4+arg1+arg2 >= 0 /\ 1+arg2 > 0), cost: 1+2*n8 New rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1+2*n8, arg2'=-1-2*n8-arg2, (arg1+arg2 >= 0 /\ -arg1+arg2 > 0), cost: 1+2*n8 Applied deletion Removed the following rules: 14 18 Accelerated simple loops Start location: __init 8: f1_0_main_Load -> f142_0_loop_EQ : arg1'=5, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 9: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=1-arg2, (-arg1-arg2 > 0 /\ -arg2 > 0), cost: 1 10: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=1-arg2, (-arg1-arg2 > 0 /\ arg2 > 0), cost: 1 11: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=0, (arg1+arg2 >= 0 /\ -arg2 > 0), cost: 1 12: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=0, (-arg1+arg2 <= 0 /\ arg2 > 0), cost: 1 13: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=-1-arg2, (arg1+arg2 >= 0 /\ -arg1+arg2 > 0), cost: 1 16: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=arg1+2*n8, arg2'=-2*n8+arg2, (-arg1-arg2 > 0 /\ -arg2 > 0 /\ 2+arg1-arg2 >= 0), cost: 2*n8 19: f142_0_loop_EQ -> [3] : (-arg1-arg2 > 0 /\ -arg2 > 0 /\ 2+arg1-arg2 >= 0), cost: NONTERM 20: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=arg1+2*n12, arg2'=arg2+2*n12, (arg1+arg2 >= 0 /\ -arg1+arg2 > 0), cost: 2*n12 21: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1+2*n12, arg2'=1-arg2+2*n12, (-arg1-arg2 > 0 /\ -arg2 > 0 /\ 2+arg1-arg2 >= 0), cost: 1+2*n12 22: f142_0_loop_EQ -> [3] : (arg1+arg2 >= 0 /\ -arg1+arg2 > 0), cost: NONTERM 23: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1+2*n8, arg2'=-1-2*n8-arg2, (arg1+arg2 >= 0 /\ -arg1+arg2 > 0), cost: 1+2*n8 7: __init -> f1_0_main_Load : arg1'=arg1P7, arg2'=arg2P7, TRUE, cost: 1 Applied chaining First rule: f1_0_main_Load -> f142_0_loop_EQ : arg1'=5, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=0, (-arg1+arg2 <= 0 /\ arg2 > 0), cost: 1 New rule: f1_0_main_Load -> f142_0_loop_EQ : arg1'=6, arg2'=0, (arg1 > 0 /\ arg2 > 0 /\ -5+arg2 <= 0), cost: 2 Applied chaining First rule: f1_0_main_Load -> f142_0_loop_EQ : arg1'=5, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1, arg2'=-1-arg2, (arg1+arg2 >= 0 /\ -arg1+arg2 > 0), cost: 1 New rule: f1_0_main_Load -> f142_0_loop_EQ : arg1'=6, arg2'=-1-arg2, (arg1 > 0 /\ -5+arg2 > 0), cost: 2 Applied chaining First rule: f1_0_main_Load -> f142_0_loop_EQ : arg1'=5, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=arg1+2*n12, arg2'=arg2+2*n12, (arg1+arg2 >= 0 /\ -arg1+arg2 > 0), cost: 2*n12 New rule: f1_0_main_Load -> f142_0_loop_EQ : arg1'=5+2*n12, arg2'=arg2+2*n12, (arg1 > 0 /\ -5+arg2 > 0), cost: 1+2*n12 Applied chaining First rule: f1_0_main_Load -> f142_0_loop_EQ : arg1'=5, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f142_0_loop_EQ -> [3] : (arg1+arg2 >= 0 /\ -arg1+arg2 > 0), cost: NONTERM New rule: f1_0_main_Load -> [3] : (arg1 > 0 /\ -5+arg2 > 0), cost: NONTERM Applied chaining First rule: f1_0_main_Load -> f142_0_loop_EQ : arg1'=5, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f142_0_loop_EQ -> f142_0_loop_EQ : arg1'=1+arg1+2*n8, arg2'=-1-2*n8-arg2, (arg1+arg2 >= 0 /\ -arg1+arg2 > 0), cost: 1+2*n8 New rule: f1_0_main_Load -> f142_0_loop_EQ : arg1'=6+2*n8, arg2'=-1-2*n8-arg2, (arg1 > 0 /\ -5+arg2 > 0), cost: 2+2*n8 Applied deletion Removed the following rules: 9 10 11 12 13 16 19 20 21 22 23 Chained accelerated rules with incoming rules Start location: __init 8: f1_0_main_Load -> f142_0_loop_EQ : arg1'=5, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 24: f1_0_main_Load -> f142_0_loop_EQ : arg1'=6, arg2'=0, (arg1 > 0 /\ arg2 > 0 /\ -5+arg2 <= 0), cost: 2 25: f1_0_main_Load -> f142_0_loop_EQ : arg1'=6, arg2'=-1-arg2, (arg1 > 0 /\ -5+arg2 > 0), cost: 2 26: f1_0_main_Load -> f142_0_loop_EQ : arg1'=5+2*n12, arg2'=arg2+2*n12, (arg1 > 0 /\ -5+arg2 > 0), cost: 1+2*n12 27: f1_0_main_Load -> [3] : (arg1 > 0 /\ -5+arg2 > 0), cost: NONTERM 28: f1_0_main_Load -> f142_0_loop_EQ : arg1'=6+2*n8, arg2'=-1-2*n8-arg2, (arg1 > 0 /\ -5+arg2 > 0), cost: 2+2*n8 7: __init -> f1_0_main_Load : arg1'=arg1P7, arg2'=arg2P7, TRUE, cost: 1 Removed unreachable locations and irrelevant leafs Start location: __init 27: f1_0_main_Load -> [3] : (arg1 > 0 /\ -5+arg2 > 0), cost: NONTERM 7: __init -> f1_0_main_Load : arg1'=arg1P7, arg2'=arg2P7, TRUE, cost: 1 Eliminating location f1_0_main_Load by chaining: Applied chaining First rule: __init -> f1_0_main_Load : arg1'=arg1P7, arg2'=arg2P7, TRUE, cost: 1 Second rule: f1_0_main_Load -> [3] : (arg1 > 0 /\ -5+arg2 > 0), cost: NONTERM New rule: __init -> [3] : (-5+arg2P7 > 0 /\ arg1P7 > 0), cost: NONTERM Applied deletion Removed the following rules: 7 27 Eliminated locations on linear paths Start location: __init 29: __init -> [3] : (-5+arg2P7 > 0 /\ arg1P7 > 0), cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 29 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: (-5+arg2P7 > 0 /\ arg1P7 > 0)