NO Initial ITS Start location: __init 0: f1_0_main_Load -> f82_0_loop_EQ : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ -arg1P0+arg2 == 0 /\ 1+arg2 > 0), cost: 1 1: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=arg1P1, arg2'=arg2P1, (arg1 < 0 /\ 5+arg1 < 0 /\ 1-arg1-arg1P1 == 0 /\ -2+arg1 < 0), cost: 1 2: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=arg1P2, arg2'=arg2P2, (arg1 > 0 /\ 1-arg1-arg1P2 == 0 /\ 5+arg1 < 0 /\ -2+arg1 < 0), cost: 1 3: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=arg1P3, arg2'=arg2P3, (arg1 < 0 /\ 6+arg1 > 0 /\ -6+arg1 < 0 /\ -arg1P3 == 0), cost: 1 4: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=arg1P4, arg2'=arg2P4, (arg1 > 0 /\ -arg1P4 == 0 /\ -6+arg1 < 0), cost: 1 5: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=arg1P5, arg2'=arg2P5, (-1-arg1-arg1P5 == 0 /\ -5+arg1 > 0), cost: 1 6: __init -> f1_0_main_Load : arg1'=arg1P6, arg2'=arg2P6, TRUE, cost: 1 Removed rules with unsatisfiable guard Start location: __init 0: f1_0_main_Load -> f82_0_loop_EQ : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ -arg1P0+arg2 == 0 /\ 1+arg2 > 0), cost: 1 1: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=arg1P1, arg2'=arg2P1, (arg1 < 0 /\ 5+arg1 < 0 /\ 1-arg1-arg1P1 == 0 /\ -2+arg1 < 0), cost: 1 3: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=arg1P3, arg2'=arg2P3, (arg1 < 0 /\ 6+arg1 > 0 /\ -6+arg1 < 0 /\ -arg1P3 == 0), cost: 1 4: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=arg1P4, arg2'=arg2P4, (arg1 > 0 /\ -arg1P4 == 0 /\ -6+arg1 < 0), cost: 1 5: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=arg1P5, arg2'=arg2P5, (-1-arg1-arg1P5 == 0 /\ -5+arg1 > 0), cost: 1 6: __init -> f1_0_main_Load : arg1'=arg1P6, arg2'=arg2P6, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_Load -> f82_0_loop_EQ : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ -arg1P0+arg2 == 0 /\ 1+arg2 > 0), cost: 1 New rule: f1_0_main_Load -> f82_0_loop_EQ : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Applied preprocessing Original rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=arg1P1, arg2'=arg2P1, (arg1 < 0 /\ 5+arg1 < 0 /\ 1-arg1-arg1P1 == 0 /\ -2+arg1 < 0), cost: 1 New rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=1-arg1, arg2'=arg2P1, -5-arg1 > 0, cost: 1 Applied preprocessing Original rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=arg1P3, arg2'=arg2P3, (arg1 < 0 /\ 6+arg1 > 0 /\ -6+arg1 < 0 /\ -arg1P3 == 0), cost: 1 New rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=0, arg2'=arg2P3, (6+arg1 > 0 /\ -arg1 > 0), cost: 1 Applied preprocessing Original rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=arg1P4, arg2'=arg2P4, (arg1 > 0 /\ -arg1P4 == 0 /\ -6+arg1 < 0), cost: 1 New rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=0, arg2'=arg2P4, (arg1 > 0 /\ 6-arg1 > 0), cost: 1 Applied preprocessing Original rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=arg1P5, arg2'=arg2P5, (-1-arg1-arg1P5 == 0 /\ -5+arg1 > 0), cost: 1 New rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=-1-arg1, arg2'=arg2P5, -5+arg1 > 0, cost: 1 Simplified rules Start location: __init 7: f1_0_main_Load -> f82_0_loop_EQ : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 8: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=1-arg1, arg2'=arg2P1, -5-arg1 > 0, cost: 1 9: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=0, arg2'=arg2P3, (6+arg1 > 0 /\ -arg1 > 0), cost: 1 10: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=0, arg2'=arg2P4, (arg1 > 0 /\ 6-arg1 > 0), cost: 1 11: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=-1-arg1, arg2'=arg2P5, -5+arg1 > 0, cost: 1 6: __init -> f1_0_main_Load : arg1'=arg1P6, arg2'=arg2P6, TRUE, cost: 1 Applied chaining First rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=1-arg1, arg2'=arg2P1, -5-arg1 > 0, cost: 1 Second rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=-1-arg1, arg2'=arg2P5, -5+arg1 > 0, cost: 1 New rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=-2+arg1, arg2'=arg2P5, -5-arg1 > 0, cost: 2 Applied nonterm Original rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=-2+arg1, arg2'=arg2P5, -5-arg1 > 0, cost: 2 New rule: f82_0_loop_EQ -> [3] : -5-arg1 > 0, cost: NONTERM Applied acceleration Original rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=-2+arg1, arg2'=arg2P5, -5-arg1 > 0, cost: 2 New rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=arg1-2*n5, arg2'=arg2P5, -5-arg1 > 0, cost: 2*n5 Applied chaining First rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=-1-arg1, arg2'=arg2P5, -5+arg1 > 0, cost: 1 Second rule: f82_0_loop_EQ -> [3] : -5-arg1 > 0, cost: NONTERM New rule: f82_0_loop_EQ -> [3] : (-4+arg1 > 0 /\ -5+arg1 > 0), cost: NONTERM Applied chaining First rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=-1-arg1, arg2'=arg2P5, -5+arg1 > 0, cost: 1 Second rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=arg1-2*n5, arg2'=arg2P5, -5-arg1 > 0, cost: 2*n5 New rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=-1-arg1-2*n5, arg2'=arg2P5, (-4+arg1 > 0 /\ -5+arg1 > 0), cost: 1+2*n5 Applied chaining First rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=-1-arg1, arg2'=arg2P5, -5+arg1 > 0, cost: 1 Second rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=1-arg1, arg2'=arg2P1, -5-arg1 > 0, cost: 1 New rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=2+arg1, arg2'=arg2P1, -5+arg1 > 0, cost: 2 Applied nonterm Original rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=2+arg1, arg2'=arg2P1, -5+arg1 > 0, cost: 2 New rule: f82_0_loop_EQ -> [3] : -5+arg1 > 0, cost: NONTERM Applied acceleration Original rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=2+arg1, arg2'=arg2P1, -5+arg1 > 0, cost: 2 New rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=arg1+2*n7, arg2'=arg2P1, -5+arg1 > 0, cost: 2*n7 Applied chaining First rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=1-arg1, arg2'=arg2P1, -5-arg1 > 0, cost: 1 Second rule: f82_0_loop_EQ -> [3] : -5+arg1 > 0, cost: NONTERM New rule: f82_0_loop_EQ -> [3] : (-4-arg1 > 0 /\ -5-arg1 > 0), cost: NONTERM Applied chaining First rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=1-arg1, arg2'=arg2P1, -5-arg1 > 0, cost: 1 Second rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=arg1+2*n7, arg2'=arg2P1, -5+arg1 > 0, cost: 2*n7 New rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=1-arg1+2*n7, arg2'=arg2P1, (-4-arg1 > 0 /\ -5-arg1 > 0), cost: 1+2*n7 Applied simplification Original rule: f82_0_loop_EQ -> [3] : (-4+arg1 > 0 /\ -5+arg1 > 0), cost: NONTERM New rule: f82_0_loop_EQ -> [3] : -5+arg1 > 0, cost: NONTERM Applied simplification Original rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=-1-arg1-2*n5, arg2'=arg2P5, (-4+arg1 > 0 /\ -5+arg1 > 0), cost: 1+2*n5 New rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=-1-arg1-2*n5, arg2'=arg2P5, -5+arg1 > 0, cost: 1+2*n5 Applied simplification Original rule: f82_0_loop_EQ -> [3] : (-4-arg1 > 0 /\ -5-arg1 > 0), cost: NONTERM New rule: f82_0_loop_EQ -> [3] : -5-arg1 > 0, cost: NONTERM Applied simplification Original rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=1-arg1+2*n7, arg2'=arg2P1, (-4-arg1 > 0 /\ -5-arg1 > 0), cost: 1+2*n7 New rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=1-arg1+2*n7, arg2'=arg2P1, -5-arg1 > 0, cost: 1+2*n7 Applied deletion Removed the following rules: 12 16 Accelerated simple loops Start location: __init 7: f1_0_main_Load -> f82_0_loop_EQ : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 8: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=1-arg1, arg2'=arg2P1, -5-arg1 > 0, cost: 1 9: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=0, arg2'=arg2P3, (6+arg1 > 0 /\ -arg1 > 0), cost: 1 10: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=0, arg2'=arg2P4, (arg1 > 0 /\ 6-arg1 > 0), cost: 1 11: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=-1-arg1, arg2'=arg2P5, -5+arg1 > 0, cost: 1 14: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=arg1-2*n5, arg2'=arg2P5, -5-arg1 > 0, cost: 2*n5 18: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=arg1+2*n7, arg2'=arg2P1, -5+arg1 > 0, cost: 2*n7 20: f82_0_loop_EQ -> [3] : -5+arg1 > 0, cost: NONTERM 21: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=-1-arg1-2*n5, arg2'=arg2P5, -5+arg1 > 0, cost: 1+2*n5 22: f82_0_loop_EQ -> [3] : -5-arg1 > 0, cost: NONTERM 23: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=1-arg1+2*n7, arg2'=arg2P1, -5-arg1 > 0, cost: 1+2*n7 6: __init -> f1_0_main_Load : arg1'=arg1P6, arg2'=arg2P6, TRUE, cost: 1 Applied chaining First rule: f1_0_main_Load -> f82_0_loop_EQ : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=0, arg2'=arg2P4, (arg1 > 0 /\ 6-arg1 > 0), cost: 1 New rule: f1_0_main_Load -> f82_0_loop_EQ : arg1'=0, arg2'=arg2P4, (arg1 > 0 /\ arg2 > 0 /\ 6-arg2 > 0), cost: 2 Applied chaining First rule: f1_0_main_Load -> f82_0_loop_EQ : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=-1-arg1, arg2'=arg2P5, -5+arg1 > 0, cost: 1 New rule: f1_0_main_Load -> f82_0_loop_EQ : arg1'=-1-arg2, arg2'=arg2P5, (arg1 > 0 /\ -5+arg2 > 0), cost: 2 Applied chaining First rule: f1_0_main_Load -> f82_0_loop_EQ : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=arg1+2*n7, arg2'=arg2P1, -5+arg1 > 0, cost: 2*n7 New rule: f1_0_main_Load -> f82_0_loop_EQ : arg1'=2*n7+arg2, arg2'=arg2P1, (arg1 > 0 /\ -5+arg2 > 0), cost: 1+2*n7 Applied chaining First rule: f1_0_main_Load -> f82_0_loop_EQ : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f82_0_loop_EQ -> [3] : -5+arg1 > 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 -> f82_0_loop_EQ : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg1'=-1-arg1-2*n5, arg2'=arg2P5, -5+arg1 > 0, cost: 1+2*n5 New rule: f1_0_main_Load -> f82_0_loop_EQ : arg1'=-1-arg2-2*n5, arg2'=arg2P5, (arg1 > 0 /\ -5+arg2 > 0), cost: 2+2*n5 Applied deletion Removed the following rules: 8 9 10 11 14 18 20 21 22 23 Chained accelerated rules with incoming rules Start location: __init 7: f1_0_main_Load -> f82_0_loop_EQ : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 24: f1_0_main_Load -> f82_0_loop_EQ : arg1'=0, arg2'=arg2P4, (arg1 > 0 /\ arg2 > 0 /\ 6-arg2 > 0), cost: 2 25: f1_0_main_Load -> f82_0_loop_EQ : arg1'=-1-arg2, arg2'=arg2P5, (arg1 > 0 /\ -5+arg2 > 0), cost: 2 26: f1_0_main_Load -> f82_0_loop_EQ : arg1'=2*n7+arg2, arg2'=arg2P1, (arg1 > 0 /\ -5+arg2 > 0), cost: 1+2*n7 27: f1_0_main_Load -> [3] : (arg1 > 0 /\ -5+arg2 > 0), cost: NONTERM 28: f1_0_main_Load -> f82_0_loop_EQ : arg1'=-1-arg2-2*n5, arg2'=arg2P5, (arg1 > 0 /\ -5+arg2 > 0), cost: 2+2*n5 6: __init -> f1_0_main_Load : arg1'=arg1P6, arg2'=arg2P6, 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 6: __init -> f1_0_main_Load : arg1'=arg1P6, arg2'=arg2P6, TRUE, cost: 1 Eliminating location f1_0_main_Load by chaining: Applied chaining First rule: __init -> f1_0_main_Load : arg1'=arg1P6, arg2'=arg2P6, TRUE, cost: 1 Second rule: f1_0_main_Load -> [3] : (arg1 > 0 /\ -5+arg2 > 0), cost: NONTERM New rule: __init -> [3] : (-5+arg2P6 > 0 /\ arg1P6 > 0), cost: NONTERM Applied deletion Removed the following rules: 6 27 Eliminated locations on linear paths Start location: __init 29: __init -> [3] : (-5+arg2P6 > 0 /\ arg1P6 > 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+arg2P6 > 0 /\ arg1P6 > 0)