NO Initial ITS Start location: __init 0: f1_0_main_Load -> f162_0_main_LT : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 > 0 /\ 1+arg1P0 > 0), cost: 1 1: f162_0_main_LT -> f162_0_main_LT : arg1'=arg1P1, arg2'=arg2P1, (-arg2P1+arg2 == 0 /\ -1+arg1-arg1P1 == 0 /\ 1+arg1 > 0 /\ -arg1+arg2 <= 0 /\ 1+arg2 > 0 /\ arg1-arg2 > 0), cost: 1 2: f162_0_main_LT -> f162_0_main_LT : arg1'=arg1P2, arg2'=arg2P2, (1+2*arg1-arg1P2 == 0 /\ 1+arg1 > 0 /\ 1-arg2P2+arg2 == 0 /\ -arg1+arg2 <= 0 /\ 1+arg2 > 0 /\ arg1-arg2 == 0 /\ 2*arg1 >= 0), cost: 1 3: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Applied preprocessing Original rule: f162_0_main_LT -> f162_0_main_LT : arg1'=arg1P1, arg2'=arg2P1, (-arg2P1+arg2 == 0 /\ -1+arg1-arg1P1 == 0 /\ 1+arg1 > 0 /\ -arg1+arg2 <= 0 /\ 1+arg2 > 0 /\ arg1-arg2 > 0), cost: 1 New rule: f162_0_main_LT -> f162_0_main_LT : arg1'=-1+arg1, (1+arg2 > 0 /\ arg1-arg2 > 0), cost: 1 Applied preprocessing Original rule: f162_0_main_LT -> f162_0_main_LT : arg1'=arg1P2, arg2'=arg2P2, (1+2*arg1-arg1P2 == 0 /\ 1+arg1 > 0 /\ 1-arg2P2+arg2 == 0 /\ -arg1+arg2 <= 0 /\ 1+arg2 > 0 /\ arg1-arg2 == 0 /\ 2*arg1 >= 0), cost: 1 New rule: f162_0_main_LT -> f162_0_main_LT : arg1'=1+2*arg1, arg2'=1+arg2, (arg1 >= 0 /\ arg1-arg2 == 0), cost: 1 Simplified rules Start location: __init 0: f1_0_main_Load -> f162_0_main_LT : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 > 0 /\ 1+arg1P0 > 0), cost: 1 4: f162_0_main_LT -> f162_0_main_LT : arg1'=-1+arg1, (1+arg2 > 0 /\ arg1-arg2 > 0), cost: 1 5: f162_0_main_LT -> f162_0_main_LT : arg1'=1+2*arg1, arg2'=1+arg2, (arg1 >= 0 /\ arg1-arg2 == 0), cost: 1 3: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Applied acceleration Original rule: f162_0_main_LT -> f162_0_main_LT : arg1'=-1+arg1, (1+arg2 > 0 /\ arg1-arg2 > 0), cost: 1 New rule: f162_0_main_LT -> f162_0_main_LT : arg1'=arg1-n1, (n1 >= 0 /\ 1+arg1-n1-arg2 > 0 /\ 1+arg2 > 0), cost: n1 Applied instantiation Original rule: f162_0_main_LT -> f162_0_main_LT : arg1'=arg1-n1, (n1 >= 0 /\ 1+arg1-n1-arg2 > 0 /\ 1+arg2 > 0), cost: n1 New rule: f162_0_main_LT -> f162_0_main_LT : arg1'=arg2, (1 > 0 /\ 1+arg2 > 0 /\ arg1-arg2 >= 0), cost: arg1-arg2 Applied chaining First rule: f162_0_main_LT -> f162_0_main_LT : arg1'=1+2*arg1, arg2'=1+arg2, (arg1 >= 0 /\ arg1-arg2 == 0), cost: 1 Second rule: f162_0_main_LT -> f162_0_main_LT : arg1'=arg2, (1 > 0 /\ 1+arg2 > 0 /\ arg1-arg2 >= 0), cost: arg1-arg2 New rule: f162_0_main_LT -> f162_0_main_LT : arg1'=1+arg2, arg2'=1+arg2, (2*arg1-arg2 >= 0 /\ arg1-arg2 == 0), cost: 1+2*arg1-arg2 Applied nonterm Original rule: f162_0_main_LT -> f162_0_main_LT : arg1'=1+arg2, arg2'=1+arg2, (2*arg1-arg2 >= 0 /\ arg1-arg2 == 0), cost: 1+2*arg1-arg2 New rule: f162_0_main_LT -> [3] : (2*arg1-arg2 >= 0 /\ -arg1+arg2 >= 0 /\ arg1-arg2 >= 0), cost: NONTERM Applied acceleration Original rule: f162_0_main_LT -> f162_0_main_LT : arg1'=1+arg2, arg2'=1+arg2, (2*arg1-arg2 >= 0 /\ arg1-arg2 == 0), cost: 1+2*arg1-arg2 New rule: f162_0_main_LT -> f162_0_main_LT : arg1'=n6+arg2, arg2'=n6+arg2, (2*arg1-arg2 >= 0 /\ -arg1+arg2 >= 0 /\ arg1-arg2 >= 0), cost: 1/2*n6+n6*arg2+1/2*n6^2 Applied chaining First rule: f162_0_main_LT -> f162_0_main_LT : arg1'=arg2, (1 > 0 /\ 1+arg2 > 0 /\ arg1-arg2 >= 0), cost: arg1-arg2 Second rule: f162_0_main_LT -> [3] : (2*arg1-arg2 >= 0 /\ -arg1+arg2 >= 0 /\ arg1-arg2 >= 0), cost: NONTERM New rule: f162_0_main_LT -> [3] : (0 >= 0 /\ 1 > 0 /\ arg2 >= 0 /\ 1+arg2 > 0 /\ arg1-arg2 >= 0), cost: NONTERM Heuristically decided not to add the following rule: f162_0_main_LT -> f162_0_main_LT : arg1'=n6+arg2, arg2'=n6+arg2, (2*arg1-arg2 >= 0 /\ -arg1+arg2 >= 0 /\ arg1-arg2 >= 0), cost: 1/2*n6+n6*arg2+1/2*n6^2 Applied chaining First rule: f162_0_main_LT -> f162_0_main_LT : arg1'=arg2, (1 > 0 /\ 1+arg2 > 0 /\ arg1-arg2 >= 0), cost: arg1-arg2 Second rule: f162_0_main_LT -> f162_0_main_LT : arg1'=1+2*arg1, arg2'=1+arg2, (arg1 >= 0 /\ arg1-arg2 == 0), cost: 1 New rule: f162_0_main_LT -> f162_0_main_LT : arg1'=1+2*arg2, arg2'=1+arg2, (1+arg2 > 0 /\ arg1-arg2 >= 0), cost: 1+arg1-arg2 Applied nonterm Original rule: f162_0_main_LT -> f162_0_main_LT : arg1'=1+2*arg2, arg2'=1+arg2, (1+arg2 > 0 /\ arg1-arg2 >= 0), cost: 1+arg1-arg2 New rule: f162_0_main_LT -> [3] : (1+arg2 > 0 /\ arg1-arg2 >= 0), cost: NONTERM Applied acceleration Original rule: f162_0_main_LT -> f162_0_main_LT : arg1'=1+2*arg2, arg2'=1+arg2, (1+arg2 > 0 /\ arg1-arg2 >= 0), cost: 1+arg1-arg2 New rule: f162_0_main_LT -> f162_0_main_LT : arg1'=-1+2*arg2+2*n8, arg2'=arg2+n8, (1+arg2 > 0 /\ arg1-arg2 >= 0), cost: arg2*n8-1/2*n8+1/2*n8^2 Applied chaining First rule: f162_0_main_LT -> f162_0_main_LT : arg1'=1+2*arg1, arg2'=1+arg2, (arg1 >= 0 /\ arg1-arg2 == 0), cost: 1 Second rule: f162_0_main_LT -> [3] : (1+arg2 > 0 /\ arg1-arg2 >= 0), cost: NONTERM New rule: f162_0_main_LT -> [3] : (arg1 >= 0 /\ 2*arg1-arg2 >= 0 /\ 2+arg2 > 0 /\ arg1-arg2 == 0), cost: NONTERM Applied chaining First rule: f162_0_main_LT -> f162_0_main_LT : arg1'=1+2*arg1, arg2'=1+arg2, (arg1 >= 0 /\ arg1-arg2 == 0), cost: 1 Second rule: f162_0_main_LT -> f162_0_main_LT : arg1'=-1+2*arg2+2*n8, arg2'=arg2+n8, (1+arg2 > 0 /\ arg1-arg2 >= 0), cost: arg2*n8-1/2*n8+1/2*n8^2 New rule: f162_0_main_LT -> f162_0_main_LT : arg1'=1+2*arg2+2*n8, arg2'=1+arg2+n8, (arg1 >= 0 /\ 2*arg1-arg2 >= 0 /\ 2+arg2 > 0 /\ arg1-arg2 == 0), cost: 1-1/2*n8+n8*(1+arg2)+1/2*n8^2 Applied simplification Original rule: f162_0_main_LT -> f162_0_main_LT : arg1'=arg2, (1 > 0 /\ 1+arg2 > 0 /\ arg1-arg2 >= 0), cost: arg1-arg2 New rule: f162_0_main_LT -> f162_0_main_LT : arg1'=arg2, (1+arg2 > 0 /\ arg1-arg2 >= 0), cost: arg1-arg2 Applied simplification Original rule: f162_0_main_LT -> [3] : (0 >= 0 /\ 1 > 0 /\ arg2 >= 0 /\ 1+arg2 > 0 /\ arg1-arg2 >= 0), cost: NONTERM New rule: f162_0_main_LT -> [3] : (1+arg2 > 0 /\ arg1-arg2 >= 0), cost: NONTERM Applied simplification Original rule: f162_0_main_LT -> [3] : (arg1 >= 0 /\ 2*arg1-arg2 >= 0 /\ 2+arg2 > 0 /\ arg1-arg2 == 0), cost: NONTERM New rule: f162_0_main_LT -> [3] : (2*arg1-arg2 >= 0 /\ arg1-arg2 == 0), cost: NONTERM Applied simplification Original rule: f162_0_main_LT -> f162_0_main_LT : arg1'=1+2*arg2+2*n8, arg2'=1+arg2+n8, (arg1 >= 0 /\ 2*arg1-arg2 >= 0 /\ 2+arg2 > 0 /\ arg1-arg2 == 0), cost: 1-1/2*n8+n8*(1+arg2)+1/2*n8^2 New rule: f162_0_main_LT -> f162_0_main_LT : arg1'=1+2*arg2+2*n8, arg2'=1+arg2+n8, (2*arg1-arg2 >= 0 /\ arg1-arg2 == 0), cost: 1-1/2*n8+n8*(1+arg2)+1/2*n8^2 Applied deletion Removed the following rules: 4 Applied deletion Removed the following rules: 9 Accelerated simple loops Start location: __init 0: f1_0_main_Load -> f162_0_main_LT : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 > 0 /\ 1+arg1P0 > 0), cost: 1 5: f162_0_main_LT -> f162_0_main_LT : arg1'=1+2*arg1, arg2'=1+arg2, (arg1 >= 0 /\ arg1-arg2 == 0), cost: 1 7: f162_0_main_LT -> [3] : (2*arg1-arg2 >= 0 /\ -arg1+arg2 >= 0 /\ arg1-arg2 >= 0), cost: NONTERM 11: f162_0_main_LT -> f162_0_main_LT : arg1'=-1+2*arg2+2*n8, arg2'=arg2+n8, (1+arg2 > 0 /\ arg1-arg2 >= 0), cost: arg2*n8-1/2*n8+1/2*n8^2 13: f162_0_main_LT -> f162_0_main_LT : arg1'=arg2, (1+arg2 > 0 /\ arg1-arg2 >= 0), cost: arg1-arg2 14: f162_0_main_LT -> [3] : (1+arg2 > 0 /\ arg1-arg2 >= 0), cost: NONTERM 15: f162_0_main_LT -> [3] : (2*arg1-arg2 >= 0 /\ arg1-arg2 == 0), cost: NONTERM 16: f162_0_main_LT -> f162_0_main_LT : arg1'=1+2*arg2+2*n8, arg2'=1+arg2+n8, (2*arg1-arg2 >= 0 /\ arg1-arg2 == 0), cost: 1-1/2*n8+n8*(1+arg2)+1/2*n8^2 3: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Applied chaining First rule: f1_0_main_Load -> f162_0_main_LT : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 > 0 /\ 1+arg1P0 > 0), cost: 1 Second rule: f162_0_main_LT -> f162_0_main_LT : arg1'=1+2*arg1, arg2'=1+arg2, (arg1 >= 0 /\ arg1-arg2 == 0), cost: 1 New rule: f1_0_main_Load -> f162_0_main_LT : arg1'=1+2*arg2P0, arg2'=1+arg2P0, (arg1 > 0 /\ -1+arg2 > 0 /\ arg2P0 >= 0), cost: 2 Applied chaining First rule: f1_0_main_Load -> f162_0_main_LT : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 > 0 /\ 1+arg1P0 > 0), cost: 1 Second rule: f162_0_main_LT -> [3] : (2*arg1-arg2 >= 0 /\ -arg1+arg2 >= 0 /\ arg1-arg2 >= 0), cost: NONTERM New rule: f1_0_main_Load -> [3] : (arg1 > 0 /\ -1+arg2 > 0), cost: NONTERM Applied chaining First rule: f1_0_main_Load -> f162_0_main_LT : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 > 0 /\ 1+arg1P0 > 0), cost: 1 Second rule: f162_0_main_LT -> f162_0_main_LT : arg1'=-1+2*arg2+2*n8, arg2'=arg2+n8, (1+arg2 > 0 /\ arg1-arg2 >= 0), cost: arg2*n8-1/2*n8+1/2*n8^2 New rule: f1_0_main_Load -> f162_0_main_LT : arg1'=-1+2*n8+2*arg2P0, arg2'=n8+arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 > 0), cost: 1+n8*arg2P0-1/2*n8+1/2*n8^2 Applied chaining First rule: f1_0_main_Load -> f162_0_main_LT : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 > 0 /\ 1+arg1P0 > 0), cost: 1 Second rule: f162_0_main_LT -> f162_0_main_LT : arg1'=arg2, (1+arg2 > 0 /\ arg1-arg2 >= 0), cost: arg1-arg2 New rule: f1_0_main_Load -> f162_0_main_LT : arg1'=arg2P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 > 0 /\ arg1P0-arg2P0 >= 0), cost: 1+arg1P0-arg2P0 Applied chaining First rule: f1_0_main_Load -> f162_0_main_LT : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 > 0 /\ 1+arg1P0 > 0), cost: 1 Second rule: f162_0_main_LT -> [3] : (1+arg2 > 0 /\ arg1-arg2 >= 0), cost: NONTERM New rule: f1_0_main_Load -> [3] : (arg1 > 0 /\ -1+arg2 > 0), cost: NONTERM Applied chaining First rule: f1_0_main_Load -> f162_0_main_LT : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 > 0 /\ 1+arg1P0 > 0), cost: 1 Second rule: f162_0_main_LT -> [3] : (2*arg1-arg2 >= 0 /\ arg1-arg2 == 0), cost: NONTERM New rule: f1_0_main_Load -> [3] : (arg1 > 0 /\ -1+arg2 > 0), cost: NONTERM Applied chaining First rule: f1_0_main_Load -> f162_0_main_LT : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 > 0 /\ 1+arg1P0 > 0), cost: 1 Second rule: f162_0_main_LT -> f162_0_main_LT : arg1'=1+2*arg2+2*n8, arg2'=1+arg2+n8, (2*arg1-arg2 >= 0 /\ arg1-arg2 == 0), cost: 1-1/2*n8+n8*(1+arg2)+1/2*n8^2 New rule: f1_0_main_Load -> f162_0_main_LT : arg1'=1+2*arg1P0+2*n8, arg2'=1+arg1P0+n8, (arg1 > 0 /\ -1+arg2 > 0 /\ arg1P0 >= 0), cost: 2+(1+arg1P0)*n8-1/2*n8+1/2*n8^2 Applied deletion Removed the following rules: 5 7 11 13 14 15 16 Chained accelerated rules with incoming rules Start location: __init 0: f1_0_main_Load -> f162_0_main_LT : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 > 0 /\ 1+arg1P0 > 0), cost: 1 17: f1_0_main_Load -> f162_0_main_LT : arg1'=1+2*arg2P0, arg2'=1+arg2P0, (arg1 > 0 /\ -1+arg2 > 0 /\ arg2P0 >= 0), cost: 2 18: f1_0_main_Load -> [3] : (arg1 > 0 /\ -1+arg2 > 0), cost: NONTERM 19: f1_0_main_Load -> f162_0_main_LT : arg1'=-1+2*n8+2*arg2P0, arg2'=n8+arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 > 0), cost: 1+n8*arg2P0-1/2*n8+1/2*n8^2 20: f1_0_main_Load -> f162_0_main_LT : arg1'=arg2P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 > 0 /\ arg1P0-arg2P0 >= 0), cost: 1+arg1P0-arg2P0 21: f1_0_main_Load -> [3] : (arg1 > 0 /\ -1+arg2 > 0), cost: NONTERM 22: f1_0_main_Load -> [3] : (arg1 > 0 /\ -1+arg2 > 0), cost: NONTERM 23: f1_0_main_Load -> f162_0_main_LT : arg1'=1+2*arg1P0+2*n8, arg2'=1+arg1P0+n8, (arg1 > 0 /\ -1+arg2 > 0 /\ arg1P0 >= 0), cost: 2+(1+arg1P0)*n8-1/2*n8+1/2*n8^2 3: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Removed unreachable locations and irrelevant leafs Start location: __init 18: f1_0_main_Load -> [3] : (arg1 > 0 /\ -1+arg2 > 0), cost: NONTERM 21: f1_0_main_Load -> [3] : (arg1 > 0 /\ -1+arg2 > 0), cost: NONTERM 22: f1_0_main_Load -> [3] : (arg1 > 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 -> [3] : (arg1 > 0 /\ -1+arg2 > 0), cost: NONTERM New rule: __init -> [3] : (-1+arg2P3 > 0 /\ arg1P3 > 0), cost: NONTERM Applied chaining First rule: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Second rule: f1_0_main_Load -> [3] : (arg1 > 0 /\ -1+arg2 > 0), cost: NONTERM New rule: __init -> [3] : (-1+arg2P3 > 0 /\ arg1P3 > 0), cost: NONTERM Applied chaining First rule: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Second rule: f1_0_main_Load -> [3] : (arg1 > 0 /\ -1+arg2 > 0), cost: NONTERM New rule: __init -> [3] : (-1+arg2P3 > 0 /\ arg1P3 > 0), cost: NONTERM Applied deletion Removed the following rules: 3 18 21 22 Eliminated locations on tree-shaped paths Start location: __init 24: __init -> [3] : (-1+arg2P3 > 0 /\ arg1P3 > 0), cost: NONTERM 25: __init -> [3] : (-1+arg2P3 > 0 /\ arg1P3 > 0), cost: NONTERM 26: __init -> [3] : (-1+arg2P3 > 0 /\ arg1P3 > 0), cost: NONTERM Removed duplicate rules (ignoring updates) Start location: __init 26: __init -> [3] : (-1+arg2P3 > 0 /\ arg1P3 > 0), cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 26 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: (-1+arg2P3 > 0 /\ arg1P3 > 0)