NO Initial ITS Start location: __init 0: f1_0_main_Load -> f1_0_main_Load\' : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+x110 > 0 /\ -1-2*x130+x120 == 0 /\ 1+x120 > 0 /\ -1+arg2 > 0 /\ arg1-arg1P0 == 0 /\ -arg2P0+arg2 == 0), cost: 1 2: f1_0_main_Load -> f1_0_main_Load\' : arg1'=arg1P2, arg2'=arg2P2, (arg1 > 0 /\ 1+x210 > 0 /\ -1+arg2 > 0 /\ arg1-arg1P2 == 0 /\ 1+x220 > 0 /\ arg2-arg2P2 == 0 /\ x220-2*x230 == 0), cost: 1 1: f1_0_main_Load\' -> f171_0_sum_EQ : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ 1+x170 > 0 /\ -1-2*x180+x170 == 0 /\ -1+arg2 > 0 /\ -2-2*x180+x170 < 0 /\ 1+arg1P1 > 0 /\ -2*x180+x170 >= 0), cost: 1 3: f1_0_main_Load\' -> f171_0_sum_EQ : arg1'=arg1P3, arg2'=arg2P3, (arg1 > 0 /\ 1+x260 > 0 /\ -arg1P3-x260 == 0 /\ -1+arg2 > 0 /\ 1+x270 > 0 /\ x270-2*x280 >= 0 /\ x270-2*x280 == 0 /\ -2+x270-2*x280 < 0), cost: 1 4: f171_0_sum_EQ -> f171_0_sum_EQ : arg1'=arg1P4, arg2'=arg2P4, (arg1 < 0 /\ -1+arg1-arg1P4 == 0), cost: 1 5: f171_0_sum_EQ -> f171_0_sum_EQ : arg1'=arg1P5, arg2'=arg2P5, (arg1 > 0 /\ -1+arg1-arg1P5 == 0), cost: 1 6: __init -> f1_0_main_Load : arg1'=arg1P6, arg2'=arg2P6, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_Load -> f1_0_main_Load\' : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+x110 > 0 /\ -1-2*x130+x120 == 0 /\ 1+x120 > 0 /\ -1+arg2 > 0 /\ arg1-arg1P0 == 0 /\ -arg2P0+arg2 == 0), cost: 1 New rule: f1_0_main_Load -> f1_0_main_Load\' : (arg1 > 0 /\ 2+2*x130 > 0 /\ -1+arg2 > 0), cost: 1 Applied preprocessing Original rule: f1_0_main_Load\' -> f171_0_sum_EQ : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ 1+x170 > 0 /\ -1-2*x180+x170 == 0 /\ -1+arg2 > 0 /\ -2-2*x180+x170 < 0 /\ 1+arg1P1 > 0 /\ -2*x180+x170 >= 0), cost: 1 New rule: f1_0_main_Load\' -> f171_0_sum_EQ : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ -1+arg2 > 0 /\ 2+2*x180 > 0 /\ 1+arg1P1 > 0), cost: 1 Applied preprocessing Original rule: f1_0_main_Load -> f1_0_main_Load\' : arg1'=arg1P2, arg2'=arg2P2, (arg1 > 0 /\ 1+x210 > 0 /\ -1+arg2 > 0 /\ arg1-arg1P2 == 0 /\ 1+x220 > 0 /\ arg2-arg2P2 == 0 /\ x220-2*x230 == 0), cost: 1 New rule: f1_0_main_Load -> f1_0_main_Load\' : (arg1 > 0 /\ 1+2*x230 > 0 /\ -1+arg2 > 0), cost: 1 Applied preprocessing Original rule: f1_0_main_Load\' -> f171_0_sum_EQ : arg1'=arg1P3, arg2'=arg2P3, (arg1 > 0 /\ 1+x260 > 0 /\ -arg1P3-x260 == 0 /\ -1+arg2 > 0 /\ 1+x270 > 0 /\ x270-2*x280 >= 0 /\ x270-2*x280 == 0 /\ -2+x270-2*x280 < 0), cost: 1 New rule: f1_0_main_Load\' -> f171_0_sum_EQ : arg1'=-x260, arg2'=arg2P3, (arg1 > 0 /\ 1+2*x280 > 0 /\ 1+x260 > 0 /\ -1+arg2 > 0), cost: 1 Applied preprocessing Original rule: f171_0_sum_EQ -> f171_0_sum_EQ : arg1'=arg1P4, arg2'=arg2P4, (arg1 < 0 /\ -1+arg1-arg1P4 == 0), cost: 1 New rule: f171_0_sum_EQ -> f171_0_sum_EQ : arg1'=-1+arg1, arg2'=arg2P4, -arg1 > 0, cost: 1 Applied preprocessing Original rule: f171_0_sum_EQ -> f171_0_sum_EQ : arg1'=arg1P5, arg2'=arg2P5, (arg1 > 0 /\ -1+arg1-arg1P5 == 0), cost: 1 New rule: f171_0_sum_EQ -> f171_0_sum_EQ : arg1'=-1+arg1, arg2'=arg2P5, arg1 > 0, cost: 1 Simplified rules Start location: __init 7: f1_0_main_Load -> f1_0_main_Load\' : (arg1 > 0 /\ 2+2*x130 > 0 /\ -1+arg2 > 0), cost: 1 9: f1_0_main_Load -> f1_0_main_Load\' : (arg1 > 0 /\ 1+2*x230 > 0 /\ -1+arg2 > 0), cost: 1 8: f1_0_main_Load\' -> f171_0_sum_EQ : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ -1+arg2 > 0 /\ 2+2*x180 > 0 /\ 1+arg1P1 > 0), cost: 1 10: f1_0_main_Load\' -> f171_0_sum_EQ : arg1'=-x260, arg2'=arg2P3, (arg1 > 0 /\ 1+2*x280 > 0 /\ 1+x260 > 0 /\ -1+arg2 > 0), cost: 1 11: f171_0_sum_EQ -> f171_0_sum_EQ : arg1'=-1+arg1, arg2'=arg2P4, -arg1 > 0, cost: 1 12: f171_0_sum_EQ -> f171_0_sum_EQ : arg1'=-1+arg1, arg2'=arg2P5, arg1 > 0, cost: 1 6: __init -> f1_0_main_Load : arg1'=arg1P6, arg2'=arg2P6, TRUE, cost: 1 Applied nonterm Original rule: f171_0_sum_EQ -> f171_0_sum_EQ : arg1'=-1+arg1, arg2'=arg2P4, -arg1 > 0, cost: 1 New rule: f171_0_sum_EQ -> [4] : -arg1 > 0, cost: NONTERM Applied acceleration Original rule: f171_0_sum_EQ -> f171_0_sum_EQ : arg1'=-1+arg1, arg2'=arg2P4, -arg1 > 0, cost: 1 New rule: f171_0_sum_EQ -> f171_0_sum_EQ : arg1'=arg1-n1, arg2'=arg2P4, -arg1 > 0, cost: n1 Applied acceleration Original rule: f171_0_sum_EQ -> f171_0_sum_EQ : arg1'=-1+arg1, arg2'=arg2P5, arg1 > 0, cost: 1 New rule: f171_0_sum_EQ -> f171_0_sum_EQ : arg1'=arg1-n3, arg2'=arg2P5, (1+arg1-n3 > 0 /\ -1+n3 >= 0), cost: n3 Applied instantiation Original rule: f171_0_sum_EQ -> f171_0_sum_EQ : arg1'=arg1-n3, arg2'=arg2P5, (1+arg1-n3 > 0 /\ -1+n3 >= 0), cost: n3 New rule: f171_0_sum_EQ -> f171_0_sum_EQ : arg1'=0, arg2'=arg2P5, (1 > 0 /\ -1+arg1 >= 0), cost: arg1 Applied simplification Original rule: f171_0_sum_EQ -> f171_0_sum_EQ : arg1'=0, arg2'=arg2P5, (1 > 0 /\ -1+arg1 >= 0), cost: arg1 New rule: f171_0_sum_EQ -> f171_0_sum_EQ : arg1'=0, arg2'=arg2P5, -1+arg1 >= 0, cost: arg1 Applied deletion Removed the following rules: 11 12 Accelerated simple loops Start location: __init 7: f1_0_main_Load -> f1_0_main_Load\' : (arg1 > 0 /\ 2+2*x130 > 0 /\ -1+arg2 > 0), cost: 1 9: f1_0_main_Load -> f1_0_main_Load\' : (arg1 > 0 /\ 1+2*x230 > 0 /\ -1+arg2 > 0), cost: 1 8: f1_0_main_Load\' -> f171_0_sum_EQ : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ -1+arg2 > 0 /\ 2+2*x180 > 0 /\ 1+arg1P1 > 0), cost: 1 10: f1_0_main_Load\' -> f171_0_sum_EQ : arg1'=-x260, arg2'=arg2P3, (arg1 > 0 /\ 1+2*x280 > 0 /\ 1+x260 > 0 /\ -1+arg2 > 0), cost: 1 13: f171_0_sum_EQ -> [4] : -arg1 > 0, cost: NONTERM 14: f171_0_sum_EQ -> f171_0_sum_EQ : arg1'=arg1-n1, arg2'=arg2P4, -arg1 > 0, cost: n1 16: f171_0_sum_EQ -> f171_0_sum_EQ : arg1'=0, arg2'=arg2P5, -1+arg1 >= 0, cost: arg1 6: __init -> f1_0_main_Load : arg1'=arg1P6, arg2'=arg2P6, TRUE, cost: 1 Applied chaining First rule: f1_0_main_Load\' -> f171_0_sum_EQ : arg1'=-x260, arg2'=arg2P3, (arg1 > 0 /\ 1+2*x280 > 0 /\ 1+x260 > 0 /\ -1+arg2 > 0), cost: 1 Second rule: f171_0_sum_EQ -> [4] : -arg1 > 0, cost: NONTERM New rule: f1_0_main_Load\' -> [4] : (arg1 > 0 /\ 1+2*x280 > 0 /\ -1+arg2 > 0), cost: NONTERM Applied chaining First rule: f1_0_main_Load\' -> f171_0_sum_EQ : arg1'=-x260, arg2'=arg2P3, (arg1 > 0 /\ 1+2*x280 > 0 /\ 1+x260 > 0 /\ -1+arg2 > 0), cost: 1 Second rule: f171_0_sum_EQ -> f171_0_sum_EQ : arg1'=arg1-n1, arg2'=arg2P4, -arg1 > 0, cost: n1 New rule: f1_0_main_Load\' -> f171_0_sum_EQ : arg1'=-x260-n1, arg2'=arg2P4, (arg1 > 0 /\ 1+2*x280 > 0 /\ -1+arg2 > 0 /\ x260 > 0), cost: 1+n1 Applied chaining First rule: f1_0_main_Load\' -> f171_0_sum_EQ : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ -1+arg2 > 0 /\ 2+2*x180 > 0 /\ 1+arg1P1 > 0), cost: 1 Second rule: f171_0_sum_EQ -> f171_0_sum_EQ : arg1'=0, arg2'=arg2P5, -1+arg1 >= 0, cost: arg1 New rule: f1_0_main_Load\' -> f171_0_sum_EQ : arg1'=0, arg2'=arg2P5, (arg1 > 0 /\ -1+arg1P1 >= 0 /\ -1+arg2 > 0 /\ 2+2*x180 > 0), cost: 1+arg1P1 Applied deletion Removed the following rules: 13 14 16 Chained accelerated rules with incoming rules Start location: __init 7: f1_0_main_Load -> f1_0_main_Load\' : (arg1 > 0 /\ 2+2*x130 > 0 /\ -1+arg2 > 0), cost: 1 9: f1_0_main_Load -> f1_0_main_Load\' : (arg1 > 0 /\ 1+2*x230 > 0 /\ -1+arg2 > 0), cost: 1 8: f1_0_main_Load\' -> f171_0_sum_EQ : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ -1+arg2 > 0 /\ 2+2*x180 > 0 /\ 1+arg1P1 > 0), cost: 1 10: f1_0_main_Load\' -> f171_0_sum_EQ : arg1'=-x260, arg2'=arg2P3, (arg1 > 0 /\ 1+2*x280 > 0 /\ 1+x260 > 0 /\ -1+arg2 > 0), cost: 1 17: f1_0_main_Load\' -> [4] : (arg1 > 0 /\ 1+2*x280 > 0 /\ -1+arg2 > 0), cost: NONTERM 18: f1_0_main_Load\' -> f171_0_sum_EQ : arg1'=-x260-n1, arg2'=arg2P4, (arg1 > 0 /\ 1+2*x280 > 0 /\ -1+arg2 > 0 /\ x260 > 0), cost: 1+n1 19: f1_0_main_Load\' -> f171_0_sum_EQ : arg1'=0, arg2'=arg2P5, (arg1 > 0 /\ -1+arg1P1 >= 0 /\ -1+arg2 > 0 /\ 2+2*x180 > 0), cost: 1+arg1P1 6: __init -> f1_0_main_Load : arg1'=arg1P6, arg2'=arg2P6, TRUE, cost: 1 Removed unreachable locations and irrelevant leafs Start location: __init 7: f1_0_main_Load -> f1_0_main_Load\' : (arg1 > 0 /\ 2+2*x130 > 0 /\ -1+arg2 > 0), cost: 1 9: f1_0_main_Load -> f1_0_main_Load\' : (arg1 > 0 /\ 1+2*x230 > 0 /\ -1+arg2 > 0), cost: 1 17: f1_0_main_Load\' -> [4] : (arg1 > 0 /\ 1+2*x280 > 0 /\ -1+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 -> f1_0_main_Load\' : (arg1 > 0 /\ 2+2*x130 > 0 /\ -1+arg2 > 0), cost: 1 New rule: __init -> f1_0_main_Load\' : arg1'=arg1P6, arg2'=arg2P6, (2+2*x130 > 0 /\ -1+arg2P6 > 0 /\ arg1P6 > 0), cost: 2 Applied chaining First rule: __init -> f1_0_main_Load : arg1'=arg1P6, arg2'=arg2P6, TRUE, cost: 1 Second rule: f1_0_main_Load -> f1_0_main_Load\' : (arg1 > 0 /\ 1+2*x230 > 0 /\ -1+arg2 > 0), cost: 1 New rule: __init -> f1_0_main_Load\' : arg1'=arg1P6, arg2'=arg2P6, (1+2*x230 > 0 /\ -1+arg2P6 > 0 /\ arg1P6 > 0), cost: 2 Applied deletion Removed the following rules: 6 7 9 Eliminated locations on tree-shaped paths Start location: __init 17: f1_0_main_Load\' -> [4] : (arg1 > 0 /\ 1+2*x280 > 0 /\ -1+arg2 > 0), cost: NONTERM 20: __init -> f1_0_main_Load\' : arg1'=arg1P6, arg2'=arg2P6, (2+2*x130 > 0 /\ -1+arg2P6 > 0 /\ arg1P6 > 0), cost: 2 21: __init -> f1_0_main_Load\' : arg1'=arg1P6, arg2'=arg2P6, (1+2*x230 > 0 /\ -1+arg2P6 > 0 /\ arg1P6 > 0), cost: 2 Eliminating location f1_0_main_Load\' by chaining: Applied chaining First rule: __init -> f1_0_main_Load\' : arg1'=arg1P6, arg2'=arg2P6, (2+2*x130 > 0 /\ -1+arg2P6 > 0 /\ arg1P6 > 0), cost: 2 Second rule: f1_0_main_Load\' -> [4] : (arg1 > 0 /\ 1+2*x280 > 0 /\ -1+arg2 > 0), cost: NONTERM New rule: __init -> [4] : (1+2*x280 > 0 /\ 2+2*x130 > 0 /\ -1+arg2P6 > 0 /\ arg1P6 > 0), cost: NONTERM Applied chaining First rule: __init -> f1_0_main_Load\' : arg1'=arg1P6, arg2'=arg2P6, (1+2*x230 > 0 /\ -1+arg2P6 > 0 /\ arg1P6 > 0), cost: 2 Second rule: f1_0_main_Load\' -> [4] : (arg1 > 0 /\ 1+2*x280 > 0 /\ -1+arg2 > 0), cost: NONTERM New rule: __init -> [4] : (1+2*x280 > 0 /\ 1+2*x230 > 0 /\ -1+arg2P6 > 0 /\ arg1P6 > 0), cost: NONTERM Applied deletion Removed the following rules: 17 20 21 Eliminated locations on tree-shaped paths Start location: __init 22: __init -> [4] : (1+2*x280 > 0 /\ 2+2*x130 > 0 /\ -1+arg2P6 > 0 /\ arg1P6 > 0), cost: NONTERM 23: __init -> [4] : (1+2*x280 > 0 /\ 1+2*x230 > 0 /\ -1+arg2P6 > 0 /\ arg1P6 > 0), cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 22 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: (1+2*x280 > 0 /\ 2+2*x130 > 0 /\ -1+arg2P6 > 0 /\ arg1P6 > 0)