NO Initial ITS Start location: __init 0: f1_0_main_Load -> f50_0_loop_EQ : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ -arg1P0+arg2 == 0 /\ 1+arg2 > 0), cost: 1 1: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=arg1P1, arg2'=arg2P1, (arg1 < 0 /\ -1+arg1 < 0 /\ 1-arg1-arg1P1 == 0 /\ -2+arg1 < 0), cost: 1 2: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=arg1P2, arg2'=arg2P2, (arg1 > 0 /\ -1-arg1-arg1P2 == 0 /\ 2+arg1 > 0), cost: 1 3: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_Load -> f50_0_loop_EQ : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ -arg1P0+arg2 == 0 /\ 1+arg2 > 0), cost: 1 New rule: f1_0_main_Load -> f50_0_loop_EQ : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Applied preprocessing Original rule: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=arg1P1, arg2'=arg2P1, (arg1 < 0 /\ -1+arg1 < 0 /\ 1-arg1-arg1P1 == 0 /\ -2+arg1 < 0), cost: 1 New rule: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=1-arg1, arg2'=arg2P1, -arg1 > 0, cost: 1 Applied preprocessing Original rule: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=arg1P2, arg2'=arg2P2, (arg1 > 0 /\ -1-arg1-arg1P2 == 0 /\ 2+arg1 > 0), cost: 1 New rule: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=-1-arg1, arg2'=arg2P2, arg1 > 0, cost: 1 Simplified rules Start location: __init 4: f1_0_main_Load -> f50_0_loop_EQ : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 5: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=1-arg1, arg2'=arg2P1, -arg1 > 0, cost: 1 6: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=-1-arg1, arg2'=arg2P2, arg1 > 0, cost: 1 3: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Applied chaining First rule: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=1-arg1, arg2'=arg2P1, -arg1 > 0, cost: 1 Second rule: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=-1-arg1, arg2'=arg2P2, arg1 > 0, cost: 1 New rule: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=-2+arg1, arg2'=arg2P2, -arg1 > 0, cost: 2 Applied nonterm Original rule: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=-2+arg1, arg2'=arg2P2, -arg1 > 0, cost: 2 New rule: f50_0_loop_EQ -> [3] : -arg1 > 0, cost: NONTERM Applied acceleration Original rule: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=-2+arg1, arg2'=arg2P2, -arg1 > 0, cost: 2 New rule: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=arg1-2*n1, arg2'=arg2P2, -arg1 > 0, cost: 2*n1 Applied chaining First rule: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=-1-arg1, arg2'=arg2P2, arg1 > 0, cost: 1 Second rule: f50_0_loop_EQ -> [3] : -arg1 > 0, cost: NONTERM New rule: f50_0_loop_EQ -> [3] : (arg1 > 0 /\ 1+arg1 > 0), cost: NONTERM Applied chaining First rule: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=-1-arg1, arg2'=arg2P2, arg1 > 0, cost: 1 Second rule: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=arg1-2*n1, arg2'=arg2P2, -arg1 > 0, cost: 2*n1 New rule: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=-1-arg1-2*n1, arg2'=arg2P2, (arg1 > 0 /\ 1+arg1 > 0), cost: 1+2*n1 Applied chaining First rule: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=-1-arg1, arg2'=arg2P2, arg1 > 0, cost: 1 Second rule: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=1-arg1, arg2'=arg2P1, -arg1 > 0, cost: 1 New rule: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=2+arg1, arg2'=arg2P1, arg1 > 0, cost: 2 Applied nonterm Original rule: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=2+arg1, arg2'=arg2P1, arg1 > 0, cost: 2 New rule: f50_0_loop_EQ -> [3] : arg1 > 0, cost: NONTERM Applied acceleration Original rule: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=2+arg1, arg2'=arg2P1, arg1 > 0, cost: 2 New rule: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=arg1+2*n3, arg2'=arg2P1, arg1 > 0, cost: 2*n3 Applied chaining First rule: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=1-arg1, arg2'=arg2P1, -arg1 > 0, cost: 1 Second rule: f50_0_loop_EQ -> [3] : arg1 > 0, cost: NONTERM New rule: f50_0_loop_EQ -> [3] : (1-arg1 > 0 /\ -arg1 > 0), cost: NONTERM Applied chaining First rule: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=1-arg1, arg2'=arg2P1, -arg1 > 0, cost: 1 Second rule: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=arg1+2*n3, arg2'=arg2P1, arg1 > 0, cost: 2*n3 New rule: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=1-arg1+2*n3, arg2'=arg2P1, (1-arg1 > 0 /\ -arg1 > 0), cost: 1+2*n3 Applied simplification Original rule: f50_0_loop_EQ -> [3] : (arg1 > 0 /\ 1+arg1 > 0), cost: NONTERM New rule: f50_0_loop_EQ -> [3] : arg1 > 0, cost: NONTERM Applied simplification Original rule: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=-1-arg1-2*n1, arg2'=arg2P2, (arg1 > 0 /\ 1+arg1 > 0), cost: 1+2*n1 New rule: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=-1-arg1-2*n1, arg2'=arg2P2, arg1 > 0, cost: 1+2*n1 Applied simplification Original rule: f50_0_loop_EQ -> [3] : (1-arg1 > 0 /\ -arg1 > 0), cost: NONTERM New rule: f50_0_loop_EQ -> [3] : -arg1 > 0, cost: NONTERM Applied simplification Original rule: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=1-arg1+2*n3, arg2'=arg2P1, (1-arg1 > 0 /\ -arg1 > 0), cost: 1+2*n3 New rule: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=1-arg1+2*n3, arg2'=arg2P1, -arg1 > 0, cost: 1+2*n3 Applied deletion Removed the following rules: 7 11 Accelerated simple loops Start location: __init 4: f1_0_main_Load -> f50_0_loop_EQ : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 5: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=1-arg1, arg2'=arg2P1, -arg1 > 0, cost: 1 6: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=-1-arg1, arg2'=arg2P2, arg1 > 0, cost: 1 9: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=arg1-2*n1, arg2'=arg2P2, -arg1 > 0, cost: 2*n1 13: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=arg1+2*n3, arg2'=arg2P1, arg1 > 0, cost: 2*n3 15: f50_0_loop_EQ -> [3] : arg1 > 0, cost: NONTERM 16: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=-1-arg1-2*n1, arg2'=arg2P2, arg1 > 0, cost: 1+2*n1 17: f50_0_loop_EQ -> [3] : -arg1 > 0, cost: NONTERM 18: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=1-arg1+2*n3, arg2'=arg2P1, -arg1 > 0, cost: 1+2*n3 3: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Applied chaining First rule: f1_0_main_Load -> f50_0_loop_EQ : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=-1-arg1, arg2'=arg2P2, arg1 > 0, cost: 1 New rule: f1_0_main_Load -> f50_0_loop_EQ : arg1'=-1-arg2, arg2'=arg2P2, (arg1 > 0 /\ arg2 > 0), cost: 2 Applied chaining First rule: f1_0_main_Load -> f50_0_loop_EQ : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=arg1+2*n3, arg2'=arg2P1, arg1 > 0, cost: 2*n3 New rule: f1_0_main_Load -> f50_0_loop_EQ : arg1'=2*n3+arg2, arg2'=arg2P1, (arg1 > 0 /\ arg2 > 0), cost: 1+2*n3 Applied chaining First rule: f1_0_main_Load -> f50_0_loop_EQ : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f50_0_loop_EQ -> [3] : arg1 > 0, cost: NONTERM New rule: f1_0_main_Load -> [3] : (arg1 > 0 /\ arg2 > 0), cost: NONTERM Applied chaining First rule: f1_0_main_Load -> f50_0_loop_EQ : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f50_0_loop_EQ -> f50_0_loop_EQ : arg1'=-1-arg1-2*n1, arg2'=arg2P2, arg1 > 0, cost: 1+2*n1 New rule: f1_0_main_Load -> f50_0_loop_EQ : arg1'=-1-arg2-2*n1, arg2'=arg2P2, (arg1 > 0 /\ arg2 > 0), cost: 2+2*n1 Applied deletion Removed the following rules: 5 6 9 13 15 16 17 18 Chained accelerated rules with incoming rules Start location: __init 4: f1_0_main_Load -> f50_0_loop_EQ : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 19: f1_0_main_Load -> f50_0_loop_EQ : arg1'=-1-arg2, arg2'=arg2P2, (arg1 > 0 /\ arg2 > 0), cost: 2 20: f1_0_main_Load -> f50_0_loop_EQ : arg1'=2*n3+arg2, arg2'=arg2P1, (arg1 > 0 /\ arg2 > 0), cost: 1+2*n3 21: f1_0_main_Load -> [3] : (arg1 > 0 /\ arg2 > 0), cost: NONTERM 22: f1_0_main_Load -> f50_0_loop_EQ : arg1'=-1-arg2-2*n1, arg2'=arg2P2, (arg1 > 0 /\ arg2 > 0), cost: 2+2*n1 3: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Removed unreachable locations and irrelevant leafs Start location: __init 21: f1_0_main_Load -> [3] : (arg1 > 0 /\ 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 /\ arg2 > 0), cost: NONTERM New rule: __init -> [3] : (arg1P3 > 0 /\ arg2P3 > 0), cost: NONTERM Applied deletion Removed the following rules: 3 21 Eliminated locations on linear paths Start location: __init 23: __init -> [3] : (arg1P3 > 0 /\ arg2P3 > 0), cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 23 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: (arg1P3 > 0 /\ arg2P3 > 0)