NO Initial ITS Start location: __init 0: f1_0_main_Load -> f116_0_flip_EQ : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 > 0 /\ 1+arg1P0 > 0), cost: 1 1: f116_0_flip_EQ -> f116_0_flip_EQ : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ arg1-arg2P1 == 0 /\ arg2 > 0 /\ -arg1P1+arg2 == 0), cost: 1 2: __init -> f1_0_main_Load : arg1'=arg1P2, arg2'=arg2P2, TRUE, cost: 1 Applied preprocessing Original rule: f116_0_flip_EQ -> f116_0_flip_EQ : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ arg1-arg2P1 == 0 /\ arg2 > 0 /\ -arg1P1+arg2 == 0), cost: 1 New rule: f116_0_flip_EQ -> f116_0_flip_EQ : arg1'=arg2, arg2'=arg1, (arg1 > 0 /\ arg2 > 0), cost: 1 Simplified rules Start location: __init 0: f1_0_main_Load -> f116_0_flip_EQ : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 > 0 /\ 1+arg1P0 > 0), cost: 1 3: f116_0_flip_EQ -> f116_0_flip_EQ : arg1'=arg2, arg2'=arg1, (arg1 > 0 /\ arg2 > 0), cost: 1 2: __init -> f1_0_main_Load : arg1'=arg1P2, arg2'=arg2P2, TRUE, cost: 1 Applied unrolling Original rule: f116_0_flip_EQ -> f116_0_flip_EQ : arg1'=arg2, arg2'=arg1, (arg1 > 0 /\ arg2 > 0), cost: 1 New rule: f116_0_flip_EQ -> f116_0_flip_EQ : arg1'=arg1, arg2'=arg2, (arg1 > 0 /\ arg2 > 0), cost: 2 Applied nonterm Original rule: f116_0_flip_EQ -> f116_0_flip_EQ : arg1'=arg1, arg2'=arg2, (arg1 > 0 /\ arg2 > 0), cost: 2 New rule: f116_0_flip_EQ -> [3] : (arg1 > 0 /\ arg2 > 0), cost: NONTERM Applied acceleration Original rule: f116_0_flip_EQ -> f116_0_flip_EQ : arg1'=arg1, arg2'=arg2, (arg1 > 0 /\ arg2 > 0), cost: 2 New rule: f116_0_flip_EQ -> f116_0_flip_EQ : arg1'=arg1, arg2'=arg2, (arg1 > 0 /\ arg2 > 0), cost: 2*n0 Applied deletion Removed the following rules: 3 Accelerated simple loops Start location: __init 0: f1_0_main_Load -> f116_0_flip_EQ : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 > 0 /\ 1+arg1P0 > 0), cost: 1 4: f116_0_flip_EQ -> [3] : (arg1 > 0 /\ arg2 > 0), cost: NONTERM 5: f116_0_flip_EQ -> f116_0_flip_EQ : arg1'=arg1, arg2'=arg2, (arg1 > 0 /\ arg2 > 0), cost: 2*n0 2: __init -> f1_0_main_Load : arg1'=arg1P2, arg2'=arg2P2, TRUE, cost: 1 Applied chaining First rule: f1_0_main_Load -> f116_0_flip_EQ : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 > 0 /\ 1+arg1P0 > 0), cost: 1 Second rule: f116_0_flip_EQ -> [3] : (arg1 > 0 /\ 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 -> f116_0_flip_EQ : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 > 0 /\ 1+arg1P0 > 0), cost: 1 Second rule: f116_0_flip_EQ -> f116_0_flip_EQ : arg1'=arg1, arg2'=arg2, (arg1 > 0 /\ arg2 > 0), cost: 2*n0 New rule: f1_0_main_Load -> f116_0_flip_EQ : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ -1+arg2 > 0 /\ arg1P0 > 0 /\ arg2P0 > 0), cost: 1+2*n0 Applied deletion Removed the following rules: 4 5 Chained accelerated rules with incoming rules Start location: __init 0: f1_0_main_Load -> f116_0_flip_EQ : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 > 0 /\ 1+arg1P0 > 0), cost: 1 6: f1_0_main_Load -> [3] : (arg1 > 0 /\ -1+arg2 > 0), cost: NONTERM 7: f1_0_main_Load -> f116_0_flip_EQ : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ -1+arg2 > 0 /\ arg1P0 > 0 /\ arg2P0 > 0), cost: 1+2*n0 2: __init -> f1_0_main_Load : arg1'=arg1P2, arg2'=arg2P2, TRUE, cost: 1 Removed unreachable locations and irrelevant leafs Start location: __init 6: f1_0_main_Load -> [3] : (arg1 > 0 /\ -1+arg2 > 0), cost: NONTERM 2: __init -> f1_0_main_Load : arg1'=arg1P2, arg2'=arg2P2, TRUE, cost: 1 Eliminating location f1_0_main_Load by chaining: Applied chaining First rule: __init -> f1_0_main_Load : arg1'=arg1P2, arg2'=arg2P2, TRUE, cost: 1 Second rule: f1_0_main_Load -> [3] : (arg1 > 0 /\ -1+arg2 > 0), cost: NONTERM New rule: __init -> [3] : (-1+arg2P2 > 0 /\ arg1P2 > 0), cost: NONTERM Applied deletion Removed the following rules: 2 6 Eliminated locations on linear paths Start location: __init 8: __init -> [3] : (-1+arg2P2 > 0 /\ arg1P2 > 0), cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 8 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: (-1+arg2P2 > 0 /\ arg1P2 > 0)