NO Initial ITS Start location: __init 0: f1_0_main_Load -> f182_0_middle_EQ : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 > 0 /\ 1+arg1P0 > 0), cost: 1 1: f182_0_middle_EQ -> f182_0_middle_EQ : arg1'=arg1P1, arg2'=arg2P1, (-1+arg1-arg1P1 == 0 /\ 1-arg2P1+arg2 == 0 /\ -arg1+arg2 > 0), cost: 1 2: f182_0_middle_EQ -> f182_0_middle_EQ : arg1'=arg1P2, arg2'=arg2P2, (-1+arg1-arg1P2 == 0 /\ 1-arg2P2+arg2 == 0 /\ -arg1+arg2 < 0), cost: 1 3: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Applied preprocessing Original rule: f182_0_middle_EQ -> f182_0_middle_EQ : arg1'=arg1P1, arg2'=arg2P1, (-1+arg1-arg1P1 == 0 /\ 1-arg2P1+arg2 == 0 /\ -arg1+arg2 > 0), cost: 1 New rule: f182_0_middle_EQ -> f182_0_middle_EQ : arg1'=-1+arg1, arg2'=1+arg2, -arg1+arg2 > 0, cost: 1 Applied preprocessing Original rule: f182_0_middle_EQ -> f182_0_middle_EQ : arg1'=arg1P2, arg2'=arg2P2, (-1+arg1-arg1P2 == 0 /\ 1-arg2P2+arg2 == 0 /\ -arg1+arg2 < 0), cost: 1 New rule: f182_0_middle_EQ -> f182_0_middle_EQ : arg1'=-1+arg1, arg2'=1+arg2, arg1-arg2 > 0, cost: 1 Simplified rules Start location: __init 0: f1_0_main_Load -> f182_0_middle_EQ : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 > 0 /\ 1+arg1P0 > 0), cost: 1 4: f182_0_middle_EQ -> f182_0_middle_EQ : arg1'=-1+arg1, arg2'=1+arg2, -arg1+arg2 > 0, cost: 1 5: f182_0_middle_EQ -> f182_0_middle_EQ : arg1'=-1+arg1, arg2'=1+arg2, arg1-arg2 > 0, cost: 1 3: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Applied nonterm Original rule: f182_0_middle_EQ -> f182_0_middle_EQ : arg1'=-1+arg1, arg2'=1+arg2, -arg1+arg2 > 0, cost: 1 New rule: f182_0_middle_EQ -> [3] : -arg1+arg2 > 0, cost: NONTERM Applied acceleration Original rule: f182_0_middle_EQ -> f182_0_middle_EQ : arg1'=-1+arg1, arg2'=1+arg2, -arg1+arg2 > 0, cost: 1 New rule: f182_0_middle_EQ -> f182_0_middle_EQ : arg1'=arg1-n1, arg2'=n1+arg2, -arg1+arg2 > 0, cost: n1 Applied acceleration Original rule: f182_0_middle_EQ -> f182_0_middle_EQ : arg1'=-1+arg1, arg2'=1+arg2, arg1-arg2 > 0, cost: 1 New rule: f182_0_middle_EQ -> f182_0_middle_EQ : arg1'=arg1-n3, arg2'=n3+arg2, (n3 >= 0 /\ 2+arg1-2*n3-arg2 > 0), cost: n3 Applied deletion Removed the following rules: 4 5 Accelerated simple loops Start location: __init 0: f1_0_main_Load -> f182_0_middle_EQ : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 > 0 /\ 1+arg1P0 > 0), cost: 1 6: f182_0_middle_EQ -> [3] : -arg1+arg2 > 0, cost: NONTERM 7: f182_0_middle_EQ -> f182_0_middle_EQ : arg1'=arg1-n1, arg2'=n1+arg2, -arg1+arg2 > 0, cost: n1 8: f182_0_middle_EQ -> f182_0_middle_EQ : arg1'=arg1-n3, arg2'=n3+arg2, (n3 >= 0 /\ 2+arg1-2*n3-arg2 > 0), cost: n3 3: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Applied chaining First rule: f1_0_main_Load -> f182_0_middle_EQ : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 > 0 /\ 1+arg1P0 > 0), cost: 1 Second rule: f182_0_middle_EQ -> [3] : -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 -> f182_0_middle_EQ : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 > 0 /\ 1+arg1P0 > 0), cost: 1 Second rule: f182_0_middle_EQ -> f182_0_middle_EQ : arg1'=arg1-n1, arg2'=n1+arg2, -arg1+arg2 > 0, cost: n1 New rule: f1_0_main_Load -> f182_0_middle_EQ : arg1'=-n1+arg1P0, arg2'=n1+arg2P0, (arg1 > 0 /\ -1+arg2 > 0 /\ 1+arg1P0 > 0 /\ -arg1P0+arg2P0 > 0), cost: 1+n1 Applied chaining First rule: f1_0_main_Load -> f182_0_middle_EQ : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 > 0 /\ 1+arg1P0 > 0), cost: 1 Second rule: f182_0_middle_EQ -> f182_0_middle_EQ : arg1'=arg1-n3, arg2'=n3+arg2, (n3 >= 0 /\ 2+arg1-2*n3-arg2 > 0), cost: n3 New rule: f1_0_main_Load -> f182_0_middle_EQ : arg1'=-n3+arg1P0, arg2'=n3+arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ n3 >= 0 /\ -1+arg2 > 0 /\ 1+arg1P0 > 0 /\ 2-2*n3+arg1P0-arg2P0 > 0), cost: 1+n3 Applied deletion Removed the following rules: 6 7 8 Chained accelerated rules with incoming rules Start location: __init 0: f1_0_main_Load -> f182_0_middle_EQ : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 > 0 /\ 1+arg1P0 > 0), cost: 1 9: f1_0_main_Load -> [3] : (arg1 > 0 /\ -1+arg2 > 0), cost: NONTERM 10: f1_0_main_Load -> f182_0_middle_EQ : arg1'=-n1+arg1P0, arg2'=n1+arg2P0, (arg1 > 0 /\ -1+arg2 > 0 /\ 1+arg1P0 > 0 /\ -arg1P0+arg2P0 > 0), cost: 1+n1 11: f1_0_main_Load -> f182_0_middle_EQ : arg1'=-n3+arg1P0, arg2'=n3+arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ n3 >= 0 /\ -1+arg2 > 0 /\ 1+arg1P0 > 0 /\ 2-2*n3+arg1P0-arg2P0 > 0), cost: 1+n3 3: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Removed unreachable locations and irrelevant leafs Start location: __init 9: 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 deletion Removed the following rules: 3 9 Eliminated locations on linear paths Start location: __init 12: __init -> [3] : (-1+arg2P3 > 0 /\ arg1P3 > 0), cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 12 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)