NO Initial ITS Start location: __init 0: f1_0_main_Load -> f169_0_loop_EQ : arg2'=arg2P0, arg1'=arg1P0, arg3'=arg3P0, (1-arg2P0 == 0 /\ 1+arg2 > 0 /\ arg1 > 0 /\ 1-arg1P0 == 0 /\ arg2-arg3P0 == 0), cost: 1 1: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=arg2P1, arg1'=arg1P1, arg3'=arg3P1, (-arg3P1 == 0 /\ 1+arg2-arg1P1 == 0 /\ arg2 > 0 /\ -1-arg2+arg3 < 0 /\ arg2+arg3 >= 0 /\ arg1 > 0 /\ 1+arg2-arg2P1 == 0 /\ arg3 < 0 /\ -arg2+arg3 <= 0), cost: 1 2: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=arg2P2, arg1'=arg1P2, arg3'=arg3P2, (arg2 > 0 /\ -1-arg2+arg3 < 0 /\ 1+arg2-arg1P2 == 0 /\ 1+arg2-arg2P2 == 0 /\ arg2+arg3 >= 0 /\ -arg3P2 == 0 /\ arg1 > 0 /\ arg3 > 0 /\ -arg2+arg3 <= 0), cost: 1 3: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=arg2P3, arg1'=arg1P3, arg3'=arg3P3, (1-arg2P3+arg2 == 0 /\ arg2 > 0 /\ arg2+arg3 < 0 /\ arg1 > 0 /\ 1-arg3P3-arg3 == 0 /\ arg3 < 0 /\ 1+arg2-arg1P3 == 0), cost: 1 4: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=arg2P4, arg1'=arg1P4, arg3'=arg3P4, (arg2 > 0 /\ 1-arg3P4-arg3 == 0 /\ arg2+arg3 < 0 /\ arg1 > 0 /\ arg3 > 0 /\ 1-arg2P4+arg2 == 0 /\ 1+arg2-arg1P4 == 0), cost: 1 5: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=arg2P5, arg1'=arg1P5, arg3'=arg3P5, (arg2 > 0 /\ 1+arg2-arg1P5 == 0 /\ -1-arg3P5-arg3 == 0 /\ arg2+arg3 >= 0 /\ -1+arg3 > 0 /\ 1-arg2P5+arg2 == 0 /\ arg1 > 0 /\ arg2-arg3 < 0 /\ 1+arg2-arg3 <= 0 /\ 2+arg3 > 0), cost: 1 6: __init -> f1_0_main_Load : arg2'=arg2P6, arg1'=arg1P6, arg3'=arg3P6, TRUE, cost: 1 Removed rules with unsatisfiable guard Start location: __init 0: f1_0_main_Load -> f169_0_loop_EQ : arg2'=arg2P0, arg1'=arg1P0, arg3'=arg3P0, (1-arg2P0 == 0 /\ 1+arg2 > 0 /\ arg1 > 0 /\ 1-arg1P0 == 0 /\ arg2-arg3P0 == 0), cost: 1 1: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=arg2P1, arg1'=arg1P1, arg3'=arg3P1, (-arg3P1 == 0 /\ 1+arg2-arg1P1 == 0 /\ arg2 > 0 /\ -1-arg2+arg3 < 0 /\ arg2+arg3 >= 0 /\ arg1 > 0 /\ 1+arg2-arg2P1 == 0 /\ arg3 < 0 /\ -arg2+arg3 <= 0), cost: 1 2: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=arg2P2, arg1'=arg1P2, arg3'=arg3P2, (arg2 > 0 /\ -1-arg2+arg3 < 0 /\ 1+arg2-arg1P2 == 0 /\ 1+arg2-arg2P2 == 0 /\ arg2+arg3 >= 0 /\ -arg3P2 == 0 /\ arg1 > 0 /\ arg3 > 0 /\ -arg2+arg3 <= 0), cost: 1 3: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=arg2P3, arg1'=arg1P3, arg3'=arg3P3, (1-arg2P3+arg2 == 0 /\ arg2 > 0 /\ arg2+arg3 < 0 /\ arg1 > 0 /\ 1-arg3P3-arg3 == 0 /\ arg3 < 0 /\ 1+arg2-arg1P3 == 0), cost: 1 5: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=arg2P5, arg1'=arg1P5, arg3'=arg3P5, (arg2 > 0 /\ 1+arg2-arg1P5 == 0 /\ -1-arg3P5-arg3 == 0 /\ arg2+arg3 >= 0 /\ -1+arg3 > 0 /\ 1-arg2P5+arg2 == 0 /\ arg1 > 0 /\ arg2-arg3 < 0 /\ 1+arg2-arg3 <= 0 /\ 2+arg3 > 0), cost: 1 6: __init -> f1_0_main_Load : arg2'=arg2P6, arg1'=arg1P6, arg3'=arg3P6, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_Load -> f169_0_loop_EQ : arg2'=arg2P0, arg1'=arg1P0, arg3'=arg3P0, (1-arg2P0 == 0 /\ 1+arg2 > 0 /\ arg1 > 0 /\ 1-arg1P0 == 0 /\ arg2-arg3P0 == 0), cost: 1 New rule: f1_0_main_Load -> f169_0_loop_EQ : arg2'=1, arg1'=1, arg3'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Applied preprocessing Original rule: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=arg2P1, arg1'=arg1P1, arg3'=arg3P1, (-arg3P1 == 0 /\ 1+arg2-arg1P1 == 0 /\ arg2 > 0 /\ -1-arg2+arg3 < 0 /\ arg2+arg3 >= 0 /\ arg1 > 0 /\ 1+arg2-arg2P1 == 0 /\ arg3 < 0 /\ -arg2+arg3 <= 0), cost: 1 New rule: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=1+arg2, arg1'=1+arg2, arg3'=0, (-arg3 > 0 /\ arg2+arg3 >= 0 /\ arg1 > 0), cost: 1 Applied preprocessing Original rule: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=arg2P2, arg1'=arg1P2, arg3'=arg3P2, (arg2 > 0 /\ -1-arg2+arg3 < 0 /\ 1+arg2-arg1P2 == 0 /\ 1+arg2-arg2P2 == 0 /\ arg2+arg3 >= 0 /\ -arg3P2 == 0 /\ arg1 > 0 /\ arg3 > 0 /\ -arg2+arg3 <= 0), cost: 1 New rule: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=1+arg2, arg1'=1+arg2, arg3'=0, (arg1 > 0 /\ arg3 > 0 /\ -arg2+arg3 <= 0), cost: 1 Applied preprocessing Original rule: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=arg2P3, arg1'=arg1P3, arg3'=arg3P3, (1-arg2P3+arg2 == 0 /\ arg2 > 0 /\ arg2+arg3 < 0 /\ arg1 > 0 /\ 1-arg3P3-arg3 == 0 /\ arg3 < 0 /\ 1+arg2-arg1P3 == 0), cost: 1 New rule: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=1+arg2, arg1'=1+arg2, arg3'=1-arg3, (-arg2-arg3 > 0 /\ arg2 > 0 /\ arg1 > 0), cost: 1 Applied preprocessing Original rule: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=arg2P5, arg1'=arg1P5, arg3'=arg3P5, (arg2 > 0 /\ 1+arg2-arg1P5 == 0 /\ -1-arg3P5-arg3 == 0 /\ arg2+arg3 >= 0 /\ -1+arg3 > 0 /\ 1-arg2P5+arg2 == 0 /\ arg1 > 0 /\ arg2-arg3 < 0 /\ 1+arg2-arg3 <= 0 /\ 2+arg3 > 0), cost: 1 New rule: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=1+arg2, arg1'=1+arg2, arg3'=-1-arg3, (arg2 > 0 /\ arg1 > 0 /\ 1+arg2-arg3 <= 0), cost: 1 Simplified rules Start location: __init 7: f1_0_main_Load -> f169_0_loop_EQ : arg2'=1, arg1'=1, arg3'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 8: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=1+arg2, arg1'=1+arg2, arg3'=0, (-arg3 > 0 /\ arg2+arg3 >= 0 /\ arg1 > 0), cost: 1 9: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=1+arg2, arg1'=1+arg2, arg3'=0, (arg1 > 0 /\ arg3 > 0 /\ -arg2+arg3 <= 0), cost: 1 10: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=1+arg2, arg1'=1+arg2, arg3'=1-arg3, (-arg2-arg3 > 0 /\ arg2 > 0 /\ arg1 > 0), cost: 1 11: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=1+arg2, arg1'=1+arg2, arg3'=-1-arg3, (arg2 > 0 /\ arg1 > 0 /\ 1+arg2-arg3 <= 0), cost: 1 6: __init -> f1_0_main_Load : arg2'=arg2P6, arg1'=arg1P6, arg3'=arg3P6, TRUE, cost: 1 Applied chaining First rule: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=1+arg2, arg1'=1+arg2, arg3'=-1-arg3, (arg2 > 0 /\ arg1 > 0 /\ 1+arg2-arg3 <= 0), cost: 1 Second rule: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=1+arg2, arg1'=1+arg2, arg3'=1-arg3, (-arg2-arg3 > 0 /\ arg2 > 0 /\ arg1 > 0), cost: 1 New rule: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=2+arg2, arg1'=2+arg2, arg3'=2+arg3, (arg2 > 0 /\ arg1 > 0 /\ -arg2+arg3 > 0), cost: 2 Applied nonterm Original rule: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=2+arg2, arg1'=2+arg2, arg3'=2+arg3, (arg2 > 0 /\ arg1 > 0 /\ -arg2+arg3 > 0), cost: 2 New rule: f169_0_loop_EQ -> [3] : (-1+n1 >= 0 /\ arg2 > 0 /\ arg1 > 0 /\ -arg2+arg3 > 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_nGGoKg.txt Applied chaining First rule: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=1+arg2, arg1'=1+arg2, arg3'=1-arg3, (-arg2-arg3 > 0 /\ arg2 > 0 /\ arg1 > 0), cost: 1 Second rule: f169_0_loop_EQ -> [3] : (-1+n1 >= 0 /\ arg2 > 0 /\ arg1 > 0 /\ -arg2+arg3 > 0), cost: NONTERM New rule: f169_0_loop_EQ -> [3] : (-1+n1 >= 0 /\ -arg2-arg3 > 0 /\ arg2 > 0 /\ 1+arg2 > 0 /\ arg1 > 0), cost: NONTERM Applied chaining First rule: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=1+arg2, arg1'=1+arg2, arg3'=1-arg3, (-arg2-arg3 > 0 /\ arg2 > 0 /\ arg1 > 0), cost: 1 Second rule: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=1+arg2, arg1'=1+arg2, arg3'=-1-arg3, (arg2 > 0 /\ arg1 > 0 /\ 1+arg2-arg3 <= 0), cost: 1 New rule: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=2+arg2, arg1'=2+arg2, arg3'=-2+arg3, (arg2 > 0 /\ 1+arg2+arg3 <= 0 /\ arg1 > 0), cost: 2 Applied nonterm Original rule: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=2+arg2, arg1'=2+arg2, arg3'=-2+arg3, (arg2 > 0 /\ 1+arg2+arg3 <= 0 /\ arg1 > 0), cost: 2 New rule: f169_0_loop_EQ -> [3] : (-1+n2 >= 0 /\ arg2 > 0 /\ arg1 > 0 /\ -1-arg2-arg3 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_hMjHcj.txt Applied chaining First rule: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=1+arg2, arg1'=1+arg2, arg3'=-1-arg3, (arg2 > 0 /\ arg1 > 0 /\ 1+arg2-arg3 <= 0), cost: 1 Second rule: f169_0_loop_EQ -> [3] : (-1+n2 >= 0 /\ arg2 > 0 /\ arg1 > 0 /\ -1-arg2-arg3 >= 0), cost: NONTERM New rule: f169_0_loop_EQ -> [3] : (-1+n2 >= 0 /\ arg2 > 0 /\ -1-arg2+arg3 >= 0 /\ 1+arg2 > 0 /\ arg1 > 0 /\ 1+arg2-arg3 <= 0), cost: NONTERM Applied simplification Original rule: f169_0_loop_EQ -> [3] : (-1+n1 >= 0 /\ -arg2-arg3 > 0 /\ arg2 > 0 /\ 1+arg2 > 0 /\ arg1 > 0), cost: NONTERM New rule: f169_0_loop_EQ -> [3] : (-1+n1 >= 0 /\ -arg2-arg3 > 0 /\ arg2 > 0 /\ arg1 > 0), cost: NONTERM Applied simplification Original rule: f169_0_loop_EQ -> [3] : (-1+n2 >= 0 /\ arg2 > 0 /\ -1-arg2+arg3 >= 0 /\ 1+arg2 > 0 /\ arg1 > 0 /\ 1+arg2-arg3 <= 0), cost: NONTERM New rule: f169_0_loop_EQ -> [3] : (-1+n2 >= 0 /\ arg2 > 0 /\ arg1 > 0 /\ 1+arg2-arg3 <= 0), cost: NONTERM Accelerated simple loops Start location: __init 7: f1_0_main_Load -> f169_0_loop_EQ : arg2'=1, arg1'=1, arg3'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 8: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=1+arg2, arg1'=1+arg2, arg3'=0, (-arg3 > 0 /\ arg2+arg3 >= 0 /\ arg1 > 0), cost: 1 9: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=1+arg2, arg1'=1+arg2, arg3'=0, (arg1 > 0 /\ arg3 > 0 /\ -arg2+arg3 <= 0), cost: 1 10: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=1+arg2, arg1'=1+arg2, arg3'=1-arg3, (-arg2-arg3 > 0 /\ arg2 > 0 /\ arg1 > 0), cost: 1 11: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=1+arg2, arg1'=1+arg2, arg3'=-1-arg3, (arg2 > 0 /\ arg1 > 0 /\ 1+arg2-arg3 <= 0), cost: 1 12: f169_0_loop_EQ -> [3] : (-1+n1 >= 0 /\ arg2 > 0 /\ arg1 > 0 /\ -arg2+arg3 > 0), cost: NONTERM 14: f169_0_loop_EQ -> [3] : (-1+n2 >= 0 /\ arg2 > 0 /\ arg1 > 0 /\ -1-arg2-arg3 >= 0), cost: NONTERM 16: f169_0_loop_EQ -> [3] : (-1+n1 >= 0 /\ -arg2-arg3 > 0 /\ arg2 > 0 /\ arg1 > 0), cost: NONTERM 17: f169_0_loop_EQ -> [3] : (-1+n2 >= 0 /\ arg2 > 0 /\ arg1 > 0 /\ 1+arg2-arg3 <= 0), cost: NONTERM 6: __init -> f1_0_main_Load : arg2'=arg2P6, arg1'=arg1P6, arg3'=arg3P6, TRUE, cost: 1 Applied chaining First rule: f1_0_main_Load -> f169_0_loop_EQ : arg2'=1, arg1'=1, arg3'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Second rule: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=1+arg2, arg1'=1+arg2, arg3'=0, (arg1 > 0 /\ arg3 > 0 /\ -arg2+arg3 <= 0), cost: 1 New rule: f1_0_main_Load -> f169_0_loop_EQ : arg2'=2, arg1'=2, arg3'=0, (arg1 > 0 /\ -1+arg2 == 0), cost: 2 Applied chaining First rule: f1_0_main_Load -> f169_0_loop_EQ : arg2'=1, arg1'=1, arg3'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Second rule: f169_0_loop_EQ -> f169_0_loop_EQ : arg2'=1+arg2, arg1'=1+arg2, arg3'=-1-arg3, (arg2 > 0 /\ arg1 > 0 /\ 1+arg2-arg3 <= 0), cost: 1 New rule: f1_0_main_Load -> f169_0_loop_EQ : arg2'=2, arg1'=2, arg3'=-1-arg2, (-2+arg2 >= 0 /\ arg1 > 0), cost: 2 Applied chaining First rule: f1_0_main_Load -> f169_0_loop_EQ : arg2'=1, arg1'=1, arg3'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Second rule: f169_0_loop_EQ -> [3] : (-1+n1 >= 0 /\ arg2 > 0 /\ arg1 > 0 /\ -arg2+arg3 > 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 -> f169_0_loop_EQ : arg2'=1, arg1'=1, arg3'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Second rule: f169_0_loop_EQ -> [3] : (-1+n2 >= 0 /\ arg2 > 0 /\ arg1 > 0 /\ 1+arg2-arg3 <= 0), cost: NONTERM New rule: f1_0_main_Load -> [3] : (-2+arg2 >= 0 /\ arg1 > 0), cost: NONTERM Applied deletion Removed the following rules: 8 9 10 11 12 14 16 17 Chained accelerated rules with incoming rules Start location: __init 7: f1_0_main_Load -> f169_0_loop_EQ : arg2'=1, arg1'=1, arg3'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 18: f1_0_main_Load -> f169_0_loop_EQ : arg2'=2, arg1'=2, arg3'=0, (arg1 > 0 /\ -1+arg2 == 0), cost: 2 19: f1_0_main_Load -> f169_0_loop_EQ : arg2'=2, arg1'=2, arg3'=-1-arg2, (-2+arg2 >= 0 /\ arg1 > 0), cost: 2 20: f1_0_main_Load -> [3] : (arg1 > 0 /\ -1+arg2 > 0), cost: NONTERM 21: f1_0_main_Load -> [3] : (-2+arg2 >= 0 /\ arg1 > 0), cost: NONTERM 6: __init -> f1_0_main_Load : arg2'=arg2P6, arg1'=arg1P6, arg3'=arg3P6, TRUE, cost: 1 Removed unreachable locations and irrelevant leafs Start location: __init 20: f1_0_main_Load -> [3] : (arg1 > 0 /\ -1+arg2 > 0), cost: NONTERM 21: f1_0_main_Load -> [3] : (-2+arg2 >= 0 /\ arg1 > 0), cost: NONTERM 6: __init -> f1_0_main_Load : arg2'=arg2P6, arg1'=arg1P6, arg3'=arg3P6, TRUE, cost: 1 Eliminating location f1_0_main_Load by chaining: Applied chaining First rule: __init -> f1_0_main_Load : arg2'=arg2P6, arg1'=arg1P6, arg3'=arg3P6, TRUE, cost: 1 Second rule: f1_0_main_Load -> [3] : (arg1 > 0 /\ -1+arg2 > 0), cost: NONTERM New rule: __init -> [3] : (arg1P6 > 0 /\ -1+arg2P6 > 0), cost: NONTERM Applied chaining First rule: __init -> f1_0_main_Load : arg2'=arg2P6, arg1'=arg1P6, arg3'=arg3P6, TRUE, cost: 1 Second rule: f1_0_main_Load -> [3] : (-2+arg2 >= 0 /\ arg1 > 0), cost: NONTERM New rule: __init -> [3] : (arg1P6 > 0 /\ -2+arg2P6 >= 0), cost: NONTERM Applied deletion Removed the following rules: 6 20 21 Eliminated locations on tree-shaped paths Start location: __init 22: __init -> [3] : (arg1P6 > 0 /\ -1+arg2P6 > 0), cost: NONTERM 23: __init -> [3] : (arg1P6 > 0 /\ -2+arg2P6 >= 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: (arg1P6 > 0 /\ -1+arg2P6 > 0)