NO Initial ITS Start location: __init 0: f1_0_main_Load -> f82_0_loop_EQ : arg2'=arg2P0, arg1'=arg1P0, (1+arg2 > 0 /\ arg1 > 0 /\ arg2-arg1P0 == 0), cost: 1 1: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P1, arg1'=arg1P1, (-2+arg1 < 0 /\ arg1 < 0 /\ 5+arg1 < 0 /\ 1-arg1-arg1P1 == 0), cost: 1 2: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P2, arg1'=arg1P2, (-2+arg1 < 0 /\ 1-arg1-arg1P2 == 0 /\ arg1 > 0 /\ 5+arg1 < 0), cost: 1 3: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P3, arg1'=arg1P3, (-arg1P3 == 0 /\ -6+arg1 < 0 /\ arg1 < 0 /\ 6+arg1 > 0), cost: 1 4: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P4, arg1'=arg1P4, (-arg1P4 == 0 /\ -6+arg1 < 0 /\ arg1 > 0), cost: 1 5: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P5, arg1'=arg1P5, (-5+arg1 > 0 /\ -1-arg1P5-arg1 == 0), cost: 1 6: __init -> f1_0_main_Load : arg2'=arg2P6, arg1'=arg1P6, TRUE, cost: 1 Removed rules with unsatisfiable guard Start location: __init 0: f1_0_main_Load -> f82_0_loop_EQ : arg2'=arg2P0, arg1'=arg1P0, (1+arg2 > 0 /\ arg1 > 0 /\ arg2-arg1P0 == 0), cost: 1 1: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P1, arg1'=arg1P1, (-2+arg1 < 0 /\ arg1 < 0 /\ 5+arg1 < 0 /\ 1-arg1-arg1P1 == 0), cost: 1 3: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P3, arg1'=arg1P3, (-arg1P3 == 0 /\ -6+arg1 < 0 /\ arg1 < 0 /\ 6+arg1 > 0), cost: 1 4: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P4, arg1'=arg1P4, (-arg1P4 == 0 /\ -6+arg1 < 0 /\ arg1 > 0), cost: 1 5: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P5, arg1'=arg1P5, (-5+arg1 > 0 /\ -1-arg1P5-arg1 == 0), cost: 1 6: __init -> f1_0_main_Load : arg2'=arg2P6, arg1'=arg1P6, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_Load -> f82_0_loop_EQ : arg2'=arg2P0, arg1'=arg1P0, (1+arg2 > 0 /\ arg1 > 0 /\ arg2-arg1P0 == 0), cost: 1 New rule: f1_0_main_Load -> f82_0_loop_EQ : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Applied preprocessing Original rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P1, arg1'=arg1P1, (-2+arg1 < 0 /\ arg1 < 0 /\ 5+arg1 < 0 /\ 1-arg1-arg1P1 == 0), cost: 1 New rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P1, arg1'=1-arg1, -5-arg1 > 0, cost: 1 Applied preprocessing Original rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P3, arg1'=arg1P3, (-arg1P3 == 0 /\ -6+arg1 < 0 /\ arg1 < 0 /\ 6+arg1 > 0), cost: 1 New rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P3, arg1'=0, (6+arg1 > 0 /\ -arg1 > 0), cost: 1 Applied preprocessing Original rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P4, arg1'=arg1P4, (-arg1P4 == 0 /\ -6+arg1 < 0 /\ arg1 > 0), cost: 1 New rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P4, arg1'=0, (6-arg1 > 0 /\ arg1 > 0), cost: 1 Applied preprocessing Original rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P5, arg1'=arg1P5, (-5+arg1 > 0 /\ -1-arg1P5-arg1 == 0), cost: 1 New rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P5, arg1'=-1-arg1, -5+arg1 > 0, cost: 1 Simplified rules Start location: __init 7: f1_0_main_Load -> f82_0_loop_EQ : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 8: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P1, arg1'=1-arg1, -5-arg1 > 0, cost: 1 9: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P3, arg1'=0, (6+arg1 > 0 /\ -arg1 > 0), cost: 1 10: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P4, arg1'=0, (6-arg1 > 0 /\ arg1 > 0), cost: 1 11: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P5, arg1'=-1-arg1, -5+arg1 > 0, cost: 1 6: __init -> f1_0_main_Load : arg2'=arg2P6, arg1'=arg1P6, TRUE, cost: 1 Applied chaining First rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P5, arg1'=-1-arg1, -5+arg1 > 0, cost: 1 Second rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P1, arg1'=1-arg1, -5-arg1 > 0, cost: 1 New rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P1, arg1'=2+arg1, -5+arg1 > 0, cost: 2 Applied nonterm Original rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P1, arg1'=2+arg1, -5+arg1 > 0, cost: 2 New rule: f82_0_loop_EQ -> [3] : (-5+arg1 > 0 /\ -1+n1 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_pKAkEA.txt Applied chaining First rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P1, arg1'=1-arg1, -5-arg1 > 0, cost: 1 Second rule: f82_0_loop_EQ -> [3] : (-5+arg1 > 0 /\ -1+n1 >= 0), cost: NONTERM New rule: f82_0_loop_EQ -> [3] : (-1+n1 >= 0 /\ -4-arg1 > 0 /\ -5-arg1 > 0), cost: NONTERM Applied chaining First rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P1, arg1'=1-arg1, -5-arg1 > 0, cost: 1 Second rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P5, arg1'=-1-arg1, -5+arg1 > 0, cost: 1 New rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P5, arg1'=-2+arg1, -5-arg1 > 0, cost: 2 Applied nonterm Original rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P5, arg1'=-2+arg1, -5-arg1 > 0, cost: 2 New rule: f82_0_loop_EQ -> [3] : (-1+n2 >= 0 /\ -5-arg1 > 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_modKKN.txt Applied chaining First rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P5, arg1'=-1-arg1, -5+arg1 > 0, cost: 1 Second rule: f82_0_loop_EQ -> [3] : (-1+n2 >= 0 /\ -5-arg1 > 0), cost: NONTERM New rule: f82_0_loop_EQ -> [3] : (-4+arg1 > 0 /\ -1+n2 >= 0 /\ -5+arg1 > 0), cost: NONTERM Applied simplification Original rule: f82_0_loop_EQ -> [3] : (-1+n1 >= 0 /\ -4-arg1 > 0 /\ -5-arg1 > 0), cost: NONTERM New rule: f82_0_loop_EQ -> [3] : (-1+n1 >= 0 /\ -5-arg1 > 0), cost: NONTERM Applied simplification Original rule: f82_0_loop_EQ -> [3] : (-4+arg1 > 0 /\ -1+n2 >= 0 /\ -5+arg1 > 0), cost: NONTERM New rule: f82_0_loop_EQ -> [3] : (-1+n2 >= 0 /\ -5+arg1 > 0), cost: NONTERM Accelerated simple loops Start location: __init 7: f1_0_main_Load -> f82_0_loop_EQ : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 8: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P1, arg1'=1-arg1, -5-arg1 > 0, cost: 1 9: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P3, arg1'=0, (6+arg1 > 0 /\ -arg1 > 0), cost: 1 10: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P4, arg1'=0, (6-arg1 > 0 /\ arg1 > 0), cost: 1 11: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P5, arg1'=-1-arg1, -5+arg1 > 0, cost: 1 12: f82_0_loop_EQ -> [3] : (-5+arg1 > 0 /\ -1+n1 >= 0), cost: NONTERM 14: f82_0_loop_EQ -> [3] : (-1+n2 >= 0 /\ -5-arg1 > 0), cost: NONTERM 16: f82_0_loop_EQ -> [3] : (-1+n1 >= 0 /\ -5-arg1 > 0), cost: NONTERM 17: f82_0_loop_EQ -> [3] : (-1+n2 >= 0 /\ -5+arg1 > 0), cost: NONTERM 6: __init -> f1_0_main_Load : arg2'=arg2P6, arg1'=arg1P6, TRUE, cost: 1 Applied chaining First rule: f1_0_main_Load -> f82_0_loop_EQ : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Second rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P4, arg1'=0, (6-arg1 > 0 /\ arg1 > 0), cost: 1 New rule: f1_0_main_Load -> f82_0_loop_EQ : arg2'=arg2P4, arg1'=0, (6-arg2 > 0 /\ arg2 > 0 /\ arg1 > 0), cost: 2 Applied chaining First rule: f1_0_main_Load -> f82_0_loop_EQ : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Second rule: f82_0_loop_EQ -> f82_0_loop_EQ : arg2'=arg2P5, arg1'=-1-arg1, -5+arg1 > 0, cost: 1 New rule: f1_0_main_Load -> f82_0_loop_EQ : arg2'=arg2P5, arg1'=-1-arg2, (-5+arg2 > 0 /\ arg1 > 0), cost: 2 Applied chaining First rule: f1_0_main_Load -> f82_0_loop_EQ : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Second rule: f82_0_loop_EQ -> [3] : (-5+arg1 > 0 /\ -1+n1 >= 0), cost: NONTERM New rule: f1_0_main_Load -> [3] : (-5+arg2 > 0 /\ arg1 > 0), cost: NONTERM Applied chaining First rule: f1_0_main_Load -> f82_0_loop_EQ : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Second rule: f82_0_loop_EQ -> [3] : (-1+n2 >= 0 /\ -5+arg1 > 0), cost: NONTERM New rule: f1_0_main_Load -> [3] : (-5+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 -> f82_0_loop_EQ : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 18: f1_0_main_Load -> f82_0_loop_EQ : arg2'=arg2P4, arg1'=0, (6-arg2 > 0 /\ arg2 > 0 /\ arg1 > 0), cost: 2 19: f1_0_main_Load -> f82_0_loop_EQ : arg2'=arg2P5, arg1'=-1-arg2, (-5+arg2 > 0 /\ arg1 > 0), cost: 2 20: f1_0_main_Load -> [3] : (-5+arg2 > 0 /\ arg1 > 0), cost: NONTERM 6: __init -> f1_0_main_Load : arg2'=arg2P6, arg1'=arg1P6, TRUE, cost: 1 Removed unreachable locations and irrelevant leafs Start location: __init 20: f1_0_main_Load -> [3] : (-5+arg2 > 0 /\ arg1 > 0), cost: NONTERM 6: __init -> f1_0_main_Load : arg2'=arg2P6, arg1'=arg1P6, TRUE, cost: 1 Eliminating location f1_0_main_Load by chaining: Applied chaining First rule: __init -> f1_0_main_Load : arg2'=arg2P6, arg1'=arg1P6, TRUE, cost: 1 Second rule: f1_0_main_Load -> [3] : (-5+arg2 > 0 /\ arg1 > 0), cost: NONTERM New rule: __init -> [3] : (arg1P6 > 0 /\ -5+arg2P6 > 0), cost: NONTERM Applied deletion Removed the following rules: 6 20 Eliminated locations on linear paths Start location: __init 21: __init -> [3] : (arg1P6 > 0 /\ -5+arg2P6 > 0), cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 21 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: (arg1P6 > 0 /\ -5+arg2P6 > 0)