NO Initial ITS Start location: __init 0: f1_0_main_Load -> f172_0_even_NE : arg2'=arg2P0, arg1'=arg1P0, (1+arg2 > 0 /\ -5 < 0 /\ arg1 > 0 /\ -5+arg2-arg1P0 == 0), cost: 1 1: f172_0_even_NE -> f137_0_odd_NE : arg2'=arg2P1, arg1'=arg1P1, (-2+arg1 < 0 /\ -1+arg1-arg1P1 == 0 /\ arg1 < 0 /\ -1 < 0 /\ -1+arg1 < 0), cost: 1 2: f172_0_even_NE -> f137_0_odd_NE : arg2'=arg2P2, arg1'=arg1P2, (-1+arg1-arg1P2 == 0 /\ -1 < 0 /\ -1+arg1 > 0), cost: 1 3: f137_0_odd_NE -> f172_0_even_NE : arg2'=arg2P3, arg1'=arg1P3, (-2+arg1 < 0 /\ -1-arg1P3+arg1 == 0 /\ arg1 < 0 /\ -1 < 0 /\ -1+arg1 < 0), cost: 1 4: f137_0_odd_NE -> f172_0_even_NE : arg2'=arg2P4, arg1'=arg1P4, (-1+arg1-arg1P4 == 0 /\ -1 < 0 /\ -1+arg1 > 0), cost: 1 5: __init -> f1_0_main_Load : arg2'=arg2P5, arg1'=arg1P5, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_Load -> f172_0_even_NE : arg2'=arg2P0, arg1'=arg1P0, (1+arg2 > 0 /\ -5 < 0 /\ arg1 > 0 /\ -5+arg2-arg1P0 == 0), cost: 1 New rule: f1_0_main_Load -> f172_0_even_NE : arg2'=arg2P0, arg1'=-5+arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Applied preprocessing Original rule: f172_0_even_NE -> f137_0_odd_NE : arg2'=arg2P1, arg1'=arg1P1, (-2+arg1 < 0 /\ -1+arg1-arg1P1 == 0 /\ arg1 < 0 /\ -1 < 0 /\ -1+arg1 < 0), cost: 1 New rule: f172_0_even_NE -> f137_0_odd_NE : arg2'=arg2P1, arg1'=-1+arg1, -arg1 > 0, cost: 1 Applied preprocessing Original rule: f172_0_even_NE -> f137_0_odd_NE : arg2'=arg2P2, arg1'=arg1P2, (-1+arg1-arg1P2 == 0 /\ -1 < 0 /\ -1+arg1 > 0), cost: 1 New rule: f172_0_even_NE -> f137_0_odd_NE : arg2'=arg2P2, arg1'=-1+arg1, -1+arg1 > 0, cost: 1 Applied preprocessing Original rule: f137_0_odd_NE -> f172_0_even_NE : arg2'=arg2P3, arg1'=arg1P3, (-2+arg1 < 0 /\ -1-arg1P3+arg1 == 0 /\ arg1 < 0 /\ -1 < 0 /\ -1+arg1 < 0), cost: 1 New rule: f137_0_odd_NE -> f172_0_even_NE : arg2'=arg2P3, arg1'=-1+arg1, -arg1 > 0, cost: 1 Applied preprocessing Original rule: f137_0_odd_NE -> f172_0_even_NE : arg2'=arg2P4, arg1'=arg1P4, (-1+arg1-arg1P4 == 0 /\ -1 < 0 /\ -1+arg1 > 0), cost: 1 New rule: f137_0_odd_NE -> f172_0_even_NE : arg2'=arg2P4, arg1'=-1+arg1, -1+arg1 > 0, cost: 1 Simplified rules Start location: __init 6: f1_0_main_Load -> f172_0_even_NE : arg2'=arg2P0, arg1'=-5+arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 7: f172_0_even_NE -> f137_0_odd_NE : arg2'=arg2P1, arg1'=-1+arg1, -arg1 > 0, cost: 1 8: f172_0_even_NE -> f137_0_odd_NE : arg2'=arg2P2, arg1'=-1+arg1, -1+arg1 > 0, cost: 1 9: f137_0_odd_NE -> f172_0_even_NE : arg2'=arg2P3, arg1'=-1+arg1, -arg1 > 0, cost: 1 10: f137_0_odd_NE -> f172_0_even_NE : arg2'=arg2P4, arg1'=-1+arg1, -1+arg1 > 0, cost: 1 5: __init -> f1_0_main_Load : arg2'=arg2P5, arg1'=arg1P5, TRUE, cost: 1 Eliminating location f1_0_main_Load by chaining: Applied chaining First rule: __init -> f1_0_main_Load : arg2'=arg2P5, arg1'=arg1P5, TRUE, cost: 1 Second rule: f1_0_main_Load -> f172_0_even_NE : arg2'=arg2P0, arg1'=-5+arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 New rule: __init -> f172_0_even_NE : arg2'=arg2P0, arg1'=-5+arg2P5, (1+arg2P5 > 0 /\ arg1P5 > 0), cost: 2 Applied deletion Removed the following rules: 5 6 Eliminated locations on linear paths Start location: __init 7: f172_0_even_NE -> f137_0_odd_NE : arg2'=arg2P1, arg1'=-1+arg1, -arg1 > 0, cost: 1 8: f172_0_even_NE -> f137_0_odd_NE : arg2'=arg2P2, arg1'=-1+arg1, -1+arg1 > 0, cost: 1 9: f137_0_odd_NE -> f172_0_even_NE : arg2'=arg2P3, arg1'=-1+arg1, -arg1 > 0, cost: 1 10: f137_0_odd_NE -> f172_0_even_NE : arg2'=arg2P4, arg1'=-1+arg1, -1+arg1 > 0, cost: 1 11: __init -> f172_0_even_NE : arg2'=arg2P0, arg1'=-5+arg2P5, (1+arg2P5 > 0 /\ arg1P5 > 0), cost: 2 Eliminating location f137_0_odd_NE by chaining: Applied chaining First rule: f172_0_even_NE -> f137_0_odd_NE : arg2'=arg2P1, arg1'=-1+arg1, -arg1 > 0, cost: 1 Second rule: f137_0_odd_NE -> f172_0_even_NE : arg2'=arg2P3, arg1'=-1+arg1, -arg1 > 0, cost: 1 New rule: f172_0_even_NE -> f172_0_even_NE : arg2'=arg2P3, arg1'=-2+arg1, (-arg1 > 0 /\ 1-arg1 > 0), cost: 2 Applied simplification Original rule: f172_0_even_NE -> f172_0_even_NE : arg2'=arg2P3, arg1'=-2+arg1, (-arg1 > 0 /\ 1-arg1 > 0), cost: 2 New rule: f172_0_even_NE -> f172_0_even_NE : arg2'=arg2P3, arg1'=-2+arg1, -arg1 > 0, cost: 2 Applied chaining First rule: f172_0_even_NE -> f137_0_odd_NE : arg2'=arg2P2, arg1'=-1+arg1, -1+arg1 > 0, cost: 1 Second rule: f137_0_odd_NE -> f172_0_even_NE : arg2'=arg2P4, arg1'=-1+arg1, -1+arg1 > 0, cost: 1 New rule: f172_0_even_NE -> f172_0_even_NE : arg2'=arg2P4, arg1'=-2+arg1, (-2+arg1 > 0 /\ -1+arg1 > 0), cost: 2 Applied simplification Original rule: f172_0_even_NE -> f172_0_even_NE : arg2'=arg2P4, arg1'=-2+arg1, (-2+arg1 > 0 /\ -1+arg1 > 0), cost: 2 New rule: f172_0_even_NE -> f172_0_even_NE : arg2'=arg2P4, arg1'=-2+arg1, -2+arg1 > 0, cost: 2 Applied deletion Removed the following rules: 7 8 9 10 Eliminated locations on tree-shaped paths Start location: __init 12: f172_0_even_NE -> f172_0_even_NE : arg2'=arg2P3, arg1'=-2+arg1, -arg1 > 0, cost: 2 13: f172_0_even_NE -> f172_0_even_NE : arg2'=arg2P4, arg1'=-2+arg1, -2+arg1 > 0, cost: 2 11: __init -> f172_0_even_NE : arg2'=arg2P0, arg1'=-5+arg2P5, (1+arg2P5 > 0 /\ arg1P5 > 0), cost: 2 Applied nonterm Original rule: f172_0_even_NE -> f172_0_even_NE : arg2'=arg2P3, arg1'=-2+arg1, -arg1 > 0, cost: 2 New rule: f172_0_even_NE -> [4] : (-1+n >= 0 /\ -arg1 > 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_AmAFaB.txt Applied acceleration Original rule: f172_0_even_NE -> f172_0_even_NE : arg2'=arg2P4, arg1'=-2+arg1, -2+arg1 > 0, cost: 2 New rule: f172_0_even_NE -> f172_0_even_NE : arg2'=arg2P4, arg1'=arg1-2*n0, (-1+n0 >= 0 /\ arg1-2*n0 > 0), cost: 2*n0 Sub-proof via acceration calculus written to file:///tmp/tmpnam_hEjLAb.txt Applied deletion Removed the following rules: 12 13 Accelerated simple loops Start location: __init 14: f172_0_even_NE -> [4] : (-1+n >= 0 /\ -arg1 > 0), cost: NONTERM 15: f172_0_even_NE -> f172_0_even_NE : arg2'=arg2P4, arg1'=arg1-2*n0, (-1+n0 >= 0 /\ arg1-2*n0 > 0), cost: 2*n0 11: __init -> f172_0_even_NE : arg2'=arg2P0, arg1'=-5+arg2P5, (1+arg2P5 > 0 /\ arg1P5 > 0), cost: 2 Applied chaining First rule: __init -> f172_0_even_NE : arg2'=arg2P0, arg1'=-5+arg2P5, (1+arg2P5 > 0 /\ arg1P5 > 0), cost: 2 Second rule: f172_0_even_NE -> [4] : (-1+n >= 0 /\ -arg1 > 0), cost: NONTERM New rule: __init -> [4] : -4 <= 0, cost: NONTERM Applied chaining First rule: __init -> f172_0_even_NE : arg2'=arg2P0, arg1'=-5+arg2P5, (1+arg2P5 > 0 /\ arg1P5 > 0), cost: 2 Second rule: f172_0_even_NE -> f172_0_even_NE : arg2'=arg2P4, arg1'=arg1-2*n0, (-1+n0 >= 0 /\ arg1-2*n0 > 0), cost: 2*n0 New rule: __init -> f172_0_even_NE : arg2'=arg2P4, arg1'=-5+arg2P5-2*n0, (-1+n0 >= 0 /\ -5+arg2P5-2*n0 > 0), cost: 2+2*n0 Applied deletion Removed the following rules: 14 15 Chained accelerated rules with incoming rules Start location: __init 11: __init -> f172_0_even_NE : arg2'=arg2P0, arg1'=-5+arg2P5, (1+arg2P5 > 0 /\ arg1P5 > 0), cost: 2 16: __init -> [4] : -4 <= 0, cost: NONTERM 17: __init -> f172_0_even_NE : arg2'=arg2P4, arg1'=-5+arg2P5-2*n0, (-1+n0 >= 0 /\ -5+arg2P5-2*n0 > 0), cost: 2+2*n0 Removed unreachable locations and irrelevant leafs Start location: __init 16: __init -> [4] : -4 <= 0, cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 16 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: -4 <= 0