NO Initial ITS Start location: __init 0: f1_0_main_Load -> f74_0_loop_LE : arg2'=arg2P0, arg4'=arg4P0, arg1'=arg1P0, arg3'=arg3P0, (arg2-arg4P0 == 0 /\ 1+arg2 > 0 /\ arg1 > 0 /\ arg1P0 > 0 /\ -arg2P0 == 0 /\ -arg1+arg1P0 <= 0 /\ arg2-arg3P0 == 0), cost: 1 1: f74_0_loop_LE -> f74_0_loop_LE\' : arg2'=arg2P1, arg4'=arg4P1, arg1'=arg1P1, arg3'=arg3P1, (x70-arg1 <= 0 /\ -arg1P1+arg1 == 0 /\ arg4-arg4P1 == 0 /\ -arg3P1+arg3 == 0 /\ x70 > 0 /\ arg1 > 0 /\ -arg2P1+arg2 == 0 /\ arg3 > 0 /\ 1+arg4 > 0), cost: 1 2: f74_0_loop_LE\' -> f74_0_loop_LE : arg2'=arg2P2, arg4'=arg4P2, arg1'=arg1P2, arg3'=arg3P2, (-arg3P2-arg2+arg4-x130 == 0 /\ -2-arg2+arg4-2*x130 < 0 /\ -arg1+arg1P2 <= 0 /\ -arg2+arg4-2*x130 >= 0 /\ arg1 > 0 /\ arg4-arg4P2 == 0 /\ arg2-arg2P2+x130 == 0 /\ arg3 > 0 /\ arg1P2 > 0 /\ 1+arg4 > 0), cost: 1 3: __init -> f1_0_main_Load : arg2'=arg2P3, arg4'=arg4P3, arg1'=arg1P3, arg3'=arg3P3, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_Load -> f74_0_loop_LE : arg2'=arg2P0, arg4'=arg4P0, arg1'=arg1P0, arg3'=arg3P0, (arg2-arg4P0 == 0 /\ 1+arg2 > 0 /\ arg1 > 0 /\ arg1P0 > 0 /\ -arg2P0 == 0 /\ -arg1+arg1P0 <= 0 /\ arg2-arg3P0 == 0), cost: 1 New rule: f1_0_main_Load -> f74_0_loop_LE : arg2'=0, arg4'=arg2, arg1'=arg1P0, arg3'=arg2, (1+arg2 > 0 /\ arg1P0 > 0 /\ -arg1+arg1P0 <= 0), cost: 1 Applied preprocessing Original rule: f74_0_loop_LE -> f74_0_loop_LE\' : arg2'=arg2P1, arg4'=arg4P1, arg1'=arg1P1, arg3'=arg3P1, (x70-arg1 <= 0 /\ -arg1P1+arg1 == 0 /\ arg4-arg4P1 == 0 /\ -arg3P1+arg3 == 0 /\ x70 > 0 /\ arg1 > 0 /\ -arg2P1+arg2 == 0 /\ arg3 > 0 /\ 1+arg4 > 0), cost: 1 New rule: f74_0_loop_LE -> f74_0_loop_LE\' : (arg3 > 0 /\ -1+arg1 >= 0 /\ 1+arg4 > 0), cost: 1 Applied preprocessing Original rule: f74_0_loop_LE\' -> f74_0_loop_LE : arg2'=arg2P2, arg4'=arg4P2, arg1'=arg1P2, arg3'=arg3P2, (-arg3P2-arg2+arg4-x130 == 0 /\ -2-arg2+arg4-2*x130 < 0 /\ -arg1+arg1P2 <= 0 /\ -arg2+arg4-2*x130 >= 0 /\ arg1 > 0 /\ arg4-arg4P2 == 0 /\ arg2-arg2P2+x130 == 0 /\ arg3 > 0 /\ arg1P2 > 0 /\ 1+arg4 > 0), cost: 1 New rule: f74_0_loop_LE\' -> f74_0_loop_LE : arg2'=arg2+x130, arg1'=arg1P2, arg3'=-arg2+arg4-x130, (-arg1+arg1P2 <= 0 /\ -arg2+arg4-2*x130 >= 0 /\ arg3 > 0 /\ 2+arg2-arg4+2*x130 > 0 /\ arg1P2 > 0 /\ 1+arg4 > 0), cost: 1 Simplified rules Start location: __init 4: f1_0_main_Load -> f74_0_loop_LE : arg2'=0, arg4'=arg2, arg1'=arg1P0, arg3'=arg2, (1+arg2 > 0 /\ arg1P0 > 0 /\ -arg1+arg1P0 <= 0), cost: 1 5: f74_0_loop_LE -> f74_0_loop_LE\' : (arg3 > 0 /\ -1+arg1 >= 0 /\ 1+arg4 > 0), cost: 1 6: f74_0_loop_LE\' -> f74_0_loop_LE : arg2'=arg2+x130, arg1'=arg1P2, arg3'=-arg2+arg4-x130, (-arg1+arg1P2 <= 0 /\ -arg2+arg4-2*x130 >= 0 /\ arg3 > 0 /\ 2+arg2-arg4+2*x130 > 0 /\ arg1P2 > 0 /\ 1+arg4 > 0), cost: 1 3: __init -> f1_0_main_Load : arg2'=arg2P3, arg4'=arg4P3, arg1'=arg1P3, arg3'=arg3P3, TRUE, cost: 1 Eliminating location f1_0_main_Load by chaining: Applied chaining First rule: __init -> f1_0_main_Load : arg2'=arg2P3, arg4'=arg4P3, arg1'=arg1P3, arg3'=arg3P3, TRUE, cost: 1 Second rule: f1_0_main_Load -> f74_0_loop_LE : arg2'=0, arg4'=arg2, arg1'=arg1P0, arg3'=arg2, (1+arg2 > 0 /\ arg1P0 > 0 /\ -arg1+arg1P0 <= 0), cost: 1 New rule: __init -> f74_0_loop_LE : arg2'=0, arg4'=arg2P3, arg1'=arg1P0, arg3'=arg2P3, (1+arg2P3 > 0 /\ arg1P0 > 0 /\ -arg1P3+arg1P0 <= 0), cost: 2 Applied deletion Removed the following rules: 3 4 Eliminating location f74_0_loop_LE\' by chaining: Applied chaining First rule: f74_0_loop_LE -> f74_0_loop_LE\' : (arg3 > 0 /\ -1+arg1 >= 0 /\ 1+arg4 > 0), cost: 1 Second rule: f74_0_loop_LE\' -> f74_0_loop_LE : arg2'=arg2+x130, arg1'=arg1P2, arg3'=-arg2+arg4-x130, (-arg1+arg1P2 <= 0 /\ -arg2+arg4-2*x130 >= 0 /\ arg3 > 0 /\ 2+arg2-arg4+2*x130 > 0 /\ arg1P2 > 0 /\ 1+arg4 > 0), cost: 1 New rule: f74_0_loop_LE -> f74_0_loop_LE : arg2'=arg2+x130, arg1'=arg1P2, arg3'=-arg2+arg4-x130, (-arg1+arg1P2 <= 0 /\ -arg2+arg4-2*x130 >= 0 /\ arg3 > 0 /\ 2+arg2-arg4+2*x130 > 0 /\ arg1P2 > 0 /\ -1+arg1 >= 0 /\ 1+arg4 > 0), cost: 2 Applied simplification Original rule: f74_0_loop_LE -> f74_0_loop_LE : arg2'=arg2+x130, arg1'=arg1P2, arg3'=-arg2+arg4-x130, (-arg1+arg1P2 <= 0 /\ -arg2+arg4-2*x130 >= 0 /\ arg3 > 0 /\ 2+arg2-arg4+2*x130 > 0 /\ arg1P2 > 0 /\ -1+arg1 >= 0 /\ 1+arg4 > 0), cost: 2 New rule: f74_0_loop_LE -> f74_0_loop_LE : arg2'=arg2+x130, arg1'=arg1P2, arg3'=-arg2+arg4-x130, (-arg1+arg1P2 <= 0 /\ -arg2+arg4-2*x130 >= 0 /\ arg3 > 0 /\ 2+arg2-arg4+2*x130 > 0 /\ arg1P2 > 0 /\ 1+arg4 > 0), cost: 2 Applied deletion Removed the following rules: 5 6 Eliminated locations on linear paths Start location: __init 8: f74_0_loop_LE -> f74_0_loop_LE : arg2'=arg2+x130, arg1'=arg1P2, arg3'=-arg2+arg4-x130, (-arg1+arg1P2 <= 0 /\ -arg2+arg4-2*x130 >= 0 /\ arg3 > 0 /\ 2+arg2-arg4+2*x130 > 0 /\ arg1P2 > 0 /\ 1+arg4 > 0), cost: 2 7: __init -> f74_0_loop_LE : arg2'=0, arg4'=arg2P3, arg1'=arg1P0, arg3'=arg2P3, (1+arg2P3 > 0 /\ arg1P0 > 0 /\ -arg1P3+arg1P0 <= 0), cost: 2 Applied acceleration Original rule: f74_0_loop_LE -> f74_0_loop_LE : arg2'=arg2+x130, arg1'=arg1P2, arg3'=-arg2+arg4-x130, (-arg1+arg1P2 <= 0 /\ -arg2+arg4-2*x130 >= 0 /\ arg3 > 0 /\ 2+arg2-arg4+2*x130 > 0 /\ arg1P2 > 0 /\ 1+arg4 > 0), cost: 2 New rule: f74_0_loop_LE -> f74_0_loop_LE : arg2'=arg2+n*x130, arg1'=arg1P2, arg3'=-arg2+arg4-x130-(-1+n)*x130, (0 == 0 /\ arg1-arg1P2 >= 0 /\ -arg2+arg4-2*x130-(-1+n)*x130 >= 0 /\ arg2-arg4+x130+arg3 == 0 /\ 2+arg2-arg4+2*x130+(-1+n)*x130 > 0 /\ -1+n >= 0 /\ -arg2+arg4-2*x130 >= 0 /\ arg3 > 0 /\ 2+arg2-arg4+2*x130 > 0 /\ arg1P2 > 0 /\ -x130 == 0 /\ 1+arg4 > 0), cost: 2*n Sub-proof via acceration calculus written to file:///tmp/tmpnam_gAEpgE.txt Applied nonterm Original rule: f74_0_loop_LE -> f74_0_loop_LE : arg2'=arg2+x130, arg1'=arg1P2, arg3'=-arg2+arg4-x130, (-arg1+arg1P2 <= 0 /\ -arg2+arg4-2*x130 >= 0 /\ arg3 > 0 /\ 2+arg2-arg4+2*x130 > 0 /\ arg1P2 > 0 /\ 1+arg4 > 0), cost: 2 New rule: f74_0_loop_LE -> [4] : (0 == 0 /\ arg1-arg1P2 >= 0 /\ arg2-arg4+x130+arg3 == 0 /\ -arg2+arg4-2*x130 >= 0 /\ x130 <= 0 /\ arg3 > 0 /\ 2+arg2-arg4+2*x130 > 0 /\ arg1P2 > 0 /\ -x130 <= 0 /\ -x130 == 0 /\ 1+arg4 > 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_hjLCiO.txt Applied simplification Original rule: f74_0_loop_LE -> f74_0_loop_LE : arg2'=arg2+n*x130, arg1'=arg1P2, arg3'=-arg2+arg4-x130-(-1+n)*x130, (0 == 0 /\ arg1-arg1P2 >= 0 /\ -arg2+arg4-2*x130-(-1+n)*x130 >= 0 /\ arg2-arg4+x130+arg3 == 0 /\ 2+arg2-arg4+2*x130+(-1+n)*x130 > 0 /\ -1+n >= 0 /\ -arg2+arg4-2*x130 >= 0 /\ arg3 > 0 /\ 2+arg2-arg4+2*x130 > 0 /\ arg1P2 > 0 /\ -x130 == 0 /\ 1+arg4 > 0), cost: 2*n New rule: f74_0_loop_LE -> f74_0_loop_LE : arg2'=arg2+n*x130, arg1'=arg1P2, arg3'=-arg2+arg4-x130-(-1+n)*x130, (arg1-arg1P2 >= 0 /\ arg2-arg4+x130+arg3 == 0 /\ -1+n >= 0 /\ x130 == 0 /\ arg3 > 0 /\ 2+arg2-arg4+2*x130 > 0 /\ arg1P2 > 0 /\ 1+arg4 > 0), cost: 2*n Applied simplification Original rule: f74_0_loop_LE -> [4] : (0 == 0 /\ arg1-arg1P2 >= 0 /\ arg2-arg4+x130+arg3 == 0 /\ -arg2+arg4-2*x130 >= 0 /\ x130 <= 0 /\ arg3 > 0 /\ 2+arg2-arg4+2*x130 > 0 /\ arg1P2 > 0 /\ -x130 <= 0 /\ -x130 == 0 /\ 1+arg4 > 0), cost: NONTERM New rule: f74_0_loop_LE -> [4] : (arg1-arg1P2 >= 0 /\ arg2-arg4+x130+arg3 == 0 /\ x130 == 0 /\ arg3 > 0 /\ 2+arg2-arg4+2*x130 > 0 /\ arg1P2 > 0 /\ 1+arg4 > 0), cost: NONTERM Applied deletion Removed the following rules: 8 Accelerated simple loops Start location: __init 11: f74_0_loop_LE -> f74_0_loop_LE : arg2'=arg2+n*x130, arg1'=arg1P2, arg3'=-arg2+arg4-x130-(-1+n)*x130, (arg1-arg1P2 >= 0 /\ arg2-arg4+x130+arg3 == 0 /\ -1+n >= 0 /\ x130 == 0 /\ arg3 > 0 /\ 2+arg2-arg4+2*x130 > 0 /\ arg1P2 > 0 /\ 1+arg4 > 0), cost: 2*n 12: f74_0_loop_LE -> [4] : (arg1-arg1P2 >= 0 /\ arg2-arg4+x130+arg3 == 0 /\ x130 == 0 /\ arg3 > 0 /\ 2+arg2-arg4+2*x130 > 0 /\ arg1P2 > 0 /\ 1+arg4 > 0), cost: NONTERM 7: __init -> f74_0_loop_LE : arg2'=0, arg4'=arg2P3, arg1'=arg1P0, arg3'=arg2P3, (1+arg2P3 > 0 /\ arg1P0 > 0 /\ -arg1P3+arg1P0 <= 0), cost: 2 Applied chaining First rule: __init -> f74_0_loop_LE : arg2'=0, arg4'=arg2P3, arg1'=arg1P0, arg3'=arg2P3, (1+arg2P3 > 0 /\ arg1P0 > 0 /\ -arg1P3+arg1P0 <= 0), cost: 2 Second rule: f74_0_loop_LE -> f74_0_loop_LE : arg2'=arg2+n*x130, arg1'=arg1P2, arg3'=-arg2+arg4-x130-(-1+n)*x130, (arg1-arg1P2 >= 0 /\ arg2-arg4+x130+arg3 == 0 /\ -1+n >= 0 /\ x130 == 0 /\ arg3 > 0 /\ 2+arg2-arg4+2*x130 > 0 /\ arg1P2 > 0 /\ 1+arg4 > 0), cost: 2*n New rule: __init -> f74_0_loop_LE : arg2'=0, arg4'=arg2P3, arg1'=arg1P2, arg3'=arg2P3, (-1+n >= 0 /\ arg2P3 > 0 /\ 2-arg2P3 > 0 /\ arg1P2 > 0), cost: 2+2*n Applied chaining First rule: __init -> f74_0_loop_LE : arg2'=0, arg4'=arg2P3, arg1'=arg1P0, arg3'=arg2P3, (1+arg2P3 > 0 /\ arg1P0 > 0 /\ -arg1P3+arg1P0 <= 0), cost: 2 Second rule: f74_0_loop_LE -> [4] : (arg1-arg1P2 >= 0 /\ arg2-arg4+x130+arg3 == 0 /\ x130 == 0 /\ arg3 > 0 /\ 2+arg2-arg4+2*x130 > 0 /\ arg1P2 > 0 /\ 1+arg4 > 0), cost: NONTERM New rule: __init -> [4] : (0 <= 0 /\ -1 <= 0), cost: NONTERM Applied deletion Removed the following rules: 11 12 Chained accelerated rules with incoming rules Start location: __init 7: __init -> f74_0_loop_LE : arg2'=0, arg4'=arg2P3, arg1'=arg1P0, arg3'=arg2P3, (1+arg2P3 > 0 /\ arg1P0 > 0 /\ -arg1P3+arg1P0 <= 0), cost: 2 13: __init -> f74_0_loop_LE : arg2'=0, arg4'=arg2P3, arg1'=arg1P2, arg3'=arg2P3, (-1+n >= 0 /\ arg2P3 > 0 /\ 2-arg2P3 > 0 /\ arg1P2 > 0), cost: 2+2*n 14: __init -> [4] : (0 <= 0 /\ -1 <= 0), cost: NONTERM Removed unreachable locations and irrelevant leafs Start location: __init 14: __init -> [4] : (0 <= 0 /\ -1 <= 0), cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 14 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: (0 <= 0 /\ -1 <= 0)