NO Initial ITS Start location: __init 0: f1_0_main_ConstantStackPush -> f79_0_loop_GE : arg2'=arg2P0, arg4'=arg4P0, arg1'=arg1P0, arg3'=arg3P0, (2-arg3P0 == 0 /\ 2-arg1P0 == 0 /\ -arg4P0 == 0 /\ 2-arg2P0 == 0), cost: 1 1: f79_0_loop_GE -> f100_0_loop_InvokeMethod : arg2'=arg2P1, arg4'=arg4P1, arg1'=arg1P1, arg3'=arg3P1, (arg1-arg1P1 == 0 /\ arg2 > 0 /\ 4+arg2-arg2P1 == 0 /\ -arg2+arg4 > 0 /\ arg2-arg3 == 0 /\ -arg3P1+arg4 == 0), cost: 1 2: f79_0_loop_GE -> f100_0_loop_InvokeMethod : arg2'=arg2P2, arg4'=arg4P2, arg1'=arg1P2, arg3'=arg3P2, (arg2 > 0 /\ 2+arg2-arg2P2 == 0 /\ -arg1P2+arg1 == 0 /\ 1-arg3P2+arg4 == 0 /\ -arg2+arg4 <= 0 /\ arg2-arg3 == 0 /\ 1+arg4 > 0), cost: 1 3: f100_0_loop_InvokeMethod -> f79_0_loop_GE : arg2'=arg2P3, arg4'=arg4P3, arg1'=arg1P3, arg3'=arg3P3, (arg2-arg3P3 == 0 /\ arg2-arg1P3 == 0 /\ arg2-arg2P3 == 0 /\ -1+arg2 > 0 /\ arg3 > 0 /\ -arg4P3+arg3 == 0 /\ -1+arg1 > 0), cost: 1 4: __init -> f1_0_main_ConstantStackPush : arg2'=arg2P4, arg4'=arg4P4, arg1'=arg1P4, arg3'=arg3P4, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_ConstantStackPush -> f79_0_loop_GE : arg2'=arg2P0, arg4'=arg4P0, arg1'=arg1P0, arg3'=arg3P0, (2-arg3P0 == 0 /\ 2-arg1P0 == 0 /\ -arg4P0 == 0 /\ 2-arg2P0 == 0), cost: 1 New rule: f1_0_main_ConstantStackPush -> f79_0_loop_GE : arg2'=2, arg4'=0, arg1'=2, arg3'=2, TRUE, cost: 1 Applied preprocessing Original rule: f79_0_loop_GE -> f100_0_loop_InvokeMethod : arg2'=arg2P1, arg4'=arg4P1, arg1'=arg1P1, arg3'=arg3P1, (arg1-arg1P1 == 0 /\ arg2 > 0 /\ 4+arg2-arg2P1 == 0 /\ -arg2+arg4 > 0 /\ arg2-arg3 == 0 /\ -arg3P1+arg4 == 0), cost: 1 New rule: f79_0_loop_GE -> f100_0_loop_InvokeMethod : arg2'=4+arg2, arg4'=arg4P1, arg3'=arg4, (arg2 > 0 /\ -arg2+arg4 > 0 /\ arg2-arg3 == 0), cost: 1 Applied preprocessing Original rule: f79_0_loop_GE -> f100_0_loop_InvokeMethod : arg2'=arg2P2, arg4'=arg4P2, arg1'=arg1P2, arg3'=arg3P2, (arg2 > 0 /\ 2+arg2-arg2P2 == 0 /\ -arg1P2+arg1 == 0 /\ 1-arg3P2+arg4 == 0 /\ -arg2+arg4 <= 0 /\ arg2-arg3 == 0 /\ 1+arg4 > 0), cost: 1 New rule: f79_0_loop_GE -> f100_0_loop_InvokeMethod : arg2'=2+arg2, arg4'=arg4P2, arg3'=1+arg4, (arg2 > 0 /\ -arg2+arg4 <= 0 /\ arg2-arg3 == 0 /\ 1+arg4 > 0), cost: 1 Applied preprocessing Original rule: f100_0_loop_InvokeMethod -> f79_0_loop_GE : arg2'=arg2P3, arg4'=arg4P3, arg1'=arg1P3, arg3'=arg3P3, (arg2-arg3P3 == 0 /\ arg2-arg1P3 == 0 /\ arg2-arg2P3 == 0 /\ -1+arg2 > 0 /\ arg3 > 0 /\ -arg4P3+arg3 == 0 /\ -1+arg1 > 0), cost: 1 New rule: f100_0_loop_InvokeMethod -> f79_0_loop_GE : arg4'=arg3, arg1'=arg2, arg3'=arg2, (-1+arg2 > 0 /\ arg3 > 0 /\ -1+arg1 > 0), cost: 1 Simplified rules Start location: __init 5: f1_0_main_ConstantStackPush -> f79_0_loop_GE : arg2'=2, arg4'=0, arg1'=2, arg3'=2, TRUE, cost: 1 6: f79_0_loop_GE -> f100_0_loop_InvokeMethod : arg2'=4+arg2, arg4'=arg4P1, arg3'=arg4, (arg2 > 0 /\ -arg2+arg4 > 0 /\ arg2-arg3 == 0), cost: 1 7: f79_0_loop_GE -> f100_0_loop_InvokeMethod : arg2'=2+arg2, arg4'=arg4P2, arg3'=1+arg4, (arg2 > 0 /\ -arg2+arg4 <= 0 /\ arg2-arg3 == 0 /\ 1+arg4 > 0), cost: 1 8: f100_0_loop_InvokeMethod -> f79_0_loop_GE : arg4'=arg3, arg1'=arg2, arg3'=arg2, (-1+arg2 > 0 /\ arg3 > 0 /\ -1+arg1 > 0), cost: 1 4: __init -> f1_0_main_ConstantStackPush : arg2'=arg2P4, arg4'=arg4P4, arg1'=arg1P4, arg3'=arg3P4, TRUE, cost: 1 Eliminating location f1_0_main_ConstantStackPush by chaining: Applied chaining First rule: __init -> f1_0_main_ConstantStackPush : arg2'=arg2P4, arg4'=arg4P4, arg1'=arg1P4, arg3'=arg3P4, TRUE, cost: 1 Second rule: f1_0_main_ConstantStackPush -> f79_0_loop_GE : arg2'=2, arg4'=0, arg1'=2, arg3'=2, TRUE, cost: 1 New rule: __init -> f79_0_loop_GE : arg2'=2, arg4'=0, arg1'=2, arg3'=2, TRUE, cost: 2 Applied deletion Removed the following rules: 4 5 Eliminated locations on linear paths Start location: __init 6: f79_0_loop_GE -> f100_0_loop_InvokeMethod : arg2'=4+arg2, arg4'=arg4P1, arg3'=arg4, (arg2 > 0 /\ -arg2+arg4 > 0 /\ arg2-arg3 == 0), cost: 1 7: f79_0_loop_GE -> f100_0_loop_InvokeMethod : arg2'=2+arg2, arg4'=arg4P2, arg3'=1+arg4, (arg2 > 0 /\ -arg2+arg4 <= 0 /\ arg2-arg3 == 0 /\ 1+arg4 > 0), cost: 1 8: f100_0_loop_InvokeMethod -> f79_0_loop_GE : arg4'=arg3, arg1'=arg2, arg3'=arg2, (-1+arg2 > 0 /\ arg3 > 0 /\ -1+arg1 > 0), cost: 1 9: __init -> f79_0_loop_GE : arg2'=2, arg4'=0, arg1'=2, arg3'=2, TRUE, cost: 2 Eliminating location f100_0_loop_InvokeMethod by chaining: Applied chaining First rule: f79_0_loop_GE -> f100_0_loop_InvokeMethod : arg2'=4+arg2, arg4'=arg4P1, arg3'=arg4, (arg2 > 0 /\ -arg2+arg4 > 0 /\ arg2-arg3 == 0), cost: 1 Second rule: f100_0_loop_InvokeMethod -> f79_0_loop_GE : arg4'=arg3, arg1'=arg2, arg3'=arg2, (-1+arg2 > 0 /\ arg3 > 0 /\ -1+arg1 > 0), cost: 1 New rule: f79_0_loop_GE -> f79_0_loop_GE : arg2'=4+arg2, arg4'=arg4, arg1'=4+arg2, arg3'=4+arg2, (arg2 > 0 /\ 3+arg2 > 0 /\ arg4 > 0 /\ -arg2+arg4 > 0 /\ arg2-arg3 == 0 /\ -1+arg1 > 0), cost: 2 Applied simplification Original rule: f79_0_loop_GE -> f79_0_loop_GE : arg2'=4+arg2, arg4'=arg4, arg1'=4+arg2, arg3'=4+arg2, (arg2 > 0 /\ 3+arg2 > 0 /\ arg4 > 0 /\ -arg2+arg4 > 0 /\ arg2-arg3 == 0 /\ -1+arg1 > 0), cost: 2 New rule: f79_0_loop_GE -> f79_0_loop_GE : arg2'=4+arg2, arg4'=arg4, arg1'=4+arg2, arg3'=4+arg2, (arg2 > 0 /\ -arg2+arg4 > 0 /\ arg2-arg3 == 0 /\ -1+arg1 > 0), cost: 2 Applied chaining First rule: f79_0_loop_GE -> f100_0_loop_InvokeMethod : arg2'=2+arg2, arg4'=arg4P2, arg3'=1+arg4, (arg2 > 0 /\ -arg2+arg4 <= 0 /\ arg2-arg3 == 0 /\ 1+arg4 > 0), cost: 1 Second rule: f100_0_loop_InvokeMethod -> f79_0_loop_GE : arg4'=arg3, arg1'=arg2, arg3'=arg2, (-1+arg2 > 0 /\ arg3 > 0 /\ -1+arg1 > 0), cost: 1 New rule: f79_0_loop_GE -> f79_0_loop_GE : arg2'=2+arg2, arg4'=1+arg4, arg1'=2+arg2, arg3'=2+arg2, (arg2 > 0 /\ 1+arg2 > 0 /\ -arg2+arg4 <= 0 /\ arg2-arg3 == 0 /\ -1+arg1 > 0 /\ 1+arg4 > 0), cost: 2 Applied simplification Original rule: f79_0_loop_GE -> f79_0_loop_GE : arg2'=2+arg2, arg4'=1+arg4, arg1'=2+arg2, arg3'=2+arg2, (arg2 > 0 /\ 1+arg2 > 0 /\ -arg2+arg4 <= 0 /\ arg2-arg3 == 0 /\ -1+arg1 > 0 /\ 1+arg4 > 0), cost: 2 New rule: f79_0_loop_GE -> f79_0_loop_GE : arg2'=2+arg2, arg4'=1+arg4, arg1'=2+arg2, arg3'=2+arg2, (arg2 > 0 /\ -arg2+arg4 <= 0 /\ arg2-arg3 == 0 /\ -1+arg1 > 0 /\ 1+arg4 > 0), cost: 2 Applied deletion Removed the following rules: 6 7 8 Eliminated locations on tree-shaped paths Start location: __init 10: f79_0_loop_GE -> f79_0_loop_GE : arg2'=4+arg2, arg4'=arg4, arg1'=4+arg2, arg3'=4+arg2, (arg2 > 0 /\ -arg2+arg4 > 0 /\ arg2-arg3 == 0 /\ -1+arg1 > 0), cost: 2 11: f79_0_loop_GE -> f79_0_loop_GE : arg2'=2+arg2, arg4'=1+arg4, arg1'=2+arg2, arg3'=2+arg2, (arg2 > 0 /\ -arg2+arg4 <= 0 /\ arg2-arg3 == 0 /\ -1+arg1 > 0 /\ 1+arg4 > 0), cost: 2 9: __init -> f79_0_loop_GE : arg2'=2, arg4'=0, arg1'=2, arg3'=2, TRUE, cost: 2 Applied simplification Original rule: f79_0_loop_GE -> f79_0_loop_GE : arg2'=4+arg2, arg4'=arg4, arg1'=4+arg2, arg3'=4+arg2, (arg2 > 0 /\ -arg2+arg4 > 0 /\ arg2-arg3 == 0 /\ -1+arg1 > 0), cost: 2 New rule: f79_0_loop_GE -> f79_0_loop_GE : arg2'=4+arg2, arg1'=4+arg2, arg3'=4+arg2, (arg2 > 0 /\ -arg2+arg4 > 0 /\ arg2-arg3 == 0 /\ -1+arg1 > 0), cost: 2 Simplified simple loops Start location: __init 11: f79_0_loop_GE -> f79_0_loop_GE : arg2'=2+arg2, arg4'=1+arg4, arg1'=2+arg2, arg3'=2+arg2, (arg2 > 0 /\ -arg2+arg4 <= 0 /\ arg2-arg3 == 0 /\ -1+arg1 > 0 /\ 1+arg4 > 0), cost: 2 12: f79_0_loop_GE -> f79_0_loop_GE : arg2'=4+arg2, arg1'=4+arg2, arg3'=4+arg2, (arg2 > 0 /\ -arg2+arg4 > 0 /\ arg2-arg3 == 0 /\ -1+arg1 > 0), cost: 2 9: __init -> f79_0_loop_GE : arg2'=2, arg4'=0, arg1'=2, arg3'=2, TRUE, cost: 2 Applied nonterm Original rule: f79_0_loop_GE -> f79_0_loop_GE : arg2'=2+arg2, arg4'=1+arg4, arg1'=2+arg2, arg3'=2+arg2, (arg2 > 0 /\ -arg2+arg4 <= 0 /\ arg2-arg3 == 0 /\ -1+arg1 > 0 /\ 1+arg4 > 0), cost: 2 New rule: f79_0_loop_GE -> [4] : (arg2 > 0 /\ -1+n >= 0 /\ arg2-arg3 >= 0 /\ -1+arg1 > 0 /\ arg2-arg4 >= 0 /\ -arg2+arg3 >= 0 /\ 1+arg4 > 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_Gbdala.txt Applied acceleration Original rule: f79_0_loop_GE -> f79_0_loop_GE : arg2'=4+arg2, arg1'=4+arg2, arg3'=4+arg2, (arg2 > 0 /\ -arg2+arg4 > 0 /\ arg2-arg3 == 0 /\ -1+arg1 > 0), cost: 2 New rule: f79_0_loop_GE -> f79_0_loop_GE : arg2'=arg2+4*n0, arg1'=arg2+4*n0, arg3'=arg2+4*n0, (arg2 > 0 /\ 4-arg2-4*n0+arg4 > 0 /\ -1+n0 >= 0 /\ arg2-arg3 >= 0 /\ -1+arg1 > 0 /\ -arg2+arg3 >= 0), cost: 2*n0 Sub-proof via acceration calculus written to file:///tmp/tmpnam_BPHnfG.txt Applied deletion Removed the following rules: 11 12 Accelerated simple loops Start location: __init 13: f79_0_loop_GE -> [4] : (arg2 > 0 /\ -1+n >= 0 /\ arg2-arg3 >= 0 /\ -1+arg1 > 0 /\ arg2-arg4 >= 0 /\ -arg2+arg3 >= 0 /\ 1+arg4 > 0), cost: NONTERM 14: f79_0_loop_GE -> f79_0_loop_GE : arg2'=arg2+4*n0, arg1'=arg2+4*n0, arg3'=arg2+4*n0, (arg2 > 0 /\ 4-arg2-4*n0+arg4 > 0 /\ -1+n0 >= 0 /\ arg2-arg3 >= 0 /\ -1+arg1 > 0 /\ -arg2+arg3 >= 0), cost: 2*n0 9: __init -> f79_0_loop_GE : arg2'=2, arg4'=0, arg1'=2, arg3'=2, TRUE, cost: 2 Applied chaining First rule: __init -> f79_0_loop_GE : arg2'=2, arg4'=0, arg1'=2, arg3'=2, TRUE, cost: 2 Second rule: f79_0_loop_GE -> [4] : (arg2 > 0 /\ -1+n >= 0 /\ arg2-arg3 >= 0 /\ -1+arg1 > 0 /\ arg2-arg4 >= 0 /\ -arg2+arg3 >= 0 /\ 1+arg4 > 0), cost: NONTERM New rule: __init -> [4] : (0 == 0 /\ 2 > 0 /\ 2 >= 0), cost: NONTERM Applied deletion Removed the following rules: 13 14 Chained accelerated rules with incoming rules Start location: __init 9: __init -> f79_0_loop_GE : arg2'=2, arg4'=0, arg1'=2, arg3'=2, TRUE, cost: 2 15: __init -> [4] : (0 == 0 /\ 2 > 0 /\ 2 >= 0), cost: NONTERM Removed unreachable locations and irrelevant leafs Start location: __init 15: __init -> [4] : (0 == 0 /\ 2 > 0 /\ 2 >= 0), cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 15 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: (0 == 0 /\ 2 > 0 /\ 2 >= 0)