NO Initial ITS Start location: __init 0: f1_0_main_ConstantStackPush -> f61_0_main_GE : arg1'=arg1P0, arg3'=arg3P0, arg2'=arg2P0, (arg1 > 0 /\ -arg1+arg1P0 <= 0 /\ arg1P0 > 0 /\ -arg2P0 == 0 /\ 1+arg2 > 0 /\ arg2-arg3P0 == 0), cost: 1 1: f61_0_main_GE -> f61_0_main_GE : arg1'=arg1P1, arg3'=arg3P1, arg2'=arg2P1, (arg1 > 0 /\ arg3-arg2 > 0 /\ arg1P1 > 0 /\ 1+x70 > 0 /\ -arg2P1+arg2+x70 == 0 /\ arg3-arg3P1 == 0 /\ 1+arg2 > 0 /\ -arg1+arg1P1 <= 0), cost: 1 2: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P2, arg3'=arg3P2, arg2'=arg2P2, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_ConstantStackPush -> f61_0_main_GE : arg1'=arg1P0, arg3'=arg3P0, arg2'=arg2P0, (arg1 > 0 /\ -arg1+arg1P0 <= 0 /\ arg1P0 > 0 /\ -arg2P0 == 0 /\ 1+arg2 > 0 /\ arg2-arg3P0 == 0), cost: 1 New rule: f1_0_main_ConstantStackPush -> f61_0_main_GE : arg1'=arg1P0, arg3'=arg2, arg2'=0, (-arg1+arg1P0 <= 0 /\ arg1P0 > 0 /\ 1+arg2 > 0), cost: 1 Applied preprocessing Original rule: f61_0_main_GE -> f61_0_main_GE : arg1'=arg1P1, arg3'=arg3P1, arg2'=arg2P1, (arg1 > 0 /\ arg3-arg2 > 0 /\ arg1P1 > 0 /\ 1+x70 > 0 /\ -arg2P1+arg2+x70 == 0 /\ arg3-arg3P1 == 0 /\ 1+arg2 > 0 /\ -arg1+arg1P1 <= 0), cost: 1 New rule: f61_0_main_GE -> f61_0_main_GE : arg1'=arg1P1, arg2'=arg2+x70, (arg3-arg2 > 0 /\ arg1P1 > 0 /\ 1+x70 > 0 /\ 1+arg2 > 0 /\ -arg1+arg1P1 <= 0), cost: 1 Simplified rules Start location: __init 3: f1_0_main_ConstantStackPush -> f61_0_main_GE : arg1'=arg1P0, arg3'=arg2, arg2'=0, (-arg1+arg1P0 <= 0 /\ arg1P0 > 0 /\ 1+arg2 > 0), cost: 1 4: f61_0_main_GE -> f61_0_main_GE : arg1'=arg1P1, arg2'=arg2+x70, (arg3-arg2 > 0 /\ arg1P1 > 0 /\ 1+x70 > 0 /\ 1+arg2 > 0 /\ -arg1+arg1P1 <= 0), cost: 1 2: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P2, arg3'=arg3P2, arg2'=arg2P2, TRUE, cost: 1 Applied acceleration Original rule: f61_0_main_GE -> f61_0_main_GE : arg1'=arg1P1, arg2'=arg2+x70, (arg3-arg2 > 0 /\ arg1P1 > 0 /\ 1+x70 > 0 /\ 1+arg2 > 0 /\ -arg1+arg1P1 <= 0), cost: 1 New rule: f61_0_main_GE -> f61_0_main_GE : arg1'=arg1P1, arg2'=arg2+n0*x70, (arg1P1 > 0 /\ 1+x70 > 0 /\ -1+n0 >= 0 /\ arg1-arg1P1 >= 0 /\ arg3-arg2-(-1+n0)*x70 > 0 /\ ((1+arg2+(-1+n0)*x70 > 0 /\ 1+arg2 > 0) \/ (1+x70 > 0 /\ 1+arg2 > 0))), cost: n0 Applied recurrent set Original rule: f61_0_main_GE -> f61_0_main_GE : arg1'=arg1P1, arg2'=arg2+x70, (arg3-arg2 > 0 /\ arg1P1 > 0 /\ 1+x70 > 0 /\ 1+arg2 > 0 /\ -arg1+arg1P1 <= 0), cost: 1 New rule: f61_0_main_GE -> [3] : (arg3-arg2 > 0 /\ 2*x70 <= 0 /\ arg1P1 > 0 /\ 1+x70 > 0 /\ 1+arg2 > 0 /\ -arg1+arg1P1 <= 0), cost: NONTERM Applied fixed-point processor Original rule: f61_0_main_GE -> f61_0_main_GE : arg1'=arg1P1, arg2'=arg2+x70, (arg3-arg2 > 0 /\ arg1P1 > 0 /\ 1+x70 > 0 /\ 1+arg2 > 0 /\ -arg1+arg1P1 <= 0), cost: 1 New rule: f61_0_main_GE -> [3] : (arg3-arg2 > 0 /\ arg1P1 > 0 /\ 1+x70 > 0 /\ 1+arg2 > 0 /\ arg1-arg1P1 == 0 /\ -arg1+arg1P1 <= 0), cost: NONTERM Applied simplification Original rule: f61_0_main_GE -> f61_0_main_GE : arg1'=arg1P1, arg2'=arg2+n0*x70, (arg1P1 > 0 /\ 1+x70 > 0 /\ -1+n0 >= 0 /\ arg1-arg1P1 >= 0 /\ arg3-arg2-(-1+n0)*x70 > 0 /\ ((1+arg2+(-1+n0)*x70 > 0 /\ 1+arg2 > 0) \/ (1+x70 > 0 /\ 1+arg2 > 0))), cost: n0 New rule: f61_0_main_GE -> f61_0_main_GE : arg1'=arg1P1, arg2'=arg2+n0*x70, (arg1P1 > 0 /\ 1+x70 > 0 /\ -1+n0 >= 0 /\ 1+arg2 > 0 /\ arg1-arg1P1 >= 0 /\ arg3-arg2-(-1+n0)*x70 > 0), cost: n0 Applied simplification Original rule: f61_0_main_GE -> [3] : (arg3-arg2 > 0 /\ 2*x70 <= 0 /\ arg1P1 > 0 /\ 1+x70 > 0 /\ 1+arg2 > 0 /\ -arg1+arg1P1 <= 0), cost: NONTERM New rule: f61_0_main_GE -> [3] : (arg3-arg2 > 0 /\ arg1P1 > 0 /\ 1+x70 > 0 /\ 1+arg2 > 0 /\ x70 <= 0 /\ -arg1+arg1P1 <= 0), cost: NONTERM Applied simplification Original rule: f61_0_main_GE -> [3] : (arg3-arg2 > 0 /\ arg1P1 > 0 /\ 1+x70 > 0 /\ 1+arg2 > 0 /\ arg1-arg1P1 == 0 /\ -arg1+arg1P1 <= 0), cost: NONTERM New rule: f61_0_main_GE -> [3] : (arg3-arg2 > 0 /\ arg1P1 > 0 /\ 1+x70 > 0 /\ 1+arg2 > 0 /\ arg1-arg1P1 == 0), cost: NONTERM Applied deletion Removed the following rules: 4 Accelerated simple loops Start location: __init 3: f1_0_main_ConstantStackPush -> f61_0_main_GE : arg1'=arg1P0, arg3'=arg2, arg2'=0, (-arg1+arg1P0 <= 0 /\ arg1P0 > 0 /\ 1+arg2 > 0), cost: 1 8: f61_0_main_GE -> f61_0_main_GE : arg1'=arg1P1, arg2'=arg2+n0*x70, (arg1P1 > 0 /\ 1+x70 > 0 /\ -1+n0 >= 0 /\ 1+arg2 > 0 /\ arg1-arg1P1 >= 0 /\ arg3-arg2-(-1+n0)*x70 > 0), cost: n0 9: f61_0_main_GE -> [3] : (arg3-arg2 > 0 /\ arg1P1 > 0 /\ 1+x70 > 0 /\ 1+arg2 > 0 /\ x70 <= 0 /\ -arg1+arg1P1 <= 0), cost: NONTERM 10: f61_0_main_GE -> [3] : (arg3-arg2 > 0 /\ arg1P1 > 0 /\ 1+x70 > 0 /\ 1+arg2 > 0 /\ arg1-arg1P1 == 0), cost: NONTERM 2: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P2, arg3'=arg3P2, arg2'=arg2P2, TRUE, cost: 1 Applied chaining First rule: f1_0_main_ConstantStackPush -> f61_0_main_GE : arg1'=arg1P0, arg3'=arg2, arg2'=0, (-arg1+arg1P0 <= 0 /\ arg1P0 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f61_0_main_GE -> f61_0_main_GE : arg1'=arg1P1, arg2'=arg2+n0*x70, (arg1P1 > 0 /\ 1+x70 > 0 /\ -1+n0 >= 0 /\ 1+arg2 > 0 /\ arg1-arg1P1 >= 0 /\ arg3-arg2-(-1+n0)*x70 > 0), cost: n0 New rule: f1_0_main_ConstantStackPush -> f61_0_main_GE : arg1'=arg1P1, arg3'=arg2, arg2'=n0*x70, (arg1P1 > 0 /\ 1+x70 > 0 /\ -1+n0 >= 0 /\ arg2-(-1+n0)*x70 > 0 /\ -arg1+arg1P1 <= 0), cost: 1+n0 Applied chaining First rule: f1_0_main_ConstantStackPush -> f61_0_main_GE : arg1'=arg1P0, arg3'=arg2, arg2'=0, (-arg1+arg1P0 <= 0 /\ arg1P0 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f61_0_main_GE -> [3] : (arg3-arg2 > 0 /\ arg1P1 > 0 /\ 1+x70 > 0 /\ 1+arg2 > 0 /\ x70 <= 0 /\ -arg1+arg1P1 <= 0), cost: NONTERM New rule: f1_0_main_ConstantStackPush -> [3] : (-1+arg1 >= 0 /\ arg2 > 0), cost: NONTERM Applied chaining First rule: f1_0_main_ConstantStackPush -> f61_0_main_GE : arg1'=arg1P0, arg3'=arg2, arg2'=0, (-arg1+arg1P0 <= 0 /\ arg1P0 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f61_0_main_GE -> [3] : (arg3-arg2 > 0 /\ arg1P1 > 0 /\ 1+x70 > 0 /\ 1+arg2 > 0 /\ arg1-arg1P1 == 0), cost: NONTERM New rule: f1_0_main_ConstantStackPush -> [3] : (-1+arg1 >= 0 /\ arg2 > 0), cost: NONTERM Applied deletion Removed the following rules: 8 9 10 Chained accelerated rules with incoming rules Start location: __init 3: f1_0_main_ConstantStackPush -> f61_0_main_GE : arg1'=arg1P0, arg3'=arg2, arg2'=0, (-arg1+arg1P0 <= 0 /\ arg1P0 > 0 /\ 1+arg2 > 0), cost: 1 11: f1_0_main_ConstantStackPush -> f61_0_main_GE : arg1'=arg1P1, arg3'=arg2, arg2'=n0*x70, (arg1P1 > 0 /\ 1+x70 > 0 /\ -1+n0 >= 0 /\ arg2-(-1+n0)*x70 > 0 /\ -arg1+arg1P1 <= 0), cost: 1+n0 12: f1_0_main_ConstantStackPush -> [3] : (-1+arg1 >= 0 /\ arg2 > 0), cost: NONTERM 13: f1_0_main_ConstantStackPush -> [3] : (-1+arg1 >= 0 /\ arg2 > 0), cost: NONTERM 2: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P2, arg3'=arg3P2, arg2'=arg2P2, TRUE, cost: 1 Removed unreachable locations and irrelevant leafs Start location: __init 12: f1_0_main_ConstantStackPush -> [3] : (-1+arg1 >= 0 /\ arg2 > 0), cost: NONTERM 13: f1_0_main_ConstantStackPush -> [3] : (-1+arg1 >= 0 /\ arg2 > 0), cost: NONTERM 2: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P2, arg3'=arg3P2, arg2'=arg2P2, TRUE, cost: 1 Eliminating location f1_0_main_ConstantStackPush by chaining: Applied chaining First rule: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P2, arg3'=arg3P2, arg2'=arg2P2, TRUE, cost: 1 Second rule: f1_0_main_ConstantStackPush -> [3] : (-1+arg1 >= 0 /\ arg2 > 0), cost: NONTERM New rule: __init -> [3] : (-1+arg1P2 >= 0 /\ arg2P2 > 0), cost: NONTERM Applied chaining First rule: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P2, arg3'=arg3P2, arg2'=arg2P2, TRUE, cost: 1 Second rule: f1_0_main_ConstantStackPush -> [3] : (-1+arg1 >= 0 /\ arg2 > 0), cost: NONTERM New rule: __init -> [3] : (-1+arg1P2 >= 0 /\ arg2P2 > 0), cost: NONTERM Applied deletion Removed the following rules: 2 12 13 Eliminated locations on tree-shaped paths Start location: __init 14: __init -> [3] : (-1+arg1P2 >= 0 /\ arg2P2 > 0), cost: NONTERM 15: __init -> [3] : (-1+arg1P2 >= 0 /\ arg2P2 > 0), cost: NONTERM Removed duplicate rules (ignoring updates) Start location: __init 15: __init -> [3] : (-1+arg1P2 >= 0 /\ arg2P2 > 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: (-1+arg1P2 >= 0 /\ arg2P2 > 0)