NO Initial ITS Start location: __init 0: f1_0_main_ConstantStackPush -> f93_0_main_GE : arg1'=arg1P0, arg3'=arg3P0, arg2'=arg2P0, (2-arg2P0 == 0 /\ 3-arg3P0 == 0 /\ 1-arg1P0 == 0), cost: 1 1: f93_0_main_GE -> f93_0_main_GE : arg1'=arg1P1, arg3'=arg3P1, arg2'=arg2P1, (arg1-arg2P1 == 0 /\ -5+arg3 < 0 /\ -arg1P1+arg2 == 0 /\ arg1+arg2-arg3P1 == 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 -> f93_0_main_GE : arg1'=arg1P0, arg3'=arg3P0, arg2'=arg2P0, (2-arg2P0 == 0 /\ 3-arg3P0 == 0 /\ 1-arg1P0 == 0), cost: 1 New rule: f1_0_main_ConstantStackPush -> f93_0_main_GE : arg1'=1, arg3'=3, arg2'=2, TRUE, cost: 1 Applied preprocessing Original rule: f93_0_main_GE -> f93_0_main_GE : arg1'=arg1P1, arg3'=arg3P1, arg2'=arg2P1, (arg1-arg2P1 == 0 /\ -5+arg3 < 0 /\ -arg1P1+arg2 == 0 /\ arg1+arg2-arg3P1 == 0), cost: 1 New rule: f93_0_main_GE -> f93_0_main_GE : arg1'=arg2, arg3'=arg1+arg2, arg2'=arg1, 5-arg3 > 0, cost: 1 Simplified rules Start location: __init 3: f1_0_main_ConstantStackPush -> f93_0_main_GE : arg1'=1, arg3'=3, arg2'=2, TRUE, cost: 1 4: f93_0_main_GE -> f93_0_main_GE : arg1'=arg2, arg3'=arg1+arg2, arg2'=arg1, 5-arg3 > 0, cost: 1 2: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P2, arg3'=arg3P2, arg2'=arg2P2, TRUE, cost: 1 Applied unrolling Original rule: f93_0_main_GE -> f93_0_main_GE : arg1'=arg2, arg3'=arg1+arg2, arg2'=arg1, 5-arg3 > 0, cost: 1 New rule: f93_0_main_GE -> f93_0_main_GE : arg1'=arg1, arg3'=arg1+arg2, arg2'=arg2, (5-arg3 > 0 /\ 5-arg1-arg2 > 0), cost: 2 Applied nonterm Original rule: f93_0_main_GE -> f93_0_main_GE : arg1'=arg1, arg3'=arg1+arg2, arg2'=arg2, (5-arg3 > 0 /\ 5-arg1-arg2 > 0), cost: 2 New rule: f93_0_main_GE -> [3] : (5-arg3 > 0 /\ 5-arg1-arg2 > 0), cost: NONTERM Applied acceleration Original rule: f93_0_main_GE -> f93_0_main_GE : arg1'=arg1, arg3'=arg1+arg2, arg2'=arg2, (5-arg3 > 0 /\ 5-arg1-arg2 > 0), cost: 2 New rule: f93_0_main_GE -> f93_0_main_GE : arg1'=arg1, arg3'=arg1+arg2, arg2'=arg2, (-1+n0 >= 0 /\ 5-arg1-arg2 > 0 /\ ((5-arg3 > 0 /\ 5-arg1-arg2 > 0) \/ (5-arg3 > 0 /\ 5-arg1-arg2 > 0))), cost: 2*n0 Applied simplification Original rule: f93_0_main_GE -> f93_0_main_GE : arg1'=arg1, arg3'=arg1+arg2, arg2'=arg2, (-1+n0 >= 0 /\ 5-arg1-arg2 > 0 /\ ((5-arg3 > 0 /\ 5-arg1-arg2 > 0) \/ (5-arg3 > 0 /\ 5-arg1-arg2 > 0))), cost: 2*n0 New rule: f93_0_main_GE -> f93_0_main_GE : arg1'=arg1, arg3'=arg1+arg2, arg2'=arg2, (5-arg3 > 0 /\ -1+n0 >= 0 /\ 5-arg1-arg2 > 0), cost: 2*n0 Applied deletion Removed the following rules: 4 Accelerated simple loops Start location: __init 3: f1_0_main_ConstantStackPush -> f93_0_main_GE : arg1'=1, arg3'=3, arg2'=2, TRUE, cost: 1 5: f93_0_main_GE -> [3] : (5-arg3 > 0 /\ 5-arg1-arg2 > 0), cost: NONTERM 7: f93_0_main_GE -> f93_0_main_GE : arg1'=arg1, arg3'=arg1+arg2, arg2'=arg2, (5-arg3 > 0 /\ -1+n0 >= 0 /\ 5-arg1-arg2 > 0), cost: 2*n0 2: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P2, arg3'=arg3P2, arg2'=arg2P2, TRUE, cost: 1 Applied chaining First rule: f1_0_main_ConstantStackPush -> f93_0_main_GE : arg1'=1, arg3'=3, arg2'=2, TRUE, cost: 1 Second rule: f93_0_main_GE -> [3] : (5-arg3 > 0 /\ 5-arg1-arg2 > 0), cost: NONTERM New rule: f1_0_main_ConstantStackPush -> [3] : 2 > 0, cost: NONTERM Applied chaining First rule: f1_0_main_ConstantStackPush -> f93_0_main_GE : arg1'=1, arg3'=3, arg2'=2, TRUE, cost: 1 Second rule: f93_0_main_GE -> f93_0_main_GE : arg1'=arg1, arg3'=arg1+arg2, arg2'=arg2, (5-arg3 > 0 /\ -1+n0 >= 0 /\ 5-arg1-arg2 > 0), cost: 2*n0 New rule: f1_0_main_ConstantStackPush -> f93_0_main_GE : arg1'=1, arg3'=3, arg2'=2, -1+n0 >= 0, cost: 1+2*n0 Applied deletion Removed the following rules: 5 7 Chained accelerated rules with incoming rules Start location: __init 3: f1_0_main_ConstantStackPush -> f93_0_main_GE : arg1'=1, arg3'=3, arg2'=2, TRUE, cost: 1 8: f1_0_main_ConstantStackPush -> [3] : 2 > 0, cost: NONTERM 9: f1_0_main_ConstantStackPush -> f93_0_main_GE : arg1'=1, arg3'=3, arg2'=2, -1+n0 >= 0, cost: 1+2*n0 2: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P2, arg3'=arg3P2, arg2'=arg2P2, TRUE, cost: 1 Removed unreachable locations and irrelevant leafs Start location: __init 8: f1_0_main_ConstantStackPush -> [3] : 2 > 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] : 2 > 0, cost: NONTERM New rule: __init -> [3] : 2 > 0, cost: NONTERM Applied deletion Removed the following rules: 2 8 Eliminated locations on linear paths Start location: __init 10: __init -> [3] : 2 > 0, cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 10 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: 2 > 0