NO Initial ITS Start location: __init 0: f1_0_main_ConstantStackPush -> f61_0_main_GE : arg2'=arg2P0, arg1'=arg1P0, arg3'=arg3P0, (-arg2P0 == 0 /\ 1+arg2 > 0 /\ arg1 > 0 /\ -arg1+arg1P0 <= 0 /\ arg1P0 > 0 /\ arg2-arg3P0 == 0), cost: 1 1: f61_0_main_GE -> f61_0_main_GE : arg2'=arg2P1, arg1'=arg1P1, arg3'=arg3P1, (arg2+x70-arg2P1 == 0 /\ arg3-arg3P1 == 0 /\ 1+x70 > 0 /\ 1+arg2 > 0 /\ arg1P1 > 0 /\ arg1 > 0 /\ arg1P1-arg1 <= 0 /\ -arg2+arg3 > 0), cost: 1 2: __init -> f1_0_main_ConstantStackPush : arg2'=arg2P2, arg1'=arg1P2, arg3'=arg3P2, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_ConstantStackPush -> f61_0_main_GE : arg2'=arg2P0, arg1'=arg1P0, arg3'=arg3P0, (-arg2P0 == 0 /\ 1+arg2 > 0 /\ arg1 > 0 /\ -arg1+arg1P0 <= 0 /\ arg1P0 > 0 /\ arg2-arg3P0 == 0), cost: 1 New rule: f1_0_main_ConstantStackPush -> f61_0_main_GE : arg2'=0, arg1'=arg1P0, arg3'=arg2, (1+arg2 > 0 /\ -arg1+arg1P0 <= 0 /\ arg1P0 > 0), cost: 1 Applied preprocessing Original rule: f61_0_main_GE -> f61_0_main_GE : arg2'=arg2P1, arg1'=arg1P1, arg3'=arg3P1, (arg2+x70-arg2P1 == 0 /\ arg3-arg3P1 == 0 /\ 1+x70 > 0 /\ 1+arg2 > 0 /\ arg1P1 > 0 /\ arg1 > 0 /\ arg1P1-arg1 <= 0 /\ -arg2+arg3 > 0), cost: 1 New rule: f61_0_main_GE -> f61_0_main_GE : arg2'=arg2+x70, arg1'=arg1P1, (1+x70 > 0 /\ 1+arg2 > 0 /\ arg1P1 > 0 /\ arg1P1-arg1 <= 0 /\ -arg2+arg3 > 0), cost: 1 Simplified rules Start location: __init 3: f1_0_main_ConstantStackPush -> f61_0_main_GE : arg2'=0, arg1'=arg1P0, arg3'=arg2, (1+arg2 > 0 /\ -arg1+arg1P0 <= 0 /\ arg1P0 > 0), cost: 1 4: f61_0_main_GE -> f61_0_main_GE : arg2'=arg2+x70, arg1'=arg1P1, (1+x70 > 0 /\ 1+arg2 > 0 /\ arg1P1 > 0 /\ arg1P1-arg1 <= 0 /\ -arg2+arg3 > 0), cost: 1 2: __init -> f1_0_main_ConstantStackPush : arg2'=arg2P2, arg1'=arg1P2, arg3'=arg3P2, TRUE, cost: 1 Applied acceleration Original rule: f61_0_main_GE -> f61_0_main_GE : arg2'=arg2+x70, arg1'=arg1P1, (1+x70 > 0 /\ 1+arg2 > 0 /\ arg1P1 > 0 /\ arg1P1-arg1 <= 0 /\ -arg2+arg3 > 0), cost: 1 New rule: f61_0_main_GE -> f61_0_main_GE : arg2'=arg2+n*x70, arg1'=arg1P1, (1+x70 > 0 /\ 1+arg2 > 0 /\ -arg2-x70*(-1+n)+arg3 > 0 /\ arg1P1 > 0 /\ -1+n >= 0 /\ -arg1P1+arg1 >= 0), cost: n Sub-proof via acceration calculus written to file:///tmp/tmpnam_AkCgLH.txt Applied nonterm Original rule: f61_0_main_GE -> f61_0_main_GE : arg2'=arg2+x70, arg1'=arg1P1, (1+x70 > 0 /\ 1+arg2 > 0 /\ arg1P1 > 0 /\ arg1P1-arg1 <= 0 /\ -arg2+arg3 > 0), cost: 1 New rule: f61_0_main_GE -> [3] : (x70 <= 0 /\ 1+x70 > 0 /\ 1+arg2 > 0 /\ arg1P1 > 0 /\ -arg2+arg3 > 0 /\ -arg1P1+arg1 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_fnhpko.txt Applied deletion Removed the following rules: 4 Accelerated simple loops Start location: __init 3: f1_0_main_ConstantStackPush -> f61_0_main_GE : arg2'=0, arg1'=arg1P0, arg3'=arg2, (1+arg2 > 0 /\ -arg1+arg1P0 <= 0 /\ arg1P0 > 0), cost: 1 5: f61_0_main_GE -> f61_0_main_GE : arg2'=arg2+n*x70, arg1'=arg1P1, (1+x70 > 0 /\ 1+arg2 > 0 /\ -arg2-x70*(-1+n)+arg3 > 0 /\ arg1P1 > 0 /\ -1+n >= 0 /\ -arg1P1+arg1 >= 0), cost: n 6: f61_0_main_GE -> [3] : (x70 <= 0 /\ 1+x70 > 0 /\ 1+arg2 > 0 /\ arg1P1 > 0 /\ -arg2+arg3 > 0 /\ -arg1P1+arg1 >= 0), cost: NONTERM 2: __init -> f1_0_main_ConstantStackPush : arg2'=arg2P2, arg1'=arg1P2, arg3'=arg3P2, TRUE, cost: 1 Applied chaining First rule: f1_0_main_ConstantStackPush -> f61_0_main_GE : arg2'=0, arg1'=arg1P0, arg3'=arg2, (1+arg2 > 0 /\ -arg1+arg1P0 <= 0 /\ arg1P0 > 0), cost: 1 Second rule: f61_0_main_GE -> f61_0_main_GE : arg2'=arg2+n*x70, arg1'=arg1P1, (1+x70 > 0 /\ 1+arg2 > 0 /\ -arg2-x70*(-1+n)+arg3 > 0 /\ arg1P1 > 0 /\ -1+n >= 0 /\ -arg1P1+arg1 >= 0), cost: n New rule: f1_0_main_ConstantStackPush -> f61_0_main_GE : arg2'=n*x70, arg1'=arg1P1, arg3'=arg2, (1+x70 > 0 /\ arg2-x70*(-1+n) > 0 /\ arg1P1 > 0 /\ arg1P1-arg1 <= 0 /\ -1+n >= 0), cost: 1+n Applied chaining First rule: f1_0_main_ConstantStackPush -> f61_0_main_GE : arg2'=0, arg1'=arg1P0, arg3'=arg2, (1+arg2 > 0 /\ -arg1+arg1P0 <= 0 /\ arg1P0 > 0), cost: 1 Second rule: f61_0_main_GE -> [3] : (x70 <= 0 /\ 1+x70 > 0 /\ 1+arg2 > 0 /\ arg1P1 > 0 /\ -arg2+arg3 > 0 /\ -arg1P1+arg1 >= 0), cost: NONTERM New rule: f1_0_main_ConstantStackPush -> [3] : (arg2 > 0 /\ -1+arg1 >= 0), cost: NONTERM Applied deletion Removed the following rules: 5 6 Chained accelerated rules with incoming rules Start location: __init 3: f1_0_main_ConstantStackPush -> f61_0_main_GE : arg2'=0, arg1'=arg1P0, arg3'=arg2, (1+arg2 > 0 /\ -arg1+arg1P0 <= 0 /\ arg1P0 > 0), cost: 1 7: f1_0_main_ConstantStackPush -> f61_0_main_GE : arg2'=n*x70, arg1'=arg1P1, arg3'=arg2, (1+x70 > 0 /\ arg2-x70*(-1+n) > 0 /\ arg1P1 > 0 /\ arg1P1-arg1 <= 0 /\ -1+n >= 0), cost: 1+n 8: f1_0_main_ConstantStackPush -> [3] : (arg2 > 0 /\ -1+arg1 >= 0), cost: NONTERM 2: __init -> f1_0_main_ConstantStackPush : arg2'=arg2P2, arg1'=arg1P2, arg3'=arg3P2, TRUE, cost: 1 Removed unreachable locations and irrelevant leafs Start location: __init 8: f1_0_main_ConstantStackPush -> [3] : (arg2 > 0 /\ -1+arg1 >= 0), cost: NONTERM 2: __init -> f1_0_main_ConstantStackPush : arg2'=arg2P2, arg1'=arg1P2, arg3'=arg3P2, TRUE, cost: 1 Eliminating location f1_0_main_ConstantStackPush by chaining: Applied chaining First rule: __init -> f1_0_main_ConstantStackPush : arg2'=arg2P2, arg1'=arg1P2, arg3'=arg3P2, TRUE, cost: 1 Second rule: f1_0_main_ConstantStackPush -> [3] : (arg2 > 0 /\ -1+arg1 >= 0), cost: NONTERM New rule: __init -> [3] : (-1+arg1P2 >= 0 /\ arg2P2 > 0), cost: NONTERM Applied deletion Removed the following rules: 2 8 Eliminated locations on linear paths Start location: __init 9: __init -> [3] : (-1+arg1P2 >= 0 /\ arg2P2 > 0), cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 9 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)