NO Initial ITS Start location: __init 0: f1_0_main_Load -> f31_0_f_NE : arg2'=arg2P0, arg1'=arg1P0, (1+arg2 > 0 /\ arg1 > 0 /\ arg2-arg1P0 == 0), cost: 1 1: f31_0_f_NE -> f31_0_f_NE : arg2'=arg2P1, arg1'=arg1P1, (-arg1P1 == 0 /\ arg1 > 0), cost: 1 2: f31_0_f_NE -> f31_0_f_NE : arg2'=arg2P2, arg1'=arg1P2, (1-arg1P2 == 0 /\ -arg1 == 0), cost: 1 3: __init -> f1_0_main_Load : arg2'=arg2P3, arg1'=arg1P3, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_Load -> f31_0_f_NE : arg2'=arg2P0, arg1'=arg1P0, (1+arg2 > 0 /\ arg1 > 0 /\ arg2-arg1P0 == 0), cost: 1 New rule: f1_0_main_Load -> f31_0_f_NE : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Applied preprocessing Original rule: f31_0_f_NE -> f31_0_f_NE : arg2'=arg2P1, arg1'=arg1P1, (-arg1P1 == 0 /\ arg1 > 0), cost: 1 New rule: f31_0_f_NE -> f31_0_f_NE : arg2'=arg2P1, arg1'=0, arg1 > 0, cost: 1 Applied preprocessing Original rule: f31_0_f_NE -> f31_0_f_NE : arg2'=arg2P2, arg1'=arg1P2, (1-arg1P2 == 0 /\ -arg1 == 0), cost: 1 New rule: f31_0_f_NE -> f31_0_f_NE : arg2'=arg2P2, arg1'=1, arg1 == 0, cost: 1 Simplified rules Start location: __init 4: f1_0_main_Load -> f31_0_f_NE : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 5: f31_0_f_NE -> f31_0_f_NE : arg2'=arg2P1, arg1'=0, arg1 > 0, cost: 1 6: f31_0_f_NE -> f31_0_f_NE : arg2'=arg2P2, arg1'=1, arg1 == 0, cost: 1 3: __init -> f1_0_main_Load : arg2'=arg2P3, arg1'=arg1P3, TRUE, cost: 1 Applied chaining First rule: f31_0_f_NE -> f31_0_f_NE : arg2'=arg2P2, arg1'=1, arg1 == 0, cost: 1 Second rule: f31_0_f_NE -> f31_0_f_NE : arg2'=arg2P1, arg1'=0, arg1 > 0, cost: 1 New rule: f31_0_f_NE -> f31_0_f_NE : arg2'=arg2P1, arg1'=0, arg1 == 0, cost: 2 Applied nonterm Original rule: f31_0_f_NE -> f31_0_f_NE : arg2'=arg2P1, arg1'=0, arg1 == 0, cost: 2 New rule: f31_0_f_NE -> [3] : (arg1 >= 0 /\ -arg1 >= 0 /\ -1+n1 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_PokDGm.txt Applied chaining First rule: f31_0_f_NE -> f31_0_f_NE : arg2'=arg2P1, arg1'=0, arg1 > 0, cost: 1 Second rule: f31_0_f_NE -> [3] : (arg1 >= 0 /\ -arg1 >= 0 /\ -1+n1 >= 0), cost: NONTERM New rule: f31_0_f_NE -> [3] : (0 >= 0 /\ arg1 > 0 /\ -1+n1 >= 0), cost: NONTERM Applied chaining First rule: f31_0_f_NE -> f31_0_f_NE : arg2'=arg2P1, arg1'=0, arg1 > 0, cost: 1 Second rule: f31_0_f_NE -> f31_0_f_NE : arg2'=arg2P2, arg1'=1, arg1 == 0, cost: 1 New rule: f31_0_f_NE -> f31_0_f_NE : arg2'=arg2P2, arg1'=1, arg1 > 0, cost: 2 Applied nonterm Original rule: f31_0_f_NE -> f31_0_f_NE : arg2'=arg2P2, arg1'=1, arg1 > 0, cost: 2 New rule: f31_0_f_NE -> [3] : (-1+n2 >= 0 /\ arg1 > 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_MgdLdN.txt Applied chaining First rule: f31_0_f_NE -> f31_0_f_NE : arg2'=arg2P2, arg1'=1, arg1 == 0, cost: 1 Second rule: f31_0_f_NE -> [3] : (-1+n2 >= 0 /\ arg1 > 0), cost: NONTERM New rule: f31_0_f_NE -> [3] : (1 > 0 /\ -1+n2 >= 0 /\ arg1 == 0), cost: NONTERM Applied simplification Original rule: f31_0_f_NE -> [3] : (arg1 >= 0 /\ -arg1 >= 0 /\ -1+n1 >= 0), cost: NONTERM New rule: f31_0_f_NE -> [3] : (arg1 <= 0 /\ arg1 >= 0 /\ -1+n1 >= 0), cost: NONTERM Applied simplification Original rule: f31_0_f_NE -> [3] : (0 >= 0 /\ arg1 > 0 /\ -1+n1 >= 0), cost: NONTERM New rule: f31_0_f_NE -> [3] : (arg1 > 0 /\ -1+n1 >= 0), cost: NONTERM Applied simplification Original rule: f31_0_f_NE -> [3] : (1 > 0 /\ -1+n2 >= 0 /\ arg1 == 0), cost: NONTERM New rule: f31_0_f_NE -> [3] : (-1+n2 >= 0 /\ arg1 == 0), cost: NONTERM Accelerated simple loops Start location: __init 4: f1_0_main_Load -> f31_0_f_NE : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 5: f31_0_f_NE -> f31_0_f_NE : arg2'=arg2P1, arg1'=0, arg1 > 0, cost: 1 6: f31_0_f_NE -> f31_0_f_NE : arg2'=arg2P2, arg1'=1, arg1 == 0, cost: 1 9: f31_0_f_NE -> [3] : (-1+n2 >= 0 /\ arg1 > 0), cost: NONTERM 11: f31_0_f_NE -> [3] : (arg1 <= 0 /\ arg1 >= 0 /\ -1+n1 >= 0), cost: NONTERM 12: f31_0_f_NE -> [3] : (arg1 > 0 /\ -1+n1 >= 0), cost: NONTERM 13: f31_0_f_NE -> [3] : (-1+n2 >= 0 /\ arg1 == 0), cost: NONTERM 3: __init -> f1_0_main_Load : arg2'=arg2P3, arg1'=arg1P3, TRUE, cost: 1 Applied chaining First rule: f1_0_main_Load -> f31_0_f_NE : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Second rule: f31_0_f_NE -> f31_0_f_NE : arg2'=arg2P1, arg1'=0, arg1 > 0, cost: 1 New rule: f1_0_main_Load -> f31_0_f_NE : arg2'=arg2P1, arg1'=0, (arg2 > 0 /\ arg1 > 0), cost: 2 Applied chaining First rule: f1_0_main_Load -> f31_0_f_NE : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Second rule: f31_0_f_NE -> f31_0_f_NE : arg2'=arg2P2, arg1'=1, arg1 == 0, cost: 1 New rule: f1_0_main_Load -> f31_0_f_NE : arg2'=arg2P2, arg1'=1, (arg2 == 0 /\ arg1 > 0), cost: 2 Applied chaining First rule: f1_0_main_Load -> f31_0_f_NE : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Second rule: f31_0_f_NE -> [3] : (-1+n2 >= 0 /\ arg1 > 0), cost: NONTERM New rule: f1_0_main_Load -> [3] : (arg2 > 0 /\ arg1 > 0), cost: NONTERM Applied chaining First rule: f1_0_main_Load -> f31_0_f_NE : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Second rule: f31_0_f_NE -> [3] : (arg1 <= 0 /\ arg1 >= 0 /\ -1+n1 >= 0), cost: NONTERM New rule: f1_0_main_Load -> [3] : (arg2 == 0 /\ arg1 > 0), cost: NONTERM Applied chaining First rule: f1_0_main_Load -> f31_0_f_NE : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Second rule: f31_0_f_NE -> [3] : (arg1 > 0 /\ -1+n1 >= 0), cost: NONTERM New rule: f1_0_main_Load -> [3] : (arg2 > 0 /\ arg1 > 0), cost: NONTERM Applied chaining First rule: f1_0_main_Load -> f31_0_f_NE : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Second rule: f31_0_f_NE -> [3] : (-1+n2 >= 0 /\ arg1 == 0), cost: NONTERM New rule: f1_0_main_Load -> [3] : (arg2 == 0 /\ arg1 > 0), cost: NONTERM Applied deletion Removed the following rules: 5 6 9 11 12 13 Chained accelerated rules with incoming rules Start location: __init 4: f1_0_main_Load -> f31_0_f_NE : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 14: f1_0_main_Load -> f31_0_f_NE : arg2'=arg2P1, arg1'=0, (arg2 > 0 /\ arg1 > 0), cost: 2 15: f1_0_main_Load -> f31_0_f_NE : arg2'=arg2P2, arg1'=1, (arg2 == 0 /\ arg1 > 0), cost: 2 16: f1_0_main_Load -> [3] : (arg2 > 0 /\ arg1 > 0), cost: NONTERM 17: f1_0_main_Load -> [3] : (arg2 == 0 /\ arg1 > 0), cost: NONTERM 3: __init -> f1_0_main_Load : arg2'=arg2P3, arg1'=arg1P3, TRUE, cost: 1 Removed unreachable locations and irrelevant leafs Start location: __init 16: f1_0_main_Load -> [3] : (arg2 > 0 /\ arg1 > 0), cost: NONTERM 17: f1_0_main_Load -> [3] : (arg2 == 0 /\ arg1 > 0), cost: NONTERM 3: __init -> f1_0_main_Load : arg2'=arg2P3, arg1'=arg1P3, TRUE, cost: 1 Eliminating location f1_0_main_Load by chaining: Applied chaining First rule: __init -> f1_0_main_Load : arg2'=arg2P3, arg1'=arg1P3, TRUE, cost: 1 Second rule: f1_0_main_Load -> [3] : (arg2 > 0 /\ arg1 > 0), cost: NONTERM New rule: __init -> [3] : (arg1P3 > 0 /\ arg2P3 > 0), cost: NONTERM Applied chaining First rule: __init -> f1_0_main_Load : arg2'=arg2P3, arg1'=arg1P3, TRUE, cost: 1 Second rule: f1_0_main_Load -> [3] : (arg2 == 0 /\ arg1 > 0), cost: NONTERM New rule: __init -> [3] : (arg1P3 > 0 /\ arg2P3 == 0), cost: NONTERM Applied deletion Removed the following rules: 3 16 17 Eliminated locations on tree-shaped paths Start location: __init 18: __init -> [3] : (arg1P3 > 0 /\ arg2P3 > 0), cost: NONTERM 19: __init -> [3] : (arg1P3 > 0 /\ arg2P3 == 0), cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 18 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: (arg1P3 > 0 /\ arg2P3 > 0)