NO Initial ITS Start location: __init 0: f1_0_main_Load -> f50_0_increase_GE : arg2'=arg2P0, arg1'=arg1P0, arg3'=arg3P0, (arg2-arg1P0 == 0 /\ 1+arg2 > 0 /\ arg1 > 0), cost: 1 1: f50_0_increase_GE -> f79_0_increase_LE : arg2'=arg2P1, arg1'=arg1P1, arg3'=arg3P1, (arg1-arg3P1 == 0 /\ -10+arg1 < 0 /\ arg1-arg1P1 == 0 /\ -arg2P1+arg1 == 0), cost: 1 2: f79_0_increase_LE -> f50_0_increase_GE : arg2'=arg2P2, arg1'=arg1P2, arg3'=arg3P2, (-arg3 == 0 /\ -arg2 == 0 /\ 1-arg1P2+arg1 == 0), cost: 1 3: f79_0_increase_LE -> f79_0_increase_LE : arg2'=arg2P3, arg1'=arg1P3, arg3'=arg3P3, (1-arg2P3+arg2 == 0 /\ arg2 > 0 /\ -arg1P3+arg1 == 0 /\ arg2-arg3 == 0 /\ 1+arg2-arg3P3 == 0), cost: 1 4: __init -> f1_0_main_Load : arg2'=arg2P4, arg1'=arg1P4, arg3'=arg3P4, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_Load -> f50_0_increase_GE : arg2'=arg2P0, arg1'=arg1P0, arg3'=arg3P0, (arg2-arg1P0 == 0 /\ 1+arg2 > 0 /\ arg1 > 0), cost: 1 New rule: f1_0_main_Load -> f50_0_increase_GE : arg2'=arg2P0, arg1'=arg2, arg3'=arg3P0, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Applied preprocessing Original rule: f50_0_increase_GE -> f79_0_increase_LE : arg2'=arg2P1, arg1'=arg1P1, arg3'=arg3P1, (arg1-arg3P1 == 0 /\ -10+arg1 < 0 /\ arg1-arg1P1 == 0 /\ -arg2P1+arg1 == 0), cost: 1 New rule: f50_0_increase_GE -> f79_0_increase_LE : arg2'=arg1, arg3'=arg1, 10-arg1 > 0, cost: 1 Applied preprocessing Original rule: f79_0_increase_LE -> f50_0_increase_GE : arg2'=arg2P2, arg1'=arg1P2, arg3'=arg3P2, (-arg3 == 0 /\ -arg2 == 0 /\ 1-arg1P2+arg1 == 0), cost: 1 New rule: f79_0_increase_LE -> f50_0_increase_GE : arg2'=arg2P2, arg1'=1+arg1, arg3'=arg3P2, (arg2 == 0 /\ arg3 == 0), cost: 1 Applied preprocessing Original rule: f79_0_increase_LE -> f79_0_increase_LE : arg2'=arg2P3, arg1'=arg1P3, arg3'=arg3P3, (1-arg2P3+arg2 == 0 /\ arg2 > 0 /\ -arg1P3+arg1 == 0 /\ arg2-arg3 == 0 /\ 1+arg2-arg3P3 == 0), cost: 1 New rule: f79_0_increase_LE -> f79_0_increase_LE : arg2'=1+arg2, arg3'=1+arg2, (arg2 > 0 /\ arg2-arg3 == 0), cost: 1 Simplified rules Start location: __init 5: f1_0_main_Load -> f50_0_increase_GE : arg2'=arg2P0, arg1'=arg2, arg3'=arg3P0, (1+arg2 > 0 /\ arg1 > 0), cost: 1 6: f50_0_increase_GE -> f79_0_increase_LE : arg2'=arg1, arg3'=arg1, 10-arg1 > 0, cost: 1 7: f79_0_increase_LE -> f50_0_increase_GE : arg2'=arg2P2, arg1'=1+arg1, arg3'=arg3P2, (arg2 == 0 /\ arg3 == 0), cost: 1 8: f79_0_increase_LE -> f79_0_increase_LE : arg2'=1+arg2, arg3'=1+arg2, (arg2 > 0 /\ arg2-arg3 == 0), cost: 1 4: __init -> f1_0_main_Load : arg2'=arg2P4, arg1'=arg1P4, arg3'=arg3P4, TRUE, cost: 1 Applied nonterm Original rule: f79_0_increase_LE -> f79_0_increase_LE : arg2'=1+arg2, arg3'=1+arg2, (arg2 > 0 /\ arg2-arg3 == 0), cost: 1 New rule: f79_0_increase_LE -> [4] : (arg2 > 0 /\ arg2-arg3 >= 0 /\ -arg2+arg3 >= 0 /\ -1+n >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_jJFNah.txt Applied deletion Removed the following rules: 8 Accelerated simple loops Start location: __init 5: f1_0_main_Load -> f50_0_increase_GE : arg2'=arg2P0, arg1'=arg2, arg3'=arg3P0, (1+arg2 > 0 /\ arg1 > 0), cost: 1 6: f50_0_increase_GE -> f79_0_increase_LE : arg2'=arg1, arg3'=arg1, 10-arg1 > 0, cost: 1 7: f79_0_increase_LE -> f50_0_increase_GE : arg2'=arg2P2, arg1'=1+arg1, arg3'=arg3P2, (arg2 == 0 /\ arg3 == 0), cost: 1 9: f79_0_increase_LE -> [4] : (arg2 > 0 /\ arg2-arg3 >= 0 /\ -arg2+arg3 >= 0 /\ -1+n >= 0), cost: NONTERM 4: __init -> f1_0_main_Load : arg2'=arg2P4, arg1'=arg1P4, arg3'=arg3P4, TRUE, cost: 1 Applied chaining First rule: f50_0_increase_GE -> f79_0_increase_LE : arg2'=arg1, arg3'=arg1, 10-arg1 > 0, cost: 1 Second rule: f79_0_increase_LE -> [4] : (arg2 > 0 /\ arg2-arg3 >= 0 /\ -arg2+arg3 >= 0 /\ -1+n >= 0), cost: NONTERM New rule: f50_0_increase_GE -> [4] : (10-arg1 > 0 /\ arg1 > 0), cost: NONTERM Applied deletion Removed the following rules: 9 Chained accelerated rules with incoming rules Start location: __init 5: f1_0_main_Load -> f50_0_increase_GE : arg2'=arg2P0, arg1'=arg2, arg3'=arg3P0, (1+arg2 > 0 /\ arg1 > 0), cost: 1 6: f50_0_increase_GE -> f79_0_increase_LE : arg2'=arg1, arg3'=arg1, 10-arg1 > 0, cost: 1 10: f50_0_increase_GE -> [4] : (10-arg1 > 0 /\ arg1 > 0), cost: NONTERM 7: f79_0_increase_LE -> f50_0_increase_GE : arg2'=arg2P2, arg1'=1+arg1, arg3'=arg3P2, (arg2 == 0 /\ arg3 == 0), cost: 1 4: __init -> f1_0_main_Load : arg2'=arg2P4, arg1'=arg1P4, arg3'=arg3P4, TRUE, cost: 1 Eliminating location f1_0_main_Load by chaining: Applied chaining First rule: __init -> f1_0_main_Load : arg2'=arg2P4, arg1'=arg1P4, arg3'=arg3P4, TRUE, cost: 1 Second rule: f1_0_main_Load -> f50_0_increase_GE : arg2'=arg2P0, arg1'=arg2, arg3'=arg3P0, (1+arg2 > 0 /\ arg1 > 0), cost: 1 New rule: __init -> f50_0_increase_GE : arg2'=arg2P0, arg1'=arg2P4, arg3'=arg3P0, (1+arg2P4 > 0 /\ arg1P4 > 0), cost: 2 Applied deletion Removed the following rules: 4 5 Eliminating location f79_0_increase_LE by chaining: Applied chaining First rule: f50_0_increase_GE -> f79_0_increase_LE : arg2'=arg1, arg3'=arg1, 10-arg1 > 0, cost: 1 Second rule: f79_0_increase_LE -> f50_0_increase_GE : arg2'=arg2P2, arg1'=1+arg1, arg3'=arg3P2, (arg2 == 0 /\ arg3 == 0), cost: 1 New rule: f50_0_increase_GE -> f50_0_increase_GE : arg2'=arg2P2, arg1'=1+arg1, arg3'=arg3P2, (10-arg1 > 0 /\ arg1 == 0), cost: 2 Applied simplification Original rule: f50_0_increase_GE -> f50_0_increase_GE : arg2'=arg2P2, arg1'=1+arg1, arg3'=arg3P2, (10-arg1 > 0 /\ arg1 == 0), cost: 2 New rule: f50_0_increase_GE -> f50_0_increase_GE : arg2'=arg2P2, arg1'=1+arg1, arg3'=arg3P2, arg1 == 0, cost: 2 Applied deletion Removed the following rules: 6 7 Eliminated locations on linear paths Start location: __init 10: f50_0_increase_GE -> [4] : (10-arg1 > 0 /\ arg1 > 0), cost: NONTERM 12: f50_0_increase_GE -> f50_0_increase_GE : arg2'=arg2P2, arg1'=1+arg1, arg3'=arg3P2, arg1 == 0, cost: 2 11: __init -> f50_0_increase_GE : arg2'=arg2P0, arg1'=arg2P4, arg3'=arg3P0, (1+arg2P4 > 0 /\ arg1P4 > 0), cost: 2 Accelerated simple loops Start location: __init 10: f50_0_increase_GE -> [4] : (10-arg1 > 0 /\ arg1 > 0), cost: NONTERM 12: f50_0_increase_GE -> f50_0_increase_GE : arg2'=arg2P2, arg1'=1+arg1, arg3'=arg3P2, arg1 == 0, cost: 2 11: __init -> f50_0_increase_GE : arg2'=arg2P0, arg1'=arg2P4, arg3'=arg3P0, (1+arg2P4 > 0 /\ arg1P4 > 0), cost: 2 Applied chaining First rule: __init -> f50_0_increase_GE : arg2'=arg2P0, arg1'=arg2P4, arg3'=arg3P0, (1+arg2P4 > 0 /\ arg1P4 > 0), cost: 2 Second rule: f50_0_increase_GE -> f50_0_increase_GE : arg2'=arg2P2, arg1'=1+arg1, arg3'=arg3P2, arg1 == 0, cost: 2 New rule: __init -> f50_0_increase_GE : arg2'=arg2P2, arg1'=1, arg3'=arg3P2, 1 > 0, cost: 4 Applied deletion Removed the following rules: 12 Chained accelerated rules with incoming rules Start location: __init 10: f50_0_increase_GE -> [4] : (10-arg1 > 0 /\ arg1 > 0), cost: NONTERM 11: __init -> f50_0_increase_GE : arg2'=arg2P0, arg1'=arg2P4, arg3'=arg3P0, (1+arg2P4 > 0 /\ arg1P4 > 0), cost: 2 13: __init -> f50_0_increase_GE : arg2'=arg2P2, arg1'=1, arg3'=arg3P2, 1 > 0, cost: 4 Eliminating location f50_0_increase_GE by chaining: Applied chaining First rule: __init -> f50_0_increase_GE : arg2'=arg2P0, arg1'=arg2P4, arg3'=arg3P0, (1+arg2P4 > 0 /\ arg1P4 > 0), cost: 2 Second rule: f50_0_increase_GE -> [4] : (10-arg1 > 0 /\ arg1 > 0), cost: NONTERM New rule: __init -> [4] : (1+arg2P4 > 0 /\ arg2P4 > 0 /\ 10-arg2P4 > 0 /\ arg1P4 > 0), cost: NONTERM Applied simplification Original rule: __init -> [4] : (1+arg2P4 > 0 /\ arg2P4 > 0 /\ 10-arg2P4 > 0 /\ arg1P4 > 0), cost: NONTERM New rule: __init -> [4] : (arg2P4 > 0 /\ 10-arg2P4 > 0 /\ arg1P4 > 0), cost: NONTERM Applied chaining First rule: __init -> f50_0_increase_GE : arg2'=arg2P2, arg1'=1, arg3'=arg3P2, 1 > 0, cost: 4 Second rule: f50_0_increase_GE -> [4] : (10-arg1 > 0 /\ arg1 > 0), cost: NONTERM New rule: __init -> [4] : (1 > 0 /\ 9 > 0), cost: NONTERM Applied deletion Removed the following rules: 10 11 13 Eliminated locations on tree-shaped paths Start location: __init 14: __init -> [4] : (arg2P4 > 0 /\ 10-arg2P4 > 0 /\ arg1P4 > 0), cost: NONTERM 15: __init -> [4] : (1 > 0 /\ 9 > 0), cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 14 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: (arg2P4 > 0 /\ 10-arg2P4 > 0 /\ arg1P4 > 0)