NO Initial ITS Start location: __init 0: f1_0_main_Load -> f71_0_main_LE : arg2'=arg2P0, arg1'=arg1P0, (1+arg2 > 0 /\ arg1 > 0 /\ arg2-arg1P0 == 0), cost: 1 1: f71_0_main_LE -> f47_0_f_LE : arg2'=arg2P1, arg1'=arg1P1, (arg1-arg1P1 == 0 /\ arg1 > 0), cost: 1 2: f71_0_main_LE -> f71_0_main_LE : arg2'=arg2P2, arg1'=arg1P2, (arg1 > 0 /\ 1+arg1-arg1P2 == 0), cost: 1 3: f47_0_f_LE -> f47_0_f_LE : arg2'=arg2P3, arg1'=arg1P3, (-1-arg1P3+arg1 == 0 /\ arg1 > 0 /\ -1 < 0), cost: 1 4: __init -> f1_0_main_Load : arg2'=arg2P4, arg1'=arg1P4, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_Load -> f71_0_main_LE : arg2'=arg2P0, arg1'=arg1P0, (1+arg2 > 0 /\ arg1 > 0 /\ arg2-arg1P0 == 0), cost: 1 New rule: f1_0_main_Load -> f71_0_main_LE : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Applied preprocessing Original rule: f71_0_main_LE -> f47_0_f_LE : arg2'=arg2P1, arg1'=arg1P1, (arg1-arg1P1 == 0 /\ arg1 > 0), cost: 1 New rule: f71_0_main_LE -> f47_0_f_LE : arg2'=arg2P1, arg1 > 0, cost: 1 Applied preprocessing Original rule: f71_0_main_LE -> f71_0_main_LE : arg2'=arg2P2, arg1'=arg1P2, (arg1 > 0 /\ 1+arg1-arg1P2 == 0), cost: 1 New rule: f71_0_main_LE -> f71_0_main_LE : arg2'=arg2P2, arg1'=1+arg1, arg1 > 0, cost: 1 Applied preprocessing Original rule: f47_0_f_LE -> f47_0_f_LE : arg2'=arg2P3, arg1'=arg1P3, (-1-arg1P3+arg1 == 0 /\ arg1 > 0 /\ -1 < 0), cost: 1 New rule: f47_0_f_LE -> f47_0_f_LE : arg2'=arg2P3, arg1'=-1+arg1, arg1 > 0, cost: 1 Simplified rules Start location: __init 5: f1_0_main_Load -> f71_0_main_LE : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 6: f71_0_main_LE -> f47_0_f_LE : arg2'=arg2P1, arg1 > 0, cost: 1 7: f71_0_main_LE -> f71_0_main_LE : arg2'=arg2P2, arg1'=1+arg1, arg1 > 0, cost: 1 8: f47_0_f_LE -> f47_0_f_LE : arg2'=arg2P3, arg1'=-1+arg1, arg1 > 0, cost: 1 4: __init -> f1_0_main_Load : arg2'=arg2P4, arg1'=arg1P4, TRUE, cost: 1 Applied nonterm Original rule: f71_0_main_LE -> f71_0_main_LE : arg2'=arg2P2, arg1'=1+arg1, arg1 > 0, cost: 1 New rule: f71_0_main_LE -> [4] : (-1+n >= 0 /\ arg1 > 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_lKLoDd.txt Applied deletion Removed the following rules: 7 Applied acceleration Original rule: f47_0_f_LE -> f47_0_f_LE : arg2'=arg2P3, arg1'=-1+arg1, arg1 > 0, cost: 1 New rule: f47_0_f_LE -> f47_0_f_LE : arg2'=arg2P3, arg1'=-n0+arg1, (1-n0+arg1 > 0 /\ -1+n0 >= 0), cost: n0 Sub-proof via acceration calculus written to file:///tmp/tmpnam_adPChE.txt Applied instantiation Original rule: f47_0_f_LE -> f47_0_f_LE : arg2'=arg2P3, arg1'=-n0+arg1, (1-n0+arg1 > 0 /\ -1+n0 >= 0), cost: n0 New rule: f47_0_f_LE -> f47_0_f_LE : arg2'=arg2P3, arg1'=0, (1 > 0 /\ -1+arg1 >= 0), cost: arg1 Applied simplification Original rule: f47_0_f_LE -> f47_0_f_LE : arg2'=arg2P3, arg1'=0, (1 > 0 /\ -1+arg1 >= 0), cost: arg1 New rule: f47_0_f_LE -> f47_0_f_LE : arg2'=arg2P3, arg1'=0, -1+arg1 >= 0, cost: arg1 Applied deletion Removed the following rules: 8 Accelerated simple loops Start location: __init 5: f1_0_main_Load -> f71_0_main_LE : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 6: f71_0_main_LE -> f47_0_f_LE : arg2'=arg2P1, arg1 > 0, cost: 1 9: f71_0_main_LE -> [4] : (-1+n >= 0 /\ arg1 > 0), cost: NONTERM 11: f47_0_f_LE -> f47_0_f_LE : arg2'=arg2P3, arg1'=0, -1+arg1 >= 0, cost: arg1 4: __init -> f1_0_main_Load : arg2'=arg2P4, arg1'=arg1P4, TRUE, cost: 1 Applied chaining First rule: f1_0_main_Load -> f71_0_main_LE : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Second rule: f71_0_main_LE -> [4] : (-1+n >= 0 /\ arg1 > 0), cost: NONTERM New rule: f1_0_main_Load -> [4] : (arg2 > 0 /\ arg1 > 0), cost: NONTERM Applied deletion Removed the following rules: 9 Applied chaining First rule: f71_0_main_LE -> f47_0_f_LE : arg2'=arg2P1, arg1 > 0, cost: 1 Second rule: f47_0_f_LE -> f47_0_f_LE : arg2'=arg2P3, arg1'=0, -1+arg1 >= 0, cost: arg1 New rule: f71_0_main_LE -> f47_0_f_LE : arg2'=arg2P3, arg1'=0, -1+arg1 >= 0, cost: 1+arg1 Applied deletion Removed the following rules: 11 Chained accelerated rules with incoming rules Start location: __init 5: f1_0_main_Load -> f71_0_main_LE : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 12: f1_0_main_Load -> [4] : (arg2 > 0 /\ arg1 > 0), cost: NONTERM 6: f71_0_main_LE -> f47_0_f_LE : arg2'=arg2P1, arg1 > 0, cost: 1 13: f71_0_main_LE -> f47_0_f_LE : arg2'=arg2P3, arg1'=0, -1+arg1 >= 0, cost: 1+arg1 4: __init -> f1_0_main_Load : arg2'=arg2P4, arg1'=arg1P4, TRUE, cost: 1 Removed unreachable locations and irrelevant leafs Start location: __init 12: f1_0_main_Load -> [4] : (arg2 > 0 /\ arg1 > 0), cost: NONTERM 4: __init -> f1_0_main_Load : arg2'=arg2P4, arg1'=arg1P4, TRUE, cost: 1 Eliminating location f1_0_main_Load by chaining: Applied chaining First rule: __init -> f1_0_main_Load : arg2'=arg2P4, arg1'=arg1P4, TRUE, cost: 1 Second rule: f1_0_main_Load -> [4] : (arg2 > 0 /\ arg1 > 0), cost: NONTERM New rule: __init -> [4] : (arg2P4 > 0 /\ arg1P4 > 0), cost: NONTERM Applied deletion Removed the following rules: 4 12 Eliminated locations on linear paths Start location: __init 14: __init -> [4] : (arg2P4 > 0 /\ arg1P4 > 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 /\ arg1P4 > 0)