NO Initial ITS Start location: __init 0: f40_0_loop_Inc -> f40_0_loop_Inc : arg2'=arg2P0, arg1'=arg1P0, arg3'=arg3P0, (-1+arg2-arg2P0 == 0 /\ arg3-arg3P0 == 0 /\ arg1 > 0 /\ -arg1+arg1P0 <= 0 /\ arg1P0 > 0), cost: 1 1: f1_0_main_Load -> f40_0_loop_Inc : arg2'=arg2P1, arg1'=arg1P1, arg3'=arg3P1, (1+arg2 > 0 /\ -1+arg2-arg2P1 == 0 /\ arg1 > 0 /\ arg1P1 > 0 /\ -arg1+arg1P1 <= 0 /\ arg2-arg3P1 == 0), cost: 1 2: __init -> f1_0_main_Load : arg2'=arg2P2, arg1'=arg1P2, arg3'=arg3P2, TRUE, cost: 1 Applied preprocessing Original rule: f40_0_loop_Inc -> f40_0_loop_Inc : arg2'=arg2P0, arg1'=arg1P0, arg3'=arg3P0, (-1+arg2-arg2P0 == 0 /\ arg3-arg3P0 == 0 /\ arg1 > 0 /\ -arg1+arg1P0 <= 0 /\ arg1P0 > 0), cost: 1 New rule: f40_0_loop_Inc -> f40_0_loop_Inc : arg2'=-1+arg2, arg1'=arg1P0, (-arg1+arg1P0 <= 0 /\ arg1P0 > 0), cost: 1 Applied preprocessing Original rule: f1_0_main_Load -> f40_0_loop_Inc : arg2'=arg2P1, arg1'=arg1P1, arg3'=arg3P1, (1+arg2 > 0 /\ -1+arg2-arg2P1 == 0 /\ arg1 > 0 /\ arg1P1 > 0 /\ -arg1+arg1P1 <= 0 /\ arg2-arg3P1 == 0), cost: 1 New rule: f1_0_main_Load -> f40_0_loop_Inc : arg2'=-1+arg2, arg1'=arg1P1, arg3'=arg2, (1+arg2 > 0 /\ arg1P1 > 0 /\ -arg1+arg1P1 <= 0), cost: 1 Simplified rules Start location: __init 3: f40_0_loop_Inc -> f40_0_loop_Inc : arg2'=-1+arg2, arg1'=arg1P0, (-arg1+arg1P0 <= 0 /\ arg1P0 > 0), cost: 1 4: f1_0_main_Load -> f40_0_loop_Inc : arg2'=-1+arg2, arg1'=arg1P1, arg3'=arg2, (1+arg2 > 0 /\ arg1P1 > 0 /\ -arg1+arg1P1 <= 0), cost: 1 2: __init -> f1_0_main_Load : arg2'=arg2P2, arg1'=arg1P2, arg3'=arg3P2, TRUE, cost: 1 Applied nonterm Original rule: f40_0_loop_Inc -> f40_0_loop_Inc : arg2'=-1+arg2, arg1'=arg1P0, (-arg1+arg1P0 <= 0 /\ arg1P0 > 0), cost: 1 New rule: f40_0_loop_Inc -> [3] : (-1+n >= 0 /\ arg1P0 > 0 /\ arg1-arg1P0 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_MApDoC.txt Applied deletion Removed the following rules: 3 Accelerated simple loops Start location: __init 5: f40_0_loop_Inc -> [3] : (-1+n >= 0 /\ arg1P0 > 0 /\ arg1-arg1P0 >= 0), cost: NONTERM 4: f1_0_main_Load -> f40_0_loop_Inc : arg2'=-1+arg2, arg1'=arg1P1, arg3'=arg2, (1+arg2 > 0 /\ arg1P1 > 0 /\ -arg1+arg1P1 <= 0), cost: 1 2: __init -> f1_0_main_Load : arg2'=arg2P2, arg1'=arg1P2, arg3'=arg3P2, TRUE, cost: 1 Applied chaining First rule: f1_0_main_Load -> f40_0_loop_Inc : arg2'=-1+arg2, arg1'=arg1P1, arg3'=arg2, (1+arg2 > 0 /\ arg1P1 > 0 /\ -arg1+arg1P1 <= 0), cost: 1 Second rule: f40_0_loop_Inc -> [3] : (-1+n >= 0 /\ arg1P0 > 0 /\ arg1-arg1P0 >= 0), cost: NONTERM New rule: f1_0_main_Load -> [3] : (1+arg2 > 0 /\ -1+arg1 >= 0), cost: NONTERM Applied deletion Removed the following rules: 5 Chained accelerated rules with incoming rules Start location: __init 4: f1_0_main_Load -> f40_0_loop_Inc : arg2'=-1+arg2, arg1'=arg1P1, arg3'=arg2, (1+arg2 > 0 /\ arg1P1 > 0 /\ -arg1+arg1P1 <= 0), cost: 1 6: f1_0_main_Load -> [3] : (1+arg2 > 0 /\ -1+arg1 >= 0), cost: NONTERM 2: __init -> f1_0_main_Load : arg2'=arg2P2, arg1'=arg1P2, arg3'=arg3P2, TRUE, cost: 1 Removed unreachable locations and irrelevant leafs Start location: __init 6: f1_0_main_Load -> [3] : (1+arg2 > 0 /\ -1+arg1 >= 0), cost: NONTERM 2: __init -> f1_0_main_Load : arg2'=arg2P2, arg1'=arg1P2, arg3'=arg3P2, TRUE, cost: 1 Eliminating location f1_0_main_Load by chaining: Applied chaining First rule: __init -> f1_0_main_Load : arg2'=arg2P2, arg1'=arg1P2, arg3'=arg3P2, TRUE, cost: 1 Second rule: f1_0_main_Load -> [3] : (1+arg2 > 0 /\ -1+arg1 >= 0), cost: NONTERM New rule: __init -> [3] : (1+arg2P2 > 0 /\ -1+arg1P2 >= 0), cost: NONTERM Applied deletion Removed the following rules: 2 6 Eliminated locations on linear paths Start location: __init 7: __init -> [3] : (1+arg2P2 > 0 /\ -1+arg1P2 >= 0), cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 7 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: (1+arg2P2 > 0 /\ -1+arg1P2 >= 0)