NO Initial ITS Start location: __init 0: f1_0_main_Load -> f31_0_loop_EQ : arg2'=arg2P0, arg1'=arg1P0, (1+arg2 > 0 /\ arg1 > 0 /\ arg2-arg1P0 == 0), cost: 1 1: f31_0_loop_EQ -> f31_0_loop_EQ : arg2'=arg2P1, arg1'=arg1P1, (1+arg1-arg1P1 == 0 /\ -5+arg1 > 0), cost: 1 2: f31_0_loop_EQ -> f31_0_loop_EQ : arg2'=arg2P2, arg1'=arg1P2, (-6+arg1 < 0 /\ arg1 > 0 /\ -arg1P2 == 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_loop_EQ : arg2'=arg2P0, arg1'=arg1P0, (1+arg2 > 0 /\ arg1 > 0 /\ arg2-arg1P0 == 0), cost: 1 New rule: f1_0_main_Load -> f31_0_loop_EQ : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Applied preprocessing Original rule: f31_0_loop_EQ -> f31_0_loop_EQ : arg2'=arg2P1, arg1'=arg1P1, (1+arg1-arg1P1 == 0 /\ -5+arg1 > 0), cost: 1 New rule: f31_0_loop_EQ -> f31_0_loop_EQ : arg2'=arg2P1, arg1'=1+arg1, -5+arg1 > 0, cost: 1 Applied preprocessing Original rule: f31_0_loop_EQ -> f31_0_loop_EQ : arg2'=arg2P2, arg1'=arg1P2, (-6+arg1 < 0 /\ arg1 > 0 /\ -arg1P2 == 0), cost: 1 New rule: f31_0_loop_EQ -> f31_0_loop_EQ : arg2'=arg2P2, arg1'=0, (6-arg1 > 0 /\ arg1 > 0), cost: 1 Simplified rules Start location: __init 4: f1_0_main_Load -> f31_0_loop_EQ : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 5: f31_0_loop_EQ -> f31_0_loop_EQ : arg2'=arg2P1, arg1'=1+arg1, -5+arg1 > 0, cost: 1 6: f31_0_loop_EQ -> f31_0_loop_EQ : arg2'=arg2P2, arg1'=0, (6-arg1 > 0 /\ arg1 > 0), cost: 1 3: __init -> f1_0_main_Load : arg2'=arg2P3, arg1'=arg1P3, TRUE, cost: 1 Applied nonterm Original rule: f31_0_loop_EQ -> f31_0_loop_EQ : arg2'=arg2P1, arg1'=1+arg1, -5+arg1 > 0, cost: 1 New rule: f31_0_loop_EQ -> [3] : (-5+arg1 > 0 /\ -1+n >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_aNmOJH.txt Applied deletion Removed the following rules: 5 Accelerated simple loops Start location: __init 4: f1_0_main_Load -> f31_0_loop_EQ : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 6: f31_0_loop_EQ -> f31_0_loop_EQ : arg2'=arg2P2, arg1'=0, (6-arg1 > 0 /\ arg1 > 0), cost: 1 7: f31_0_loop_EQ -> [3] : (-5+arg1 > 0 /\ -1+n >= 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_loop_EQ : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Second rule: f31_0_loop_EQ -> f31_0_loop_EQ : arg2'=arg2P2, arg1'=0, (6-arg1 > 0 /\ arg1 > 0), cost: 1 New rule: f1_0_main_Load -> f31_0_loop_EQ : arg2'=arg2P2, arg1'=0, (6-arg2 > 0 /\ arg2 > 0 /\ arg1 > 0), cost: 2 Applied chaining First rule: f1_0_main_Load -> f31_0_loop_EQ : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Second rule: f31_0_loop_EQ -> [3] : (-5+arg1 > 0 /\ -1+n >= 0), cost: NONTERM New rule: f1_0_main_Load -> [3] : (-5+arg2 > 0 /\ arg1 > 0), cost: NONTERM Applied deletion Removed the following rules: 6 7 Chained accelerated rules with incoming rules Start location: __init 4: f1_0_main_Load -> f31_0_loop_EQ : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 8: f1_0_main_Load -> f31_0_loop_EQ : arg2'=arg2P2, arg1'=0, (6-arg2 > 0 /\ arg2 > 0 /\ arg1 > 0), cost: 2 9: f1_0_main_Load -> [3] : (-5+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 9: f1_0_main_Load -> [3] : (-5+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] : (-5+arg2 > 0 /\ arg1 > 0), cost: NONTERM New rule: __init -> [3] : (arg1P3 > 0 /\ -5+arg2P3 > 0), cost: NONTERM Applied deletion Removed the following rules: 3 9 Eliminated locations on linear paths Start location: __init 10: __init -> [3] : (arg1P3 > 0 /\ -5+arg2P3 > 0), cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 10 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: (arg1P3 > 0 /\ -5+arg2P3 > 0)