NO Initial ITS Start location: __init 0: f1_0_main_Load -> f76_0_loop_GT : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ -arg1P0+arg2 == 0 /\ 1+arg2 > 0), cost: 1 1: f76_0_loop_GT -> f76_0_loop_GT : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ 1+arg1-arg1P1 == 0), cost: 1 2: f76_0_loop_GT -> f76_0_loop_GT : arg1'=arg1P2, arg2'=arg2P2, (-1+arg1 < 0 /\ -1+arg1-arg1P2 == 0 /\ -2+arg1 < 0), cost: 1 3: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_Load -> f76_0_loop_GT : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ -arg1P0+arg2 == 0 /\ 1+arg2 > 0), cost: 1 New rule: f1_0_main_Load -> f76_0_loop_GT : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Applied preprocessing Original rule: f76_0_loop_GT -> f76_0_loop_GT : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ 1+arg1-arg1P1 == 0), cost: 1 New rule: f76_0_loop_GT -> f76_0_loop_GT : arg1'=1+arg1, arg2'=arg2P1, arg1 > 0, cost: 1 Applied preprocessing Original rule: f76_0_loop_GT -> f76_0_loop_GT : arg1'=arg1P2, arg2'=arg2P2, (-1+arg1 < 0 /\ -1+arg1-arg1P2 == 0 /\ -2+arg1 < 0), cost: 1 New rule: f76_0_loop_GT -> f76_0_loop_GT : arg1'=-1+arg1, arg2'=arg2P2, 1-arg1 > 0, cost: 1 Simplified rules Start location: __init 4: f1_0_main_Load -> f76_0_loop_GT : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 5: f76_0_loop_GT -> f76_0_loop_GT : arg1'=1+arg1, arg2'=arg2P1, arg1 > 0, cost: 1 6: f76_0_loop_GT -> f76_0_loop_GT : arg1'=-1+arg1, arg2'=arg2P2, 1-arg1 > 0, cost: 1 3: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Applied nonterm Original rule: f76_0_loop_GT -> f76_0_loop_GT : arg1'=1+arg1, arg2'=arg2P1, arg1 > 0, cost: 1 New rule: f76_0_loop_GT -> [3] : arg1 > 0, cost: NONTERM Applied acceleration Original rule: f76_0_loop_GT -> f76_0_loop_GT : arg1'=1+arg1, arg2'=arg2P1, arg1 > 0, cost: 1 New rule: f76_0_loop_GT -> f76_0_loop_GT : arg1'=arg1+n1, arg2'=arg2P1, arg1 > 0, cost: n1 Applied nonterm Original rule: f76_0_loop_GT -> f76_0_loop_GT : arg1'=-1+arg1, arg2'=arg2P2, 1-arg1 > 0, cost: 1 New rule: f76_0_loop_GT -> [3] : 1-arg1 > 0, cost: NONTERM Applied acceleration Original rule: f76_0_loop_GT -> f76_0_loop_GT : arg1'=-1+arg1, arg2'=arg2P2, 1-arg1 > 0, cost: 1 New rule: f76_0_loop_GT -> f76_0_loop_GT : arg1'=arg1-n3, arg2'=arg2P2, 1-arg1 > 0, cost: n3 Applied deletion Removed the following rules: 5 6 Accelerated simple loops Start location: __init 4: f1_0_main_Load -> f76_0_loop_GT : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 7: f76_0_loop_GT -> [3] : arg1 > 0, cost: NONTERM 8: f76_0_loop_GT -> f76_0_loop_GT : arg1'=arg1+n1, arg2'=arg2P1, arg1 > 0, cost: n1 9: f76_0_loop_GT -> [3] : 1-arg1 > 0, cost: NONTERM 10: f76_0_loop_GT -> f76_0_loop_GT : arg1'=arg1-n3, arg2'=arg2P2, 1-arg1 > 0, cost: n3 3: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Applied chaining First rule: f1_0_main_Load -> f76_0_loop_GT : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f76_0_loop_GT -> [3] : arg1 > 0, cost: NONTERM New rule: f1_0_main_Load -> [3] : (arg1 > 0 /\ arg2 > 0), cost: NONTERM Applied chaining First rule: f1_0_main_Load -> f76_0_loop_GT : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f76_0_loop_GT -> f76_0_loop_GT : arg1'=arg1+n1, arg2'=arg2P1, arg1 > 0, cost: n1 New rule: f1_0_main_Load -> f76_0_loop_GT : arg1'=arg2+n1, arg2'=arg2P1, (arg1 > 0 /\ arg2 > 0), cost: 1+n1 Applied chaining First rule: f1_0_main_Load -> f76_0_loop_GT : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f76_0_loop_GT -> [3] : 1-arg1 > 0, cost: NONTERM New rule: f1_0_main_Load -> [3] : (arg1 > 0 /\ arg2 == 0), cost: NONTERM Applied chaining First rule: f1_0_main_Load -> f76_0_loop_GT : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 Second rule: f76_0_loop_GT -> f76_0_loop_GT : arg1'=arg1-n3, arg2'=arg2P2, 1-arg1 > 0, cost: n3 New rule: f1_0_main_Load -> f76_0_loop_GT : arg1'=-n3+arg2, arg2'=arg2P2, (arg1 > 0 /\ arg2 == 0), cost: 1+n3 Applied deletion Removed the following rules: 7 8 9 10 Chained accelerated rules with incoming rules Start location: __init 4: f1_0_main_Load -> f76_0_loop_GT : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1 11: f1_0_main_Load -> [3] : (arg1 > 0 /\ arg2 > 0), cost: NONTERM 12: f1_0_main_Load -> f76_0_loop_GT : arg1'=arg2+n1, arg2'=arg2P1, (arg1 > 0 /\ arg2 > 0), cost: 1+n1 13: f1_0_main_Load -> [3] : (arg1 > 0 /\ arg2 == 0), cost: NONTERM 14: f1_0_main_Load -> f76_0_loop_GT : arg1'=-n3+arg2, arg2'=arg2P2, (arg1 > 0 /\ arg2 == 0), cost: 1+n3 3: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Removed unreachable locations and irrelevant leafs Start location: __init 11: f1_0_main_Load -> [3] : (arg1 > 0 /\ arg2 > 0), cost: NONTERM 13: f1_0_main_Load -> [3] : (arg1 > 0 /\ arg2 == 0), cost: NONTERM 3: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Eliminating location f1_0_main_Load by chaining: Applied chaining First rule: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Second rule: f1_0_main_Load -> [3] : (arg1 > 0 /\ arg2 > 0), cost: NONTERM New rule: __init -> [3] : (arg1P3 > 0 /\ arg2P3 > 0), cost: NONTERM Applied chaining First rule: __init -> f1_0_main_Load : arg1'=arg1P3, arg2'=arg2P3, TRUE, cost: 1 Second rule: f1_0_main_Load -> [3] : (arg1 > 0 /\ arg2 == 0), cost: NONTERM New rule: __init -> [3] : (arg1P3 > 0 /\ arg2P3 == 0), cost: NONTERM Applied deletion Removed the following rules: 3 11 13 Eliminated locations on tree-shaped paths Start location: __init 15: __init -> [3] : (arg1P3 > 0 /\ arg2P3 > 0), cost: NONTERM 16: __init -> [3] : (arg1P3 > 0 /\ arg2P3 == 0), cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 15 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: (arg1P3 > 0 /\ arg2P3 > 0)