NO Initial ITS Start location: __init 0: f1_0_main_Load -> f112_0_loop_GE : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0 /\ -1+arg2 > 0), cost: 1 1: f112_0_loop_GE -> f112_0_loop_GE : arg2'=arg2P1, arg1'=arg1P1, (1+arg1 > 0 /\ arg2-arg1 > 0 /\ arg2-arg2P1 == 0 /\ 4+arg1-arg1P1 == 0), cost: 1 2: f112_0_loop_GE -> f112_0_loop_GE : arg2'=arg2P2, arg1'=arg1P2, (1+arg1 > 0 /\ arg2-arg1 <= 0 /\ 1+arg2 > 0 /\ 2+arg1-arg1P2 == 0 /\ 1+arg2-arg2P2 == 0), cost: 1 3: __init -> f1_0_main_Load : arg2'=arg2P3, arg1'=arg1P3, TRUE, cost: 1 Applied preprocessing Original rule: f112_0_loop_GE -> f112_0_loop_GE : arg2'=arg2P1, arg1'=arg1P1, (1+arg1 > 0 /\ arg2-arg1 > 0 /\ arg2-arg2P1 == 0 /\ 4+arg1-arg1P1 == 0), cost: 1 New rule: f112_0_loop_GE -> f112_0_loop_GE : arg1'=4+arg1, (1+arg1 > 0 /\ arg2-arg1 > 0), cost: 1 Applied preprocessing Original rule: f112_0_loop_GE -> f112_0_loop_GE : arg2'=arg2P2, arg1'=arg1P2, (1+arg1 > 0 /\ arg2-arg1 <= 0 /\ 1+arg2 > 0 /\ 2+arg1-arg1P2 == 0 /\ 1+arg2-arg2P2 == 0), cost: 1 New rule: f112_0_loop_GE -> f112_0_loop_GE : arg2'=1+arg2, arg1'=2+arg1, (arg2-arg1 <= 0 /\ 1+arg2 > 0), cost: 1 Simplified rules Start location: __init 0: f1_0_main_Load -> f112_0_loop_GE : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0 /\ -1+arg2 > 0), cost: 1 4: f112_0_loop_GE -> f112_0_loop_GE : arg1'=4+arg1, (1+arg1 > 0 /\ arg2-arg1 > 0), cost: 1 5: f112_0_loop_GE -> f112_0_loop_GE : arg2'=1+arg2, arg1'=2+arg1, (arg2-arg1 <= 0 /\ 1+arg2 > 0), cost: 1 3: __init -> f1_0_main_Load : arg2'=arg2P3, arg1'=arg1P3, TRUE, cost: 1 Applied acceleration Original rule: f112_0_loop_GE -> f112_0_loop_GE : arg1'=4+arg1, (1+arg1 > 0 /\ arg2-arg1 > 0), cost: 1 New rule: f112_0_loop_GE -> f112_0_loop_GE : arg1'=arg1+4*n, (1+arg1 > 0 /\ n >= 0 /\ 4+arg2-arg1-4*n > 0), cost: n Sub-proof via acceration calculus written to file:///tmp/tmpnam_jNhfGM.txt Applied nonterm Original rule: f112_0_loop_GE -> f112_0_loop_GE : arg2'=1+arg2, arg1'=2+arg1, (arg2-arg1 <= 0 /\ 1+arg2 > 0), cost: 1 New rule: f112_0_loop_GE -> [3] : (n0 >= 0 /\ 1+arg2 > 0 /\ -arg2+arg1 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_ofOIfC.txt Applied deletion Removed the following rules: 4 5 Accelerated simple loops Start location: __init 0: f1_0_main_Load -> f112_0_loop_GE : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0 /\ -1+arg2 > 0), cost: 1 6: f112_0_loop_GE -> f112_0_loop_GE : arg1'=arg1+4*n, (1+arg1 > 0 /\ n >= 0 /\ 4+arg2-arg1-4*n > 0), cost: n 7: f112_0_loop_GE -> [3] : (n0 >= 0 /\ 1+arg2 > 0 /\ -arg2+arg1 >= 0), cost: NONTERM 3: __init -> f1_0_main_Load : arg2'=arg2P3, arg1'=arg1P3, TRUE, cost: 1 Applied chaining First rule: f1_0_main_Load -> f112_0_loop_GE : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0 /\ -1+arg2 > 0), cost: 1 Second rule: f112_0_loop_GE -> f112_0_loop_GE : arg1'=arg1+4*n, (1+arg1 > 0 /\ n >= 0 /\ 4+arg2-arg1-4*n > 0), cost: n New rule: f1_0_main_Load -> f112_0_loop_GE : arg2'=arg2P0, arg1'=arg1P0+4*n, (1+arg2P0 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0 /\ n >= 0 /\ -1+arg2 > 0 /\ 4+arg2P0-arg1P0-4*n > 0), cost: 1+n Applied chaining First rule: f1_0_main_Load -> f112_0_loop_GE : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0 /\ -1+arg2 > 0), cost: 1 Second rule: f112_0_loop_GE -> [3] : (n0 >= 0 /\ 1+arg2 > 0 /\ -arg2+arg1 >= 0), cost: NONTERM New rule: f1_0_main_Load -> [3] : (arg1 > 0 /\ -1+arg2 > 0), cost: NONTERM Applied deletion Removed the following rules: 6 7 Chained accelerated rules with incoming rules Start location: __init 0: f1_0_main_Load -> f112_0_loop_GE : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0 /\ -1+arg2 > 0), cost: 1 8: f1_0_main_Load -> f112_0_loop_GE : arg2'=arg2P0, arg1'=arg1P0+4*n, (1+arg2P0 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0 /\ n >= 0 /\ -1+arg2 > 0 /\ 4+arg2P0-arg1P0-4*n > 0), cost: 1+n 9: f1_0_main_Load -> [3] : (arg1 > 0 /\ -1+arg2 > 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] : (arg1 > 0 /\ -1+arg2 > 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] : (arg1 > 0 /\ -1+arg2 > 0), cost: NONTERM New rule: __init -> [3] : (-1+arg2P3 > 0 /\ arg1P3 > 0), cost: NONTERM Applied deletion Removed the following rules: 3 9 Eliminated locations on linear paths Start location: __init 10: __init -> [3] : (-1+arg2P3 > 0 /\ arg1P3 > 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: (-1+arg2P3 > 0 /\ arg1P3 > 0)