NO Initial ITS Start location: __init 0: f1_0_main_Load -> f53_0_loop_LE : arg2'=arg2P0, arg1'=arg1P0, (1+arg2 > 0 /\ arg1 > 0 /\ arg2-arg1P0 == 0), cost: 1 1: f53_0_loop_LE -> f74_0_loop_NE : arg2'=arg2P1, arg1'=arg1P1, (-21+arg1 < 0 /\ -10+arg1 > 0 /\ -1+arg1-arg1P1 == 0), cost: 1 2: f53_0_loop_LE -> f74_0_loop_NE : arg2'=arg2P2, arg1'=arg1P2, (-20+arg1 > 0 /\ 1+arg1-arg1P2 == 0), cost: 1 3: f74_0_loop_NE -> f53_0_loop_LE : arg2'=arg2P3, arg1'=arg1P3, (-30+arg1 < 0 /\ -arg1P3+arg1 == 0), cost: 1 4: f74_0_loop_NE -> f53_0_loop_LE : arg2'=arg2P4, arg1'=arg1P4, (-30+arg1 > 0 /\ arg1-arg1P4 == 0), cost: 1 5: __init -> f1_0_main_Load : arg2'=arg2P5, arg1'=arg1P5, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_Load -> f53_0_loop_LE : arg2'=arg2P0, arg1'=arg1P0, (1+arg2 > 0 /\ arg1 > 0 /\ arg2-arg1P0 == 0), cost: 1 New rule: f1_0_main_Load -> f53_0_loop_LE : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 Applied preprocessing Original rule: f53_0_loop_LE -> f74_0_loop_NE : arg2'=arg2P1, arg1'=arg1P1, (-21+arg1 < 0 /\ -10+arg1 > 0 /\ -1+arg1-arg1P1 == 0), cost: 1 New rule: f53_0_loop_LE -> f74_0_loop_NE : arg2'=arg2P1, arg1'=-1+arg1, (21-arg1 > 0 /\ -10+arg1 > 0), cost: 1 Applied preprocessing Original rule: f53_0_loop_LE -> f74_0_loop_NE : arg2'=arg2P2, arg1'=arg1P2, (-20+arg1 > 0 /\ 1+arg1-arg1P2 == 0), cost: 1 New rule: f53_0_loop_LE -> f74_0_loop_NE : arg2'=arg2P2, arg1'=1+arg1, -20+arg1 > 0, cost: 1 Applied preprocessing Original rule: f74_0_loop_NE -> f53_0_loop_LE : arg2'=arg2P3, arg1'=arg1P3, (-30+arg1 < 0 /\ -arg1P3+arg1 == 0), cost: 1 New rule: f74_0_loop_NE -> f53_0_loop_LE : arg2'=arg2P3, 30-arg1 > 0, cost: 1 Applied preprocessing Original rule: f74_0_loop_NE -> f53_0_loop_LE : arg2'=arg2P4, arg1'=arg1P4, (-30+arg1 > 0 /\ arg1-arg1P4 == 0), cost: 1 New rule: f74_0_loop_NE -> f53_0_loop_LE : arg2'=arg2P4, -30+arg1 > 0, cost: 1 Simplified rules Start location: __init 6: f1_0_main_Load -> f53_0_loop_LE : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 7: f53_0_loop_LE -> f74_0_loop_NE : arg2'=arg2P1, arg1'=-1+arg1, (21-arg1 > 0 /\ -10+arg1 > 0), cost: 1 8: f53_0_loop_LE -> f74_0_loop_NE : arg2'=arg2P2, arg1'=1+arg1, -20+arg1 > 0, cost: 1 9: f74_0_loop_NE -> f53_0_loop_LE : arg2'=arg2P3, 30-arg1 > 0, cost: 1 10: f74_0_loop_NE -> f53_0_loop_LE : arg2'=arg2P4, -30+arg1 > 0, cost: 1 5: __init -> f1_0_main_Load : arg2'=arg2P5, arg1'=arg1P5, TRUE, cost: 1 Eliminating location f1_0_main_Load by chaining: Applied chaining First rule: __init -> f1_0_main_Load : arg2'=arg2P5, arg1'=arg1P5, TRUE, cost: 1 Second rule: f1_0_main_Load -> f53_0_loop_LE : arg2'=arg2P0, arg1'=arg2, (1+arg2 > 0 /\ arg1 > 0), cost: 1 New rule: __init -> f53_0_loop_LE : arg2'=arg2P0, arg1'=arg2P5, (1+arg2P5 > 0 /\ arg1P5 > 0), cost: 2 Applied deletion Removed the following rules: 5 6 Eliminated locations on linear paths Start location: __init 7: f53_0_loop_LE -> f74_0_loop_NE : arg2'=arg2P1, arg1'=-1+arg1, (21-arg1 > 0 /\ -10+arg1 > 0), cost: 1 8: f53_0_loop_LE -> f74_0_loop_NE : arg2'=arg2P2, arg1'=1+arg1, -20+arg1 > 0, cost: 1 9: f74_0_loop_NE -> f53_0_loop_LE : arg2'=arg2P3, 30-arg1 > 0, cost: 1 10: f74_0_loop_NE -> f53_0_loop_LE : arg2'=arg2P4, -30+arg1 > 0, cost: 1 11: __init -> f53_0_loop_LE : arg2'=arg2P0, arg1'=arg2P5, (1+arg2P5 > 0 /\ arg1P5 > 0), cost: 2 Eliminating location f74_0_loop_NE by chaining: Applied chaining First rule: f53_0_loop_LE -> f74_0_loop_NE : arg2'=arg2P1, arg1'=-1+arg1, (21-arg1 > 0 /\ -10+arg1 > 0), cost: 1 Second rule: f74_0_loop_NE -> f53_0_loop_LE : arg2'=arg2P3, 30-arg1 > 0, cost: 1 New rule: f53_0_loop_LE -> f53_0_loop_LE : arg2'=arg2P3, arg1'=-1+arg1, (31-arg1 > 0 /\ 21-arg1 > 0 /\ -10+arg1 > 0), cost: 2 Applied simplification Original rule: f53_0_loop_LE -> f53_0_loop_LE : arg2'=arg2P3, arg1'=-1+arg1, (31-arg1 > 0 /\ 21-arg1 > 0 /\ -10+arg1 > 0), cost: 2 New rule: f53_0_loop_LE -> f53_0_loop_LE : arg2'=arg2P3, arg1'=-1+arg1, (21-arg1 > 0 /\ -10+arg1 > 0), cost: 2 Applied chaining First rule: f53_0_loop_LE -> f74_0_loop_NE : arg2'=arg2P2, arg1'=1+arg1, -20+arg1 > 0, cost: 1 Second rule: f74_0_loop_NE -> f53_0_loop_LE : arg2'=arg2P3, 30-arg1 > 0, cost: 1 New rule: f53_0_loop_LE -> f53_0_loop_LE : arg2'=arg2P3, arg1'=1+arg1, (-20+arg1 > 0 /\ 29-arg1 > 0), cost: 2 Applied chaining First rule: f53_0_loop_LE -> f74_0_loop_NE : arg2'=arg2P2, arg1'=1+arg1, -20+arg1 > 0, cost: 1 Second rule: f74_0_loop_NE -> f53_0_loop_LE : arg2'=arg2P4, -30+arg1 > 0, cost: 1 New rule: f53_0_loop_LE -> f53_0_loop_LE : arg2'=arg2P4, arg1'=1+arg1, (-29+arg1 > 0 /\ -20+arg1 > 0), cost: 2 Applied simplification Original rule: f53_0_loop_LE -> f53_0_loop_LE : arg2'=arg2P4, arg1'=1+arg1, (-29+arg1 > 0 /\ -20+arg1 > 0), cost: 2 New rule: f53_0_loop_LE -> f53_0_loop_LE : arg2'=arg2P4, arg1'=1+arg1, -29+arg1 > 0, cost: 2 Applied deletion Removed the following rules: 7 8 9 10 Eliminated locations on tree-shaped paths Start location: __init 12: f53_0_loop_LE -> f53_0_loop_LE : arg2'=arg2P3, arg1'=-1+arg1, (21-arg1 > 0 /\ -10+arg1 > 0), cost: 2 13: f53_0_loop_LE -> f53_0_loop_LE : arg2'=arg2P3, arg1'=1+arg1, (-20+arg1 > 0 /\ 29-arg1 > 0), cost: 2 14: f53_0_loop_LE -> f53_0_loop_LE : arg2'=arg2P4, arg1'=1+arg1, -29+arg1 > 0, cost: 2 11: __init -> f53_0_loop_LE : arg2'=arg2P0, arg1'=arg2P5, (1+arg2P5 > 0 /\ arg1P5 > 0), cost: 2 Applied acceleration Original rule: f53_0_loop_LE -> f53_0_loop_LE : arg2'=arg2P3, arg1'=-1+arg1, (21-arg1 > 0 /\ -10+arg1 > 0), cost: 2 New rule: f53_0_loop_LE -> f53_0_loop_LE : arg2'=arg2P3, arg1'=arg1-n, (-9+arg1-n > 0 /\ -1+n >= 0 /\ 21-arg1 > 0), cost: 2*n Sub-proof via acceration calculus written to file:///tmp/tmpnam_FlHOKH.txt Applied instantiation Original rule: f53_0_loop_LE -> f53_0_loop_LE : arg2'=arg2P3, arg1'=arg1-n, (-9+arg1-n > 0 /\ -1+n >= 0 /\ 21-arg1 > 0), cost: 2*n New rule: f53_0_loop_LE -> f53_0_loop_LE : arg2'=arg2P3, arg1'=10, (1 > 0 /\ -11+arg1 >= 0 /\ 21-arg1 > 0), cost: -20+2*arg1 Applied acceleration Original rule: f53_0_loop_LE -> f53_0_loop_LE : arg2'=arg2P3, arg1'=1+arg1, (-20+arg1 > 0 /\ 29-arg1 > 0), cost: 2 New rule: f53_0_loop_LE -> f53_0_loop_LE : arg2'=arg2P3, arg1'=arg1+n0, (30-arg1-n0 > 0 /\ -20+arg1 > 0 /\ -1+n0 >= 0), cost: 2*n0 Sub-proof via acceration calculus written to file:///tmp/tmpnam_KOCBOk.txt Applied instantiation Original rule: f53_0_loop_LE -> f53_0_loop_LE : arg2'=arg2P3, arg1'=arg1+n0, (30-arg1-n0 > 0 /\ -20+arg1 > 0 /\ -1+n0 >= 0), cost: 2*n0 New rule: f53_0_loop_LE -> f53_0_loop_LE : arg2'=arg2P3, arg1'=29, (1 > 0 /\ -20+arg1 > 0 /\ 28-arg1 >= 0), cost: 58-2*arg1 Applied nonterm Original rule: f53_0_loop_LE -> f53_0_loop_LE : arg2'=arg2P4, arg1'=1+arg1, -29+arg1 > 0, cost: 2 New rule: f53_0_loop_LE -> [4] : (-29+arg1 > 0 /\ -1+n1 >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_CIkmKK.txt Applied simplification Original rule: f53_0_loop_LE -> f53_0_loop_LE : arg2'=arg2P3, arg1'=10, (1 > 0 /\ -11+arg1 >= 0 /\ 21-arg1 > 0), cost: -20+2*arg1 New rule: f53_0_loop_LE -> f53_0_loop_LE : arg2'=arg2P3, arg1'=10, (-11+arg1 >= 0 /\ 21-arg1 > 0), cost: -20+2*arg1 Applied simplification Original rule: f53_0_loop_LE -> f53_0_loop_LE : arg2'=arg2P3, arg1'=29, (1 > 0 /\ -20+arg1 > 0 /\ 28-arg1 >= 0), cost: 58-2*arg1 New rule: f53_0_loop_LE -> f53_0_loop_LE : arg2'=arg2P3, arg1'=29, (-20+arg1 > 0 /\ -28+arg1 <= 0), cost: 58-2*arg1 Applied deletion Removed the following rules: 12 13 14 Accelerated simple loops Start location: __init 17: f53_0_loop_LE -> [4] : (-29+arg1 > 0 /\ -1+n1 >= 0), cost: NONTERM 18: f53_0_loop_LE -> f53_0_loop_LE : arg2'=arg2P3, arg1'=10, (-11+arg1 >= 0 /\ 21-arg1 > 0), cost: -20+2*arg1 19: f53_0_loop_LE -> f53_0_loop_LE : arg2'=arg2P3, arg1'=29, (-20+arg1 > 0 /\ -28+arg1 <= 0), cost: 58-2*arg1 11: __init -> f53_0_loop_LE : arg2'=arg2P0, arg1'=arg2P5, (1+arg2P5 > 0 /\ arg1P5 > 0), cost: 2 Applied chaining First rule: __init -> f53_0_loop_LE : arg2'=arg2P0, arg1'=arg2P5, (1+arg2P5 > 0 /\ arg1P5 > 0), cost: 2 Second rule: f53_0_loop_LE -> [4] : (-29+arg1 > 0 /\ -1+n1 >= 0), cost: NONTERM New rule: __init -> [4] : TRUE, cost: NONTERM Applied chaining First rule: __init -> f53_0_loop_LE : arg2'=arg2P0, arg1'=arg2P5, (1+arg2P5 > 0 /\ arg1P5 > 0), cost: 2 Second rule: f53_0_loop_LE -> f53_0_loop_LE : arg2'=arg2P3, arg1'=10, (-11+arg1 >= 0 /\ 21-arg1 > 0), cost: -20+2*arg1 New rule: __init -> f53_0_loop_LE : arg2'=arg2P3, arg1'=10, (21-arg2P5 > 0 /\ -11+arg2P5 >= 0), cost: -18+2*arg2P5 Applied chaining First rule: __init -> f53_0_loop_LE : arg2'=arg2P0, arg1'=arg2P5, (1+arg2P5 > 0 /\ arg1P5 > 0), cost: 2 Second rule: f53_0_loop_LE -> f53_0_loop_LE : arg2'=arg2P3, arg1'=29, (-20+arg1 > 0 /\ -28+arg1 <= 0), cost: 58-2*arg1 New rule: __init -> f53_0_loop_LE : arg2'=arg2P3, arg1'=29, (-20+arg2P5 > 0 /\ -28+arg2P5 <= 0), cost: 60-2*arg2P5 Applied deletion Removed the following rules: 17 18 19 Chained accelerated rules with incoming rules Start location: __init 11: __init -> f53_0_loop_LE : arg2'=arg2P0, arg1'=arg2P5, (1+arg2P5 > 0 /\ arg1P5 > 0), cost: 2 20: __init -> [4] : TRUE, cost: NONTERM 21: __init -> f53_0_loop_LE : arg2'=arg2P3, arg1'=10, (21-arg2P5 > 0 /\ -11+arg2P5 >= 0), cost: -18+2*arg2P5 22: __init -> f53_0_loop_LE : arg2'=arg2P3, arg1'=29, (-20+arg2P5 > 0 /\ -28+arg2P5 <= 0), cost: 60-2*arg2P5 Removed unreachable locations and irrelevant leafs Start location: __init 20: __init -> [4] : TRUE, cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 20 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: TRUE