NO Initial ITS Start location: __init 0: f1_0_main_Load -> f182_0_middle_EQ : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0 /\ -1+arg2 > 0), cost: 1 1: f182_0_middle_EQ -> f182_0_middle_EQ : arg2'=arg2P1, arg1'=arg1P1, (arg2-arg1 > 0 /\ 1+arg2-arg2P1 == 0 /\ -1+arg1-arg1P1 == 0), cost: 1 2: f182_0_middle_EQ -> f182_0_middle_EQ : arg2'=arg2P2, arg1'=arg1P2, (-1+arg1-arg1P2 == 0 /\ arg2-arg1 < 0 /\ 1+arg2-arg2P2 == 0), cost: 1 3: __init -> f1_0_main_Load : arg2'=arg2P3, arg1'=arg1P3, TRUE, cost: 1 Applied preprocessing Original rule: f182_0_middle_EQ -> f182_0_middle_EQ : arg2'=arg2P1, arg1'=arg1P1, (arg2-arg1 > 0 /\ 1+arg2-arg2P1 == 0 /\ -1+arg1-arg1P1 == 0), cost: 1 New rule: f182_0_middle_EQ -> f182_0_middle_EQ : arg2'=1+arg2, arg1'=-1+arg1, arg2-arg1 > 0, cost: 1 Applied preprocessing Original rule: f182_0_middle_EQ -> f182_0_middle_EQ : arg2'=arg2P2, arg1'=arg1P2, (-1+arg1-arg1P2 == 0 /\ arg2-arg1 < 0 /\ 1+arg2-arg2P2 == 0), cost: 1 New rule: f182_0_middle_EQ -> f182_0_middle_EQ : arg2'=1+arg2, arg1'=-1+arg1, -arg2+arg1 > 0, cost: 1 Simplified rules Start location: __init 0: f1_0_main_Load -> f182_0_middle_EQ : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0 /\ -1+arg2 > 0), cost: 1 4: f182_0_middle_EQ -> f182_0_middle_EQ : arg2'=1+arg2, arg1'=-1+arg1, arg2-arg1 > 0, cost: 1 5: f182_0_middle_EQ -> f182_0_middle_EQ : arg2'=1+arg2, arg1'=-1+arg1, -arg2+arg1 > 0, cost: 1 3: __init -> f1_0_main_Load : arg2'=arg2P3, arg1'=arg1P3, TRUE, cost: 1 Applied nonterm Original rule: f182_0_middle_EQ -> f182_0_middle_EQ : arg2'=1+arg2, arg1'=-1+arg1, arg2-arg1 > 0, cost: 1 New rule: f182_0_middle_EQ -> [3] : (arg2-arg1 > 0 /\ n >= 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_jgKmgj.txt Applied acceleration Original rule: f182_0_middle_EQ -> f182_0_middle_EQ : arg2'=1+arg2, arg1'=-1+arg1, -arg2+arg1 > 0, cost: 1 New rule: f182_0_middle_EQ -> f182_0_middle_EQ : arg2'=arg2+n0, arg1'=-n0+arg1, (2-arg2-2*n0+arg1 > 0 /\ n0 >= 0), cost: n0 Sub-proof via acceration calculus written to file:///tmp/tmpnam_bAfLLa.txt Applied deletion Removed the following rules: 4 5 Accelerated simple loops Start location: __init 0: f1_0_main_Load -> f182_0_middle_EQ : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0 /\ -1+arg2 > 0), cost: 1 6: f182_0_middle_EQ -> [3] : (arg2-arg1 > 0 /\ n >= 0), cost: NONTERM 7: f182_0_middle_EQ -> f182_0_middle_EQ : arg2'=arg2+n0, arg1'=-n0+arg1, (2-arg2-2*n0+arg1 > 0 /\ n0 >= 0), cost: n0 3: __init -> f1_0_main_Load : arg2'=arg2P3, arg1'=arg1P3, TRUE, cost: 1 Applied chaining First rule: f1_0_main_Load -> f182_0_middle_EQ : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0 /\ -1+arg2 > 0), cost: 1 Second rule: f182_0_middle_EQ -> [3] : (arg2-arg1 > 0 /\ n >= 0), cost: NONTERM New rule: f1_0_main_Load -> [3] : (arg1 > 0 /\ -1+arg2 > 0), cost: NONTERM Applied chaining First rule: f1_0_main_Load -> f182_0_middle_EQ : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0 /\ -1+arg2 > 0), cost: 1 Second rule: f182_0_middle_EQ -> f182_0_middle_EQ : arg2'=arg2+n0, arg1'=-n0+arg1, (2-arg2-2*n0+arg1 > 0 /\ n0 >= 0), cost: n0 New rule: f1_0_main_Load -> f182_0_middle_EQ : arg2'=arg2P0+n0, arg1'=arg1P0-n0, (1+arg2P0 > 0 /\ 2-arg2P0+arg1P0-2*n0 > 0 /\ n0 >= 0 /\ arg1 > 0 /\ 1+arg1P0 > 0 /\ -1+arg2 > 0), cost: 1+n0 Applied deletion Removed the following rules: 6 7 Chained accelerated rules with incoming rules Start location: __init 0: f1_0_main_Load -> f182_0_middle_EQ : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P0 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0 /\ -1+arg2 > 0), cost: 1 8: f1_0_main_Load -> [3] : (arg1 > 0 /\ -1+arg2 > 0), cost: NONTERM 9: f1_0_main_Load -> f182_0_middle_EQ : arg2'=arg2P0+n0, arg1'=arg1P0-n0, (1+arg2P0 > 0 /\ 2-arg2P0+arg1P0-2*n0 > 0 /\ n0 >= 0 /\ arg1 > 0 /\ 1+arg1P0 > 0 /\ -1+arg2 > 0), cost: 1+n0 3: __init -> f1_0_main_Load : arg2'=arg2P3, arg1'=arg1P3, TRUE, cost: 1 Removed unreachable locations and irrelevant leafs Start location: __init 8: 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 8 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)