NO Initial ITS Start location: __init 0: f1_0_main_Load -> f1_0_main_Load\' : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+x120 > 0 /\ -1-2*x140+x130 == 0 /\ 1+x130 > 0 /\ -1+arg2 > 0 /\ arg1-arg1P0 == 0 /\ -arg2P0+arg2 == 0), cost: 1 3: f1_0_main_Load -> f1_0_main_Load\' : arg1'=arg1P3, arg2'=arg2P3, (arg1 > 0 /\ arg1-arg1P3 == 0 /\ -1+arg2 > 0 /\ -arg2P3+arg2 == 0 /\ 1+x230 > 0 /\ x230-2*x240 == 0 /\ 1+x220 > 0), cost: 1 1: f1_0_main_Load\' -> f122_0_even_EQ : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ 1+x180 > 0 /\ -1-2*x190+x180 == 0 /\ -1+arg2 > 0 /\ -2-2*x190+x180 < 0 /\ 1+arg1P1 > 0 /\ -2*x190+x180 >= 0), cost: 1 4: f1_0_main_Load\' -> f146_0_even_EQ : arg1'=arg1P4, arg2'=arg2P4, (arg1 > 0 /\ 1+x270 > 0 /\ -1+arg2 > 0 /\ 1+x280 > 0 /\ -x270-arg1P4 == 0 /\ x280-2*x290 >= 0 /\ x280-2*x290 == 0 /\ -2+x280-2*x290 < 0), cost: 1 2: f122_0_even_EQ -> f146_0_even_EQ : arg1'=arg1P2, arg2'=arg2P2, (-arg1 == 0 /\ -arg1P2 == 0), cost: 1 5: f122_0_even_EQ -> f122_0_even_EQ : arg1'=arg1P5, arg2'=arg2P5, (-2+arg1-arg1P5 == 0 /\ -1+arg1 > 0), cost: 1 6: f146_0_even_EQ -> f146_0_even_EQ : arg1'=arg1P6, arg2'=arg2P6, (arg1 < 0 /\ -3+arg1 < 0 /\ -2+arg1-arg1P6 == 0), cost: 1 7: __init -> f1_0_main_Load : arg1'=arg1P7, arg2'=arg2P7, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_Load -> f1_0_main_Load\' : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+x120 > 0 /\ -1-2*x140+x130 == 0 /\ 1+x130 > 0 /\ -1+arg2 > 0 /\ arg1-arg1P0 == 0 /\ -arg2P0+arg2 == 0), cost: 1 New rule: f1_0_main_Load -> f1_0_main_Load\' : (arg1 > 0 /\ 2+2*x140 > 0 /\ -1+arg2 > 0), cost: 1 Applied preprocessing Original rule: f1_0_main_Load\' -> f122_0_even_EQ : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ 1+x180 > 0 /\ -1-2*x190+x180 == 0 /\ -1+arg2 > 0 /\ -2-2*x190+x180 < 0 /\ 1+arg1P1 > 0 /\ -2*x190+x180 >= 0), cost: 1 New rule: f1_0_main_Load\' -> f122_0_even_EQ : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ -1+arg2 > 0 /\ 2+2*x190 > 0 /\ 1+arg1P1 > 0), cost: 1 Applied preprocessing Original rule: f122_0_even_EQ -> f146_0_even_EQ : arg1'=arg1P2, arg2'=arg2P2, (-arg1 == 0 /\ -arg1P2 == 0), cost: 1 New rule: f122_0_even_EQ -> f146_0_even_EQ : arg1'=0, arg2'=arg2P2, arg1 == 0, cost: 1 Applied preprocessing Original rule: f1_0_main_Load -> f1_0_main_Load\' : arg1'=arg1P3, arg2'=arg2P3, (arg1 > 0 /\ arg1-arg1P3 == 0 /\ -1+arg2 > 0 /\ -arg2P3+arg2 == 0 /\ 1+x230 > 0 /\ x230-2*x240 == 0 /\ 1+x220 > 0), cost: 1 New rule: f1_0_main_Load -> f1_0_main_Load\' : (arg1 > 0 /\ 1+2*x240 > 0 /\ -1+arg2 > 0), cost: 1 Applied preprocessing Original rule: f1_0_main_Load\' -> f146_0_even_EQ : arg1'=arg1P4, arg2'=arg2P4, (arg1 > 0 /\ 1+x270 > 0 /\ -1+arg2 > 0 /\ 1+x280 > 0 /\ -x270-arg1P4 == 0 /\ x280-2*x290 >= 0 /\ x280-2*x290 == 0 /\ -2+x280-2*x290 < 0), cost: 1 New rule: f1_0_main_Load\' -> f146_0_even_EQ : arg1'=-x270, arg2'=arg2P4, (arg1 > 0 /\ 1+2*x290 > 0 /\ 1+x270 > 0 /\ -1+arg2 > 0), cost: 1 Applied preprocessing Original rule: f122_0_even_EQ -> f122_0_even_EQ : arg1'=arg1P5, arg2'=arg2P5, (-2+arg1-arg1P5 == 0 /\ -1+arg1 > 0), cost: 1 New rule: f122_0_even_EQ -> f122_0_even_EQ : arg1'=-2+arg1, arg2'=arg2P5, -1+arg1 > 0, cost: 1 Applied preprocessing Original rule: f146_0_even_EQ -> f146_0_even_EQ : arg1'=arg1P6, arg2'=arg2P6, (arg1 < 0 /\ -3+arg1 < 0 /\ -2+arg1-arg1P6 == 0), cost: 1 New rule: f146_0_even_EQ -> f146_0_even_EQ : arg1'=-2+arg1, arg2'=arg2P6, -arg1 > 0, cost: 1 Simplified rules Start location: __init 8: f1_0_main_Load -> f1_0_main_Load\' : (arg1 > 0 /\ 2+2*x140 > 0 /\ -1+arg2 > 0), cost: 1 11: f1_0_main_Load -> f1_0_main_Load\' : (arg1 > 0 /\ 1+2*x240 > 0 /\ -1+arg2 > 0), cost: 1 9: f1_0_main_Load\' -> f122_0_even_EQ : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ -1+arg2 > 0 /\ 2+2*x190 > 0 /\ 1+arg1P1 > 0), cost: 1 12: f1_0_main_Load\' -> f146_0_even_EQ : arg1'=-x270, arg2'=arg2P4, (arg1 > 0 /\ 1+2*x290 > 0 /\ 1+x270 > 0 /\ -1+arg2 > 0), cost: 1 10: f122_0_even_EQ -> f146_0_even_EQ : arg1'=0, arg2'=arg2P2, arg1 == 0, cost: 1 13: f122_0_even_EQ -> f122_0_even_EQ : arg1'=-2+arg1, arg2'=arg2P5, -1+arg1 > 0, cost: 1 14: f146_0_even_EQ -> f146_0_even_EQ : arg1'=-2+arg1, arg2'=arg2P6, -arg1 > 0, cost: 1 7: __init -> f1_0_main_Load : arg1'=arg1P7, arg2'=arg2P7, TRUE, cost: 1 Applied acceleration Original rule: f122_0_even_EQ -> f122_0_even_EQ : arg1'=-2+arg1, arg2'=arg2P5, -1+arg1 > 0, cost: 1 New rule: f122_0_even_EQ -> f122_0_even_EQ : arg1'=arg1-2*n0, arg2'=arg2P5, (1+arg1-2*n0 > 0 /\ -1+n0 >= 0), cost: n0 Applied deletion Removed the following rules: 13 Applied nonterm Original rule: f146_0_even_EQ -> f146_0_even_EQ : arg1'=-2+arg1, arg2'=arg2P6, -arg1 > 0, cost: 1 New rule: f146_0_even_EQ -> [6] : -arg1 > 0, cost: NONTERM Applied acceleration Original rule: f146_0_even_EQ -> f146_0_even_EQ : arg1'=-2+arg1, arg2'=arg2P6, -arg1 > 0, cost: 1 New rule: f146_0_even_EQ -> f146_0_even_EQ : arg1'=arg1-2*n3, arg2'=arg2P6, -arg1 > 0, cost: n3 Applied deletion Removed the following rules: 14 Accelerated simple loops Start location: __init 8: f1_0_main_Load -> f1_0_main_Load\' : (arg1 > 0 /\ 2+2*x140 > 0 /\ -1+arg2 > 0), cost: 1 11: f1_0_main_Load -> f1_0_main_Load\' : (arg1 > 0 /\ 1+2*x240 > 0 /\ -1+arg2 > 0), cost: 1 9: f1_0_main_Load\' -> f122_0_even_EQ : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ -1+arg2 > 0 /\ 2+2*x190 > 0 /\ 1+arg1P1 > 0), cost: 1 12: f1_0_main_Load\' -> f146_0_even_EQ : arg1'=-x270, arg2'=arg2P4, (arg1 > 0 /\ 1+2*x290 > 0 /\ 1+x270 > 0 /\ -1+arg2 > 0), cost: 1 10: f122_0_even_EQ -> f146_0_even_EQ : arg1'=0, arg2'=arg2P2, arg1 == 0, cost: 1 15: f122_0_even_EQ -> f122_0_even_EQ : arg1'=arg1-2*n0, arg2'=arg2P5, (1+arg1-2*n0 > 0 /\ -1+n0 >= 0), cost: n0 16: f146_0_even_EQ -> [6] : -arg1 > 0, cost: NONTERM 17: f146_0_even_EQ -> f146_0_even_EQ : arg1'=arg1-2*n3, arg2'=arg2P6, -arg1 > 0, cost: n3 7: __init -> f1_0_main_Load : arg1'=arg1P7, arg2'=arg2P7, TRUE, cost: 1 Applied chaining First rule: f1_0_main_Load\' -> f122_0_even_EQ : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ -1+arg2 > 0 /\ 2+2*x190 > 0 /\ 1+arg1P1 > 0), cost: 1 Second rule: f122_0_even_EQ -> f122_0_even_EQ : arg1'=arg1-2*n0, arg2'=arg2P5, (1+arg1-2*n0 > 0 /\ -1+n0 >= 0), cost: n0 New rule: f1_0_main_Load\' -> f122_0_even_EQ : arg1'=arg1P1-2*n0, arg2'=arg2P5, (arg1 > 0 /\ -1+arg2 > 0 /\ 2+2*x190 > 0 /\ -1+n0 >= 0 /\ 1+arg1P1-2*n0 > 0), cost: 1+n0 Applied deletion Removed the following rules: 15 Applied chaining First rule: f1_0_main_Load\' -> f146_0_even_EQ : arg1'=-x270, arg2'=arg2P4, (arg1 > 0 /\ 1+2*x290 > 0 /\ 1+x270 > 0 /\ -1+arg2 > 0), cost: 1 Second rule: f146_0_even_EQ -> [6] : -arg1 > 0, cost: NONTERM New rule: f1_0_main_Load\' -> [6] : (arg1 > 0 /\ 1+2*x290 > 0 /\ -1+arg2 > 0), cost: NONTERM Applied chaining First rule: f1_0_main_Load\' -> f146_0_even_EQ : arg1'=-x270, arg2'=arg2P4, (arg1 > 0 /\ 1+2*x290 > 0 /\ 1+x270 > 0 /\ -1+arg2 > 0), cost: 1 Second rule: f146_0_even_EQ -> f146_0_even_EQ : arg1'=arg1-2*n3, arg2'=arg2P6, -arg1 > 0, cost: n3 New rule: f1_0_main_Load\' -> f146_0_even_EQ : arg1'=-x270-2*n3, arg2'=arg2P6, (arg1 > 0 /\ 1+2*x290 > 0 /\ x270 > 0 /\ -1+arg2 > 0), cost: 1+n3 Applied deletion Removed the following rules: 16 17 Chained accelerated rules with incoming rules Start location: __init 8: f1_0_main_Load -> f1_0_main_Load\' : (arg1 > 0 /\ 2+2*x140 > 0 /\ -1+arg2 > 0), cost: 1 11: f1_0_main_Load -> f1_0_main_Load\' : (arg1 > 0 /\ 1+2*x240 > 0 /\ -1+arg2 > 0), cost: 1 9: f1_0_main_Load\' -> f122_0_even_EQ : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ -1+arg2 > 0 /\ 2+2*x190 > 0 /\ 1+arg1P1 > 0), cost: 1 12: f1_0_main_Load\' -> f146_0_even_EQ : arg1'=-x270, arg2'=arg2P4, (arg1 > 0 /\ 1+2*x290 > 0 /\ 1+x270 > 0 /\ -1+arg2 > 0), cost: 1 18: f1_0_main_Load\' -> f122_0_even_EQ : arg1'=arg1P1-2*n0, arg2'=arg2P5, (arg1 > 0 /\ -1+arg2 > 0 /\ 2+2*x190 > 0 /\ -1+n0 >= 0 /\ 1+arg1P1-2*n0 > 0), cost: 1+n0 19: f1_0_main_Load\' -> [6] : (arg1 > 0 /\ 1+2*x290 > 0 /\ -1+arg2 > 0), cost: NONTERM 20: f1_0_main_Load\' -> f146_0_even_EQ : arg1'=-x270-2*n3, arg2'=arg2P6, (arg1 > 0 /\ 1+2*x290 > 0 /\ x270 > 0 /\ -1+arg2 > 0), cost: 1+n3 10: f122_0_even_EQ -> f146_0_even_EQ : arg1'=0, arg2'=arg2P2, arg1 == 0, cost: 1 7: __init -> f1_0_main_Load : arg1'=arg1P7, arg2'=arg2P7, TRUE, cost: 1 Removed unreachable locations and irrelevant leafs Start location: __init 8: f1_0_main_Load -> f1_0_main_Load\' : (arg1 > 0 /\ 2+2*x140 > 0 /\ -1+arg2 > 0), cost: 1 11: f1_0_main_Load -> f1_0_main_Load\' : (arg1 > 0 /\ 1+2*x240 > 0 /\ -1+arg2 > 0), cost: 1 19: f1_0_main_Load\' -> [6] : (arg1 > 0 /\ 1+2*x290 > 0 /\ -1+arg2 > 0), cost: NONTERM 7: __init -> f1_0_main_Load : arg1'=arg1P7, arg2'=arg2P7, TRUE, cost: 1 Eliminating location f1_0_main_Load by chaining: Applied chaining First rule: __init -> f1_0_main_Load : arg1'=arg1P7, arg2'=arg2P7, TRUE, cost: 1 Second rule: f1_0_main_Load -> f1_0_main_Load\' : (arg1 > 0 /\ 2+2*x140 > 0 /\ -1+arg2 > 0), cost: 1 New rule: __init -> f1_0_main_Load\' : arg1'=arg1P7, arg2'=arg2P7, (2+2*x140 > 0 /\ arg1P7 > 0 /\ -1+arg2P7 > 0), cost: 2 Applied chaining First rule: __init -> f1_0_main_Load : arg1'=arg1P7, arg2'=arg2P7, TRUE, cost: 1 Second rule: f1_0_main_Load -> f1_0_main_Load\' : (arg1 > 0 /\ 1+2*x240 > 0 /\ -1+arg2 > 0), cost: 1 New rule: __init -> f1_0_main_Load\' : arg1'=arg1P7, arg2'=arg2P7, (1+2*x240 > 0 /\ arg1P7 > 0 /\ -1+arg2P7 > 0), cost: 2 Applied deletion Removed the following rules: 7 8 11 Eliminated locations on tree-shaped paths Start location: __init 19: f1_0_main_Load\' -> [6] : (arg1 > 0 /\ 1+2*x290 > 0 /\ -1+arg2 > 0), cost: NONTERM 21: __init -> f1_0_main_Load\' : arg1'=arg1P7, arg2'=arg2P7, (2+2*x140 > 0 /\ arg1P7 > 0 /\ -1+arg2P7 > 0), cost: 2 22: __init -> f1_0_main_Load\' : arg1'=arg1P7, arg2'=arg2P7, (1+2*x240 > 0 /\ arg1P7 > 0 /\ -1+arg2P7 > 0), cost: 2 Eliminating location f1_0_main_Load\' by chaining: Applied chaining First rule: __init -> f1_0_main_Load\' : arg1'=arg1P7, arg2'=arg2P7, (2+2*x140 > 0 /\ arg1P7 > 0 /\ -1+arg2P7 > 0), cost: 2 Second rule: f1_0_main_Load\' -> [6] : (arg1 > 0 /\ 1+2*x290 > 0 /\ -1+arg2 > 0), cost: NONTERM New rule: __init -> [6] : (1+2*x290 > 0 /\ 2+2*x140 > 0 /\ arg1P7 > 0 /\ -1+arg2P7 > 0), cost: NONTERM Applied chaining First rule: __init -> f1_0_main_Load\' : arg1'=arg1P7, arg2'=arg2P7, (1+2*x240 > 0 /\ arg1P7 > 0 /\ -1+arg2P7 > 0), cost: 2 Second rule: f1_0_main_Load\' -> [6] : (arg1 > 0 /\ 1+2*x290 > 0 /\ -1+arg2 > 0), cost: NONTERM New rule: __init -> [6] : (1+2*x240 > 0 /\ 1+2*x290 > 0 /\ arg1P7 > 0 /\ -1+arg2P7 > 0), cost: NONTERM Applied deletion Removed the following rules: 19 21 22 Eliminated locations on tree-shaped paths Start location: __init 23: __init -> [6] : (1+2*x290 > 0 /\ 2+2*x140 > 0 /\ arg1P7 > 0 /\ -1+arg2P7 > 0), cost: NONTERM 24: __init -> [6] : (1+2*x240 > 0 /\ 1+2*x290 > 0 /\ arg1P7 > 0 /\ -1+arg2P7 > 0), cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 23 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: (1+2*x290 > 0 /\ 2+2*x140 > 0 /\ arg1P7 > 0 /\ -1+arg2P7 > 0)