NO Initial ITS Start location: __init 0: f226_0_createIntList_Return -> f570_0_main_NULL : arg2'=arg2P0, arg1'=arg1P0, (-1-arg2+arg1P0 <= 0 /\ 1+arg2P0 > 0 /\ arg1P0 > 0 /\ 1+arg2 > 0 /\ arg1 > 0 /\ arg1P0-arg1 <= 0 /\ arg2P0-arg2 <= 0), cost: 1 2: f570_0_main_NULL -> f570_0_main_NULL : arg2'=arg2P2, arg1'=arg1P2, (1-arg2+arg1P2 <= 0 /\ 1+arg2P2-arg1 <= 0 /\ arg1 > 0 /\ -arg1+arg1P2 <= 0 /\ -1+arg2 > 0 /\ arg1P2 > 0 /\ 2-arg2+arg2P2 <= 0 /\ 1+arg2P2 > 0), cost: 1 3: f570_0_main_NULL -> f570_0_main_NULL : arg2'=arg2P3, arg1'=arg1P3, (x190 > 0 /\ 1+arg2P3 > 0 /\ -arg1+arg1P3 <= 0 /\ -2+arg2 > 0 /\ x140 > 0 /\ arg1 > 0 /\ 2-arg2+arg1P3 <= 0 /\ arg1P3 > 0), cost: 1 6: f570_0_main_NULL -> f726_0_reverse_NULL : arg2'=arg2P6, arg1'=arg1P6, (-2+arg2 > 0 /\ x290 > 0 /\ arg1 > 0 /\ 2-arg2+arg1P6 <= 0 /\ arg1P6 > 0 /\ x250 > 0), cost: 1 1: f1_0_main_Load -> f570_0_main_NULL : arg2'=arg2P1, arg1'=arg1P1, (-arg1+arg1P1 <= 0 /\ 1+arg2P1 > 0 /\ arg1 > 0 /\ arg1P1 > 0), cost: 1 4: f1_0_main_Load -> f507_0_createIntList_LE : arg2'=arg2P4, arg1'=arg1P4, (1-arg2P4 == 0 /\ 1+arg2 > 0 /\ arg1 > 0 /\ 1+arg1P4 > 0), cost: 1 5: f507_0_createIntList_LE -> f507_0_createIntList_LE : arg2'=arg2P5, arg1'=arg1P5, (arg2 > 0 /\ arg1 > 0 /\ -1-arg1P5+arg1 == 0 /\ 1-arg2P5+arg2 == 0), cost: 1 7: f726_0_reverse_NULL -> f726_0_reverse_NULL : arg2'=arg2P7, arg1'=arg1P7, (1+arg1P7 > 0 /\ arg1 > 0 /\ 1+arg1P7-arg1 <= 0), cost: 1 8: __init -> f1_0_main_Load : arg2'=arg2P8, arg1'=arg1P8, TRUE, cost: 1 Removed unreachable rules and leafs Start location: __init 2: f570_0_main_NULL -> f570_0_main_NULL : arg2'=arg2P2, arg1'=arg1P2, (1-arg2+arg1P2 <= 0 /\ 1+arg2P2-arg1 <= 0 /\ arg1 > 0 /\ -arg1+arg1P2 <= 0 /\ -1+arg2 > 0 /\ arg1P2 > 0 /\ 2-arg2+arg2P2 <= 0 /\ 1+arg2P2 > 0), cost: 1 3: f570_0_main_NULL -> f570_0_main_NULL : arg2'=arg2P3, arg1'=arg1P3, (x190 > 0 /\ 1+arg2P3 > 0 /\ -arg1+arg1P3 <= 0 /\ -2+arg2 > 0 /\ x140 > 0 /\ arg1 > 0 /\ 2-arg2+arg1P3 <= 0 /\ arg1P3 > 0), cost: 1 6: f570_0_main_NULL -> f726_0_reverse_NULL : arg2'=arg2P6, arg1'=arg1P6, (-2+arg2 > 0 /\ x290 > 0 /\ arg1 > 0 /\ 2-arg2+arg1P6 <= 0 /\ arg1P6 > 0 /\ x250 > 0), cost: 1 1: f1_0_main_Load -> f570_0_main_NULL : arg2'=arg2P1, arg1'=arg1P1, (-arg1+arg1P1 <= 0 /\ 1+arg2P1 > 0 /\ arg1 > 0 /\ arg1P1 > 0), cost: 1 4: f1_0_main_Load -> f507_0_createIntList_LE : arg2'=arg2P4, arg1'=arg1P4, (1-arg2P4 == 0 /\ 1+arg2 > 0 /\ arg1 > 0 /\ 1+arg1P4 > 0), cost: 1 5: f507_0_createIntList_LE -> f507_0_createIntList_LE : arg2'=arg2P5, arg1'=arg1P5, (arg2 > 0 /\ arg1 > 0 /\ -1-arg1P5+arg1 == 0 /\ 1-arg2P5+arg2 == 0), cost: 1 7: f726_0_reverse_NULL -> f726_0_reverse_NULL : arg2'=arg2P7, arg1'=arg1P7, (1+arg1P7 > 0 /\ arg1 > 0 /\ 1+arg1P7-arg1 <= 0), cost: 1 8: __init -> f1_0_main_Load : arg2'=arg2P8, arg1'=arg1P8, TRUE, cost: 1 Applied preprocessing Original rule: f1_0_main_Load -> f570_0_main_NULL : arg2'=arg2P1, arg1'=arg1P1, (-arg1+arg1P1 <= 0 /\ 1+arg2P1 > 0 /\ arg1 > 0 /\ arg1P1 > 0), cost: 1 New rule: f1_0_main_Load -> f570_0_main_NULL : arg2'=arg2P1, arg1'=arg1P1, (-arg1+arg1P1 <= 0 /\ 1+arg2P1 > 0 /\ arg1P1 > 0), cost: 1 Applied preprocessing Original rule: f570_0_main_NULL -> f570_0_main_NULL : arg2'=arg2P2, arg1'=arg1P2, (1-arg2+arg1P2 <= 0 /\ 1+arg2P2-arg1 <= 0 /\ arg1 > 0 /\ -arg1+arg1P2 <= 0 /\ -1+arg2 > 0 /\ arg1P2 > 0 /\ 2-arg2+arg2P2 <= 0 /\ 1+arg2P2 > 0), cost: 1 New rule: f570_0_main_NULL -> f570_0_main_NULL : arg2'=arg2P2, arg1'=arg1P2, (1-arg2+arg1P2 <= 0 /\ 1+arg2P2-arg1 <= 0 /\ -arg1+arg1P2 <= 0 /\ arg1P2 > 0 /\ 2-arg2+arg2P2 <= 0 /\ 1+arg2P2 > 0), cost: 1 Applied preprocessing Original rule: f570_0_main_NULL -> f570_0_main_NULL : arg2'=arg2P3, arg1'=arg1P3, (x190 > 0 /\ 1+arg2P3 > 0 /\ -arg1+arg1P3 <= 0 /\ -2+arg2 > 0 /\ x140 > 0 /\ arg1 > 0 /\ 2-arg2+arg1P3 <= 0 /\ arg1P3 > 0), cost: 1 New rule: f570_0_main_NULL -> f570_0_main_NULL : arg2'=arg2P3, arg1'=arg1P3, (1+arg2P3 > 0 /\ -arg1+arg1P3 <= 0 /\ 2-arg2+arg1P3 <= 0 /\ arg1P3 > 0), cost: 1 Applied preprocessing Original rule: f1_0_main_Load -> f507_0_createIntList_LE : arg2'=arg2P4, arg1'=arg1P4, (1-arg2P4 == 0 /\ 1+arg2 > 0 /\ arg1 > 0 /\ 1+arg1P4 > 0), cost: 1 New rule: f1_0_main_Load -> f507_0_createIntList_LE : arg2'=1, arg1'=arg1P4, (1+arg2 > 0 /\ arg1 > 0 /\ 1+arg1P4 > 0), cost: 1 Applied preprocessing Original rule: f507_0_createIntList_LE -> f507_0_createIntList_LE : arg2'=arg2P5, arg1'=arg1P5, (arg2 > 0 /\ arg1 > 0 /\ -1-arg1P5+arg1 == 0 /\ 1-arg2P5+arg2 == 0), cost: 1 New rule: f507_0_createIntList_LE -> f507_0_createIntList_LE : arg2'=1+arg2, arg1'=-1+arg1, (arg2 > 0 /\ arg1 > 0), cost: 1 Applied preprocessing Original rule: f570_0_main_NULL -> f726_0_reverse_NULL : arg2'=arg2P6, arg1'=arg1P6, (-2+arg2 > 0 /\ x290 > 0 /\ arg1 > 0 /\ 2-arg2+arg1P6 <= 0 /\ arg1P6 > 0 /\ x250 > 0), cost: 1 New rule: f570_0_main_NULL -> f726_0_reverse_NULL : arg2'=arg2P6, arg1'=arg1P6, (arg1 > 0 /\ 2-arg2+arg1P6 <= 0 /\ arg1P6 > 0), cost: 1 Applied preprocessing Original rule: f726_0_reverse_NULL -> f726_0_reverse_NULL : arg2'=arg2P7, arg1'=arg1P7, (1+arg1P7 > 0 /\ arg1 > 0 /\ 1+arg1P7-arg1 <= 0), cost: 1 New rule: f726_0_reverse_NULL -> f726_0_reverse_NULL : arg2'=arg2P7, arg1'=arg1P7, (1+arg1P7 > 0 /\ 1+arg1P7-arg1 <= 0), cost: 1 Simplified rules Start location: __init 10: f570_0_main_NULL -> f570_0_main_NULL : arg2'=arg2P2, arg1'=arg1P2, (1-arg2+arg1P2 <= 0 /\ 1+arg2P2-arg1 <= 0 /\ -arg1+arg1P2 <= 0 /\ arg1P2 > 0 /\ 2-arg2+arg2P2 <= 0 /\ 1+arg2P2 > 0), cost: 1 11: f570_0_main_NULL -> f570_0_main_NULL : arg2'=arg2P3, arg1'=arg1P3, (1+arg2P3 > 0 /\ -arg1+arg1P3 <= 0 /\ 2-arg2+arg1P3 <= 0 /\ arg1P3 > 0), cost: 1 14: f570_0_main_NULL -> f726_0_reverse_NULL : arg2'=arg2P6, arg1'=arg1P6, (arg1 > 0 /\ 2-arg2+arg1P6 <= 0 /\ arg1P6 > 0), cost: 1 9: f1_0_main_Load -> f570_0_main_NULL : arg2'=arg2P1, arg1'=arg1P1, (-arg1+arg1P1 <= 0 /\ 1+arg2P1 > 0 /\ arg1P1 > 0), cost: 1 12: f1_0_main_Load -> f507_0_createIntList_LE : arg2'=1, arg1'=arg1P4, (1+arg2 > 0 /\ arg1 > 0 /\ 1+arg1P4 > 0), cost: 1 13: f507_0_createIntList_LE -> f507_0_createIntList_LE : arg2'=1+arg2, arg1'=-1+arg1, (arg2 > 0 /\ arg1 > 0), cost: 1 15: f726_0_reverse_NULL -> f726_0_reverse_NULL : arg2'=arg2P7, arg1'=arg1P7, (1+arg1P7 > 0 /\ 1+arg1P7-arg1 <= 0), cost: 1 8: __init -> f1_0_main_Load : arg2'=arg2P8, arg1'=arg1P8, TRUE, cost: 1 Applied acceleration Original rule: f570_0_main_NULL -> f570_0_main_NULL : arg2'=arg2P3, arg1'=arg1P3, (1+arg2P3 > 0 /\ -arg1+arg1P3 <= 0 /\ 2-arg2+arg1P3 <= 0 /\ arg1P3 > 0), cost: 1 New rule: f570_0_main_NULL -> f570_0_main_NULL : arg2'=arg2P3, arg1'=arg1P3, (arg1-arg1P3 >= 0 /\ 1+arg2P3 > 0 /\ -2+arg2-arg1P3 >= 0 /\ arg1P3 > 0 /\ -1+n0 >= 0 /\ -2+arg2P3-arg1P3 >= 0), cost: n0 Sub-proof via acceration calculus written to file:///tmp/tmpnam_hNaFNh.txt Applied nonterm Original rule: f570_0_main_NULL -> f570_0_main_NULL : arg2'=arg2P3, arg1'=arg1P3, (1+arg2P3 > 0 /\ -arg1+arg1P3 <= 0 /\ 2-arg2+arg1P3 <= 0 /\ arg1P3 > 0), cost: 1 New rule: f570_0_main_NULL -> [6] : (arg1-arg1P3 >= 0 /\ arg2-arg2P3 <= 0 /\ 1+arg2P3 > 0 /\ -2+arg2-arg1P3 >= 0 /\ arg1P3 > 0), cost: NONTERM Sub-proof via acceration calculus written to file:///tmp/tmpnam_GgHIGD.txt Applied simplification Original rule: f570_0_main_NULL -> f570_0_main_NULL : arg2'=arg2P3, arg1'=arg1P3, (arg1-arg1P3 >= 0 /\ 1+arg2P3 > 0 /\ -2+arg2-arg1P3 >= 0 /\ arg1P3 > 0 /\ -1+n0 >= 0 /\ -2+arg2P3-arg1P3 >= 0), cost: n0 New rule: f570_0_main_NULL -> f570_0_main_NULL : arg2'=arg2P3, arg1'=arg1P3, (arg1-arg1P3 >= 0 /\ -2+arg2-arg1P3 >= 0 /\ arg1P3 > 0 /\ -1+n0 >= 0 /\ -2+arg2P3-arg1P3 >= 0), cost: n0 Applied simplification Original rule: f570_0_main_NULL -> [6] : (arg1-arg1P3 >= 0 /\ arg2-arg2P3 <= 0 /\ 1+arg2P3 > 0 /\ -2+arg2-arg1P3 >= 0 /\ arg1P3 > 0), cost: NONTERM New rule: f570_0_main_NULL -> [6] : (arg1-arg1P3 >= 0 /\ arg2-arg2P3 <= 0 /\ -2+arg2-arg1P3 >= 0 /\ arg1P3 > 0), cost: NONTERM Applied deletion Removed the following rules: 11 Applied acceleration Original rule: f507_0_createIntList_LE -> f507_0_createIntList_LE : arg2'=1+arg2, arg1'=-1+arg1, (arg2 > 0 /\ arg1 > 0), cost: 1 New rule: f507_0_createIntList_LE -> f507_0_createIntList_LE : arg2'=arg2+n5, arg1'=-n5+arg1, (arg2 > 0 /\ n5 >= 0 /\ 1-n5+arg1 > 0), cost: n5 Sub-proof via acceration calculus written to file:///tmp/tmpnam_bPcChe.txt Applied instantiation Original rule: f507_0_createIntList_LE -> f507_0_createIntList_LE : arg2'=arg2+n5, arg1'=-n5+arg1, (arg2 > 0 /\ n5 >= 0 /\ 1-n5+arg1 > 0), cost: n5 New rule: f507_0_createIntList_LE -> f507_0_createIntList_LE : arg2'=arg2+arg1, arg1'=0, (1 > 0 /\ arg2 > 0 /\ arg1 >= 0), cost: arg1 Applied simplification Original rule: f507_0_createIntList_LE -> f507_0_createIntList_LE : arg2'=arg2+arg1, arg1'=0, (1 > 0 /\ arg2 > 0 /\ arg1 >= 0), cost: arg1 New rule: f507_0_createIntList_LE -> f507_0_createIntList_LE : arg2'=arg2+arg1, arg1'=0, (arg2 > 0 /\ arg1 >= 0), cost: arg1 Applied deletion Removed the following rules: 13 Accelerated simple loops Start location: __init 10: f570_0_main_NULL -> f570_0_main_NULL : arg2'=arg2P2, arg1'=arg1P2, (1-arg2+arg1P2 <= 0 /\ 1+arg2P2-arg1 <= 0 /\ -arg1+arg1P2 <= 0 /\ arg1P2 > 0 /\ 2-arg2+arg2P2 <= 0 /\ 1+arg2P2 > 0), cost: 1 14: f570_0_main_NULL -> f726_0_reverse_NULL : arg2'=arg2P6, arg1'=arg1P6, (arg1 > 0 /\ 2-arg2+arg1P6 <= 0 /\ arg1P6 > 0), cost: 1 18: f570_0_main_NULL -> f570_0_main_NULL : arg2'=arg2P3, arg1'=arg1P3, (arg1-arg1P3 >= 0 /\ -2+arg2-arg1P3 >= 0 /\ arg1P3 > 0 /\ -1+n0 >= 0 /\ -2+arg2P3-arg1P3 >= 0), cost: n0 19: f570_0_main_NULL -> [6] : (arg1-arg1P3 >= 0 /\ arg2-arg2P3 <= 0 /\ -2+arg2-arg1P3 >= 0 /\ arg1P3 > 0), cost: NONTERM 9: f1_0_main_Load -> f570_0_main_NULL : arg2'=arg2P1, arg1'=arg1P1, (-arg1+arg1P1 <= 0 /\ 1+arg2P1 > 0 /\ arg1P1 > 0), cost: 1 12: f1_0_main_Load -> f507_0_createIntList_LE : arg2'=1, arg1'=arg1P4, (1+arg2 > 0 /\ arg1 > 0 /\ 1+arg1P4 > 0), cost: 1 21: f507_0_createIntList_LE -> f507_0_createIntList_LE : arg2'=arg2+arg1, arg1'=0, (arg2 > 0 /\ arg1 >= 0), cost: arg1 15: f726_0_reverse_NULL -> f726_0_reverse_NULL : arg2'=arg2P7, arg1'=arg1P7, (1+arg1P7 > 0 /\ 1+arg1P7-arg1 <= 0), cost: 1 8: __init -> f1_0_main_Load : arg2'=arg2P8, arg1'=arg1P8, TRUE, cost: 1 Applied chaining First rule: f1_0_main_Load -> f570_0_main_NULL : arg2'=arg2P1, arg1'=arg1P1, (-arg1+arg1P1 <= 0 /\ 1+arg2P1 > 0 /\ arg1P1 > 0), cost: 1 Second rule: f570_0_main_NULL -> f570_0_main_NULL : arg2'=arg2P2, arg1'=arg1P2, (1-arg2+arg1P2 <= 0 /\ 1+arg2P2-arg1 <= 0 /\ -arg1+arg1P2 <= 0 /\ arg1P2 > 0 /\ 2-arg2+arg2P2 <= 0 /\ 1+arg2P2 > 0), cost: 1 New rule: f1_0_main_Load -> f570_0_main_NULL : arg2'=arg2P2, arg1'=arg1P2, (1+arg2P2-arg1 <= 0 /\ -arg1+arg1P2 <= 0 /\ arg1P2 > 0 /\ 1+arg2P2 > 0), cost: 2 Applied chaining First rule: f1_0_main_Load -> f570_0_main_NULL : arg2'=arg2P1, arg1'=arg1P1, (-arg1+arg1P1 <= 0 /\ 1+arg2P1 > 0 /\ arg1P1 > 0), cost: 1 Second rule: f570_0_main_NULL -> f570_0_main_NULL : arg2'=arg2P3, arg1'=arg1P3, (arg1-arg1P3 >= 0 /\ -2+arg2-arg1P3 >= 0 /\ arg1P3 > 0 /\ -1+n0 >= 0 /\ -2+arg2P3-arg1P3 >= 0), cost: n0 New rule: f1_0_main_Load -> f570_0_main_NULL : arg2'=arg2P3, arg1'=arg1P3, (-arg1+arg1P3 <= 0 /\ arg1P3 > 0 /\ -1+n0 >= 0 /\ -2+arg2P3-arg1P3 >= 0), cost: 1+n0 Applied chaining First rule: f1_0_main_Load -> f570_0_main_NULL : arg2'=arg2P1, arg1'=arg1P1, (-arg1+arg1P1 <= 0 /\ 1+arg2P1 > 0 /\ arg1P1 > 0), cost: 1 Second rule: f570_0_main_NULL -> [6] : (arg1-arg1P3 >= 0 /\ arg2-arg2P3 <= 0 /\ -2+arg2-arg1P3 >= 0 /\ arg1P3 > 0), cost: NONTERM New rule: f1_0_main_Load -> [6] : -1+arg1 >= 0, cost: NONTERM Applied deletion Removed the following rules: 10 18 19 Applied chaining First rule: f1_0_main_Load -> f507_0_createIntList_LE : arg2'=1, arg1'=arg1P4, (1+arg2 > 0 /\ arg1 > 0 /\ 1+arg1P4 > 0), cost: 1 Second rule: f507_0_createIntList_LE -> f507_0_createIntList_LE : arg2'=arg2+arg1, arg1'=0, (arg2 > 0 /\ arg1 >= 0), cost: arg1 New rule: f1_0_main_Load -> f507_0_createIntList_LE : arg2'=1+arg1P4, arg1'=0, (1+arg2 > 0 /\ arg1 > 0 /\ arg1P4 >= 0), cost: 1+arg1P4 Applied deletion Removed the following rules: 21 Applied chaining First rule: f570_0_main_NULL -> f726_0_reverse_NULL : arg2'=arg2P6, arg1'=arg1P6, (arg1 > 0 /\ 2-arg2+arg1P6 <= 0 /\ arg1P6 > 0), cost: 1 Second rule: f726_0_reverse_NULL -> f726_0_reverse_NULL : arg2'=arg2P7, arg1'=arg1P7, (1+arg1P7 > 0 /\ 1+arg1P7-arg1 <= 0), cost: 1 New rule: f570_0_main_NULL -> f726_0_reverse_NULL : arg2'=arg2P7, arg1'=arg1P7, (1+arg1P7 > 0 /\ 3-arg2+arg1P7 <= 0 /\ arg1 > 0), cost: 2 Applied deletion Removed the following rules: 15 Chained accelerated rules with incoming rules Start location: __init 14: f570_0_main_NULL -> f726_0_reverse_NULL : arg2'=arg2P6, arg1'=arg1P6, (arg1 > 0 /\ 2-arg2+arg1P6 <= 0 /\ arg1P6 > 0), cost: 1 26: f570_0_main_NULL -> f726_0_reverse_NULL : arg2'=arg2P7, arg1'=arg1P7, (1+arg1P7 > 0 /\ 3-arg2+arg1P7 <= 0 /\ arg1 > 0), cost: 2 9: f1_0_main_Load -> f570_0_main_NULL : arg2'=arg2P1, arg1'=arg1P1, (-arg1+arg1P1 <= 0 /\ 1+arg2P1 > 0 /\ arg1P1 > 0), cost: 1 12: f1_0_main_Load -> f507_0_createIntList_LE : arg2'=1, arg1'=arg1P4, (1+arg2 > 0 /\ arg1 > 0 /\ 1+arg1P4 > 0), cost: 1 22: f1_0_main_Load -> f570_0_main_NULL : arg2'=arg2P2, arg1'=arg1P2, (1+arg2P2-arg1 <= 0 /\ -arg1+arg1P2 <= 0 /\ arg1P2 > 0 /\ 1+arg2P2 > 0), cost: 2 23: f1_0_main_Load -> f570_0_main_NULL : arg2'=arg2P3, arg1'=arg1P3, (-arg1+arg1P3 <= 0 /\ arg1P3 > 0 /\ -1+n0 >= 0 /\ -2+arg2P3-arg1P3 >= 0), cost: 1+n0 24: f1_0_main_Load -> [6] : -1+arg1 >= 0, cost: NONTERM 25: f1_0_main_Load -> f507_0_createIntList_LE : arg2'=1+arg1P4, arg1'=0, (1+arg2 > 0 /\ arg1 > 0 /\ arg1P4 >= 0), cost: 1+arg1P4 8: __init -> f1_0_main_Load : arg2'=arg2P8, arg1'=arg1P8, TRUE, cost: 1 Removed unreachable locations and irrelevant leafs Start location: __init 24: f1_0_main_Load -> [6] : -1+arg1 >= 0, cost: NONTERM 8: __init -> f1_0_main_Load : arg2'=arg2P8, arg1'=arg1P8, TRUE, cost: 1 Eliminating location f1_0_main_Load by chaining: Applied chaining First rule: __init -> f1_0_main_Load : arg2'=arg2P8, arg1'=arg1P8, TRUE, cost: 1 Second rule: f1_0_main_Load -> [6] : -1+arg1 >= 0, cost: NONTERM New rule: __init -> [6] : -1+arg1P8 >= 0, cost: NONTERM Applied deletion Removed the following rules: 8 24 Eliminated locations on linear paths Start location: __init 27: __init -> [6] : -1+arg1P8 >= 0, cost: NONTERM Computing asymptotic complexity Proved nontermination of rule 27 via SMT. Proved the following lower bound Complexity: Nonterm Cpx degree: Nonterm Solved cost: NONTERM Rule cost: NONTERM Rule guard: -1+arg1P8 >= 0