NO proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be disproven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof [EQUIVALENT, 868 ms] (4) AND (5) IRSwT (6) IntTRSCompressionProof [EQUIVALENT, 8 ms] (7) IRSwT (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (9) IRSwT (10) FilterProof [EQUIVALENT, 0 ms] (11) IntTRS (12) IntTRSCompressionProof [EQUIVALENT, 0 ms] (13) IntTRS (14) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (15) YES (16) IRSwT (17) IntTRSCompressionProof [EQUIVALENT, 8 ms] (18) IRSwT (19) IRSwTChainingProof [EQUIVALENT, 0 ms] (20) IRSwT (21) IRSwTTerminationDigraphProof [EQUIVALENT, 73 ms] (22) IRSwT (23) IntTRSCompressionProof [EQUIVALENT, 9 ms] (24) IRSwT (25) TempFilterProof [SOUND, 5318 ms] (26) IRSwT (27) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] (28) IRSwT (29) IntTRSCompressionProof [EQUIVALENT, 0 ms] (30) IRSwT (31) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (32) IRSwT (33) IRSwT (34) IntTRSCompressionProof [EQUIVALENT, 4 ms] (35) IRSwT (36) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (37) IRSwT (38) TempFilterProof [SOUND, 15 ms] (39) IntTRS (40) RankingReductionPairProof [EQUIVALENT, 4 ms] (41) YES (42) IRSwT (43) IntTRSCompressionProof [EQUIVALENT, 1 ms] (44) IRSwT (45) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (46) IRSwT (47) FilterProof [EQUIVALENT, 0 ms] (48) IntTRS (49) IntTRSCompressionProof [EQUIVALENT, 0 ms] (50) IntTRS (51) IntTRSPeriodicNontermProof [COMPLETE, 4 ms] (52) NO ---------------------------------------- (0) Obligation: Rules: f1_0_main_New(arg1, arg2, arg3, arg4, arg5, arg6) -> f216_0_main_GE(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P) :|: arg2 = arg6P && 0 = arg5P && arg2 + 1 = arg4P && 0 = arg3P && 1 <= arg2P - 1 && 0 <= arg1P - 1 && 0 <= arg1 - 1 && arg2P - 1 <= arg1 && -1 <= arg2 - 1 && arg1P <= arg1 f216_0_main_GE(x, x1, x2, x3, x4, x5) -> f216_0_main_GE(x6, x7, x8, x9, x10, x11) :|: x5 = x11 && x5 + 1 = x9 && x2 + 1 = x8 && 0 <= x7 - 1 && 0 <= x6 - 1 && 0 <= x1 - 1 && 0 <= x - 1 && x6 <= x1 && x6 <= x && x4 <= x10 - 1 && -1 <= x5 - 1 && 0 <= x4 - 1 && x2 <= x3 - 1 f216_0_main_GE(x12, x13, x14, x15, x16, x17) -> f216_0_main_GE(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && 1 = x22 && x17 + 1 = x21 && x14 + 1 = x20 && 3 <= x19 - 1 && 0 <= x18 - 1 && 1 <= x13 - 1 && 0 <= x12 - 1 && x19 - 2 <= x13 && x19 - 3 <= x12 && x18 + 1 <= x13 && x18 <= x12 && x14 <= x15 - 1 && -1 <= x17 - 1 f339_0_length_Load(x24, x25, x26, x27, x28, x29) -> f339_0_length_Load(x30, x31, x32, x33, x34, x35) :|: x26 = x32 && x25 + 1 = x31 && 0 <= x30 - 1 && 0 <= x24 - 1 && x30 <= x24 f216_0_main_GE(x36, x37, x38, x39, x40, x41) -> f339_0_length_Load(x42, x43, x44, x45, x46, x47) :|: x41 = x44 && 1 = x43 && 0 <= x42 - 1 && 1 <= x37 - 1 && 0 <= x36 - 1 && x42 + 1 <= x37 && x39 <= x38 && x42 <= x36 f216_0_main_GE(x48, x49, x50, x51, x52, x53) -> f340_0_length_FieldAccess(x55, x56, x57, x58, x59, x60) :|: x52 = x60 && 0 = x59 && 0 = x58 && 0 = x57 && x52 = x56 && 0 <= x55 - 1 && 0 <= x49 - 1 && 0 <= x48 - 1 && x51 <= x50 && 0 <= x52 - 1 f340_0_length_FieldAccess(x61, x62, x63, x64, x65, x66) -> f340_0_length_FieldAccess(x67, x68, x69, x70, x71, x72) :|: x63 = x69 && x62 = x68 && 0 <= x67 - 1 && 2 <= x61 - 1 && x65 <= x62 - 1 && x70 <= x64 - 1 && 0 <= x63 - 1 && x65 <= x63 - 1 && x65 <= x71 - 1 && 0 <= x64 - 1 && 0 <= x65 - 1 f340_0_length_FieldAccess(x73, x74, x75, x76, x77, x78) -> f340_0_length_FieldAccess(x79, x80, x81, x82, x83, x84) :|: x84 <= x74 - 1 && -1 <= x74 - 1 && -1 <= x75 - 1 && x82 <= x75 - 1 && 2 <= x73 - 1 && 0 <= x79 - 1 && x85 + 3 <= x73 && x74 = x78 && 0 = x81 && 1 = x83 __init(x86, x87, x88, x89, x90, x91) -> f1_0_main_New(x92, x93, x94, x95, x96, x97) :|: 0 <= 0 Start term: __init(arg1, arg2, arg3, arg4, arg5, arg6) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: f1_0_main_New(arg1, arg2, arg3, arg4, arg5, arg6) -> f216_0_main_GE(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P) :|: arg2 = arg6P && 0 = arg5P && arg2 + 1 = arg4P && 0 = arg3P && 1 <= arg2P - 1 && 0 <= arg1P - 1 && 0 <= arg1 - 1 && arg2P - 1 <= arg1 && -1 <= arg2 - 1 && arg1P <= arg1 f216_0_main_GE(x, x1, x2, x3, x4, x5) -> f216_0_main_GE(x6, x7, x8, x9, x10, x11) :|: x5 = x11 && x5 + 1 = x9 && x2 + 1 = x8 && 0 <= x7 - 1 && 0 <= x6 - 1 && 0 <= x1 - 1 && 0 <= x - 1 && x6 <= x1 && x6 <= x && x4 <= x10 - 1 && -1 <= x5 - 1 && 0 <= x4 - 1 && x2 <= x3 - 1 f216_0_main_GE(x12, x13, x14, x15, x16, x17) -> f216_0_main_GE(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && 1 = x22 && x17 + 1 = x21 && x14 + 1 = x20 && 3 <= x19 - 1 && 0 <= x18 - 1 && 1 <= x13 - 1 && 0 <= x12 - 1 && x19 - 2 <= x13 && x19 - 3 <= x12 && x18 + 1 <= x13 && x18 <= x12 && x14 <= x15 - 1 && -1 <= x17 - 1 f339_0_length_Load(x24, x25, x26, x27, x28, x29) -> f339_0_length_Load(x30, x31, x32, x33, x34, x35) :|: x26 = x32 && x25 + 1 = x31 && 0 <= x30 - 1 && 0 <= x24 - 1 && x30 <= x24 f216_0_main_GE(x36, x37, x38, x39, x40, x41) -> f339_0_length_Load(x42, x43, x44, x45, x46, x47) :|: x41 = x44 && 1 = x43 && 0 <= x42 - 1 && 1 <= x37 - 1 && 0 <= x36 - 1 && x42 + 1 <= x37 && x39 <= x38 && x42 <= x36 f216_0_main_GE(x48, x49, x50, x51, x52, x53) -> f340_0_length_FieldAccess(x55, x56, x57, x58, x59, x60) :|: x52 = x60 && 0 = x59 && 0 = x58 && 0 = x57 && x52 = x56 && 0 <= x55 - 1 && 0 <= x49 - 1 && 0 <= x48 - 1 && x51 <= x50 && 0 <= x52 - 1 f340_0_length_FieldAccess(x61, x62, x63, x64, x65, x66) -> f340_0_length_FieldAccess(x67, x68, x69, x70, x71, x72) :|: x63 = x69 && x62 = x68 && 0 <= x67 - 1 && 2 <= x61 - 1 && x65 <= x62 - 1 && x70 <= x64 - 1 && 0 <= x63 - 1 && x65 <= x63 - 1 && x65 <= x71 - 1 && 0 <= x64 - 1 && 0 <= x65 - 1 f340_0_length_FieldAccess(x73, x74, x75, x76, x77, x78) -> f340_0_length_FieldAccess(x79, x80, x81, x82, x83, x84) :|: x84 <= x74 - 1 && -1 <= x74 - 1 && -1 <= x75 - 1 && x82 <= x75 - 1 && 2 <= x73 - 1 && 0 <= x79 - 1 && x85 + 3 <= x73 && x74 = x78 && 0 = x81 && 1 = x83 __init(x86, x87, x88, x89, x90, x91) -> f1_0_main_New(x92, x93, x94, x95, x96, x97) :|: 0 <= 0 Start term: __init(arg1, arg2, arg3, arg4, arg5, arg6) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f1_0_main_New(arg1, arg2, arg3, arg4, arg5, arg6) -> f216_0_main_GE(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P) :|: arg2 = arg6P && 0 = arg5P && arg2 + 1 = arg4P && 0 = arg3P && 1 <= arg2P - 1 && 0 <= arg1P - 1 && 0 <= arg1 - 1 && arg2P - 1 <= arg1 && -1 <= arg2 - 1 && arg1P <= arg1 (2) f216_0_main_GE(x, x1, x2, x3, x4, x5) -> f216_0_main_GE(x6, x7, x8, x9, x10, x11) :|: x5 = x11 && x5 + 1 = x9 && x2 + 1 = x8 && 0 <= x7 - 1 && 0 <= x6 - 1 && 0 <= x1 - 1 && 0 <= x - 1 && x6 <= x1 && x6 <= x && x4 <= x10 - 1 && -1 <= x5 - 1 && 0 <= x4 - 1 && x2 <= x3 - 1 (3) f216_0_main_GE(x12, x13, x14, x15, x16, x17) -> f216_0_main_GE(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && 1 = x22 && x17 + 1 = x21 && x14 + 1 = x20 && 3 <= x19 - 1 && 0 <= x18 - 1 && 1 <= x13 - 1 && 0 <= x12 - 1 && x19 - 2 <= x13 && x19 - 3 <= x12 && x18 + 1 <= x13 && x18 <= x12 && x14 <= x15 - 1 && -1 <= x17 - 1 (4) f339_0_length_Load(x24, x25, x26, x27, x28, x29) -> f339_0_length_Load(x30, x31, x32, x33, x34, x35) :|: x26 = x32 && x25 + 1 = x31 && 0 <= x30 - 1 && 0 <= x24 - 1 && x30 <= x24 (5) f216_0_main_GE(x36, x37, x38, x39, x40, x41) -> f339_0_length_Load(x42, x43, x44, x45, x46, x47) :|: x41 = x44 && 1 = x43 && 0 <= x42 - 1 && 1 <= x37 - 1 && 0 <= x36 - 1 && x42 + 1 <= x37 && x39 <= x38 && x42 <= x36 (6) f216_0_main_GE(x48, x49, x50, x51, x52, x53) -> f340_0_length_FieldAccess(x55, x56, x57, x58, x59, x60) :|: x52 = x60 && 0 = x59 && 0 = x58 && 0 = x57 && x52 = x56 && 0 <= x55 - 1 && 0 <= x49 - 1 && 0 <= x48 - 1 && x51 <= x50 && 0 <= x52 - 1 (7) f340_0_length_FieldAccess(x61, x62, x63, x64, x65, x66) -> f340_0_length_FieldAccess(x67, x68, x69, x70, x71, x72) :|: x63 = x69 && x62 = x68 && 0 <= x67 - 1 && 2 <= x61 - 1 && x65 <= x62 - 1 && x70 <= x64 - 1 && 0 <= x63 - 1 && x65 <= x63 - 1 && x65 <= x71 - 1 && 0 <= x64 - 1 && 0 <= x65 - 1 (8) f340_0_length_FieldAccess(x73, x74, x75, x76, x77, x78) -> f340_0_length_FieldAccess(x79, x80, x81, x82, x83, x84) :|: x84 <= x74 - 1 && -1 <= x74 - 1 && -1 <= x75 - 1 && x82 <= x75 - 1 && 2 <= x73 - 1 && 0 <= x79 - 1 && x85 + 3 <= x73 && x74 = x78 && 0 = x81 && 1 = x83 (9) __init(x86, x87, x88, x89, x90, x91) -> f1_0_main_New(x92, x93, x94, x95, x96, x97) :|: 0 <= 0 Arcs: (1) -> (3) (2) -> (2), (3), (5), (6) (3) -> (2), (3), (5), (6) (4) -> (4) (5) -> (4) (6) -> (8) (7) -> (7), (8) (8) -> (8) (9) -> (1) This digraph is fully evaluated! ---------------------------------------- (4) Complex Obligation (AND) ---------------------------------------- (5) Obligation: Termination digraph: Nodes: (1) f340_0_length_FieldAccess(x61, x62, x63, x64, x65, x66) -> f340_0_length_FieldAccess(x67, x68, x69, x70, x71, x72) :|: x63 = x69 && x62 = x68 && 0 <= x67 - 1 && 2 <= x61 - 1 && x65 <= x62 - 1 && x70 <= x64 - 1 && 0 <= x63 - 1 && x65 <= x63 - 1 && x65 <= x71 - 1 && 0 <= x64 - 1 && 0 <= x65 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (6) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (7) Obligation: Rules: f340_0_length_FieldAccess(x61:0, x62:0, x63:0, x64:0, x65:0, x66:0) -> f340_0_length_FieldAccess(x67:0, x62:0, x63:0, x70:0, x71:0, x72:0) :|: x64:0 > 0 && x65:0 > 0 && x71:0 - 1 >= x65:0 && x65:0 <= x63:0 - 1 && x63:0 > 0 && x70:0 <= x64:0 - 1 && x65:0 <= x62:0 - 1 && x67:0 > 0 && x61:0 > 2 ---------------------------------------- (8) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f340_0_length_FieldAccess(x1, x2, x3, x4, x5, x6) -> f340_0_length_FieldAccess(x1, x2, x3, x4, x5) ---------------------------------------- (9) Obligation: Rules: f340_0_length_FieldAccess(x61:0, x62:0, x63:0, x64:0, x65:0) -> f340_0_length_FieldAccess(x67:0, x62:0, x63:0, x70:0, x71:0) :|: x64:0 > 0 && x65:0 > 0 && x71:0 - 1 >= x65:0 && x65:0 <= x63:0 - 1 && x63:0 > 0 && x70:0 <= x64:0 - 1 && x65:0 <= x62:0 - 1 && x67:0 > 0 && x61:0 > 2 ---------------------------------------- (10) FilterProof (EQUIVALENT) Used the following sort dictionary for filtering: f340_0_length_FieldAccess(INTEGER, INTEGER, INTEGER, INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (11) Obligation: Rules: f340_0_length_FieldAccess(x61:0, x62:0, x63:0, x64:0, x65:0) -> f340_0_length_FieldAccess(x67:0, x62:0, x63:0, x70:0, x71:0) :|: x64:0 > 0 && x65:0 > 0 && x71:0 - 1 >= x65:0 && x65:0 <= x63:0 - 1 && x63:0 > 0 && x70:0 <= x64:0 - 1 && x65:0 <= x62:0 - 1 && x67:0 > 0 && x61:0 > 2 ---------------------------------------- (12) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (13) Obligation: Rules: f340_0_length_FieldAccess(x61:0:0, x62:0:0, x63:0:0, x64:0:0, x65:0:0) -> f340_0_length_FieldAccess(x67:0:0, x62:0:0, x63:0:0, x70:0:0, x71:0:0) :|: x67:0:0 > 0 && x61:0:0 > 2 && x65:0:0 <= x62:0:0 - 1 && x70:0:0 <= x64:0:0 - 1 && x63:0:0 > 0 && x65:0:0 <= x63:0:0 - 1 && x71:0:0 - 1 >= x65:0:0 && x65:0:0 > 0 && x64:0:0 > 0 ---------------------------------------- (14) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f340_0_length_FieldAccess(x, x1, x2, x3, x4)] = x3 The following rules are decreasing: f340_0_length_FieldAccess(x61:0:0, x62:0:0, x63:0:0, x64:0:0, x65:0:0) -> f340_0_length_FieldAccess(x67:0:0, x62:0:0, x63:0:0, x70:0:0, x71:0:0) :|: x67:0:0 > 0 && x61:0:0 > 2 && x65:0:0 <= x62:0:0 - 1 && x70:0:0 <= x64:0:0 - 1 && x63:0:0 > 0 && x65:0:0 <= x63:0:0 - 1 && x71:0:0 - 1 >= x65:0:0 && x65:0:0 > 0 && x64:0:0 > 0 The following rules are bounded: f340_0_length_FieldAccess(x61:0:0, x62:0:0, x63:0:0, x64:0:0, x65:0:0) -> f340_0_length_FieldAccess(x67:0:0, x62:0:0, x63:0:0, x70:0:0, x71:0:0) :|: x67:0:0 > 0 && x61:0:0 > 2 && x65:0:0 <= x62:0:0 - 1 && x70:0:0 <= x64:0:0 - 1 && x63:0:0 > 0 && x65:0:0 <= x63:0:0 - 1 && x71:0:0 - 1 >= x65:0:0 && x65:0:0 > 0 && x64:0:0 > 0 ---------------------------------------- (15) YES ---------------------------------------- (16) Obligation: Termination digraph: Nodes: (1) f216_0_main_GE(x12, x13, x14, x15, x16, x17) -> f216_0_main_GE(x18, x19, x20, x21, x22, x23) :|: x17 = x23 && 1 = x22 && x17 + 1 = x21 && x14 + 1 = x20 && 3 <= x19 - 1 && 0 <= x18 - 1 && 1 <= x13 - 1 && 0 <= x12 - 1 && x19 - 2 <= x13 && x19 - 3 <= x12 && x18 + 1 <= x13 && x18 <= x12 && x14 <= x15 - 1 && -1 <= x17 - 1 (2) f216_0_main_GE(x, x1, x2, x3, x4, x5) -> f216_0_main_GE(x6, x7, x8, x9, x10, x11) :|: x5 = x11 && x5 + 1 = x9 && x2 + 1 = x8 && 0 <= x7 - 1 && 0 <= x6 - 1 && 0 <= x1 - 1 && 0 <= x - 1 && x6 <= x1 && x6 <= x && x4 <= x10 - 1 && -1 <= x5 - 1 && 0 <= x4 - 1 && x2 <= x3 - 1 Arcs: (1) -> (1), (2) (2) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (17) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (18) Obligation: Rules: f216_0_main_GE(x:0, x1:0, x2:0, x3:0, x4:0, x11:0) -> f216_0_main_GE(x6:0, x7:0, x2:0 + 1, x11:0 + 1, x10:0, x11:0) :|: x4:0 > 0 && x3:0 - 1 >= x2:0 && x11:0 > -1 && x4:0 <= x10:0 - 1 && x:0 >= x6:0 && x6:0 <= x1:0 && x:0 > 0 && x1:0 > 0 && x7:0 > 0 && x6:0 > 0 f216_0_main_GE(x12:0, x13:0, x14:0, x15:0, x16:0, x17:0) -> f216_0_main_GE(x18:0, x19:0, x14:0 + 1, x17:0 + 1, 1, x17:0) :|: x15:0 - 1 >= x14:0 && x17:0 > -1 && x18:0 <= x12:0 && x18:0 + 1 <= x13:0 && x19:0 - 3 <= x12:0 && x19:0 - 2 <= x13:0 && x12:0 > 0 && x13:0 > 1 && x19:0 > 3 && x18:0 > 0 ---------------------------------------- (19) IRSwTChainingProof (EQUIVALENT) Chaining! ---------------------------------------- (20) Obligation: Rules: f216_0_main_GE(x, x1, x2, x3, x4, x5) -> f216_0_main_GE(x15, x16, x2 + 2, x5 + 1, x17, x5) :|: TRUE && x4 >= 1 && x3 + -1 * x2 >= 1 && x5 >= 0 && x4 + -1 * x8 <= -1 && x + -1 * x6 >= 0 && x6 + -1 * x1 <= 0 && x >= 1 && x1 >= 1 && x7 >= 1 && x6 >= 1 && x8 >= 1 && x5 + -1 * x2 >= 1 && x8 + -1 * x17 <= -1 && x6 + -1 * x15 >= 0 && x15 + -1 * x7 <= 0 && x16 >= 1 && x15 >= 1 f216_0_main_GE(x12:0, x13:0, x14:0, x15:0, x16:0, x17:0) -> f216_0_main_GE(x18:0, x19:0, x14:0 + 1, x17:0 + 1, 1, x17:0) :|: x15:0 - 1 >= x14:0 && x17:0 > -1 && x18:0 <= x12:0 && x18:0 + 1 <= x13:0 && x19:0 - 3 <= x12:0 && x19:0 - 2 <= x13:0 && x12:0 > 0 && x13:0 > 1 && x19:0 > 3 && x18:0 > 0 f216_0_main_GE(x18, x19, x20, x21, x22, x23) -> f216_0_main_GE(x33, x34, x20 + 2, x23 + 1, 1, x23) :|: TRUE && x22 >= 1 && x21 + -1 * x20 >= 1 && x23 >= 0 && x22 + -1 * x26 <= -1 && x18 + -1 * x24 >= 0 && x24 + -1 * x19 <= 0 && x18 >= 1 && x19 >= 1 && x24 >= 1 && x23 + -1 * x20 >= 1 && x33 + -1 * x24 <= 0 && x33 + -1 * x25 <= -1 && x34 + -1 * x24 <= 3 && x34 + -1 * x25 <= 2 && x25 >= 2 && x34 >= 4 && x33 >= 1 ---------------------------------------- (21) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f216_0_main_GE(x, x1, x2, x3, x4, x5) -> f216_0_main_GE(x15, x16, x2 + 2, x5 + 1, x17, x5) :|: TRUE && x4 >= 1 && x3 + -1 * x2 >= 1 && x5 >= 0 && x4 + -1 * x8 <= -1 && x + -1 * x6 >= 0 && x6 + -1 * x1 <= 0 && x >= 1 && x1 >= 1 && x7 >= 1 && x6 >= 1 && x8 >= 1 && x5 + -1 * x2 >= 1 && x8 + -1 * x17 <= -1 && x6 + -1 * x15 >= 0 && x15 + -1 * x7 <= 0 && x16 >= 1 && x15 >= 1 (2) f216_0_main_GE(x12:0, x13:0, x14:0, x15:0, x16:0, x17:0) -> f216_0_main_GE(x18:0, x19:0, x14:0 + 1, x17:0 + 1, 1, x17:0) :|: x15:0 - 1 >= x14:0 && x17:0 > -1 && x18:0 <= x12:0 && x18:0 + 1 <= x13:0 && x19:0 - 3 <= x12:0 && x19:0 - 2 <= x13:0 && x12:0 > 0 && x13:0 > 1 && x19:0 > 3 && x18:0 > 0 (3) f216_0_main_GE(x18, x19, x20, x21, x22, x23) -> f216_0_main_GE(x33, x34, x20 + 2, x23 + 1, 1, x23) :|: TRUE && x22 >= 1 && x21 + -1 * x20 >= 1 && x23 >= 0 && x22 + -1 * x26 <= -1 && x18 + -1 * x24 >= 0 && x24 + -1 * x19 <= 0 && x18 >= 1 && x19 >= 1 && x24 >= 1 && x23 + -1 * x20 >= 1 && x33 + -1 * x24 <= 0 && x33 + -1 * x25 <= -1 && x34 + -1 * x24 <= 3 && x34 + -1 * x25 <= 2 && x25 >= 2 && x34 >= 4 && x33 >= 1 Arcs: (1) -> (1), (2), (3) (2) -> (1), (2), (3) (3) -> (1), (2), (3) This digraph is fully evaluated! ---------------------------------------- (22) Obligation: Termination digraph: Nodes: (1) f216_0_main_GE(x, x1, x2, x3, x4, x5) -> f216_0_main_GE(x15, x16, x2 + 2, x5 + 1, x17, x5) :|: TRUE && x4 >= 1 && x3 + -1 * x2 >= 1 && x5 >= 0 && x4 + -1 * x8 <= -1 && x + -1 * x6 >= 0 && x6 + -1 * x1 <= 0 && x >= 1 && x1 >= 1 && x7 >= 1 && x6 >= 1 && x8 >= 1 && x5 + -1 * x2 >= 1 && x8 + -1 * x17 <= -1 && x6 + -1 * x15 >= 0 && x15 + -1 * x7 <= 0 && x16 >= 1 && x15 >= 1 (2) f216_0_main_GE(x12:0, x13:0, x14:0, x15:0, x16:0, x17:0) -> f216_0_main_GE(x18:0, x19:0, x14:0 + 1, x17:0 + 1, 1, x17:0) :|: x15:0 - 1 >= x14:0 && x17:0 > -1 && x18:0 <= x12:0 && x18:0 + 1 <= x13:0 && x19:0 - 3 <= x12:0 && x19:0 - 2 <= x13:0 && x12:0 > 0 && x13:0 > 1 && x19:0 > 3 && x18:0 > 0 (3) f216_0_main_GE(x18, x19, x20, x21, x22, x23) -> f216_0_main_GE(x33, x34, x20 + 2, x23 + 1, 1, x23) :|: TRUE && x22 >= 1 && x21 + -1 * x20 >= 1 && x23 >= 0 && x22 + -1 * x26 <= -1 && x18 + -1 * x24 >= 0 && x24 + -1 * x19 <= 0 && x18 >= 1 && x19 >= 1 && x24 >= 1 && x23 + -1 * x20 >= 1 && x33 + -1 * x24 <= 0 && x33 + -1 * x25 <= -1 && x34 + -1 * x24 <= 3 && x34 + -1 * x25 <= 2 && x25 >= 2 && x34 >= 4 && x33 >= 1 Arcs: (1) -> (1), (2), (3) (2) -> (1), (2), (3) (3) -> (1), (2), (3) This digraph is fully evaluated! ---------------------------------------- (23) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (24) Obligation: Rules: f216_0_main_GE(x18:0, x19:0, x20:0, x21:0, x22:0, x23:0) -> f216_0_main_GE(x33:0, x34:0, x20:0 + 2, x23:0 + 1, 1, x23:0) :|: x34:0 > 3 && x33:0 > 0 && x25:0 > 1 && x34:0 + -1 * x25:0 <= 2 && x34:0 + -1 * x24:0 <= 3 && x33:0 + -1 * x25:0 <= -1 && x33:0 + -1 * x24:0 <= 0 && x23:0 + -1 * x20:0 >= 1 && x24:0 > 0 && x19:0 > 0 && x18:0 > 0 && x24:0 + -1 * x19:0 <= 0 && x18:0 + -1 * x24:0 >= 0 && x22:0 + -1 * x26:0 <= -1 && x23:0 > -1 && x22:0 > 0 && x21:0 + -1 * x20:0 >= 1 f216_0_main_GE(x:0, x1:0, x2:0, x3:0, x4:0, x5:0) -> f216_0_main_GE(x15:0, x16:0, x2:0 + 2, x5:0 + 1, x17:0, x5:0) :|: x16:0 > 0 && x15:0 > 0 && x15:0 + -1 * x7:0 <= 0 && x6:0 + -1 * x15:0 >= 0 && x8:0 + -1 * x17:0 <= -1 && x5:0 + -1 * x2:0 >= 1 && x8:0 > 0 && x6:0 > 0 && x7:0 > 0 && x1:0 > 0 && x:0 > 0 && x6:0 + -1 * x1:0 <= 0 && x:0 + -1 * x6:0 >= 0 && x4:0 + -1 * x8:0 <= -1 && x5:0 > -1 && x4:0 > 0 && x3:0 + -1 * x2:0 >= 1 f216_0_main_GE(x12:0:0, x13:0:0, x14:0:0, x15:0:0, x16:0:0, x17:0:0) -> f216_0_main_GE(x18:0:0, x19:0:0, x14:0:0 + 1, x17:0:0 + 1, 1, x17:0:0) :|: x19:0:0 > 3 && x18:0:0 > 0 && x13:0:0 > 1 && x12:0:0 > 0 && x19:0:0 - 2 <= x13:0:0 && x19:0:0 - 3 <= x12:0:0 && x18:0:0 + 1 <= x13:0:0 && x18:0:0 <= x12:0:0 && x17:0:0 > -1 && x15:0:0 - 1 >= x14:0:0 ---------------------------------------- (25) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f216_0_main_GE(INTEGER, INTEGER, INTEGER, INTEGER, VARIABLE, INTEGER) Replaced non-predefined constructor symbols by 0.The following proof was generated: # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IntTRS could not be shown: - IntTRS - PolynomialOrderProcessor Rules: f216_0_main_GE(x18:0, x19:0, x20:0, x21:0, x22:0, x23:0) -> f216_0_main_GE(x33:0, x34:0, c, c1, c2, x23:0) :|: c2 = 1 && (c1 = x23:0 + 1 && c = x20:0 + 2) && (x34:0 > 3 && x33:0 > 0 && x25:0 > 1 && x34:0 + -1 * x25:0 <= 2 && x34:0 + -1 * x24:0 <= 3 && x33:0 + -1 * x25:0 <= -1 && x33:0 + -1 * x24:0 <= 0 && x23:0 + -1 * x20:0 >= 1 && x24:0 > 0 && x19:0 > 0 && x18:0 > 0 && x24:0 + -1 * x19:0 <= 0 && x18:0 + -1 * x24:0 >= 0 && x22:0 + -1 * x26:0 <= -1 && x23:0 > -1 && x22:0 > 0 && x21:0 + -1 * x20:0 >= 1) f216_0_main_GE(x:0, x1:0, x2:0, x3:0, x4:0, x5:0) -> f216_0_main_GE(x15:0, x16:0, c3, c4, x17:0, x5:0) :|: c4 = x5:0 + 1 && c3 = x2:0 + 2 && (x16:0 > 0 && x15:0 > 0 && x15:0 + -1 * x7:0 <= 0 && x6:0 + -1 * x15:0 >= 0 && x8:0 + -1 * x17:0 <= -1 && x5:0 + -1 * x2:0 >= 1 && x8:0 > 0 && x6:0 > 0 && x7:0 > 0 && x1:0 > 0 && x:0 > 0 && x6:0 + -1 * x1:0 <= 0 && x:0 + -1 * x6:0 >= 0 && x4:0 + -1 * x8:0 <= -1 && x5:0 > -1 && x4:0 > 0 && x3:0 + -1 * x2:0 >= 1) f216_0_main_GE(x12:0:0, x13:0:0, x14:0:0, x15:0:0, x16:0:0, x17:0:0) -> f216_0_main_GE(x18:0:0, x19:0:0, c5, c6, c7, x17:0:0) :|: c7 = 1 && (c6 = x17:0:0 + 1 && c5 = x14:0:0 + 1) && (x19:0:0 > 3 && x18:0:0 > 0 && x13:0:0 > 1 && x12:0:0 > 0 && x19:0:0 - 2 <= x13:0:0 && x19:0:0 - 3 <= x12:0:0 && x18:0:0 + 1 <= x13:0:0 && x18:0:0 <= x12:0:0 && x17:0:0 > -1 && x15:0:0 - 1 >= x14:0:0) Found the following polynomial interpretation: [f216_0_main_GE(x, x1, x2, x3, x4, x5)] = -1 - x2 + x5 The following rules are decreasing: f216_0_main_GE(x18:0, x19:0, x20:0, x21:0, x22:0, x23:0) -> f216_0_main_GE(x33:0, x34:0, c, c1, c2, x23:0) :|: c2 = 1 && (c1 = x23:0 + 1 && c = x20:0 + 2) && (x34:0 > 3 && x33:0 > 0 && x25:0 > 1 && x34:0 + -1 * x25:0 <= 2 && x34:0 + -1 * x24:0 <= 3 && x33:0 + -1 * x25:0 <= -1 && x33:0 + -1 * x24:0 <= 0 && x23:0 + -1 * x20:0 >= 1 && x24:0 > 0 && x19:0 > 0 && x18:0 > 0 && x24:0 + -1 * x19:0 <= 0 && x18:0 + -1 * x24:0 >= 0 && x22:0 + -1 * x26:0 <= -1 && x23:0 > -1 && x22:0 > 0 && x21:0 + -1 * x20:0 >= 1) f216_0_main_GE(x:0, x1:0, x2:0, x3:0, x4:0, x5:0) -> f216_0_main_GE(x15:0, x16:0, c3, c4, x17:0, x5:0) :|: c4 = x5:0 + 1 && c3 = x2:0 + 2 && (x16:0 > 0 && x15:0 > 0 && x15:0 + -1 * x7:0 <= 0 && x6:0 + -1 * x15:0 >= 0 && x8:0 + -1 * x17:0 <= -1 && x5:0 + -1 * x2:0 >= 1 && x8:0 > 0 && x6:0 > 0 && x7:0 > 0 && x1:0 > 0 && x:0 > 0 && x6:0 + -1 * x1:0 <= 0 && x:0 + -1 * x6:0 >= 0 && x4:0 + -1 * x8:0 <= -1 && x5:0 > -1 && x4:0 > 0 && x3:0 + -1 * x2:0 >= 1) f216_0_main_GE(x12:0:0, x13:0:0, x14:0:0, x15:0:0, x16:0:0, x17:0:0) -> f216_0_main_GE(x18:0:0, x19:0:0, c5, c6, c7, x17:0:0) :|: c7 = 1 && (c6 = x17:0:0 + 1 && c5 = x14:0:0 + 1) && (x19:0:0 > 3 && x18:0:0 > 0 && x13:0:0 > 1 && x12:0:0 > 0 && x19:0:0 - 2 <= x13:0:0 && x19:0:0 - 3 <= x12:0:0 && x18:0:0 + 1 <= x13:0:0 && x18:0:0 <= x12:0:0 && x17:0:0 > -1 && x15:0:0 - 1 >= x14:0:0) The following rules are bounded: f216_0_main_GE(x18:0, x19:0, x20:0, x21:0, x22:0, x23:0) -> f216_0_main_GE(x33:0, x34:0, c, c1, c2, x23:0) :|: c2 = 1 && (c1 = x23:0 + 1 && c = x20:0 + 2) && (x34:0 > 3 && x33:0 > 0 && x25:0 > 1 && x34:0 + -1 * x25:0 <= 2 && x34:0 + -1 * x24:0 <= 3 && x33:0 + -1 * x25:0 <= -1 && x33:0 + -1 * x24:0 <= 0 && x23:0 + -1 * x20:0 >= 1 && x24:0 > 0 && x19:0 > 0 && x18:0 > 0 && x24:0 + -1 * x19:0 <= 0 && x18:0 + -1 * x24:0 >= 0 && x22:0 + -1 * x26:0 <= -1 && x23:0 > -1 && x22:0 > 0 && x21:0 + -1 * x20:0 >= 1) f216_0_main_GE(x:0, x1:0, x2:0, x3:0, x4:0, x5:0) -> f216_0_main_GE(x15:0, x16:0, c3, c4, x17:0, x5:0) :|: c4 = x5:0 + 1 && c3 = x2:0 + 2 && (x16:0 > 0 && x15:0 > 0 && x15:0 + -1 * x7:0 <= 0 && x6:0 + -1 * x15:0 >= 0 && x8:0 + -1 * x17:0 <= -1 && x5:0 + -1 * x2:0 >= 1 && x8:0 > 0 && x6:0 > 0 && x7:0 > 0 && x1:0 > 0 && x:0 > 0 && x6:0 + -1 * x1:0 <= 0 && x:0 + -1 * x6:0 >= 0 && x4:0 + -1 * x8:0 <= -1 && x5:0 > -1 && x4:0 > 0 && x3:0 + -1 * x2:0 >= 1) - IntTRS - PolynomialOrderProcessor - IntTRS Rules: f216_0_main_GE(x12:0:0, x13:0:0, x14:0:0, x15:0:0, x16:0:0, x17:0:0) -> f216_0_main_GE(x18:0:0, x19:0:0, c5, c6, c7, x17:0:0) :|: c7 = 1 && (c6 = x17:0:0 + 1 && c5 = x14:0:0 + 1) && (x19:0:0 > 3 && x18:0:0 > 0 && x13:0:0 > 1 && x12:0:0 > 0 && x19:0:0 - 2 <= x13:0:0 && x19:0:0 - 3 <= x12:0:0 && x18:0:0 + 1 <= x13:0:0 && x18:0:0 <= x12:0:0 && x17:0:0 > -1 && x15:0:0 - 1 >= x14:0:0) ---------------------------------------- (26) Obligation: Rules: f216_0_main_GE(x12:0:0, x13:0:0, x14:0:0, x15:0:0, x16:0:0, x17:0:0) -> f216_0_main_GE(x18:0:0, x19:0:0, x14:0:0 + 1, x17:0:0 + 1, 1, x17:0:0) :|: x19:0:0 > 3 && x18:0:0 > 0 && x13:0:0 > 1 && x12:0:0 > 0 && x19:0:0 - 2 <= x13:0:0 && x19:0:0 - 3 <= x12:0:0 && x18:0:0 + 1 <= x13:0:0 && x18:0:0 <= x12:0:0 && x17:0:0 > -1 && x15:0:0 - 1 >= x14:0:0 ---------------------------------------- (27) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f216_0_main_GE(x12:0:0, x13:0:0, x14:0:0, x15:0:0, x16:0:0, x17:0:0) -> f216_0_main_GE(x18:0:0, x19:0:0, x14:0:0 + 1, x17:0:0 + 1, 1, x17:0:0) :|: x19:0:0 > 3 && x18:0:0 > 0 && x13:0:0 > 1 && x12:0:0 > 0 && x19:0:0 - 2 <= x13:0:0 && x19:0:0 - 3 <= x12:0:0 && x18:0:0 + 1 <= x13:0:0 && x18:0:0 <= x12:0:0 && x17:0:0 > -1 && x15:0:0 - 1 >= x14:0:0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (28) Obligation: Termination digraph: Nodes: (1) f216_0_main_GE(x12:0:0, x13:0:0, x14:0:0, x15:0:0, x16:0:0, x17:0:0) -> f216_0_main_GE(x18:0:0, x19:0:0, x14:0:0 + 1, x17:0:0 + 1, 1, x17:0:0) :|: x19:0:0 > 3 && x18:0:0 > 0 && x13:0:0 > 1 && x12:0:0 > 0 && x19:0:0 - 2 <= x13:0:0 && x19:0:0 - 3 <= x12:0:0 && x18:0:0 + 1 <= x13:0:0 && x18:0:0 <= x12:0:0 && x17:0:0 > -1 && x15:0:0 - 1 >= x14:0:0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (29) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (30) Obligation: Rules: f216_0_main_GE(x12:0:0:0, x13:0:0:0, x14:0:0:0, x15:0:0:0, x16:0:0:0, x17:0:0:0) -> f216_0_main_GE(x18:0:0:0, x19:0:0:0, x14:0:0:0 + 1, x17:0:0:0 + 1, 1, x17:0:0:0) :|: x17:0:0:0 > -1 && x15:0:0:0 - 1 >= x14:0:0:0 && x18:0:0:0 <= x12:0:0:0 && x18:0:0:0 + 1 <= x13:0:0:0 && x19:0:0:0 - 3 <= x12:0:0:0 && x19:0:0:0 - 2 <= x13:0:0:0 && x12:0:0:0 > 0 && x13:0:0:0 > 1 && x18:0:0:0 > 0 && x19:0:0:0 > 3 ---------------------------------------- (31) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f216_0_main_GE(x1, x2, x3, x4, x5, x6) -> f216_0_main_GE(x1, x2, x3, x4, x6) ---------------------------------------- (32) Obligation: Rules: f216_0_main_GE(x12:0:0:0, x13:0:0:0, x14:0:0:0, x15:0:0:0, x17:0:0:0) -> f216_0_main_GE(x18:0:0:0, x19:0:0:0, x14:0:0:0 + 1, x17:0:0:0 + 1, x17:0:0:0) :|: x17:0:0:0 > -1 && x15:0:0:0 - 1 >= x14:0:0:0 && x18:0:0:0 <= x12:0:0:0 && x18:0:0:0 + 1 <= x13:0:0:0 && x19:0:0:0 - 3 <= x12:0:0:0 && x19:0:0:0 - 2 <= x13:0:0:0 && x12:0:0:0 > 0 && x13:0:0:0 > 1 && x18:0:0:0 > 0 && x19:0:0:0 > 3 ---------------------------------------- (33) Obligation: Termination digraph: Nodes: (1) f340_0_length_FieldAccess(x73, x74, x75, x76, x77, x78) -> f340_0_length_FieldAccess(x79, x80, x81, x82, x83, x84) :|: x84 <= x74 - 1 && -1 <= x74 - 1 && -1 <= x75 - 1 && x82 <= x75 - 1 && 2 <= x73 - 1 && 0 <= x79 - 1 && x85 + 3 <= x73 && x74 = x78 && 0 = x81 && 1 = x83 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (34) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (35) Obligation: Rules: f340_0_length_FieldAccess(x73:0, x74:0, x75:0, x76:0, x77:0, x74:0) -> f340_0_length_FieldAccess(x79:0, x80:0, 0, x82:0, 1, x84:0) :|: x79:0 > 0 && x85:0 + 3 <= x73:0 && x73:0 > 2 && x82:0 <= x75:0 - 1 && x75:0 > -1 && x74:0 > -1 && x84:0 <= x74:0 - 1 ---------------------------------------- (36) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f340_0_length_FieldAccess(x1, x2, x3, x4, x5, x6) -> f340_0_length_FieldAccess(x1, x2, x3, x4, x6) ---------------------------------------- (37) Obligation: Rules: f340_0_length_FieldAccess(x73:0, x74:0, x75:0, x76:0, x74:0) -> f340_0_length_FieldAccess(x79:0, x80:0, 0, x82:0, x84:0) :|: x79:0 > 0 && x85:0 + 3 <= x73:0 && x73:0 > 2 && x82:0 <= x75:0 - 1 && x75:0 > -1 && x74:0 > -1 && x84:0 <= x74:0 - 1 ---------------------------------------- (38) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f340_0_length_FieldAccess(INTEGER, VARIABLE, VARIABLE, VARIABLE, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (39) Obligation: Rules: f340_0_length_FieldAccess(x73:0, x74:0, x75:0, x76:0, x74:0) -> f340_0_length_FieldAccess(x79:0, x80:0, c, x82:0, x84:0) :|: c = 0 && (x79:0 > 0 && x85:0 + 3 <= x73:0 && x73:0 > 2 && x82:0 <= x75:0 - 1 && x75:0 > -1 && x74:0 > -1 && x84:0 <= x74:0 - 1) ---------------------------------------- (40) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f340_0_length_FieldAccess ] = f340_0_length_FieldAccess_5 The following rules are decreasing: f340_0_length_FieldAccess(x73:0, x74:0, x75:0, x76:0, x74:0) -> f340_0_length_FieldAccess(x79:0, x80:0, c, x82:0, x84:0) :|: c = 0 && (x79:0 > 0 && x85:0 + 3 <= x73:0 && x73:0 > 2 && x82:0 <= x75:0 - 1 && x75:0 > -1 && x74:0 > -1 && x84:0 <= x74:0 - 1) The following rules are bounded: f340_0_length_FieldAccess(x73:0, x74:0, x75:0, x76:0, x74:0) -> f340_0_length_FieldAccess(x79:0, x80:0, c, x82:0, x84:0) :|: c = 0 && (x79:0 > 0 && x85:0 + 3 <= x73:0 && x73:0 > 2 && x82:0 <= x75:0 - 1 && x75:0 > -1 && x74:0 > -1 && x84:0 <= x74:0 - 1) ---------------------------------------- (41) YES ---------------------------------------- (42) Obligation: Termination digraph: Nodes: (1) f339_0_length_Load(x24, x25, x26, x27, x28, x29) -> f339_0_length_Load(x30, x31, x32, x33, x34, x35) :|: x26 = x32 && x25 + 1 = x31 && 0 <= x30 - 1 && 0 <= x24 - 1 && x30 <= x24 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (43) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (44) Obligation: Rules: f339_0_length_Load(x24:0, x25:0, x26:0, x27:0, x28:0, x29:0) -> f339_0_length_Load(x30:0, x25:0 + 1, x26:0, x33:0, x34:0, x35:0) :|: x24:0 > 0 && x30:0 > 0 && x30:0 <= x24:0 ---------------------------------------- (45) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f339_0_length_Load(x1, x2, x3, x4, x5, x6) -> f339_0_length_Load(x1) ---------------------------------------- (46) Obligation: Rules: f339_0_length_Load(x24:0) -> f339_0_length_Load(x30:0) :|: x24:0 > 0 && x30:0 > 0 && x30:0 <= x24:0 ---------------------------------------- (47) FilterProof (EQUIVALENT) Used the following sort dictionary for filtering: f339_0_length_Load(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (48) Obligation: Rules: f339_0_length_Load(x24:0) -> f339_0_length_Load(x30:0) :|: x24:0 > 0 && x30:0 > 0 && x30:0 <= x24:0 ---------------------------------------- (49) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (50) Obligation: Rules: f339_0_length_Load(x24:0:0) -> f339_0_length_Load(x30:0:0) :|: x24:0:0 > 0 && x30:0:0 > 0 && x30:0:0 <= x24:0:0 ---------------------------------------- (51) IntTRSPeriodicNontermProof (COMPLETE) Normalized system to the following form: f(pc, x24:0:0) -> f(1, x30:0:0) :|: pc = 1 && (x24:0:0 > 0 && x30:0:0 > 0 && x30:0:0 <= x24:0:0) Witness term starting non-terminating reduction: f(1, 16) ---------------------------------------- (52) NO