NO proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be disproven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 473 ms] (4) AND (5) IRSwT (6) IntTRSCompressionProof [EQUIVALENT, 7 ms] (7) IRSwT (8) TempFilterProof [SOUND, 59 ms] (9) IntTRS (10) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (11) IntTRS (12) RankingReductionPairProof [EQUIVALENT, 6 ms] (13) YES (14) IRSwT (15) IntTRSCompressionProof [EQUIVALENT, 9 ms] (16) IRSwT (17) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (18) IRSwT (19) FilterProof [EQUIVALENT, 0 ms] (20) IntTRS (21) IntTRSCompressionProof [EQUIVALENT, 0 ms] (22) IntTRS (23) IntTRSPeriodicNontermProof [COMPLETE, 0 ms] (24) NO ---------------------------------------- (0) Obligation: Rules: f269_0_createMetaList_Return(arg1, arg2, arg3, arg4) -> f462_0_main_InvokeMethod(arg1P, arg2P, arg3P, arg4P) :|: -1 <= arg2P - 1 && 0 <= arg1P - 1 && -1 <= arg2 - 1 && 0 <= arg1 - 1 && arg2P <= arg2 && arg1P - 1 <= arg2 && arg1P <= arg1 f1_0_main_Load(x, x1, x2, x3) -> f462_0_main_InvokeMethod(x4, x5, x6, x7) :|: -1 <= x5 - 1 && 0 <= x4 - 1 && 0 <= x - 1 && x4 <= x f462_0_main_InvokeMethod(x8, x10, x11, x12) -> f479_0_countMetaList_NONNULL(x14, x15, x16, x17) :|: 0 <= x18 - 1 && 0 <= x19 - 1 && x14 <= x10 && 0 <= x8 - 1 && -1 <= x10 - 1 && -1 <= x14 - 1 f1_0_main_Load(x20, x21, x22, x23) -> f703_0_createMetaList_GE(x24, x25, x26, x27) :|: 1 = x26 && 0 = x24 && 0 <= x20 - 1 && -1 <= x25 - 1 && -1 <= x21 - 1 f703_0_createMetaList_GE(x28, x29, x30, x32) -> f922_0_createMetaList_LE(x33, x34, x36, x37) :|: x30 + 1 = x37 && x28 = x34 && x29 = x33 && 0 <= x30 - 1 && x28 <= x29 - 1 && -1 <= x36 - 1 f922_0_createMetaList_LE(x38, x40, x41, x42) -> f703_0_createMetaList_GE(x43, x44, x45, x46) :|: x42 = x45 && x38 = x44 && x40 + 1 = x43 && 0 = x41 f922_0_createMetaList_LE(x47, x48, x49, x50) -> f922_0_createMetaList_LE(x51, x52, x53, x54) :|: x50 = x54 && x49 - 1 = x53 && x48 = x52 && x47 = x51 && 0 <= x49 - 1 f479_0_countMetaList_NONNULL(x55, x56, x57, x58) -> f479_0_countMetaList_NONNULL(x59, x60, x61, x62) :|: x59 + 2 <= x55 && 0 <= x63 - 1 && 1 <= x55 - 1 && -1 <= x59 - 1 f479_0_countMetaList_NONNULL(x64, x65, x66, x67) -> f479_0_countMetaList_NONNULL(x68, x69, x70, x71) :|: x68 + 2 <= x64 && 0 <= x72 - 1 && 2 <= x64 - 1 && -1 <= x68 - 1 f479_0_countMetaList_NONNULL(x73, x74, x75, x76) -> f479_0_countMetaList_NONNULL(x77, x78, x79, x80) :|: x77 <= x73 && 0 <= x81 - 1 && 2 <= x73 - 1 && 0 <= x77 - 1 __init(x82, x83, x84, x85) -> f1_0_main_Load(x86, x87, x88, x89) :|: 0 <= 0 Start term: __init(arg1, arg2, arg3, arg4) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: f269_0_createMetaList_Return(arg1, arg2, arg3, arg4) -> f462_0_main_InvokeMethod(arg1P, arg2P, arg3P, arg4P) :|: -1 <= arg2P - 1 && 0 <= arg1P - 1 && -1 <= arg2 - 1 && 0 <= arg1 - 1 && arg2P <= arg2 && arg1P - 1 <= arg2 && arg1P <= arg1 f1_0_main_Load(x, x1, x2, x3) -> f462_0_main_InvokeMethod(x4, x5, x6, x7) :|: -1 <= x5 - 1 && 0 <= x4 - 1 && 0 <= x - 1 && x4 <= x f462_0_main_InvokeMethod(x8, x10, x11, x12) -> f479_0_countMetaList_NONNULL(x14, x15, x16, x17) :|: 0 <= x18 - 1 && 0 <= x19 - 1 && x14 <= x10 && 0 <= x8 - 1 && -1 <= x10 - 1 && -1 <= x14 - 1 f1_0_main_Load(x20, x21, x22, x23) -> f703_0_createMetaList_GE(x24, x25, x26, x27) :|: 1 = x26 && 0 = x24 && 0 <= x20 - 1 && -1 <= x25 - 1 && -1 <= x21 - 1 f703_0_createMetaList_GE(x28, x29, x30, x32) -> f922_0_createMetaList_LE(x33, x34, x36, x37) :|: x30 + 1 = x37 && x28 = x34 && x29 = x33 && 0 <= x30 - 1 && x28 <= x29 - 1 && -1 <= x36 - 1 f922_0_createMetaList_LE(x38, x40, x41, x42) -> f703_0_createMetaList_GE(x43, x44, x45, x46) :|: x42 = x45 && x38 = x44 && x40 + 1 = x43 && 0 = x41 f922_0_createMetaList_LE(x47, x48, x49, x50) -> f922_0_createMetaList_LE(x51, x52, x53, x54) :|: x50 = x54 && x49 - 1 = x53 && x48 = x52 && x47 = x51 && 0 <= x49 - 1 f479_0_countMetaList_NONNULL(x55, x56, x57, x58) -> f479_0_countMetaList_NONNULL(x59, x60, x61, x62) :|: x59 + 2 <= x55 && 0 <= x63 - 1 && 1 <= x55 - 1 && -1 <= x59 - 1 f479_0_countMetaList_NONNULL(x64, x65, x66, x67) -> f479_0_countMetaList_NONNULL(x68, x69, x70, x71) :|: x68 + 2 <= x64 && 0 <= x72 - 1 && 2 <= x64 - 1 && -1 <= x68 - 1 f479_0_countMetaList_NONNULL(x73, x74, x75, x76) -> f479_0_countMetaList_NONNULL(x77, x78, x79, x80) :|: x77 <= x73 && 0 <= x81 - 1 && 2 <= x73 - 1 && 0 <= x77 - 1 __init(x82, x83, x84, x85) -> f1_0_main_Load(x86, x87, x88, x89) :|: 0 <= 0 Start term: __init(arg1, arg2, arg3, arg4) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f269_0_createMetaList_Return(arg1, arg2, arg3, arg4) -> f462_0_main_InvokeMethod(arg1P, arg2P, arg3P, arg4P) :|: -1 <= arg2P - 1 && 0 <= arg1P - 1 && -1 <= arg2 - 1 && 0 <= arg1 - 1 && arg2P <= arg2 && arg1P - 1 <= arg2 && arg1P <= arg1 (2) f1_0_main_Load(x, x1, x2, x3) -> f462_0_main_InvokeMethod(x4, x5, x6, x7) :|: -1 <= x5 - 1 && 0 <= x4 - 1 && 0 <= x - 1 && x4 <= x (3) f462_0_main_InvokeMethod(x8, x10, x11, x12) -> f479_0_countMetaList_NONNULL(x14, x15, x16, x17) :|: 0 <= x18 - 1 && 0 <= x19 - 1 && x14 <= x10 && 0 <= x8 - 1 && -1 <= x10 - 1 && -1 <= x14 - 1 (4) f1_0_main_Load(x20, x21, x22, x23) -> f703_0_createMetaList_GE(x24, x25, x26, x27) :|: 1 = x26 && 0 = x24 && 0 <= x20 - 1 && -1 <= x25 - 1 && -1 <= x21 - 1 (5) f703_0_createMetaList_GE(x28, x29, x30, x32) -> f922_0_createMetaList_LE(x33, x34, x36, x37) :|: x30 + 1 = x37 && x28 = x34 && x29 = x33 && 0 <= x30 - 1 && x28 <= x29 - 1 && -1 <= x36 - 1 (6) f922_0_createMetaList_LE(x38, x40, x41, x42) -> f703_0_createMetaList_GE(x43, x44, x45, x46) :|: x42 = x45 && x38 = x44 && x40 + 1 = x43 && 0 = x41 (7) f922_0_createMetaList_LE(x47, x48, x49, x50) -> f922_0_createMetaList_LE(x51, x52, x53, x54) :|: x50 = x54 && x49 - 1 = x53 && x48 = x52 && x47 = x51 && 0 <= x49 - 1 (8) f479_0_countMetaList_NONNULL(x55, x56, x57, x58) -> f479_0_countMetaList_NONNULL(x59, x60, x61, x62) :|: x59 + 2 <= x55 && 0 <= x63 - 1 && 1 <= x55 - 1 && -1 <= x59 - 1 (9) f479_0_countMetaList_NONNULL(x64, x65, x66, x67) -> f479_0_countMetaList_NONNULL(x68, x69, x70, x71) :|: x68 + 2 <= x64 && 0 <= x72 - 1 && 2 <= x64 - 1 && -1 <= x68 - 1 (10) f479_0_countMetaList_NONNULL(x73, x74, x75, x76) -> f479_0_countMetaList_NONNULL(x77, x78, x79, x80) :|: x77 <= x73 && 0 <= x81 - 1 && 2 <= x73 - 1 && 0 <= x77 - 1 (11) __init(x82, x83, x84, x85) -> f1_0_main_Load(x86, x87, x88, x89) :|: 0 <= 0 Arcs: (1) -> (3) (2) -> (3) (3) -> (8), (9), (10) (4) -> (5) (5) -> (6), (7) (6) -> (5) (7) -> (6), (7) (8) -> (8), (9), (10) (9) -> (8), (9), (10) (10) -> (8), (9), (10) (11) -> (2), (4) This digraph is fully evaluated! ---------------------------------------- (4) Complex Obligation (AND) ---------------------------------------- (5) Obligation: Termination digraph: Nodes: (1) f703_0_createMetaList_GE(x28, x29, x30, x32) -> f922_0_createMetaList_LE(x33, x34, x36, x37) :|: x30 + 1 = x37 && x28 = x34 && x29 = x33 && 0 <= x30 - 1 && x28 <= x29 - 1 && -1 <= x36 - 1 (2) f922_0_createMetaList_LE(x38, x40, x41, x42) -> f703_0_createMetaList_GE(x43, x44, x45, x46) :|: x42 = x45 && x38 = x44 && x40 + 1 = x43 && 0 = x41 (3) f922_0_createMetaList_LE(x47, x48, x49, x50) -> f922_0_createMetaList_LE(x51, x52, x53, x54) :|: x50 = x54 && x49 - 1 = x53 && x48 = x52 && x47 = x51 && 0 <= x49 - 1 Arcs: (1) -> (2), (3) (2) -> (1) (3) -> (2), (3) This digraph is fully evaluated! ---------------------------------------- (6) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (7) Obligation: Rules: f922_0_createMetaList_LE(x33:0, x40:0, cons_0, x42:0) -> f922_0_createMetaList_LE(x33:0, x40:0 + 1, x36:0, x42:0 + 1) :|: x40:0 + 1 <= x33:0 - 1 && x42:0 > 0 && x36:0 > -1 && cons_0 = 0 f922_0_createMetaList_LE(x47:0, x48:0, x49:0, x50:0) -> f922_0_createMetaList_LE(x47:0, x48:0, x49:0 - 1, x50:0) :|: x49:0 > 0 ---------------------------------------- (8) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f922_0_createMetaList_LE(VARIABLE, VARIABLE, INTEGER, VARIABLE) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (9) Obligation: Rules: f922_0_createMetaList_LE(x33:0, x40:0, c, x42:0) -> f922_0_createMetaList_LE(x33:0, c1, x36:0, c2) :|: c2 = x42:0 + 1 && (c1 = x40:0 + 1 && c = 0) && (x40:0 + 1 <= x33:0 - 1 && x42:0 > 0 && x36:0 > -1 && cons_0 = 0) f922_0_createMetaList_LE(x47:0, x48:0, x49:0, x50:0) -> f922_0_createMetaList_LE(x47:0, x48:0, c3, x50:0) :|: c3 = x49:0 - 1 && x49:0 > 0 ---------------------------------------- (10) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f922_0_createMetaList_LE(x, x1, x2, x3)] = -1 + 2*x - 2*x1 + x3 The following rules are decreasing: f922_0_createMetaList_LE(x33:0, x40:0, c, x42:0) -> f922_0_createMetaList_LE(x33:0, c1, x36:0, c2) :|: c2 = x42:0 + 1 && (c1 = x40:0 + 1 && c = 0) && (x40:0 + 1 <= x33:0 - 1 && x42:0 > 0 && x36:0 > -1 && cons_0 = 0) The following rules are bounded: f922_0_createMetaList_LE(x33:0, x40:0, c, x42:0) -> f922_0_createMetaList_LE(x33:0, c1, x36:0, c2) :|: c2 = x42:0 + 1 && (c1 = x40:0 + 1 && c = 0) && (x40:0 + 1 <= x33:0 - 1 && x42:0 > 0 && x36:0 > -1 && cons_0 = 0) ---------------------------------------- (11) Obligation: Rules: f922_0_createMetaList_LE(x47:0, x48:0, x49:0, x50:0) -> f922_0_createMetaList_LE(x47:0, x48:0, c3, x50:0) :|: c3 = x49:0 - 1 && x49:0 > 0 ---------------------------------------- (12) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f922_0_createMetaList_LE ] = f922_0_createMetaList_LE_3 The following rules are decreasing: f922_0_createMetaList_LE(x47:0, x48:0, x49:0, x50:0) -> f922_0_createMetaList_LE(x47:0, x48:0, c3, x50:0) :|: c3 = x49:0 - 1 && x49:0 > 0 The following rules are bounded: f922_0_createMetaList_LE(x47:0, x48:0, x49:0, x50:0) -> f922_0_createMetaList_LE(x47:0, x48:0, c3, x50:0) :|: c3 = x49:0 - 1 && x49:0 > 0 ---------------------------------------- (13) YES ---------------------------------------- (14) Obligation: Termination digraph: Nodes: (1) f479_0_countMetaList_NONNULL(x55, x56, x57, x58) -> f479_0_countMetaList_NONNULL(x59, x60, x61, x62) :|: x59 + 2 <= x55 && 0 <= x63 - 1 && 1 <= x55 - 1 && -1 <= x59 - 1 (2) f479_0_countMetaList_NONNULL(x64, x65, x66, x67) -> f479_0_countMetaList_NONNULL(x68, x69, x70, x71) :|: x68 + 2 <= x64 && 0 <= x72 - 1 && 2 <= x64 - 1 && -1 <= x68 - 1 (3) f479_0_countMetaList_NONNULL(x73, x74, x75, x76) -> f479_0_countMetaList_NONNULL(x77, x78, x79, x80) :|: x77 <= x73 && 0 <= x81 - 1 && 2 <= x73 - 1 && 0 <= x77 - 1 Arcs: (1) -> (1), (2), (3) (2) -> (1), (2), (3) (3) -> (1), (2), (3) This digraph is fully evaluated! ---------------------------------------- (15) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (16) Obligation: Rules: f479_0_countMetaList_NONNULL(x73:0, x74:0, x75:0, x76:0) -> f479_0_countMetaList_NONNULL(x77:0, x78:0, x79:0, x80:0) :|: x73:0 > 2 && x77:0 > 0 && x81:0 > 0 && x77:0 <= x73:0 f479_0_countMetaList_NONNULL(x55:0, x56:0, x57:0, x58:0) -> f479_0_countMetaList_NONNULL(x59:0, x60:0, x61:0, x62:0) :|: x55:0 > 1 && x59:0 > -1 && x63:0 > 0 && x59:0 + 2 <= x55:0 f479_0_countMetaList_NONNULL(x64:0, x65:0, x66:0, x67:0) -> f479_0_countMetaList_NONNULL(x68:0, x69:0, x70:0, x71:0) :|: x64:0 > 2 && x68:0 > -1 && x72:0 > 0 && x68:0 + 2 <= x64:0 ---------------------------------------- (17) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f479_0_countMetaList_NONNULL(x1, x2, x3, x4) -> f479_0_countMetaList_NONNULL(x1) ---------------------------------------- (18) Obligation: Rules: f479_0_countMetaList_NONNULL(x73:0) -> f479_0_countMetaList_NONNULL(x77:0) :|: x73:0 > 2 && x77:0 > 0 && x81:0 > 0 && x77:0 <= x73:0 f479_0_countMetaList_NONNULL(x55:0) -> f479_0_countMetaList_NONNULL(x59:0) :|: x55:0 > 1 && x59:0 > -1 && x63:0 > 0 && x59:0 + 2 <= x55:0 f479_0_countMetaList_NONNULL(x64:0) -> f479_0_countMetaList_NONNULL(x68:0) :|: x64:0 > 2 && x68:0 > -1 && x72:0 > 0 && x68:0 + 2 <= x64:0 ---------------------------------------- (19) FilterProof (EQUIVALENT) Used the following sort dictionary for filtering: f479_0_countMetaList_NONNULL(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (20) Obligation: Rules: f479_0_countMetaList_NONNULL(x73:0) -> f479_0_countMetaList_NONNULL(x77:0) :|: x73:0 > 2 && x77:0 > 0 && x81:0 > 0 && x77:0 <= x73:0 f479_0_countMetaList_NONNULL(x55:0) -> f479_0_countMetaList_NONNULL(x59:0) :|: x55:0 > 1 && x59:0 > -1 && x63:0 > 0 && x59:0 + 2 <= x55:0 f479_0_countMetaList_NONNULL(x64:0) -> f479_0_countMetaList_NONNULL(x68:0) :|: x64:0 > 2 && x68:0 > -1 && x72:0 > 0 && x68:0 + 2 <= x64:0 ---------------------------------------- (21) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (22) Obligation: Rules: f479_0_countMetaList_NONNULL(x64:0:0) -> f479_0_countMetaList_NONNULL(x68:0:0) :|: x72:0:0 > 0 && x68:0:0 + 2 <= x64:0:0 && x68:0:0 > -1 && x64:0:0 > 2 f479_0_countMetaList_NONNULL(x73:0:0) -> f479_0_countMetaList_NONNULL(x77:0:0) :|: x81:0:0 > 0 && x77:0:0 <= x73:0:0 && x77:0:0 > 0 && x73:0:0 > 2 f479_0_countMetaList_NONNULL(x55:0:0) -> f479_0_countMetaList_NONNULL(x59:0:0) :|: x63:0:0 > 0 && x59:0:0 + 2 <= x55:0:0 && x59:0:0 > -1 && x55:0:0 > 1 ---------------------------------------- (23) IntTRSPeriodicNontermProof (COMPLETE) Normalized system to the following form: f(pc, x64:0:0) -> f(1, x68:0:0) :|: pc = 1 && (x72:0:0 > 0 && x68:0:0 + 2 <= x64:0:0 && x68:0:0 > -1 && x64:0:0 > 2) f(pc, x73:0:0) -> f(1, x77:0:0) :|: pc = 1 && (x81:0:0 > 0 && x77:0:0 <= x73:0:0 && x77:0:0 > 0 && x73:0:0 > 2) f(pc, x55:0:0) -> f(1, x59:0:0) :|: pc = 1 && (x63:0:0 > 0 && x59:0:0 + 2 <= x55:0:0 && x59:0:0 > -1 && x55:0:0 > 1) Witness term starting non-terminating reduction: f(1, 7) ---------------------------------------- (24) NO