YES proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be proven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof [EQUIVALENT, 1560 ms] (4) AND (5) IRSwT (6) IntTRSCompressionProof [EQUIVALENT, 0 ms] (7) IRSwT (8) TempFilterProof [SOUND, 102 ms] (9) IntTRS (10) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (11) YES (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT (15) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (16) IRSwT (17) FilterProof [EQUIVALENT, 0 ms] (18) IntTRS (19) IntTRSCompressionProof [EQUIVALENT, 0 ms] (20) IntTRS (21) RankingReductionPairProof [EQUIVALENT, 5 ms] (22) YES ---------------------------------------- (0) Obligation: Rules: f1_0_main_Load(arg1, arg2, arg3, arg4, arg5) -> f1612_0_main_NULL(arg1P, arg2P, arg3P, arg4P, arg5P) :|: -1 <= arg2P - 1 && 0 <= arg1P - 1 && 0 <= arg1 - 1 f408_0_createTree_Return(x, x1, x2, x3, x4) -> f1612_0_main_NULL(x5, x6, x7, x8, x9) :|: x1 + 2 <= x && -1 <= x6 - 1 && 1 <= x5 - 1 && 1 <= x - 1 && x6 + 2 <= x && x5 <= x f1612_0_main_NULL(x10, x11, x12, x13, x14) -> f1612_0_main_NULL(x15, x16, x17, x18, x19) :|: -1 <= x16 - 1 && 2 <= x15 - 1 && 0 <= x11 - 1 && 2 <= x10 - 1 && x16 + 1 <= x11 && x16 + 3 <= x10 && x15 - 2 <= x10 f1_0_main_Load(x20, x21, x22, x23, x24) -> f1301_0_createTree_LE(x25, x26, x27, x28, x29) :|: 1 = x29 && x21 = x28 && 1 <= x26 - 1 && 1 <= x25 - 1 && 0 <= x20 - 1 && x26 - 1 <= x20 && x25 - 1 <= x20 && 0 <= x27 - 1 && 0 <= x21 - 1 f1301_0_createTree_LE(x30, x32, x33, x34, x35) -> f1301_0_createTree_LE(x36, x37, x38, x40, x41) :|: x35 + 1 = x41 && x34 = x40 && x33 - 1 = x38 && 0 <= x37 - 1 && 0 <= x36 - 1 && 2 <= x32 - 1 && 0 <= x30 - 1 && x37 + 2 <= x32 && x36 <= x30 && x35 <= x34 - 1 && -1 <= x35 - 1 && 0 <= x33 - 1 f1301_0_createTree_LE(x42, x43, x44, x45, x46) -> f1301_0_createTree_LE(x47, x48, x49, x50, x51) :|: -1 <= x46 - 1 && 0 <= x52 - 1 && 0 <= x44 - 1 && x46 <= x45 - 1 && x47 <= x42 && x48 + 2 <= x43 && 0 <= x42 - 1 && 2 <= x43 - 1 && 0 <= x47 - 1 && 0 <= x48 - 1 && x44 - 1 = x49 && x45 = x50 && x46 + 1 = x51 f1301_0_createTree_LE(x53, x54, x55, x56, x57) -> f1301_0_createTree_LE(x58, x59, x60, x62, x63) :|: -1 <= x57 - 1 && 0 <= x64 - 1 && 0 <= x55 - 1 && x57 <= x56 - 1 && 0 <= x53 - 1 && 1 <= x54 - 1 && 0 <= x58 - 1 && 0 <= x59 - 1 && x55 - 1 = x60 && x56 = x62 && x57 + 1 = x63 f1301_0_createTree_LE(x65, x66, x67, x68, x69) -> f1301_0_createTree_LE(x70, x71, x72, x73, x74) :|: x69 + 1 = x74 && x68 = x73 && x67 - 1 = x72 && 0 <= x71 - 1 && 0 <= x70 - 1 && 1 <= x66 - 1 && 0 <= x65 - 1 && x69 <= x68 - 1 && -1 <= x69 - 1 && 0 <= x67 - 1 f1301_0_createTree_LE(x75, x76, x77, x78, x79) -> f1301_0_createTree_LE(x80, x81, x82, x83, x84) :|: x79 + 1 = x84 && x78 = x83 && x77 - 1 = x82 && 3 <= x81 - 1 && 3 <= x80 - 1 && 1 <= x76 - 1 && 1 <= x75 - 1 && x81 - 2 <= x76 && x81 - 2 <= x75 && x80 - 2 <= x76 && x80 - 2 <= x75 && x79 <= x78 - 1 && -1 <= x79 - 1 && 0 <= x77 - 1 f1301_0_createTree_LE(x85, x86, x87, x88, x89) -> f1301_0_createTree_LE(x90, x91, x92, x93, x94) :|: -1 <= x89 - 1 && 0 <= x95 - 1 && 0 <= x87 - 1 && x89 <= x88 - 1 && x90 - 2 <= x85 && x90 - 2 <= x86 && x91 - 2 <= x85 && x91 - 2 <= x86 && 1 <= x85 - 1 && 1 <= x86 - 1 && 3 <= x90 - 1 && 3 <= x91 - 1 && x87 - 1 = x92 && x88 = x93 && x89 + 1 = x94 __init(x96, x97, x98, x99, x100) -> f1_0_main_Load(x101, x102, x103, x104, x105) :|: 0 <= 0 Start term: __init(arg1, arg2, arg3, arg4, arg5) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: f1_0_main_Load(arg1, arg2, arg3, arg4, arg5) -> f1612_0_main_NULL(arg1P, arg2P, arg3P, arg4P, arg5P) :|: -1 <= arg2P - 1 && 0 <= arg1P - 1 && 0 <= arg1 - 1 f408_0_createTree_Return(x, x1, x2, x3, x4) -> f1612_0_main_NULL(x5, x6, x7, x8, x9) :|: x1 + 2 <= x && -1 <= x6 - 1 && 1 <= x5 - 1 && 1 <= x - 1 && x6 + 2 <= x && x5 <= x f1612_0_main_NULL(x10, x11, x12, x13, x14) -> f1612_0_main_NULL(x15, x16, x17, x18, x19) :|: -1 <= x16 - 1 && 2 <= x15 - 1 && 0 <= x11 - 1 && 2 <= x10 - 1 && x16 + 1 <= x11 && x16 + 3 <= x10 && x15 - 2 <= x10 f1_0_main_Load(x20, x21, x22, x23, x24) -> f1301_0_createTree_LE(x25, x26, x27, x28, x29) :|: 1 = x29 && x21 = x28 && 1 <= x26 - 1 && 1 <= x25 - 1 && 0 <= x20 - 1 && x26 - 1 <= x20 && x25 - 1 <= x20 && 0 <= x27 - 1 && 0 <= x21 - 1 f1301_0_createTree_LE(x30, x32, x33, x34, x35) -> f1301_0_createTree_LE(x36, x37, x38, x40, x41) :|: x35 + 1 = x41 && x34 = x40 && x33 - 1 = x38 && 0 <= x37 - 1 && 0 <= x36 - 1 && 2 <= x32 - 1 && 0 <= x30 - 1 && x37 + 2 <= x32 && x36 <= x30 && x35 <= x34 - 1 && -1 <= x35 - 1 && 0 <= x33 - 1 f1301_0_createTree_LE(x42, x43, x44, x45, x46) -> f1301_0_createTree_LE(x47, x48, x49, x50, x51) :|: -1 <= x46 - 1 && 0 <= x52 - 1 && 0 <= x44 - 1 && x46 <= x45 - 1 && x47 <= x42 && x48 + 2 <= x43 && 0 <= x42 - 1 && 2 <= x43 - 1 && 0 <= x47 - 1 && 0 <= x48 - 1 && x44 - 1 = x49 && x45 = x50 && x46 + 1 = x51 f1301_0_createTree_LE(x53, x54, x55, x56, x57) -> f1301_0_createTree_LE(x58, x59, x60, x62, x63) :|: -1 <= x57 - 1 && 0 <= x64 - 1 && 0 <= x55 - 1 && x57 <= x56 - 1 && 0 <= x53 - 1 && 1 <= x54 - 1 && 0 <= x58 - 1 && 0 <= x59 - 1 && x55 - 1 = x60 && x56 = x62 && x57 + 1 = x63 f1301_0_createTree_LE(x65, x66, x67, x68, x69) -> f1301_0_createTree_LE(x70, x71, x72, x73, x74) :|: x69 + 1 = x74 && x68 = x73 && x67 - 1 = x72 && 0 <= x71 - 1 && 0 <= x70 - 1 && 1 <= x66 - 1 && 0 <= x65 - 1 && x69 <= x68 - 1 && -1 <= x69 - 1 && 0 <= x67 - 1 f1301_0_createTree_LE(x75, x76, x77, x78, x79) -> f1301_0_createTree_LE(x80, x81, x82, x83, x84) :|: x79 + 1 = x84 && x78 = x83 && x77 - 1 = x82 && 3 <= x81 - 1 && 3 <= x80 - 1 && 1 <= x76 - 1 && 1 <= x75 - 1 && x81 - 2 <= x76 && x81 - 2 <= x75 && x80 - 2 <= x76 && x80 - 2 <= x75 && x79 <= x78 - 1 && -1 <= x79 - 1 && 0 <= x77 - 1 f1301_0_createTree_LE(x85, x86, x87, x88, x89) -> f1301_0_createTree_LE(x90, x91, x92, x93, x94) :|: -1 <= x89 - 1 && 0 <= x95 - 1 && 0 <= x87 - 1 && x89 <= x88 - 1 && x90 - 2 <= x85 && x90 - 2 <= x86 && x91 - 2 <= x85 && x91 - 2 <= x86 && 1 <= x85 - 1 && 1 <= x86 - 1 && 3 <= x90 - 1 && 3 <= x91 - 1 && x87 - 1 = x92 && x88 = x93 && x89 + 1 = x94 __init(x96, x97, x98, x99, x100) -> f1_0_main_Load(x101, x102, x103, x104, x105) :|: 0 <= 0 Start term: __init(arg1, arg2, arg3, arg4, arg5) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f1_0_main_Load(arg1, arg2, arg3, arg4, arg5) -> f1612_0_main_NULL(arg1P, arg2P, arg3P, arg4P, arg5P) :|: -1 <= arg2P - 1 && 0 <= arg1P - 1 && 0 <= arg1 - 1 (2) f408_0_createTree_Return(x, x1, x2, x3, x4) -> f1612_0_main_NULL(x5, x6, x7, x8, x9) :|: x1 + 2 <= x && -1 <= x6 - 1 && 1 <= x5 - 1 && 1 <= x - 1 && x6 + 2 <= x && x5 <= x (3) f1612_0_main_NULL(x10, x11, x12, x13, x14) -> f1612_0_main_NULL(x15, x16, x17, x18, x19) :|: -1 <= x16 - 1 && 2 <= x15 - 1 && 0 <= x11 - 1 && 2 <= x10 - 1 && x16 + 1 <= x11 && x16 + 3 <= x10 && x15 - 2 <= x10 (4) f1_0_main_Load(x20, x21, x22, x23, x24) -> f1301_0_createTree_LE(x25, x26, x27, x28, x29) :|: 1 = x29 && x21 = x28 && 1 <= x26 - 1 && 1 <= x25 - 1 && 0 <= x20 - 1 && x26 - 1 <= x20 && x25 - 1 <= x20 && 0 <= x27 - 1 && 0 <= x21 - 1 (5) f1301_0_createTree_LE(x30, x32, x33, x34, x35) -> f1301_0_createTree_LE(x36, x37, x38, x40, x41) :|: x35 + 1 = x41 && x34 = x40 && x33 - 1 = x38 && 0 <= x37 - 1 && 0 <= x36 - 1 && 2 <= x32 - 1 && 0 <= x30 - 1 && x37 + 2 <= x32 && x36 <= x30 && x35 <= x34 - 1 && -1 <= x35 - 1 && 0 <= x33 - 1 (6) f1301_0_createTree_LE(x42, x43, x44, x45, x46) -> f1301_0_createTree_LE(x47, x48, x49, x50, x51) :|: -1 <= x46 - 1 && 0 <= x52 - 1 && 0 <= x44 - 1 && x46 <= x45 - 1 && x47 <= x42 && x48 + 2 <= x43 && 0 <= x42 - 1 && 2 <= x43 - 1 && 0 <= x47 - 1 && 0 <= x48 - 1 && x44 - 1 = x49 && x45 = x50 && x46 + 1 = x51 (7) f1301_0_createTree_LE(x53, x54, x55, x56, x57) -> f1301_0_createTree_LE(x58, x59, x60, x62, x63) :|: -1 <= x57 - 1 && 0 <= x64 - 1 && 0 <= x55 - 1 && x57 <= x56 - 1 && 0 <= x53 - 1 && 1 <= x54 - 1 && 0 <= x58 - 1 && 0 <= x59 - 1 && x55 - 1 = x60 && x56 = x62 && x57 + 1 = x63 (8) f1301_0_createTree_LE(x65, x66, x67, x68, x69) -> f1301_0_createTree_LE(x70, x71, x72, x73, x74) :|: x69 + 1 = x74 && x68 = x73 && x67 - 1 = x72 && 0 <= x71 - 1 && 0 <= x70 - 1 && 1 <= x66 - 1 && 0 <= x65 - 1 && x69 <= x68 - 1 && -1 <= x69 - 1 && 0 <= x67 - 1 (9) f1301_0_createTree_LE(x75, x76, x77, x78, x79) -> f1301_0_createTree_LE(x80, x81, x82, x83, x84) :|: x79 + 1 = x84 && x78 = x83 && x77 - 1 = x82 && 3 <= x81 - 1 && 3 <= x80 - 1 && 1 <= x76 - 1 && 1 <= x75 - 1 && x81 - 2 <= x76 && x81 - 2 <= x75 && x80 - 2 <= x76 && x80 - 2 <= x75 && x79 <= x78 - 1 && -1 <= x79 - 1 && 0 <= x77 - 1 (10) f1301_0_createTree_LE(x85, x86, x87, x88, x89) -> f1301_0_createTree_LE(x90, x91, x92, x93, x94) :|: -1 <= x89 - 1 && 0 <= x95 - 1 && 0 <= x87 - 1 && x89 <= x88 - 1 && x90 - 2 <= x85 && x90 - 2 <= x86 && x91 - 2 <= x85 && x91 - 2 <= x86 && 1 <= x85 - 1 && 1 <= x86 - 1 && 3 <= x90 - 1 && 3 <= x91 - 1 && x87 - 1 = x92 && x88 = x93 && x89 + 1 = x94 (11) __init(x96, x97, x98, x99, x100) -> f1_0_main_Load(x101, x102, x103, x104, x105) :|: 0 <= 0 Arcs: (1) -> (3) (2) -> (3) (3) -> (3) (4) -> (5), (6), (7), (8), (9), (10) (5) -> (5), (6), (7), (8), (9), (10) (6) -> (5), (6), (7), (8), (9), (10) (7) -> (5), (6), (7), (8), (9), (10) (8) -> (5), (6), (7), (8), (9), (10) (9) -> (5), (6), (7), (8), (9), (10) (10) -> (5), (6), (7), (8), (9), (10) (11) -> (1), (4) This digraph is fully evaluated! ---------------------------------------- (4) Complex Obligation (AND) ---------------------------------------- (5) Obligation: Termination digraph: Nodes: (1) f1301_0_createTree_LE(x30, x32, x33, x34, x35) -> f1301_0_createTree_LE(x36, x37, x38, x40, x41) :|: x35 + 1 = x41 && x34 = x40 && x33 - 1 = x38 && 0 <= x37 - 1 && 0 <= x36 - 1 && 2 <= x32 - 1 && 0 <= x30 - 1 && x37 + 2 <= x32 && x36 <= x30 && x35 <= x34 - 1 && -1 <= x35 - 1 && 0 <= x33 - 1 (2) f1301_0_createTree_LE(x42, x43, x44, x45, x46) -> f1301_0_createTree_LE(x47, x48, x49, x50, x51) :|: -1 <= x46 - 1 && 0 <= x52 - 1 && 0 <= x44 - 1 && x46 <= x45 - 1 && x47 <= x42 && x48 + 2 <= x43 && 0 <= x42 - 1 && 2 <= x43 - 1 && 0 <= x47 - 1 && 0 <= x48 - 1 && x44 - 1 = x49 && x45 = x50 && x46 + 1 = x51 (3) f1301_0_createTree_LE(x53, x54, x55, x56, x57) -> f1301_0_createTree_LE(x58, x59, x60, x62, x63) :|: -1 <= x57 - 1 && 0 <= x64 - 1 && 0 <= x55 - 1 && x57 <= x56 - 1 && 0 <= x53 - 1 && 1 <= x54 - 1 && 0 <= x58 - 1 && 0 <= x59 - 1 && x55 - 1 = x60 && x56 = x62 && x57 + 1 = x63 (4) f1301_0_createTree_LE(x65, x66, x67, x68, x69) -> f1301_0_createTree_LE(x70, x71, x72, x73, x74) :|: x69 + 1 = x74 && x68 = x73 && x67 - 1 = x72 && 0 <= x71 - 1 && 0 <= x70 - 1 && 1 <= x66 - 1 && 0 <= x65 - 1 && x69 <= x68 - 1 && -1 <= x69 - 1 && 0 <= x67 - 1 (5) f1301_0_createTree_LE(x75, x76, x77, x78, x79) -> f1301_0_createTree_LE(x80, x81, x82, x83, x84) :|: x79 + 1 = x84 && x78 = x83 && x77 - 1 = x82 && 3 <= x81 - 1 && 3 <= x80 - 1 && 1 <= x76 - 1 && 1 <= x75 - 1 && x81 - 2 <= x76 && x81 - 2 <= x75 && x80 - 2 <= x76 && x80 - 2 <= x75 && x79 <= x78 - 1 && -1 <= x79 - 1 && 0 <= x77 - 1 (6) f1301_0_createTree_LE(x85, x86, x87, x88, x89) -> f1301_0_createTree_LE(x90, x91, x92, x93, x94) :|: -1 <= x89 - 1 && 0 <= x95 - 1 && 0 <= x87 - 1 && x89 <= x88 - 1 && x90 - 2 <= x85 && x90 - 2 <= x86 && x91 - 2 <= x85 && x91 - 2 <= x86 && 1 <= x85 - 1 && 1 <= x86 - 1 && 3 <= x90 - 1 && 3 <= x91 - 1 && x87 - 1 = x92 && x88 = x93 && x89 + 1 = x94 Arcs: (1) -> (1), (2), (3), (4), (5), (6) (2) -> (1), (2), (3), (4), (5), (6) (3) -> (1), (2), (3), (4), (5), (6) (4) -> (1), (2), (3), (4), (5), (6) (5) -> (1), (2), (3), (4), (5), (6) (6) -> (1), (2), (3), (4), (5), (6) This digraph is fully evaluated! ---------------------------------------- (6) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (7) Obligation: Rules: f1301_0_createTree_LE(x85:0, x86:0, x87:0, x88:0, x89:0) -> f1301_0_createTree_LE(x90:0, x91:0, x87:0 - 1, x88:0, x89:0 + 1) :|: x90:0 > 3 && x91:0 > 3 && x86:0 > 1 && x85:0 > 1 && x91:0 - 2 <= x86:0 && x91:0 - 2 <= x85:0 && x90:0 - 2 <= x86:0 && x90:0 - 2 <= x85:0 && x89:0 <= x88:0 - 1 && x87:0 > 0 && x95:0 > 0 && x89:0 > -1 f1301_0_createTree_LE(x42:0, x43:0, x44:0, x45:0, x46:0) -> f1301_0_createTree_LE(x47:0, x48:0, x44:0 - 1, x45:0, x46:0 + 1) :|: x47:0 > 0 && x48:0 > 0 && x43:0 > 2 && x42:0 > 0 && x48:0 + 2 <= x43:0 && x47:0 <= x42:0 && x46:0 <= x45:0 - 1 && x44:0 > 0 && x52:0 > 0 && x46:0 > -1 f1301_0_createTree_LE(x53:0, x54:0, x55:0, x56:0, x57:0) -> f1301_0_createTree_LE(x58:0, x59:0, x55:0 - 1, x56:0, x57:0 + 1) :|: x58:0 > 0 && x59:0 > 0 && x54:0 > 1 && x53:0 > 0 && x57:0 <= x56:0 - 1 && x55:0 > 0 && x64:0 > 0 && x57:0 > -1 f1301_0_createTree_LE(x65:0, x66:0, x67:0, x68:0, x69:0) -> f1301_0_createTree_LE(x70:0, x71:0, x67:0 - 1, x68:0, x69:0 + 1) :|: x69:0 > -1 && x67:0 > 0 && x69:0 <= x68:0 - 1 && x65:0 > 0 && x66:0 > 1 && x71:0 > 0 && x70:0 > 0 f1301_0_createTree_LE(x30:0, x32:0, x33:0, x34:0, x35:0) -> f1301_0_createTree_LE(x36:0, x37:0, x33:0 - 1, x34:0, x35:0 + 1) :|: x35:0 > -1 && x33:0 > 0 && x35:0 <= x34:0 - 1 && x36:0 <= x30:0 && x37:0 + 2 <= x32:0 && x30:0 > 0 && x32:0 > 2 && x37:0 > 0 && x36:0 > 0 f1301_0_createTree_LE(x75:0, x76:0, x77:0, x78:0, x79:0) -> f1301_0_createTree_LE(x80:0, x81:0, x77:0 - 1, x78:0, x79:0 + 1) :|: x79:0 > -1 && x77:0 > 0 && x79:0 <= x78:0 - 1 && x80:0 - 2 <= x75:0 && x80:0 - 2 <= x76:0 && x81:0 - 2 <= x75:0 && x81:0 - 2 <= x76:0 && x75:0 > 1 && x76:0 > 1 && x81:0 > 3 && x80:0 > 3 ---------------------------------------- (8) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f1301_0_createTree_LE(INTEGER, INTEGER, INTEGER, INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (9) Obligation: Rules: f1301_0_createTree_LE(x85:0, x86:0, x87:0, x88:0, x89:0) -> f1301_0_createTree_LE(x90:0, x91:0, c, x88:0, c1) :|: c1 = x89:0 + 1 && c = x87:0 - 1 && (x90:0 > 3 && x91:0 > 3 && x86:0 > 1 && x85:0 > 1 && x91:0 - 2 <= x86:0 && x91:0 - 2 <= x85:0 && x90:0 - 2 <= x86:0 && x90:0 - 2 <= x85:0 && x89:0 <= x88:0 - 1 && x87:0 > 0 && x95:0 > 0 && x89:0 > -1) f1301_0_createTree_LE(x42:0, x43:0, x44:0, x45:0, x46:0) -> f1301_0_createTree_LE(x47:0, x48:0, c2, x45:0, c3) :|: c3 = x46:0 + 1 && c2 = x44:0 - 1 && (x47:0 > 0 && x48:0 > 0 && x43:0 > 2 && x42:0 > 0 && x48:0 + 2 <= x43:0 && x47:0 <= x42:0 && x46:0 <= x45:0 - 1 && x44:0 > 0 && x52:0 > 0 && x46:0 > -1) f1301_0_createTree_LE(x53:0, x54:0, x55:0, x56:0, x57:0) -> f1301_0_createTree_LE(x58:0, x59:0, c4, x56:0, c5) :|: c5 = x57:0 + 1 && c4 = x55:0 - 1 && (x58:0 > 0 && x59:0 > 0 && x54:0 > 1 && x53:0 > 0 && x57:0 <= x56:0 - 1 && x55:0 > 0 && x64:0 > 0 && x57:0 > -1) f1301_0_createTree_LE(x65:0, x66:0, x67:0, x68:0, x69:0) -> f1301_0_createTree_LE(x70:0, x71:0, c6, x68:0, c7) :|: c7 = x69:0 + 1 && c6 = x67:0 - 1 && (x69:0 > -1 && x67:0 > 0 && x69:0 <= x68:0 - 1 && x65:0 > 0 && x66:0 > 1 && x71:0 > 0 && x70:0 > 0) f1301_0_createTree_LE(x30:0, x32:0, x33:0, x34:0, x35:0) -> f1301_0_createTree_LE(x36:0, x37:0, c8, x34:0, c9) :|: c9 = x35:0 + 1 && c8 = x33:0 - 1 && (x35:0 > -1 && x33:0 > 0 && x35:0 <= x34:0 - 1 && x36:0 <= x30:0 && x37:0 + 2 <= x32:0 && x30:0 > 0 && x32:0 > 2 && x37:0 > 0 && x36:0 > 0) f1301_0_createTree_LE(x75:0, x76:0, x77:0, x78:0, x79:0) -> f1301_0_createTree_LE(x80:0, x81:0, c10, x78:0, c11) :|: c11 = x79:0 + 1 && c10 = x77:0 - 1 && (x79:0 > -1 && x77:0 > 0 && x79:0 <= x78:0 - 1 && x80:0 - 2 <= x75:0 && x80:0 - 2 <= x76:0 && x81:0 - 2 <= x75:0 && x81:0 - 2 <= x76:0 && x75:0 > 1 && x76:0 > 1 && x81:0 > 3 && x80:0 > 3) ---------------------------------------- (10) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f1301_0_createTree_LE(x, x1, x2, x3, x4)] = x2 The following rules are decreasing: f1301_0_createTree_LE(x85:0, x86:0, x87:0, x88:0, x89:0) -> f1301_0_createTree_LE(x90:0, x91:0, c, x88:0, c1) :|: c1 = x89:0 + 1 && c = x87:0 - 1 && (x90:0 > 3 && x91:0 > 3 && x86:0 > 1 && x85:0 > 1 && x91:0 - 2 <= x86:0 && x91:0 - 2 <= x85:0 && x90:0 - 2 <= x86:0 && x90:0 - 2 <= x85:0 && x89:0 <= x88:0 - 1 && x87:0 > 0 && x95:0 > 0 && x89:0 > -1) f1301_0_createTree_LE(x42:0, x43:0, x44:0, x45:0, x46:0) -> f1301_0_createTree_LE(x47:0, x48:0, c2, x45:0, c3) :|: c3 = x46:0 + 1 && c2 = x44:0 - 1 && (x47:0 > 0 && x48:0 > 0 && x43:0 > 2 && x42:0 > 0 && x48:0 + 2 <= x43:0 && x47:0 <= x42:0 && x46:0 <= x45:0 - 1 && x44:0 > 0 && x52:0 > 0 && x46:0 > -1) f1301_0_createTree_LE(x53:0, x54:0, x55:0, x56:0, x57:0) -> f1301_0_createTree_LE(x58:0, x59:0, c4, x56:0, c5) :|: c5 = x57:0 + 1 && c4 = x55:0 - 1 && (x58:0 > 0 && x59:0 > 0 && x54:0 > 1 && x53:0 > 0 && x57:0 <= x56:0 - 1 && x55:0 > 0 && x64:0 > 0 && x57:0 > -1) f1301_0_createTree_LE(x65:0, x66:0, x67:0, x68:0, x69:0) -> f1301_0_createTree_LE(x70:0, x71:0, c6, x68:0, c7) :|: c7 = x69:0 + 1 && c6 = x67:0 - 1 && (x69:0 > -1 && x67:0 > 0 && x69:0 <= x68:0 - 1 && x65:0 > 0 && x66:0 > 1 && x71:0 > 0 && x70:0 > 0) f1301_0_createTree_LE(x30:0, x32:0, x33:0, x34:0, x35:0) -> f1301_0_createTree_LE(x36:0, x37:0, c8, x34:0, c9) :|: c9 = x35:0 + 1 && c8 = x33:0 - 1 && (x35:0 > -1 && x33:0 > 0 && x35:0 <= x34:0 - 1 && x36:0 <= x30:0 && x37:0 + 2 <= x32:0 && x30:0 > 0 && x32:0 > 2 && x37:0 > 0 && x36:0 > 0) f1301_0_createTree_LE(x75:0, x76:0, x77:0, x78:0, x79:0) -> f1301_0_createTree_LE(x80:0, x81:0, c10, x78:0, c11) :|: c11 = x79:0 + 1 && c10 = x77:0 - 1 && (x79:0 > -1 && x77:0 > 0 && x79:0 <= x78:0 - 1 && x80:0 - 2 <= x75:0 && x80:0 - 2 <= x76:0 && x81:0 - 2 <= x75:0 && x81:0 - 2 <= x76:0 && x75:0 > 1 && x76:0 > 1 && x81:0 > 3 && x80:0 > 3) The following rules are bounded: f1301_0_createTree_LE(x85:0, x86:0, x87:0, x88:0, x89:0) -> f1301_0_createTree_LE(x90:0, x91:0, c, x88:0, c1) :|: c1 = x89:0 + 1 && c = x87:0 - 1 && (x90:0 > 3 && x91:0 > 3 && x86:0 > 1 && x85:0 > 1 && x91:0 - 2 <= x86:0 && x91:0 - 2 <= x85:0 && x90:0 - 2 <= x86:0 && x90:0 - 2 <= x85:0 && x89:0 <= x88:0 - 1 && x87:0 > 0 && x95:0 > 0 && x89:0 > -1) f1301_0_createTree_LE(x42:0, x43:0, x44:0, x45:0, x46:0) -> f1301_0_createTree_LE(x47:0, x48:0, c2, x45:0, c3) :|: c3 = x46:0 + 1 && c2 = x44:0 - 1 && (x47:0 > 0 && x48:0 > 0 && x43:0 > 2 && x42:0 > 0 && x48:0 + 2 <= x43:0 && x47:0 <= x42:0 && x46:0 <= x45:0 - 1 && x44:0 > 0 && x52:0 > 0 && x46:0 > -1) f1301_0_createTree_LE(x53:0, x54:0, x55:0, x56:0, x57:0) -> f1301_0_createTree_LE(x58:0, x59:0, c4, x56:0, c5) :|: c5 = x57:0 + 1 && c4 = x55:0 - 1 && (x58:0 > 0 && x59:0 > 0 && x54:0 > 1 && x53:0 > 0 && x57:0 <= x56:0 - 1 && x55:0 > 0 && x64:0 > 0 && x57:0 > -1) f1301_0_createTree_LE(x65:0, x66:0, x67:0, x68:0, x69:0) -> f1301_0_createTree_LE(x70:0, x71:0, c6, x68:0, c7) :|: c7 = x69:0 + 1 && c6 = x67:0 - 1 && (x69:0 > -1 && x67:0 > 0 && x69:0 <= x68:0 - 1 && x65:0 > 0 && x66:0 > 1 && x71:0 > 0 && x70:0 > 0) f1301_0_createTree_LE(x30:0, x32:0, x33:0, x34:0, x35:0) -> f1301_0_createTree_LE(x36:0, x37:0, c8, x34:0, c9) :|: c9 = x35:0 + 1 && c8 = x33:0 - 1 && (x35:0 > -1 && x33:0 > 0 && x35:0 <= x34:0 - 1 && x36:0 <= x30:0 && x37:0 + 2 <= x32:0 && x30:0 > 0 && x32:0 > 2 && x37:0 > 0 && x36:0 > 0) f1301_0_createTree_LE(x75:0, x76:0, x77:0, x78:0, x79:0) -> f1301_0_createTree_LE(x80:0, x81:0, c10, x78:0, c11) :|: c11 = x79:0 + 1 && c10 = x77:0 - 1 && (x79:0 > -1 && x77:0 > 0 && x79:0 <= x78:0 - 1 && x80:0 - 2 <= x75:0 && x80:0 - 2 <= x76:0 && x81:0 - 2 <= x75:0 && x81:0 - 2 <= x76:0 && x75:0 > 1 && x76:0 > 1 && x81:0 > 3 && x80:0 > 3) ---------------------------------------- (11) YES ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) f1612_0_main_NULL(x10, x11, x12, x13, x14) -> f1612_0_main_NULL(x15, x16, x17, x18, x19) :|: -1 <= x16 - 1 && 2 <= x15 - 1 && 0 <= x11 - 1 && 2 <= x10 - 1 && x16 + 1 <= x11 && x16 + 3 <= x10 && x15 - 2 <= x10 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: f1612_0_main_NULL(x10:0, x11:0, x12:0, x13:0, x14:0) -> f1612_0_main_NULL(x15:0, x16:0, x17:0, x18:0, x19:0) :|: x16:0 + 3 <= x10:0 && x15:0 - 2 <= x10:0 && x16:0 + 1 <= x11:0 && x10:0 > 2 && x11:0 > 0 && x15:0 > 2 && x16:0 > -1 ---------------------------------------- (15) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f1612_0_main_NULL(x1, x2, x3, x4, x5) -> f1612_0_main_NULL(x1, x2) ---------------------------------------- (16) Obligation: Rules: f1612_0_main_NULL(x10:0, x11:0) -> f1612_0_main_NULL(x15:0, x16:0) :|: x16:0 + 3 <= x10:0 && x15:0 - 2 <= x10:0 && x16:0 + 1 <= x11:0 && x10:0 > 2 && x11:0 > 0 && x15:0 > 2 && x16:0 > -1 ---------------------------------------- (17) FilterProof (EQUIVALENT) Used the following sort dictionary for filtering: f1612_0_main_NULL(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (18) Obligation: Rules: f1612_0_main_NULL(x10:0, x11:0) -> f1612_0_main_NULL(x15:0, x16:0) :|: x16:0 + 3 <= x10:0 && x15:0 - 2 <= x10:0 && x16:0 + 1 <= x11:0 && x10:0 > 2 && x11:0 > 0 && x15:0 > 2 && x16:0 > -1 ---------------------------------------- (19) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (20) Obligation: Rules: f1612_0_main_NULL(x10:0:0, x11:0:0) -> f1612_0_main_NULL(x15:0:0, x16:0:0) :|: x15:0:0 > 2 && x16:0:0 > -1 && x11:0:0 > 0 && x10:0:0 > 2 && x16:0:0 + 1 <= x11:0:0 && x15:0:0 - 2 <= x10:0:0 && x16:0:0 + 3 <= x10:0:0 ---------------------------------------- (21) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f1612_0_main_NULL ] = f1612_0_main_NULL_2 The following rules are decreasing: f1612_0_main_NULL(x10:0:0, x11:0:0) -> f1612_0_main_NULL(x15:0:0, x16:0:0) :|: x15:0:0 > 2 && x16:0:0 > -1 && x11:0:0 > 0 && x10:0:0 > 2 && x16:0:0 + 1 <= x11:0:0 && x15:0:0 - 2 <= x10:0:0 && x16:0:0 + 3 <= x10:0:0 The following rules are bounded: f1612_0_main_NULL(x10:0:0, x11:0:0) -> f1612_0_main_NULL(x15:0:0, x16:0:0) :|: x15:0:0 > 2 && x16:0:0 > -1 && x11:0:0 > 0 && x10:0:0 > 2 && x16:0:0 + 1 <= x11:0:0 && x15:0:0 - 2 <= x10:0:0 && x16:0:0 + 3 <= x10:0:0 ---------------------------------------- (22) YES