MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof [EQUIVALENT, 191 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 0 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 101 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 5 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT ---------------------------------------- (0) Obligation: Rules: f1_0_main_Load(arg1, arg2) -> f49_0_loop_LE(arg1P, arg2P) :|: arg2 = arg1P && -1 <= arg2 - 1 && 0 <= arg1 - 1 f49_0_loop_LE(x, x1) -> f49_0_loop_LE'(x2, x3) :|: x - 5 * x4 = 0 && 2 <= x - 1 && x = x2 f49_0_loop_LE'(x6, x8) -> f49_0_loop_LE(x10, x12) :|: 2 <= x6 - 1 && x6 - 5 * x13 = 0 && x6 - 5 * x13 <= 4 && 0 <= x6 - 5 * x13 && x6 = x10 f49_0_loop_LE(x14, x15) -> f49_0_loop_LE'(x16, x17) :|: 0 <= x14 - 5 * x18 - 1 && 2 <= x14 - 1 && x14 = x16 f49_0_loop_LE'(x19, x20) -> f49_0_loop_LE(x21, x22) :|: 0 <= x19 - 5 * x23 - 1 && x19 - 5 * x23 <= 4 && 2 <= x19 - 1 && x19 - 1 = x21 __init(x24, x25) -> f1_0_main_Load(x26, x27) :|: 0 <= 0 Start term: __init(arg1, arg2) ---------------------------------------- (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) -> f49_0_loop_LE(arg1P, arg2P) :|: arg2 = arg1P && -1 <= arg2 - 1 && 0 <= arg1 - 1 f49_0_loop_LE(x, x1) -> f49_0_loop_LE'(x2, x3) :|: x - 5 * x4 = 0 && 2 <= x - 1 && x = x2 f49_0_loop_LE'(x6, x8) -> f49_0_loop_LE(x10, x12) :|: 2 <= x6 - 1 && x6 - 5 * x13 = 0 && x6 - 5 * x13 <= 4 && 0 <= x6 - 5 * x13 && x6 = x10 f49_0_loop_LE(x14, x15) -> f49_0_loop_LE'(x16, x17) :|: 0 <= x14 - 5 * x18 - 1 && 2 <= x14 - 1 && x14 = x16 f49_0_loop_LE'(x19, x20) -> f49_0_loop_LE(x21, x22) :|: 0 <= x19 - 5 * x23 - 1 && x19 - 5 * x23 <= 4 && 2 <= x19 - 1 && x19 - 1 = x21 __init(x24, x25) -> f1_0_main_Load(x26, x27) :|: 0 <= 0 Start term: __init(arg1, arg2) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f1_0_main_Load(arg1, arg2) -> f49_0_loop_LE(arg1P, arg2P) :|: arg2 = arg1P && -1 <= arg2 - 1 && 0 <= arg1 - 1 (2) f49_0_loop_LE(x, x1) -> f49_0_loop_LE'(x2, x3) :|: x - 5 * x4 = 0 && 2 <= x - 1 && x = x2 (3) f49_0_loop_LE'(x6, x8) -> f49_0_loop_LE(x10, x12) :|: 2 <= x6 - 1 && x6 - 5 * x13 = 0 && x6 - 5 * x13 <= 4 && 0 <= x6 - 5 * x13 && x6 = x10 (4) f49_0_loop_LE(x14, x15) -> f49_0_loop_LE'(x16, x17) :|: 0 <= x14 - 5 * x18 - 1 && 2 <= x14 - 1 && x14 = x16 (5) f49_0_loop_LE'(x19, x20) -> f49_0_loop_LE(x21, x22) :|: 0 <= x19 - 5 * x23 - 1 && x19 - 5 * x23 <= 4 && 2 <= x19 - 1 && x19 - 1 = x21 (6) __init(x24, x25) -> f1_0_main_Load(x26, x27) :|: 0 <= 0 Arcs: (1) -> (2), (4) (2) -> (3) (3) -> (2), (4) (4) -> (3), (5) (5) -> (2), (4) (6) -> (1) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) f49_0_loop_LE(x, x1) -> f49_0_loop_LE'(x2, x3) :|: x - 5 * x4 = 0 && 2 <= x - 1 && x = x2 (2) f49_0_loop_LE'(x6, x8) -> f49_0_loop_LE(x10, x12) :|: 2 <= x6 - 1 && x6 - 5 * x13 = 0 && x6 - 5 * x13 <= 4 && 0 <= x6 - 5 * x13 && x6 = x10 (3) f49_0_loop_LE(x14, x15) -> f49_0_loop_LE'(x16, x17) :|: 0 <= x14 - 5 * x18 - 1 && 2 <= x14 - 1 && x14 = x16 (4) f49_0_loop_LE'(x19, x20) -> f49_0_loop_LE(x21, x22) :|: 0 <= x19 - 5 * x23 - 1 && x19 - 5 * x23 <= 4 && 2 <= x19 - 1 && x19 - 1 = x21 Arcs: (1) -> (2) (2) -> (1), (3) (3) -> (2), (4) (4) -> (1), (3) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: f49_0_loop_LE'(x10:0, x8:0) -> f49_0_loop_LE(x10:0, x12:0) :|: x10:0 - 5 * x13:0 <= 4 && x10:0 - 5 * x13:0 >= 0 && x10:0 - 5 * x13:0 = 0 && x10:0 > 2 f49_0_loop_LE'(x19:0, x20:0) -> f49_0_loop_LE(x19:0 - 1, x22:0) :|: x19:0 - 5 * x23:0 >= 1 && x19:0 - 5 * x23:0 <= 4 && x19:0 > 2 f49_0_loop_LE(x14:0, x15:0) -> f49_0_loop_LE'(x14:0, x17:0) :|: x14:0 - 5 * x18:0 >= 1 && x14:0 > 2 f49_0_loop_LE(x2:0, x1:0) -> f49_0_loop_LE'(x2:0, x3:0) :|: x2:0 - 5 * x4:0 = 0 && x2:0 > 2 ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f49_0_loop_LE'(x1, x2) -> f49_0_loop_LE'(x1) f49_0_loop_LE(x1, x2) -> f49_0_loop_LE(x1) ---------------------------------------- (8) Obligation: Rules: f49_0_loop_LE'(x10:0) -> f49_0_loop_LE(x10:0) :|: x10:0 - 5 * x13:0 <= 4 && x10:0 - 5 * x13:0 >= 0 && x10:0 - 5 * x13:0 = 0 && x10:0 > 2 f49_0_loop_LE'(x19:0) -> f49_0_loop_LE(x19:0 - 1) :|: x19:0 - 5 * x23:0 >= 1 && x19:0 - 5 * x23:0 <= 4 && x19:0 > 2 f49_0_loop_LE(x14:0) -> f49_0_loop_LE'(x14:0) :|: x14:0 - 5 * x18:0 >= 1 && x14:0 > 2 f49_0_loop_LE(x2:0) -> f49_0_loop_LE'(x2:0) :|: x2:0 - 5 * x4:0 = 0 && x2:0 > 2 ---------------------------------------- (9) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f49_0_loop_LE'(INTEGER) f49_0_loop_LE(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: f49_0_loop_LE'(x10:0) -> f49_0_loop_LE(x10:0) :|: x10:0 - 5 * x13:0 <= 4 && x10:0 - 5 * x13:0 >= 0 && x10:0 - 5 * x13:0 = 0 && x10:0 > 2 f49_0_loop_LE'(x19:0) -> f49_0_loop_LE(c) :|: c = x19:0 - 1 && (x19:0 - 5 * x23:0 >= 1 && x19:0 - 5 * x23:0 <= 4 && x19:0 > 2) f49_0_loop_LE(x14:0) -> f49_0_loop_LE'(x14:0) :|: x14:0 - 5 * x18:0 >= 1 && x14:0 > 2 f49_0_loop_LE(x2:0) -> f49_0_loop_LE'(x2:0) :|: x2:0 - 5 * x4:0 = 0 && x2:0 > 2 Found the following polynomial interpretation: [f49_0_loop_LE'(x)] = x [f49_0_loop_LE(x1)] = x1 The following rules are decreasing: f49_0_loop_LE'(x19:0) -> f49_0_loop_LE(c) :|: c = x19:0 - 1 && (x19:0 - 5 * x23:0 >= 1 && x19:0 - 5 * x23:0 <= 4 && x19:0 > 2) The following rules are bounded: f49_0_loop_LE'(x10:0) -> f49_0_loop_LE(x10:0) :|: x10:0 - 5 * x13:0 <= 4 && x10:0 - 5 * x13:0 >= 0 && x10:0 - 5 * x13:0 = 0 && x10:0 > 2 f49_0_loop_LE'(x19:0) -> f49_0_loop_LE(c) :|: c = x19:0 - 1 && (x19:0 - 5 * x23:0 >= 1 && x19:0 - 5 * x23:0 <= 4 && x19:0 > 2) f49_0_loop_LE(x14:0) -> f49_0_loop_LE'(x14:0) :|: x14:0 - 5 * x18:0 >= 1 && x14:0 > 2 f49_0_loop_LE(x2:0) -> f49_0_loop_LE'(x2:0) :|: x2:0 - 5 * x4:0 = 0 && x2:0 > 2 - IntTRS - PolynomialOrderProcessor - IntTRS Rules: f49_0_loop_LE'(x10:0) -> f49_0_loop_LE(x10:0) :|: x10:0 - 5 * x13:0 <= 4 && x10:0 - 5 * x13:0 >= 0 && x10:0 - 5 * x13:0 = 0 && x10:0 > 2 f49_0_loop_LE(x14:0) -> f49_0_loop_LE'(x14:0) :|: x14:0 - 5 * x18:0 >= 1 && x14:0 > 2 f49_0_loop_LE(x2:0) -> f49_0_loop_LE'(x2:0) :|: x2:0 - 5 * x4:0 = 0 && x2:0 > 2 ---------------------------------------- (10) Obligation: Rules: f49_0_loop_LE'(x10:0) -> f49_0_loop_LE(x10:0) :|: x10:0 - 5 * x13:0 <= 4 && x10:0 - 5 * x13:0 >= 0 && x10:0 - 5 * x13:0 = 0 && x10:0 > 2 f49_0_loop_LE(x14:0) -> f49_0_loop_LE'(x14:0) :|: x14:0 - 5 * x18:0 >= 1 && x14:0 > 2 f49_0_loop_LE(x2:0) -> f49_0_loop_LE'(x2:0) :|: x2:0 - 5 * x4:0 = 0 && x2:0 > 2 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f49_0_loop_LE'(x10:0) -> f49_0_loop_LE(x10:0) :|: x10:0 - 5 * x13:0 <= 4 && x10:0 - 5 * x13:0 >= 0 && x10:0 - 5 * x13:0 = 0 && x10:0 > 2 (2) f49_0_loop_LE(x14:0) -> f49_0_loop_LE'(x14:0) :|: x14:0 - 5 * x18:0 >= 1 && x14:0 > 2 (3) f49_0_loop_LE(x2:0) -> f49_0_loop_LE'(x2:0) :|: x2:0 - 5 * x4:0 = 0 && x2:0 > 2 Arcs: (1) -> (2), (3) (2) -> (1) (3) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) f49_0_loop_LE'(x10:0) -> f49_0_loop_LE(x10:0) :|: x10:0 - 5 * x13:0 <= 4 && x10:0 - 5 * x13:0 >= 0 && x10:0 - 5 * x13:0 = 0 && x10:0 > 2 (2) f49_0_loop_LE(x2:0) -> f49_0_loop_LE'(x2:0) :|: x2:0 - 5 * x4:0 = 0 && x2:0 > 2 (3) f49_0_loop_LE(x14:0) -> f49_0_loop_LE'(x14:0) :|: x14:0 - 5 * x18:0 >= 1 && x14:0 > 2 Arcs: (1) -> (2), (3) (2) -> (1) (3) -> (1) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: f49_0_loop_LE'(x10:0:0) -> f49_0_loop_LE'(x10:0:0) :|: x10:0:0 - 5 * x4:0:0 = 0 && x10:0:0 > 2 && x10:0:0 - 5 * x13:0:0 = 0 && x10:0:0 - 5 * x13:0:0 >= 0 && x10:0:0 - 5 * x13:0:0 <= 4 f49_0_loop_LE'(x) -> f49_0_loop_LE'(x) :|: x - 5 * x1 >= 1 && x > 2 && x - 5 * x2 = 0 && x - 5 * x2 >= 0 && x - 5 * x2 <= 4