MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 440 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 28 ms] (6) IRSwT (7) TempFilterProof [SOUND, 310 ms] (8) IRSwT (9) IRSwTTerminationDigraphProof [EQUIVALENT, 9 ms] (10) IRSwT (11) IntTRSCompressionProof [EQUIVALENT, 0 ms] (12) IRSwT ---------------------------------------- (0) Obligation: Rules: f1_0_main_Load(arg1, arg2) -> f142_0_loop_EQ(arg1P, arg2P) :|: arg2 = arg2P && 5 = arg1P && -1 <= arg2 - 1 && 0 <= arg1 - 1 f142_0_loop_EQ(x, x1) -> f142_0_loop_EQ(x2, x3) :|: -1 * x1 + 1 = x3 && x + 1 = x2 && x1 <= 0 - x - 1 && x1 <= -1 f142_0_loop_EQ(x4, x5) -> f142_0_loop_EQ(x6, x7) :|: -1 * x5 + 1 = x7 && x4 + 1 = x6 && x5 <= 0 - x4 - 1 && 0 <= x5 - 1 f142_0_loop_EQ(x8, x9) -> f142_0_loop_EQ(x10, x11) :|: 0 = x11 && x8 + 1 = x10 && 0 - x8 <= x9 && x9 <= -1 && x9 <= x8 f142_0_loop_EQ(x12, x13) -> f142_0_loop_EQ(x14, x15) :|: 0 = x15 && x12 + 1 = x14 && 0 - x12 <= x13 && 0 <= x13 - 1 && x13 <= x12 f142_0_loop_EQ(x16, x17) -> f142_0_loop_EQ(x18, x19) :|: -1 * x17 - 1 = x19 && x16 + 1 = x18 && 0 - x16 <= x17 && x17 <= -1 && x16 <= x17 - 1 f142_0_loop_EQ(x20, x21) -> f142_0_loop_EQ(x22, x23) :|: -1 * x21 - 1 = x23 && x20 + 1 = x22 && 0 - x20 <= x21 && 0 <= x21 - 1 && x20 <= x21 - 1 __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) -> f142_0_loop_EQ(arg1P, arg2P) :|: arg2 = arg2P && 5 = arg1P && -1 <= arg2 - 1 && 0 <= arg1 - 1 f142_0_loop_EQ(x, x1) -> f142_0_loop_EQ(x2, x3) :|: -1 * x1 + 1 = x3 && x + 1 = x2 && x1 <= 0 - x - 1 && x1 <= -1 f142_0_loop_EQ(x4, x5) -> f142_0_loop_EQ(x6, x7) :|: -1 * x5 + 1 = x7 && x4 + 1 = x6 && x5 <= 0 - x4 - 1 && 0 <= x5 - 1 f142_0_loop_EQ(x8, x9) -> f142_0_loop_EQ(x10, x11) :|: 0 = x11 && x8 + 1 = x10 && 0 - x8 <= x9 && x9 <= -1 && x9 <= x8 f142_0_loop_EQ(x12, x13) -> f142_0_loop_EQ(x14, x15) :|: 0 = x15 && x12 + 1 = x14 && 0 - x12 <= x13 && 0 <= x13 - 1 && x13 <= x12 f142_0_loop_EQ(x16, x17) -> f142_0_loop_EQ(x18, x19) :|: -1 * x17 - 1 = x19 && x16 + 1 = x18 && 0 - x16 <= x17 && x17 <= -1 && x16 <= x17 - 1 f142_0_loop_EQ(x20, x21) -> f142_0_loop_EQ(x22, x23) :|: -1 * x21 - 1 = x23 && x20 + 1 = x22 && 0 - x20 <= x21 && 0 <= x21 - 1 && x20 <= x21 - 1 __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) -> f142_0_loop_EQ(arg1P, arg2P) :|: arg2 = arg2P && 5 = arg1P && -1 <= arg2 - 1 && 0 <= arg1 - 1 (2) f142_0_loop_EQ(x, x1) -> f142_0_loop_EQ(x2, x3) :|: -1 * x1 + 1 = x3 && x + 1 = x2 && x1 <= 0 - x - 1 && x1 <= -1 (3) f142_0_loop_EQ(x4, x5) -> f142_0_loop_EQ(x6, x7) :|: -1 * x5 + 1 = x7 && x4 + 1 = x6 && x5 <= 0 - x4 - 1 && 0 <= x5 - 1 (4) f142_0_loop_EQ(x8, x9) -> f142_0_loop_EQ(x10, x11) :|: 0 = x11 && x8 + 1 = x10 && 0 - x8 <= x9 && x9 <= -1 && x9 <= x8 (5) f142_0_loop_EQ(x12, x13) -> f142_0_loop_EQ(x14, x15) :|: 0 = x15 && x12 + 1 = x14 && 0 - x12 <= x13 && 0 <= x13 - 1 && x13 <= x12 (6) f142_0_loop_EQ(x16, x17) -> f142_0_loop_EQ(x18, x19) :|: -1 * x17 - 1 = x19 && x16 + 1 = x18 && 0 - x16 <= x17 && x17 <= -1 && x16 <= x17 - 1 (7) f142_0_loop_EQ(x20, x21) -> f142_0_loop_EQ(x22, x23) :|: -1 * x21 - 1 = x23 && x20 + 1 = x22 && 0 - x20 <= x21 && 0 <= x21 - 1 && x20 <= x21 - 1 (8) __init(x24, x25) -> f1_0_main_Load(x26, x27) :|: 0 <= 0 Arcs: (1) -> (5), (7) (2) -> (3), (7) (3) -> (2) (7) -> (2) (8) -> (1) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) f142_0_loop_EQ(x20, x21) -> f142_0_loop_EQ(x22, x23) :|: -1 * x21 - 1 = x23 && x20 + 1 = x22 && 0 - x20 <= x21 && 0 <= x21 - 1 && x20 <= x21 - 1 (2) f142_0_loop_EQ(x, x1) -> f142_0_loop_EQ(x2, x3) :|: -1 * x1 + 1 = x3 && x + 1 = x2 && x1 <= 0 - x - 1 && x1 <= -1 (3) f142_0_loop_EQ(x4, x5) -> f142_0_loop_EQ(x6, x7) :|: -1 * x5 + 1 = x7 && x4 + 1 = x6 && x5 <= 0 - x4 - 1 && 0 <= x5 - 1 Arcs: (1) -> (2) (2) -> (1), (3) (3) -> (2) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: f142_0_loop_EQ(x:0, x1:0) -> f142_0_loop_EQ(x:0 + 1, -1 * x1:0 + 1) :|: x1:0 < 0 && x1:0 <= 0 - x:0 - 1 f142_0_loop_EQ(x20:0, x21:0) -> f142_0_loop_EQ(x20:0 + 1, -1 * x21:0 - 1) :|: x21:0 > 0 && x21:0 >= 0 - x20:0 && x21:0 - 1 >= x20:0 f142_0_loop_EQ(x4:0, x5:0) -> f142_0_loop_EQ(x4:0 + 1, -1 * x5:0 + 1) :|: x5:0 > 0 && x5:0 <= 0 - x4:0 - 1 ---------------------------------------- (7) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f142_0_loop_EQ(INTEGER, 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: f142_0_loop_EQ(x:0, x1:0) -> f142_0_loop_EQ(c, c1) :|: c1 = -1 * x1:0 + 1 && c = x:0 + 1 && (x1:0 < 0 && x1:0 <= 0 - x:0 - 1) f142_0_loop_EQ(x20:0, x21:0) -> f142_0_loop_EQ(c2, c3) :|: c3 = -1 * x21:0 - 1 && c2 = x20:0 + 1 && (x21:0 > 0 && x21:0 >= 0 - x20:0 && x21:0 - 1 >= x20:0) f142_0_loop_EQ(x4:0, x5:0) -> f142_0_loop_EQ(c4, c5) :|: c5 = -1 * x5:0 + 1 && c4 = x4:0 + 1 && (x5:0 > 0 && x5:0 <= 0 - x4:0 - 1) Found the following polynomial interpretation: [f142_0_loop_EQ(x, x1)] = -1 - x The following rules are decreasing: f142_0_loop_EQ(x:0, x1:0) -> f142_0_loop_EQ(c, c1) :|: c1 = -1 * x1:0 + 1 && c = x:0 + 1 && (x1:0 < 0 && x1:0 <= 0 - x:0 - 1) f142_0_loop_EQ(x20:0, x21:0) -> f142_0_loop_EQ(c2, c3) :|: c3 = -1 * x21:0 - 1 && c2 = x20:0 + 1 && (x21:0 > 0 && x21:0 >= 0 - x20:0 && x21:0 - 1 >= x20:0) f142_0_loop_EQ(x4:0, x5:0) -> f142_0_loop_EQ(c4, c5) :|: c5 = -1 * x5:0 + 1 && c4 = x4:0 + 1 && (x5:0 > 0 && x5:0 <= 0 - x4:0 - 1) The following rules are bounded: f142_0_loop_EQ(x4:0, x5:0) -> f142_0_loop_EQ(c4, c5) :|: c5 = -1 * x5:0 + 1 && c4 = x4:0 + 1 && (x5:0 > 0 && x5:0 <= 0 - x4:0 - 1) - IntTRS - PolynomialOrderProcessor - IntTRS Rules: f142_0_loop_EQ(x:0, x1:0) -> f142_0_loop_EQ(c, c1) :|: c1 = -1 * x1:0 + 1 && c = x:0 + 1 && (x1:0 < 0 && x1:0 <= 0 - x:0 - 1) f142_0_loop_EQ(x20:0, x21:0) -> f142_0_loop_EQ(c2, c3) :|: c3 = -1 * x21:0 - 1 && c2 = x20:0 + 1 && (x21:0 > 0 && x21:0 >= 0 - x20:0 && x21:0 - 1 >= x20:0) ---------------------------------------- (8) Obligation: Rules: f142_0_loop_EQ(x:0, x1:0) -> f142_0_loop_EQ(x:0 + 1, -1 * x1:0 + 1) :|: x1:0 < 0 && x1:0 <= 0 - x:0 - 1 f142_0_loop_EQ(x20:0, x21:0) -> f142_0_loop_EQ(x20:0 + 1, -1 * x21:0 - 1) :|: x21:0 > 0 && x21:0 >= 0 - x20:0 && x21:0 - 1 >= x20:0 ---------------------------------------- (9) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f142_0_loop_EQ(x:0, x1:0) -> f142_0_loop_EQ(x:0 + 1, -1 * x1:0 + 1) :|: x1:0 < 0 && x1:0 <= 0 - x:0 - 1 (2) f142_0_loop_EQ(x20:0, x21:0) -> f142_0_loop_EQ(x20:0 + 1, -1 * x21:0 - 1) :|: x21:0 > 0 && x21:0 >= 0 - x20:0 && x21:0 - 1 >= x20:0 Arcs: (1) -> (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (10) Obligation: Termination digraph: Nodes: (1) f142_0_loop_EQ(x:0, x1:0) -> f142_0_loop_EQ(x:0 + 1, -1 * x1:0 + 1) :|: x1:0 < 0 && x1:0 <= 0 - x:0 - 1 (2) f142_0_loop_EQ(x20:0, x21:0) -> f142_0_loop_EQ(x20:0 + 1, -1 * x21:0 - 1) :|: x21:0 > 0 && x21:0 >= 0 - x20:0 && x21:0 - 1 >= x20:0 Arcs: (1) -> (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (11) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (12) Obligation: Rules: f142_0_loop_EQ(x20:0:0, x21:0:0) -> f142_0_loop_EQ(x20:0:0 + 1, -1 * x21:0:0 - 1) :|: x21:0:0 > 0 && x21:0:0 >= 0 - x20:0:0 && x21:0:0 - 1 >= x20:0:0 f142_0_loop_EQ(x:0:0, x1:0:0) -> f142_0_loop_EQ(x:0:0 + 1, -1 * x1:0:0 + 1) :|: x1:0:0 < 0 && x1:0:0 <= 0 - x:0:0 - 1