MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 233 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 0 ms] (6) IRSwT (7) TempFilterProof [SOUND, 1353 ms] (8) IRSwT (9) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IntTRSCompressionProof [EQUIVALENT, 0 ms] (12) IRSwT ---------------------------------------- (0) Obligation: Rules: f1_0_main_ConstantStackPush(arg1, arg2, arg3, arg4) -> f79_0_loop_GE(arg1P, arg2P, arg3P, arg4P) :|: 0 = arg4P && 2 = arg3P && 2 = arg2P && 2 = arg1P f79_0_loop_GE(x, x1, x2, x3) -> f100_0_loop_InvokeMethod(x4, x5, x6, x7) :|: x3 = x6 && x1 + 4 = x5 && x = x4 && x1 = x2 && 0 <= x1 - 1 && x1 <= x3 - 1 f79_0_loop_GE(x8, x9, x10, x11) -> f100_0_loop_InvokeMethod(x12, x13, x14, x15) :|: x11 + 1 = x14 && x9 + 2 = x13 && x8 = x12 && x9 = x10 && -1 <= x11 - 1 && 0 <= x9 - 1 && x11 <= x9 f100_0_loop_InvokeMethod(x16, x17, x18, x19) -> f79_0_loop_GE(x20, x21, x22, x23) :|: x18 = x23 && x17 = x22 && x17 = x21 && x17 = x20 && 1 <= x17 - 1 && 1 <= x16 - 1 && 0 <= x18 - 1 __init(x24, x25, x26, x27) -> f1_0_main_ConstantStackPush(x28, x29, x30, x31) :|: 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: f1_0_main_ConstantStackPush(arg1, arg2, arg3, arg4) -> f79_0_loop_GE(arg1P, arg2P, arg3P, arg4P) :|: 0 = arg4P && 2 = arg3P && 2 = arg2P && 2 = arg1P f79_0_loop_GE(x, x1, x2, x3) -> f100_0_loop_InvokeMethod(x4, x5, x6, x7) :|: x3 = x6 && x1 + 4 = x5 && x = x4 && x1 = x2 && 0 <= x1 - 1 && x1 <= x3 - 1 f79_0_loop_GE(x8, x9, x10, x11) -> f100_0_loop_InvokeMethod(x12, x13, x14, x15) :|: x11 + 1 = x14 && x9 + 2 = x13 && x8 = x12 && x9 = x10 && -1 <= x11 - 1 && 0 <= x9 - 1 && x11 <= x9 f100_0_loop_InvokeMethod(x16, x17, x18, x19) -> f79_0_loop_GE(x20, x21, x22, x23) :|: x18 = x23 && x17 = x22 && x17 = x21 && x17 = x20 && 1 <= x17 - 1 && 1 <= x16 - 1 && 0 <= x18 - 1 __init(x24, x25, x26, x27) -> f1_0_main_ConstantStackPush(x28, x29, x30, x31) :|: 0 <= 0 Start term: __init(arg1, arg2, arg3, arg4) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f1_0_main_ConstantStackPush(arg1, arg2, arg3, arg4) -> f79_0_loop_GE(arg1P, arg2P, arg3P, arg4P) :|: 0 = arg4P && 2 = arg3P && 2 = arg2P && 2 = arg1P (2) f79_0_loop_GE(x, x1, x2, x3) -> f100_0_loop_InvokeMethod(x4, x5, x6, x7) :|: x3 = x6 && x1 + 4 = x5 && x = x4 && x1 = x2 && 0 <= x1 - 1 && x1 <= x3 - 1 (3) f79_0_loop_GE(x8, x9, x10, x11) -> f100_0_loop_InvokeMethod(x12, x13, x14, x15) :|: x11 + 1 = x14 && x9 + 2 = x13 && x8 = x12 && x9 = x10 && -1 <= x11 - 1 && 0 <= x9 - 1 && x11 <= x9 (4) f100_0_loop_InvokeMethod(x16, x17, x18, x19) -> f79_0_loop_GE(x20, x21, x22, x23) :|: x18 = x23 && x17 = x22 && x17 = x21 && x17 = x20 && 1 <= x17 - 1 && 1 <= x16 - 1 && 0 <= x18 - 1 (5) __init(x24, x25, x26, x27) -> f1_0_main_ConstantStackPush(x28, x29, x30, x31) :|: 0 <= 0 Arcs: (1) -> (3) (2) -> (4) (3) -> (4) (4) -> (2), (3) (5) -> (1) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) f79_0_loop_GE(x8, x9, x10, x11) -> f100_0_loop_InvokeMethod(x12, x13, x14, x15) :|: x11 + 1 = x14 && x9 + 2 = x13 && x8 = x12 && x9 = x10 && -1 <= x11 - 1 && 0 <= x9 - 1 && x11 <= x9 (2) f100_0_loop_InvokeMethod(x16, x17, x18, x19) -> f79_0_loop_GE(x20, x21, x22, x23) :|: x18 = x23 && x17 = x22 && x17 = x21 && x17 = x20 && 1 <= x17 - 1 && 1 <= x16 - 1 && 0 <= x18 - 1 (3) f79_0_loop_GE(x, x1, x2, x3) -> f100_0_loop_InvokeMethod(x4, x5, x6, x7) :|: x3 = x6 && x1 + 4 = x5 && x = x4 && x1 = x2 && 0 <= x1 - 1 && x1 <= x3 - 1 Arcs: (1) -> (2) (2) -> (1), (3) (3) -> (2) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: f79_0_loop_GE(x4:0, x1:0, x1:0, x23:0) -> f79_0_loop_GE(x1:0 + 4, x1:0 + 4, x1:0 + 4, x23:0) :|: x23:0 > 0 && x23:0 - 1 >= x1:0 && x1:0 > 0 && x4:0 > 1 f79_0_loop_GE(x12:0, x10:0, x10:0, x11:0) -> f79_0_loop_GE(x10:0 + 2, x10:0 + 2, x10:0 + 2, x11:0 + 1) :|: x11:0 <= x10:0 && x12:0 > 1 && x10:0 > 0 && x11:0 > -1 ---------------------------------------- (7) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f79_0_loop_GE(INTEGER, INTEGER, 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: f79_0_loop_GE(x4:0, x1:0, x1:0, x23:0) -> f79_0_loop_GE(c, c1, c2, x23:0) :|: c2 = x1:0 + 4 && (c1 = x1:0 + 4 && c = x1:0 + 4) && (x23:0 > 0 && x23:0 - 1 >= x1:0 && x1:0 > 0 && x4:0 > 1) f79_0_loop_GE(x12:0, x10:0, x10:0, x11:0) -> f79_0_loop_GE(c3, c4, c5, c6) :|: c6 = x11:0 + 1 && (c5 = x10:0 + 2 && (c4 = x10:0 + 2 && c3 = x10:0 + 2)) && (x11:0 <= x10:0 && x12:0 > 1 && x10:0 > 0 && x11:0 > -1) Found the following polynomial interpretation: [f79_0_loop_GE(x, x1, x2, x3)] = -2 - x1 + 2*x3 The following rules are decreasing: f79_0_loop_GE(x4:0, x1:0, x1:0, x23:0) -> f79_0_loop_GE(c, c1, c2, x23:0) :|: c2 = x1:0 + 4 && (c1 = x1:0 + 4 && c = x1:0 + 4) && (x23:0 > 0 && x23:0 - 1 >= x1:0 && x1:0 > 0 && x4:0 > 1) The following rules are bounded: f79_0_loop_GE(x4:0, x1:0, x1:0, x23:0) -> f79_0_loop_GE(c, c1, c2, x23:0) :|: c2 = x1:0 + 4 && (c1 = x1:0 + 4 && c = x1:0 + 4) && (x23:0 > 0 && x23:0 - 1 >= x1:0 && x1:0 > 0 && x4:0 > 1) - IntTRS - PolynomialOrderProcessor - IntTRS Rules: f79_0_loop_GE(x12:0, x10:0, x10:0, x11:0) -> f79_0_loop_GE(c3, c4, c5, c6) :|: c6 = x11:0 + 1 && (c5 = x10:0 + 2 && (c4 = x10:0 + 2 && c3 = x10:0 + 2)) && (x11:0 <= x10:0 && x12:0 > 1 && x10:0 > 0 && x11:0 > -1) ---------------------------------------- (8) Obligation: Rules: f79_0_loop_GE(x12:0, x10:0, x10:0, x11:0) -> f79_0_loop_GE(x10:0 + 2, x10:0 + 2, x10:0 + 2, x11:0 + 1) :|: x11:0 <= x10:0 && x12:0 > 1 && x10:0 > 0 && x11:0 > -1 ---------------------------------------- (9) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f79_0_loop_GE(x12:0, x10:0, x10:0, x11:0) -> f79_0_loop_GE(x10:0 + 2, x10:0 + 2, x10:0 + 2, x11:0 + 1) :|: x11:0 <= x10:0 && x12:0 > 1 && x10:0 > 0 && x11:0 > -1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (10) Obligation: Termination digraph: Nodes: (1) f79_0_loop_GE(x12:0, x10:0, x10:0, x11:0) -> f79_0_loop_GE(x10:0 + 2, x10:0 + 2, x10:0 + 2, x11:0 + 1) :|: x11:0 <= x10:0 && x12:0 > 1 && x10:0 > 0 && x11:0 > -1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (11) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (12) Obligation: Rules: f79_0_loop_GE(x12:0:0, x10:0:0, x10:0:0, x11:0:0) -> f79_0_loop_GE(x10:0:0 + 2, x10:0:0 + 2, x10:0:0 + 2, x11:0:0 + 1) :|: x10:0:0 > 0 && x11:0:0 > -1 && x12:0:0 > 1 && x11:0:0 <= x10:0:0