MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 237 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 35 ms] (6) IRSwT (7) IRSwTChainingProof [EQUIVALENT, 0 ms] (8) IRSwT (9) IRSwTTerminationDigraphProof [EQUIVALENT, 11 ms] (10) IRSwT (11) IntTRSCompressionProof [EQUIVALENT, 0 ms] (12) IRSwT (13) IRSwTChainingProof [EQUIVALENT, 0 ms] (14) IRSwT (15) IRSwTTerminationDigraphProof [EQUIVALENT, 42 ms] (16) IRSwT (17) IntTRSCompressionProof [EQUIVALENT, 4 ms] (18) IRSwT (19) TempFilterProof [SOUND, 3466 ms] (20) IRSwT (21) IRSwTTerminationDigraphProof [EQUIVALENT, 6 ms] (22) IRSwT (23) IntTRSCompressionProof [EQUIVALENT, 0 ms] (24) IRSwT ---------------------------------------- (0) Obligation: Rules: f1_0_main_Load(arg1, arg2, arg3, arg4, arg5) -> f362_0_gt_LE(arg1P, arg2P, arg3P, arg4P, arg5P) :|: arg1P = arg5P && arg2P = arg4P && arg1P = arg3P && 0 <= arg1 - 1 && -1 <= arg1P - 1 && -1 <= arg2 - 1 && -1 <= arg2P - 1 f362_0_gt_LE(x, x1, x2, x3, x4) -> f362_0_gt_LE(x5, x6, x7, x8, x9) :|: x2 - 1 = x9 && x3 - 1 = x8 && x2 - 1 = x7 && x1 = x6 && x = x5 && x2 = x4 && 0 <= x3 - 1 && 0 <= x2 - 1 f362_0_gt_LE(x10, x11, x12, x13, x14) -> f362_0_gt_LE(x15, x16, x17, x18, x19) :|: x10 = x19 && x11 + 1 = x18 && x10 = x17 && x11 + 1 = x16 && x10 = x15 && x12 = x14 && 0 = x13 && 0 <= x12 - 1 __init(x20, x21, x22, x23, x24) -> f1_0_main_Load(x25, x26, x27, x28, x29) :|: 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) -> f362_0_gt_LE(arg1P, arg2P, arg3P, arg4P, arg5P) :|: arg1P = arg5P && arg2P = arg4P && arg1P = arg3P && 0 <= arg1 - 1 && -1 <= arg1P - 1 && -1 <= arg2 - 1 && -1 <= arg2P - 1 f362_0_gt_LE(x, x1, x2, x3, x4) -> f362_0_gt_LE(x5, x6, x7, x8, x9) :|: x2 - 1 = x9 && x3 - 1 = x8 && x2 - 1 = x7 && x1 = x6 && x = x5 && x2 = x4 && 0 <= x3 - 1 && 0 <= x2 - 1 f362_0_gt_LE(x10, x11, x12, x13, x14) -> f362_0_gt_LE(x15, x16, x17, x18, x19) :|: x10 = x19 && x11 + 1 = x18 && x10 = x17 && x11 + 1 = x16 && x10 = x15 && x12 = x14 && 0 = x13 && 0 <= x12 - 1 __init(x20, x21, x22, x23, x24) -> f1_0_main_Load(x25, x26, x27, x28, x29) :|: 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) -> f362_0_gt_LE(arg1P, arg2P, arg3P, arg4P, arg5P) :|: arg1P = arg5P && arg2P = arg4P && arg1P = arg3P && 0 <= arg1 - 1 && -1 <= arg1P - 1 && -1 <= arg2 - 1 && -1 <= arg2P - 1 (2) f362_0_gt_LE(x, x1, x2, x3, x4) -> f362_0_gt_LE(x5, x6, x7, x8, x9) :|: x2 - 1 = x9 && x3 - 1 = x8 && x2 - 1 = x7 && x1 = x6 && x = x5 && x2 = x4 && 0 <= x3 - 1 && 0 <= x2 - 1 (3) f362_0_gt_LE(x10, x11, x12, x13, x14) -> f362_0_gt_LE(x15, x16, x17, x18, x19) :|: x10 = x19 && x11 + 1 = x18 && x10 = x17 && x11 + 1 = x16 && x10 = x15 && x12 = x14 && 0 = x13 && 0 <= x12 - 1 (4) __init(x20, x21, x22, x23, x24) -> f1_0_main_Load(x25, x26, x27, x28, x29) :|: 0 <= 0 Arcs: (1) -> (2), (3) (2) -> (2), (3) (3) -> (2), (3) (4) -> (1) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) f362_0_gt_LE(x, x1, x2, x3, x4) -> f362_0_gt_LE(x5, x6, x7, x8, x9) :|: x2 - 1 = x9 && x3 - 1 = x8 && x2 - 1 = x7 && x1 = x6 && x = x5 && x2 = x4 && 0 <= x3 - 1 && 0 <= x2 - 1 (2) f362_0_gt_LE(x10, x11, x12, x13, x14) -> f362_0_gt_LE(x15, x16, x17, x18, x19) :|: x10 = x19 && x11 + 1 = x18 && x10 = x17 && x11 + 1 = x16 && x10 = x15 && x12 = x14 && 0 = x13 && 0 <= x12 - 1 Arcs: (1) -> (1), (2) (2) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: f362_0_gt_LE(x5:0, x1:0, x2:0, x3:0, x2:0) -> f362_0_gt_LE(x5:0, x1:0, x2:0 - 1, x3:0 - 1, x2:0 - 1) :|: x2:0 > 0 && x3:0 > 0 f362_0_gt_LE(x10:0, x11:0, x12:0, cons_0, x12:0) -> f362_0_gt_LE(x10:0, x11:0 + 1, x10:0, x11:0 + 1, x10:0) :|: x12:0 > 0 && cons_0 = 0 ---------------------------------------- (7) IRSwTChainingProof (EQUIVALENT) Chaining! ---------------------------------------- (8) Obligation: Rules: f362_0_gt_LE(x, x1, x2, x3, x2) -> f362_0_gt_LE(x, x1, x2 + -2, x3 + -2, x2 + -2) :|: TRUE && x2 >= 2 && x3 >= 2 f362_0_gt_LE(x10:0, x11:0, x12:0, cons_0, x12:0) -> f362_0_gt_LE(x10:0, x11:0 + 1, x10:0, x11:0 + 1, x10:0) :|: x12:0 > 0 && cons_0 = 0 f362_0_gt_LE(x8, x9, x10, x11, x10) -> f362_0_gt_LE(x8, x9 + 1, x8, x9 + 1, x8) :|: TRUE && x10 >= 2 && x11 = 1 ---------------------------------------- (9) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f362_0_gt_LE(x, x1, x2, x3, x2) -> f362_0_gt_LE(x, x1, x2 + -2, x3 + -2, x2 + -2) :|: TRUE && x2 >= 2 && x3 >= 2 (2) f362_0_gt_LE(x10:0, x11:0, x12:0, cons_0, x12:0) -> f362_0_gt_LE(x10:0, x11:0 + 1, x10:0, x11:0 + 1, x10:0) :|: x12:0 > 0 && cons_0 = 0 (3) f362_0_gt_LE(x8, x9, x10, x11, x10) -> f362_0_gt_LE(x8, x9 + 1, x8, x9 + 1, x8) :|: TRUE && x10 >= 2 && x11 = 1 Arcs: (1) -> (1), (2), (3) (2) -> (1), (2), (3) (3) -> (1), (2), (3) This digraph is fully evaluated! ---------------------------------------- (10) Obligation: Termination digraph: Nodes: (1) f362_0_gt_LE(x, x1, x2, x3, x2) -> f362_0_gt_LE(x, x1, x2 + -2, x3 + -2, x2 + -2) :|: TRUE && x2 >= 2 && x3 >= 2 (2) f362_0_gt_LE(x10:0, x11:0, x12:0, cons_0, x12:0) -> f362_0_gt_LE(x10:0, x11:0 + 1, x10:0, x11:0 + 1, x10:0) :|: x12:0 > 0 && cons_0 = 0 (3) f362_0_gt_LE(x8, x9, x10, x11, x10) -> f362_0_gt_LE(x8, x9 + 1, x8, x9 + 1, x8) :|: TRUE && x10 >= 2 && x11 = 1 Arcs: (1) -> (1), (2), (3) (2) -> (1), (2), (3) (3) -> (1), (2), (3) This digraph is fully evaluated! ---------------------------------------- (11) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (12) Obligation: Rules: f362_0_gt_LE(x8:0, x9:0, x10:0, cons_1, x10:0) -> f362_0_gt_LE(x8:0, x9:0 + 1, x8:0, x9:0 + 1, x8:0) :|: x10:0 > 1 && cons_1 = 1 f362_0_gt_LE(x:0, x1:0, x2:0, x3:0, x2:0) -> f362_0_gt_LE(x:0, x1:0, x2:0 - 2, x3:0 - 2, x2:0 - 2) :|: x3:0 > 1 && x2:0 > 1 f362_0_gt_LE(x10:0:0, x11:0:0, x12:0:0, cons_0, x12:0:0) -> f362_0_gt_LE(x10:0:0, x11:0:0 + 1, x10:0:0, x11:0:0 + 1, x10:0:0) :|: x12:0:0 > 0 && cons_0 = 0 ---------------------------------------- (13) IRSwTChainingProof (EQUIVALENT) Chaining! ---------------------------------------- (14) Obligation: Rules: f362_0_gt_LE(x, x1, x2, x3, x2) -> f362_0_gt_LE(x, 0 + 2, x, 0 + 2, x) :|: TRUE && x2 >= 2 && x3 = 1 && x >= 2 && x1 = 0 f362_0_gt_LE(x:0, x1:0, x2:0, x3:0, x2:0) -> f362_0_gt_LE(x:0, x1:0, x2:0 - 2, x3:0 - 2, x2:0 - 2) :|: x3:0 > 1 && x2:0 > 1 f362_0_gt_LE(x8, x9, x10, x11, x10) -> f362_0_gt_LE(x8, x9 + 1, x8 + -2, x9 + -1, x8 + -2) :|: TRUE && x10 >= 2 && x11 = 1 && x9 >= 1 && x8 >= 2 f362_0_gt_LE(x10:0:0, x11:0:0, x12:0:0, cons_0, x12:0:0) -> f362_0_gt_LE(x10:0:0, x11:0:0 + 1, x10:0:0, x11:0:0 + 1, x10:0:0) :|: x12:0:0 > 0 && cons_0 = 0 f362_0_gt_LE(x16, x17, x18, x19, x18) -> f362_0_gt_LE(x16, x17 + 2, x16, x17 + 2, x16) :|: TRUE && x18 >= 2 && x19 = 1 && x16 >= 1 && x17 = -1 ---------------------------------------- (15) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f362_0_gt_LE(x, x1, x2, x3, x2) -> f362_0_gt_LE(x, 0 + 2, x, 0 + 2, x) :|: TRUE && x2 >= 2 && x3 = 1 && x >= 2 && x1 = 0 (2) f362_0_gt_LE(x:0, x1:0, x2:0, x3:0, x2:0) -> f362_0_gt_LE(x:0, x1:0, x2:0 - 2, x3:0 - 2, x2:0 - 2) :|: x3:0 > 1 && x2:0 > 1 (3) f362_0_gt_LE(x8, x9, x10, x11, x10) -> f362_0_gt_LE(x8, x9 + 1, x8 + -2, x9 + -1, x8 + -2) :|: TRUE && x10 >= 2 && x11 = 1 && x9 >= 1 && x8 >= 2 (4) f362_0_gt_LE(x10:0:0, x11:0:0, x12:0:0, cons_0, x12:0:0) -> f362_0_gt_LE(x10:0:0, x11:0:0 + 1, x10:0:0, x11:0:0 + 1, x10:0:0) :|: x12:0:0 > 0 && cons_0 = 0 (5) f362_0_gt_LE(x16, x17, x18, x19, x18) -> f362_0_gt_LE(x16, x17 + 2, x16, x17 + 2, x16) :|: TRUE && x18 >= 2 && x19 = 1 && x16 >= 1 && x17 = -1 Arcs: (1) -> (2) (2) -> (1), (2), (3), (4), (5) (3) -> (2), (3), (4) (4) -> (2), (3), (4) (5) -> (3) This digraph is fully evaluated! ---------------------------------------- (16) Obligation: Termination digraph: Nodes: (1) f362_0_gt_LE(x, x1, x2, x3, x2) -> f362_0_gt_LE(x, 0 + 2, x, 0 + 2, x) :|: TRUE && x2 >= 2 && x3 = 1 && x >= 2 && x1 = 0 (2) f362_0_gt_LE(x:0, x1:0, x2:0, x3:0, x2:0) -> f362_0_gt_LE(x:0, x1:0, x2:0 - 2, x3:0 - 2, x2:0 - 2) :|: x3:0 > 1 && x2:0 > 1 (3) f362_0_gt_LE(x8, x9, x10, x11, x10) -> f362_0_gt_LE(x8, x9 + 1, x8 + -2, x9 + -1, x8 + -2) :|: TRUE && x10 >= 2 && x11 = 1 && x9 >= 1 && x8 >= 2 (4) f362_0_gt_LE(x16, x17, x18, x19, x18) -> f362_0_gt_LE(x16, x17 + 2, x16, x17 + 2, x16) :|: TRUE && x18 >= 2 && x19 = 1 && x16 >= 1 && x17 = -1 (5) f362_0_gt_LE(x10:0:0, x11:0:0, x12:0:0, cons_0, x12:0:0) -> f362_0_gt_LE(x10:0:0, x11:0:0 + 1, x10:0:0, x11:0:0 + 1, x10:0:0) :|: x12:0:0 > 0 && cons_0 = 0 Arcs: (1) -> (2) (2) -> (1), (2), (3), (4), (5) (3) -> (2), (3), (5) (4) -> (3) (5) -> (2), (3), (5) This digraph is fully evaluated! ---------------------------------------- (17) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (18) Obligation: Rules: f362_0_gt_LE(x16:0, cons_-1, x18:0, cons_1, x18:0) -> f362_0_gt_LE(x16:0, 1, x16:0, 1, x16:0) :|: x16:0 > 0 && x18:0 > 1 && cons_-1 = -1 && cons_1 = 1 f362_0_gt_LE(x, x1, x2, x3, x2) -> f362_0_gt_LE(x, 2, x, 2, x) :|: x > 1 && x2 > 1 && x1 = 0 && x3 = 1 f362_0_gt_LE(x4, x5, x6, x7, x6) -> f362_0_gt_LE(x4, x5 + 1, x4 - 2, x5 - 1, x4 - 2) :|: x5 > 0 && x6 > 1 && x4 > 1 && x7 = 1 f362_0_gt_LE(x:0:0, x1:0:0, x2:0:0, x3:0:0, x2:0:0) -> f362_0_gt_LE(x:0:0, x1:0:0, x2:0:0 - 2, x3:0:0 - 2, x2:0:0 - 2) :|: x3:0:0 > 1 && x2:0:0 > 1 f362_0_gt_LE(x10:0:0:0, x11:0:0:0, x12:0:0:0, cons_0, x12:0:0:0) -> f362_0_gt_LE(x10:0:0:0, x11:0:0:0 + 1, x10:0:0:0, x11:0:0:0 + 1, x10:0:0:0) :|: x12:0:0:0 > 0 && cons_0 = 0 ---------------------------------------- (19) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f362_0_gt_LE(VARIABLE, VARIABLE, VARIABLE, VARIABLE, VARIABLE) 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: f362_0_gt_LE(x16:0, c, x18:0, c1, x18:0) -> f362_0_gt_LE(x16:0, c2, x16:0, c3, x16:0) :|: c3 = 1 && (c2 = 1 && (c1 = 1 && c = -1)) && (x16:0 > 0 && x18:0 > 1 && cons_-1 = -1 && cons_1 = 1) f362_0_gt_LE(x, c4, x2, c5, x2) -> f362_0_gt_LE(x, c6, x, c7, x) :|: c7 = 2 && (c6 = 2 && (c5 = 1 && c4 = 0)) && (x > 1 && x2 > 1 && x1 = 0 && x3 = 1) f362_0_gt_LE(x4, x5, x6, c8, x6) -> f362_0_gt_LE(x4, c9, c10, c11, c12) :|: c12 = x4 - 2 && (c11 = x5 - 1 && (c10 = x4 - 2 && (c9 = x5 + 1 && c8 = 1))) && (x5 > 0 && x6 > 1 && x4 > 1 && x7 = 1) f362_0_gt_LE(x:0:0, x1:0:0, x2:0:0, x3:0:0, x2:0:0) -> f362_0_gt_LE(x:0:0, x1:0:0, c13, c14, c15) :|: c15 = x2:0:0 - 2 && (c14 = x3:0:0 - 2 && c13 = x2:0:0 - 2) && (x3:0:0 > 1 && x2:0:0 > 1) f362_0_gt_LE(x10:0:0:0, x11:0:0:0, x12:0:0:0, c16, x12:0:0:0) -> f362_0_gt_LE(x10:0:0:0, c17, x10:0:0:0, c18, x10:0:0:0) :|: c18 = x11:0:0:0 + 1 && (c17 = x11:0:0:0 + 1 && c16 = 0) && (x12:0:0:0 > 0 && cons_0 = 0) Found the following polynomial interpretation: [f362_0_gt_LE(x, x1, x2, x3, x4)] = -2 + x - x1 The following rules are decreasing: f362_0_gt_LE(x16:0, c, x18:0, c1, x18:0) -> f362_0_gt_LE(x16:0, c2, x16:0, c3, x16:0) :|: c3 = 1 && (c2 = 1 && (c1 = 1 && c = -1)) && (x16:0 > 0 && x18:0 > 1 && cons_-1 = -1 && cons_1 = 1) f362_0_gt_LE(x, c4, x2, c5, x2) -> f362_0_gt_LE(x, c6, x, c7, x) :|: c7 = 2 && (c6 = 2 && (c5 = 1 && c4 = 0)) && (x > 1 && x2 > 1 && x1 = 0 && x3 = 1) f362_0_gt_LE(x4, x5, x6, c8, x6) -> f362_0_gt_LE(x4, c9, c10, c11, c12) :|: c12 = x4 - 2 && (c11 = x5 - 1 && (c10 = x4 - 2 && (c9 = x5 + 1 && c8 = 1))) && (x5 > 0 && x6 > 1 && x4 > 1 && x7 = 1) f362_0_gt_LE(x10:0:0:0, x11:0:0:0, x12:0:0:0, c16, x12:0:0:0) -> f362_0_gt_LE(x10:0:0:0, c17, x10:0:0:0, c18, x10:0:0:0) :|: c18 = x11:0:0:0 + 1 && (c17 = x11:0:0:0 + 1 && c16 = 0) && (x12:0:0:0 > 0 && cons_0 = 0) The following rules are bounded: f362_0_gt_LE(x16:0, c, x18:0, c1, x18:0) -> f362_0_gt_LE(x16:0, c2, x16:0, c3, x16:0) :|: c3 = 1 && (c2 = 1 && (c1 = 1 && c = -1)) && (x16:0 > 0 && x18:0 > 1 && cons_-1 = -1 && cons_1 = 1) f362_0_gt_LE(x, c4, x2, c5, x2) -> f362_0_gt_LE(x, c6, x, c7, x) :|: c7 = 2 && (c6 = 2 && (c5 = 1 && c4 = 0)) && (x > 1 && x2 > 1 && x1 = 0 && x3 = 1) - IntTRS - PolynomialOrderProcessor - IntTRS Rules: f362_0_gt_LE(x4, x5, x6, c8, x6) -> f362_0_gt_LE(x4, c9, c10, c11, c12) :|: c12 = x4 - 2 && (c11 = x5 - 1 && (c10 = x4 - 2 && (c9 = x5 + 1 && c8 = 1))) && (x5 > 0 && x6 > 1 && x4 > 1 && x7 = 1) f362_0_gt_LE(x:0:0, x1:0:0, x2:0:0, x3:0:0, x2:0:0) -> f362_0_gt_LE(x:0:0, x1:0:0, c13, c14, c15) :|: c15 = x2:0:0 - 2 && (c14 = x3:0:0 - 2 && c13 = x2:0:0 - 2) && (x3:0:0 > 1 && x2:0:0 > 1) f362_0_gt_LE(x10:0:0:0, x11:0:0:0, x12:0:0:0, c16, x12:0:0:0) -> f362_0_gt_LE(x10:0:0:0, c17, x10:0:0:0, c18, x10:0:0:0) :|: c18 = x11:0:0:0 + 1 && (c17 = x11:0:0:0 + 1 && c16 = 0) && (x12:0:0:0 > 0 && cons_0 = 0) ---------------------------------------- (20) Obligation: Rules: f362_0_gt_LE(x4, x5, x6, x7, x6) -> f362_0_gt_LE(x4, x5 + 1, x4 - 2, x5 - 1, x4 - 2) :|: x5 > 0 && x6 > 1 && x4 > 1 && x7 = 1 f362_0_gt_LE(x:0:0, x1:0:0, x2:0:0, x3:0:0, x2:0:0) -> f362_0_gt_LE(x:0:0, x1:0:0, x2:0:0 - 2, x3:0:0 - 2, x2:0:0 - 2) :|: x3:0:0 > 1 && x2:0:0 > 1 f362_0_gt_LE(x10:0:0:0, x11:0:0:0, x12:0:0:0, cons_0, x12:0:0:0) -> f362_0_gt_LE(x10:0:0:0, x11:0:0:0 + 1, x10:0:0:0, x11:0:0:0 + 1, x10:0:0:0) :|: x12:0:0:0 > 0 && cons_0 = 0 ---------------------------------------- (21) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f362_0_gt_LE(x4, x5, x6, x7, x6) -> f362_0_gt_LE(x4, x5 + 1, x4 - 2, x5 - 1, x4 - 2) :|: x5 > 0 && x6 > 1 && x4 > 1 && x7 = 1 (2) f362_0_gt_LE(x:0:0, x1:0:0, x2:0:0, x3:0:0, x2:0:0) -> f362_0_gt_LE(x:0:0, x1:0:0, x2:0:0 - 2, x3:0:0 - 2, x2:0:0 - 2) :|: x3:0:0 > 1 && x2:0:0 > 1 (3) f362_0_gt_LE(x10:0:0:0, x11:0:0:0, x12:0:0:0, cons_0, x12:0:0:0) -> f362_0_gt_LE(x10:0:0:0, x11:0:0:0 + 1, x10:0:0:0, x11:0:0:0 + 1, x10:0:0:0) :|: x12:0:0:0 > 0 && cons_0 = 0 Arcs: (1) -> (1), (2), (3) (2) -> (1), (2), (3) (3) -> (1), (2), (3) This digraph is fully evaluated! ---------------------------------------- (22) Obligation: Termination digraph: Nodes: (1) f362_0_gt_LE(x4, x5, x6, x7, x6) -> f362_0_gt_LE(x4, x5 + 1, x4 - 2, x5 - 1, x4 - 2) :|: x5 > 0 && x6 > 1 && x4 > 1 && x7 = 1 (2) f362_0_gt_LE(x:0:0, x1:0:0, x2:0:0, x3:0:0, x2:0:0) -> f362_0_gt_LE(x:0:0, x1:0:0, x2:0:0 - 2, x3:0:0 - 2, x2:0:0 - 2) :|: x3:0:0 > 1 && x2:0:0 > 1 (3) f362_0_gt_LE(x10:0:0:0, x11:0:0:0, x12:0:0:0, cons_0, x12:0:0:0) -> f362_0_gt_LE(x10:0:0:0, x11:0:0:0 + 1, x10:0:0:0, x11:0:0:0 + 1, x10:0:0:0) :|: x12:0:0:0 > 0 && cons_0 = 0 Arcs: (1) -> (1), (2), (3) (2) -> (1), (2), (3) (3) -> (1), (2), (3) This digraph is fully evaluated! ---------------------------------------- (23) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (24) Obligation: Rules: f362_0_gt_LE(x4:0, x5:0, x6:0, cons_1, x6:0) -> f362_0_gt_LE(x4:0, x5:0 + 1, x4:0 - 2, x5:0 - 1, x4:0 - 2) :|: x5:0 > 0 && x6:0 > 1 && x4:0 > 1 && cons_1 = 1 f362_0_gt_LE(x:0:0:0, x1:0:0:0, x2:0:0:0, x3:0:0:0, x2:0:0:0) -> f362_0_gt_LE(x:0:0:0, x1:0:0:0, x2:0:0:0 - 2, x3:0:0:0 - 2, x2:0:0:0 - 2) :|: x3:0:0:0 > 1 && x2:0:0:0 > 1 f362_0_gt_LE(x10:0:0:0:0, x11:0:0:0:0, x12:0:0:0:0, cons_0, x12:0:0:0:0) -> f362_0_gt_LE(x10:0:0:0:0, x11:0:0:0:0 + 1, x10:0:0:0:0, x11:0:0:0:0 + 1, x10:0:0:0:0) :|: x12:0:0:0:0 > 0 && cons_0 = 0