MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 712 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 0 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) IRSwTChainingProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 100 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT (15) IRSwTChainingProof [EQUIVALENT, 0 ms] (16) IRSwT (17) IRSwTTerminationDigraphProof [EQUIVALENT, 157 ms] (18) AND (19) IRSwT (20) IntTRSCompressionProof [EQUIVALENT, 0 ms] (21) IRSwT (22) TempFilterProof [SOUND, 5 ms] (23) IntTRS (24) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (25) YES (26) IRSwT (27) IntTRSCompressionProof [EQUIVALENT, 4 ms] (28) IRSwT (29) IRSwTChainingProof [EQUIVALENT, 0 ms] (30) IRSwT (31) IRSwTTerminationDigraphProof [EQUIVALENT, 170 ms] (32) IRSwT (33) IntTRSCompressionProof [EQUIVALENT, 0 ms] (34) IRSwT (35) IRSwTChainingProof [EQUIVALENT, 0 ms] (36) IRSwT (37) IRSwTTerminationDigraphProof [EQUIVALENT, 139 ms] (38) IRSwT (39) IntTRSCompressionProof [EQUIVALENT, 0 ms] (40) IRSwT (41) TempFilterProof [SOUND, 8232 ms] (42) IRSwT (43) IRSwTTerminationDigraphProof [EQUIVALENT, 21 ms] (44) IRSwT (45) IntTRSCompressionProof [EQUIVALENT, 0 ms] (46) IRSwT ---------------------------------------- (0) Obligation: Rules: f1_0_main_Load(arg1, arg2, arg3, arg4) -> f74_0_loop_aux_LE(arg1P, arg2P, arg3P, arg4P) :|: arg2 = arg3P && arg2 = arg2P && arg2 = arg1P && -1 <= arg2 - 1 && 0 <= arg1 - 1 f74_0_loop_aux_LE(x, x1, x2, x3) -> f74_0_loop_aux_LE(x4, x5, x6, x7) :|: x - 1 = x6 && x1 - 1 = x5 && x - 1 = x4 && x = x2 && 4 <= x1 - 1 && 1 <= x - 1 && x1 <= x f74_0_loop_aux_LE(x8, x9, x10, x11) -> f135_0_loop_aux_InvokeMethod(x12, x13, x14, x15) :|: x9 + 1 = x15 && x8 + 1 = x14 && x9 = x13 && x8 = x12 && x8 = x10 && 0 <= x8 - 1 && 2 * x9 <= x8 + 1 && 1 <= x9 - 1 && x8 <= x9 - 1 f74_0_loop_aux_LE(x16, x17, x18, x19) -> f135_0_loop_aux_InvokeMethod(x20, x21, x22, x23) :|: x17 - 1 = x23 && x16 + 1 = x22 && x17 = x21 && x16 = x20 && x16 = x18 && 0 <= x16 - 1 && x16 + 1 <= 2 * x17 - 1 && 1 <= x17 - 1 && x16 <= x17 - 1 f135_0_loop_aux_InvokeMethod(x24, x25, x26, x27) -> f74_0_loop_aux_LE(x28, x29, x30, x31) :|: x26 = x30 && x27 = x29 && x26 = x28 && x24 <= x27 && x26 <= x25 && x24 <= x25 - 1 && 0 <= x27 - 1 && 1 <= x26 - 1 && 1 <= x25 - 1 && 0 <= x24 - 1 f74_0_loop_aux_LE(x32, x33, x34, x35) -> f74_0_loop_aux_LE(x36, x37, x38, x39) :|: x32 - 1 = x38 && x33 + 2 = x37 && x32 - 1 = x36 && x32 = x34 && -1 <= x33 - 1 && x32 - 1 - (x33 + 1) <= 2 && x33 <= 4 && x33 <= x32 && 0 <= x32 - 1 f74_0_loop_aux_LE(x40, x41, x42, x43) -> f74_0_loop_aux_LE(x44, x45, x46, x47) :|: x40 = x46 && x41 + 1 = x45 && x40 = x44 && x40 = x42 && -1 <= x41 - 1 && 2 <= x40 - 1 - (x41 + 1) - 1 && x41 <= 4 && x41 <= x40 && 0 <= x40 - 1 __init(x48, x49, x50, x51) -> f1_0_main_Load(x52, x53, x54, x55) :|: 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_Load(arg1, arg2, arg3, arg4) -> f74_0_loop_aux_LE(arg1P, arg2P, arg3P, arg4P) :|: arg2 = arg3P && arg2 = arg2P && arg2 = arg1P && -1 <= arg2 - 1 && 0 <= arg1 - 1 f74_0_loop_aux_LE(x, x1, x2, x3) -> f74_0_loop_aux_LE(x4, x5, x6, x7) :|: x - 1 = x6 && x1 - 1 = x5 && x - 1 = x4 && x = x2 && 4 <= x1 - 1 && 1 <= x - 1 && x1 <= x f74_0_loop_aux_LE(x8, x9, x10, x11) -> f135_0_loop_aux_InvokeMethod(x12, x13, x14, x15) :|: x9 + 1 = x15 && x8 + 1 = x14 && x9 = x13 && x8 = x12 && x8 = x10 && 0 <= x8 - 1 && 2 * x9 <= x8 + 1 && 1 <= x9 - 1 && x8 <= x9 - 1 f74_0_loop_aux_LE(x16, x17, x18, x19) -> f135_0_loop_aux_InvokeMethod(x20, x21, x22, x23) :|: x17 - 1 = x23 && x16 + 1 = x22 && x17 = x21 && x16 = x20 && x16 = x18 && 0 <= x16 - 1 && x16 + 1 <= 2 * x17 - 1 && 1 <= x17 - 1 && x16 <= x17 - 1 f135_0_loop_aux_InvokeMethod(x24, x25, x26, x27) -> f74_0_loop_aux_LE(x28, x29, x30, x31) :|: x26 = x30 && x27 = x29 && x26 = x28 && x24 <= x27 && x26 <= x25 && x24 <= x25 - 1 && 0 <= x27 - 1 && 1 <= x26 - 1 && 1 <= x25 - 1 && 0 <= x24 - 1 f74_0_loop_aux_LE(x32, x33, x34, x35) -> f74_0_loop_aux_LE(x36, x37, x38, x39) :|: x32 - 1 = x38 && x33 + 2 = x37 && x32 - 1 = x36 && x32 = x34 && -1 <= x33 - 1 && x32 - 1 - (x33 + 1) <= 2 && x33 <= 4 && x33 <= x32 && 0 <= x32 - 1 f74_0_loop_aux_LE(x40, x41, x42, x43) -> f74_0_loop_aux_LE(x44, x45, x46, x47) :|: x40 = x46 && x41 + 1 = x45 && x40 = x44 && x40 = x42 && -1 <= x41 - 1 && 2 <= x40 - 1 - (x41 + 1) - 1 && x41 <= 4 && x41 <= x40 && 0 <= x40 - 1 __init(x48, x49, x50, x51) -> f1_0_main_Load(x52, x53, x54, x55) :|: 0 <= 0 Start term: __init(arg1, arg2, arg3, arg4) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f1_0_main_Load(arg1, arg2, arg3, arg4) -> f74_0_loop_aux_LE(arg1P, arg2P, arg3P, arg4P) :|: arg2 = arg3P && arg2 = arg2P && arg2 = arg1P && -1 <= arg2 - 1 && 0 <= arg1 - 1 (2) f74_0_loop_aux_LE(x, x1, x2, x3) -> f74_0_loop_aux_LE(x4, x5, x6, x7) :|: x - 1 = x6 && x1 - 1 = x5 && x - 1 = x4 && x = x2 && 4 <= x1 - 1 && 1 <= x - 1 && x1 <= x (3) f74_0_loop_aux_LE(x8, x9, x10, x11) -> f135_0_loop_aux_InvokeMethod(x12, x13, x14, x15) :|: x9 + 1 = x15 && x8 + 1 = x14 && x9 = x13 && x8 = x12 && x8 = x10 && 0 <= x8 - 1 && 2 * x9 <= x8 + 1 && 1 <= x9 - 1 && x8 <= x9 - 1 (4) f74_0_loop_aux_LE(x16, x17, x18, x19) -> f135_0_loop_aux_InvokeMethod(x20, x21, x22, x23) :|: x17 - 1 = x23 && x16 + 1 = x22 && x17 = x21 && x16 = x20 && x16 = x18 && 0 <= x16 - 1 && x16 + 1 <= 2 * x17 - 1 && 1 <= x17 - 1 && x16 <= x17 - 1 (5) f135_0_loop_aux_InvokeMethod(x24, x25, x26, x27) -> f74_0_loop_aux_LE(x28, x29, x30, x31) :|: x26 = x30 && x27 = x29 && x26 = x28 && x24 <= x27 && x26 <= x25 && x24 <= x25 - 1 && 0 <= x27 - 1 && 1 <= x26 - 1 && 1 <= x25 - 1 && 0 <= x24 - 1 (6) f74_0_loop_aux_LE(x32, x33, x34, x35) -> f74_0_loop_aux_LE(x36, x37, x38, x39) :|: x32 - 1 = x38 && x33 + 2 = x37 && x32 - 1 = x36 && x32 = x34 && -1 <= x33 - 1 && x32 - 1 - (x33 + 1) <= 2 && x33 <= 4 && x33 <= x32 && 0 <= x32 - 1 (7) f74_0_loop_aux_LE(x40, x41, x42, x43) -> f74_0_loop_aux_LE(x44, x45, x46, x47) :|: x40 = x46 && x41 + 1 = x45 && x40 = x44 && x40 = x42 && -1 <= x41 - 1 && 2 <= x40 - 1 - (x41 + 1) - 1 && x41 <= 4 && x41 <= x40 && 0 <= x40 - 1 (8) __init(x48, x49, x50, x51) -> f1_0_main_Load(x52, x53, x54, x55) :|: 0 <= 0 Arcs: (1) -> (2), (6) (2) -> (2), (6), (7) (4) -> (5) (5) -> (2), (4), (6), (7) (6) -> (2), (4), (6) (7) -> (2), (6), (7) (8) -> (1) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) f74_0_loop_aux_LE(x, x1, x2, x3) -> f74_0_loop_aux_LE(x4, x5, x6, x7) :|: x - 1 = x6 && x1 - 1 = x5 && x - 1 = x4 && x = x2 && 4 <= x1 - 1 && 1 <= x - 1 && x1 <= x (2) f135_0_loop_aux_InvokeMethod(x24, x25, x26, x27) -> f74_0_loop_aux_LE(x28, x29, x30, x31) :|: x26 = x30 && x27 = x29 && x26 = x28 && x24 <= x27 && x26 <= x25 && x24 <= x25 - 1 && 0 <= x27 - 1 && 1 <= x26 - 1 && 1 <= x25 - 1 && 0 <= x24 - 1 (3) f74_0_loop_aux_LE(x16, x17, x18, x19) -> f135_0_loop_aux_InvokeMethod(x20, x21, x22, x23) :|: x17 - 1 = x23 && x16 + 1 = x22 && x17 = x21 && x16 = x20 && x16 = x18 && 0 <= x16 - 1 && x16 + 1 <= 2 * x17 - 1 && 1 <= x17 - 1 && x16 <= x17 - 1 (4) f74_0_loop_aux_LE(x32, x33, x34, x35) -> f74_0_loop_aux_LE(x36, x37, x38, x39) :|: x32 - 1 = x38 && x33 + 2 = x37 && x32 - 1 = x36 && x32 = x34 && -1 <= x33 - 1 && x32 - 1 - (x33 + 1) <= 2 && x33 <= 4 && x33 <= x32 && 0 <= x32 - 1 (5) f74_0_loop_aux_LE(x40, x41, x42, x43) -> f74_0_loop_aux_LE(x44, x45, x46, x47) :|: x40 = x46 && x41 + 1 = x45 && x40 = x44 && x40 = x42 && -1 <= x41 - 1 && 2 <= x40 - 1 - (x41 + 1) - 1 && x41 <= 4 && x41 <= x40 && 0 <= x40 - 1 Arcs: (1) -> (1), (4), (5) (2) -> (1), (3), (4), (5) (3) -> (2) (4) -> (1), (3), (4) (5) -> (1), (4), (5) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: f74_0_loop_aux_LE(x2:0, x1:0, x2:0, x3:0) -> f74_0_loop_aux_LE(x2:0 - 1, x1:0 - 1, x2:0 - 1, x7:0) :|: x2:0 > 1 && x1:0 > 4 && x2:0 >= x1:0 f74_0_loop_aux_LE(x32:0, x33:0, x32:0, x35:0) -> f74_0_loop_aux_LE(x32:0 - 1, x33:0 + 2, x32:0 - 1, x39:0) :|: x33:0 <= x32:0 && x32:0 > 0 && x33:0 < 5 && x33:0 > -1 && x32:0 - 1 - (x33:0 + 1) <= 2 f74_0_loop_aux_LE(x16:0, x17:0, x16:0, x19:0) -> f74_0_loop_aux_LE(x16:0 + 1, x17:0 - 1, x16:0 + 1, x31:0) :|: x16:0 + 1 <= 2 * x17:0 - 1 && x16:0 > 0 && x17:0 > 1 && x17:0 - 1 >= x16:0 && x17:0 >= x16:0 + 1 f74_0_loop_aux_LE(x40:0, x41:0, x40:0, x43:0) -> f74_0_loop_aux_LE(x40:0, x41:0 + 1, x40:0, x47:0) :|: x41:0 <= x40:0 && x40:0 > 0 && x41:0 < 5 && x41:0 > -1 && x40:0 - 1 - (x41:0 + 1) >= 3 ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f74_0_loop_aux_LE(x1, x2, x3, x4) -> f74_0_loop_aux_LE(x1, x2, x3) ---------------------------------------- (8) Obligation: Rules: f74_0_loop_aux_LE(x2:0, x1:0, x2:0) -> f74_0_loop_aux_LE(x2:0 - 1, x1:0 - 1, x2:0 - 1) :|: x2:0 > 1 && x1:0 > 4 && x2:0 >= x1:0 f74_0_loop_aux_LE(x32:0, x33:0, x32:0) -> f74_0_loop_aux_LE(x32:0 - 1, x33:0 + 2, x32:0 - 1) :|: x33:0 <= x32:0 && x32:0 > 0 && x33:0 < 5 && x33:0 > -1 && x32:0 - 1 - (x33:0 + 1) <= 2 f74_0_loop_aux_LE(x16:0, x17:0, x16:0) -> f74_0_loop_aux_LE(x16:0 + 1, x17:0 - 1, x16:0 + 1) :|: x16:0 + 1 <= 2 * x17:0 - 1 && x16:0 > 0 && x17:0 > 1 && x17:0 - 1 >= x16:0 && x17:0 >= x16:0 + 1 f74_0_loop_aux_LE(x40:0, x41:0, x40:0) -> f74_0_loop_aux_LE(x40:0, x41:0 + 1, x40:0) :|: x41:0 <= x40:0 && x40:0 > 0 && x41:0 < 5 && x41:0 > -1 && x40:0 - 1 - (x41:0 + 1) >= 3 ---------------------------------------- (9) IRSwTChainingProof (EQUIVALENT) Chaining! ---------------------------------------- (10) Obligation: Rules: f74_0_loop_aux_LE(x, x1, x) -> f74_0_loop_aux_LE(x + -2, x1 + -2, x + -2) :|: TRUE && x + -1 * x1 >= 0 && x >= 3 && x1 >= 6 f74_0_loop_aux_LE(x32:0, x33:0, x32:0) -> f74_0_loop_aux_LE(x32:0 - 1, x33:0 + 2, x32:0 - 1) :|: x33:0 <= x32:0 && x32:0 > 0 && x33:0 < 5 && x33:0 > -1 && x32:0 - 1 - (x33:0 + 1) <= 2 f74_0_loop_aux_LE(x4, x5, x4) -> f74_0_loop_aux_LE(x4 + -2, x5 + 1, x4 + -2) :|: TRUE && x4 >= 2 && x5 >= 5 && x4 + -1 * x5 >= 0 && x5 <= 5 && x4 + -1 * x5 <= 4 f74_0_loop_aux_LE(x16:0, x17:0, x16:0) -> f74_0_loop_aux_LE(x16:0 + 1, x17:0 - 1, x16:0 + 1) :|: x16:0 + 1 <= 2 * x17:0 - 1 && x16:0 > 0 && x17:0 > 1 && x17:0 - 1 >= x16:0 && x17:0 >= x16:0 + 1 f74_0_loop_aux_LE(x40:0, x41:0, x40:0) -> f74_0_loop_aux_LE(x40:0, x41:0 + 1, x40:0) :|: x41:0 <= x40:0 && x40:0 > 0 && x41:0 < 5 && x41:0 > -1 && x40:0 - 1 - (x41:0 + 1) >= 3 f74_0_loop_aux_LE(x12, x13, x12) -> f74_0_loop_aux_LE(x12 + -1, x13, x12 + -1) :|: TRUE && x12 >= 2 && x13 >= 5 && x13 <= 5 && x12 + -1 * x13 >= 5 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f74_0_loop_aux_LE(x, x1, x) -> f74_0_loop_aux_LE(x + -2, x1 + -2, x + -2) :|: TRUE && x + -1 * x1 >= 0 && x >= 3 && x1 >= 6 (2) f74_0_loop_aux_LE(x32:0, x33:0, x32:0) -> f74_0_loop_aux_LE(x32:0 - 1, x33:0 + 2, x32:0 - 1) :|: x33:0 <= x32:0 && x32:0 > 0 && x33:0 < 5 && x33:0 > -1 && x32:0 - 1 - (x33:0 + 1) <= 2 (3) f74_0_loop_aux_LE(x4, x5, x4) -> f74_0_loop_aux_LE(x4 + -2, x5 + 1, x4 + -2) :|: TRUE && x4 >= 2 && x5 >= 5 && x4 + -1 * x5 >= 0 && x5 <= 5 && x4 + -1 * x5 <= 4 (4) f74_0_loop_aux_LE(x16:0, x17:0, x16:0) -> f74_0_loop_aux_LE(x16:0 + 1, x17:0 - 1, x16:0 + 1) :|: x16:0 + 1 <= 2 * x17:0 - 1 && x16:0 > 0 && x17:0 > 1 && x17:0 - 1 >= x16:0 && x17:0 >= x16:0 + 1 (5) f74_0_loop_aux_LE(x40:0, x41:0, x40:0) -> f74_0_loop_aux_LE(x40:0, x41:0 + 1, x40:0) :|: x41:0 <= x40:0 && x40:0 > 0 && x41:0 < 5 && x41:0 > -1 && x40:0 - 1 - (x41:0 + 1) >= 3 (6) f74_0_loop_aux_LE(x12, x13, x12) -> f74_0_loop_aux_LE(x12 + -1, x13, x12 + -1) :|: TRUE && x12 >= 2 && x13 >= 5 && x13 <= 5 && x12 + -1 * x13 >= 5 Arcs: (1) -> (1), (2), (3), (5), (6) (2) -> (1), (2), (3), (4) (3) -> (1), (4) (4) -> (1), (2), (3), (4) (5) -> (2), (3), (5), (6) (6) -> (3), (6) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) f74_0_loop_aux_LE(x, x1, x) -> f74_0_loop_aux_LE(x + -2, x1 + -2, x + -2) :|: TRUE && x + -1 * x1 >= 0 && x >= 3 && x1 >= 6 (2) f74_0_loop_aux_LE(x32:0, x33:0, x32:0) -> f74_0_loop_aux_LE(x32:0 - 1, x33:0 + 2, x32:0 - 1) :|: x33:0 <= x32:0 && x32:0 > 0 && x33:0 < 5 && x33:0 > -1 && x32:0 - 1 - (x33:0 + 1) <= 2 (3) f74_0_loop_aux_LE(x16:0, x17:0, x16:0) -> f74_0_loop_aux_LE(x16:0 + 1, x17:0 - 1, x16:0 + 1) :|: x16:0 + 1 <= 2 * x17:0 - 1 && x16:0 > 0 && x17:0 > 1 && x17:0 - 1 >= x16:0 && x17:0 >= x16:0 + 1 (4) f74_0_loop_aux_LE(x4, x5, x4) -> f74_0_loop_aux_LE(x4 + -2, x5 + 1, x4 + -2) :|: TRUE && x4 >= 2 && x5 >= 5 && x4 + -1 * x5 >= 0 && x5 <= 5 && x4 + -1 * x5 <= 4 (5) f74_0_loop_aux_LE(x12, x13, x12) -> f74_0_loop_aux_LE(x12 + -1, x13, x12 + -1) :|: TRUE && x12 >= 2 && x13 >= 5 && x13 <= 5 && x12 + -1 * x13 >= 5 (6) f74_0_loop_aux_LE(x40:0, x41:0, x40:0) -> f74_0_loop_aux_LE(x40:0, x41:0 + 1, x40:0) :|: x41:0 <= x40:0 && x40:0 > 0 && x41:0 < 5 && x41:0 > -1 && x40:0 - 1 - (x41:0 + 1) >= 3 Arcs: (1) -> (1), (2), (4), (5), (6) (2) -> (1), (2), (3), (4) (3) -> (1), (2), (3), (4) (4) -> (1), (3) (5) -> (4), (5) (6) -> (2), (4), (5), (6) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: f74_0_loop_aux_LE(x40:0:0, x41:0:0, x40:0:0) -> f74_0_loop_aux_LE(x40:0:0, x41:0:0 + 1, x40:0:0) :|: x41:0:0 > -1 && x40:0:0 - 1 - (x41:0:0 + 1) >= 3 && x41:0:0 < 5 && x40:0:0 > 0 && x41:0:0 <= x40:0:0 f74_0_loop_aux_LE(x:0, x1:0, x:0) -> f74_0_loop_aux_LE(x:0 - 2, x1:0 - 2, x:0 - 2) :|: x:0 > 2 && x:0 + -1 * x1:0 >= 0 && x1:0 > 5 f74_0_loop_aux_LE(x16:0:0, x17:0:0, x16:0:0) -> f74_0_loop_aux_LE(x16:0:0 + 1, x17:0:0 - 1, x16:0:0 + 1) :|: x17:0:0 - 1 >= x16:0:0 && x17:0:0 >= x16:0:0 + 1 && x17:0:0 > 1 && x16:0:0 > 0 && x16:0:0 + 1 <= 2 * x17:0:0 - 1 f74_0_loop_aux_LE(x12:0, x13:0, x12:0) -> f74_0_loop_aux_LE(x12:0 - 1, x13:0, x12:0 - 1) :|: x13:0 < 6 && x12:0 + -1 * x13:0 >= 5 && x12:0 > 1 && x13:0 > 4 f74_0_loop_aux_LE(x32:0:0, x33:0:0, x32:0:0) -> f74_0_loop_aux_LE(x32:0:0 - 1, x33:0:0 + 2, x32:0:0 - 1) :|: x33:0:0 > -1 && x32:0:0 - 1 - (x33:0:0 + 1) <= 2 && x33:0:0 < 5 && x32:0:0 > 0 && x33:0:0 <= x32:0:0 f74_0_loop_aux_LE(x4:0, x5:0, x4:0) -> f74_0_loop_aux_LE(x4:0 - 2, x5:0 + 1, x4:0 - 2) :|: x5:0 < 6 && x4:0 + -1 * x5:0 <= 4 && x4:0 + -1 * x5:0 >= 0 && x4:0 > 1 && x5:0 > 4 ---------------------------------------- (15) IRSwTChainingProof (EQUIVALENT) Chaining! ---------------------------------------- (16) Obligation: Rules: f74_0_loop_aux_LE(x, x1, x) -> f74_0_loop_aux_LE(x, x1 + 2, x) :|: TRUE && x1 >= 0 && x >= 1 && x + -1 * x1 >= 6 && x1 <= 3 f74_0_loop_aux_LE(x:0, x1:0, x:0) -> f74_0_loop_aux_LE(x:0 - 2, x1:0 - 2, x:0 - 2) :|: x:0 > 2 && x:0 + -1 * x1:0 >= 0 && x1:0 > 5 f74_0_loop_aux_LE(x16:0:0, x17:0:0, x16:0:0) -> f74_0_loop_aux_LE(x16:0:0 + 1, x17:0:0 - 1, x16:0:0 + 1) :|: x17:0:0 - 1 >= x16:0:0 && x17:0:0 >= x16:0:0 + 1 && x17:0:0 > 1 && x16:0:0 > 0 && x16:0:0 + 1 <= 2 * x17:0:0 - 1 f74_0_loop_aux_LE(x12:0, x13:0, x12:0) -> f74_0_loop_aux_LE(x12:0 - 1, x13:0, x12:0 - 1) :|: x13:0 < 6 && x12:0 + -1 * x13:0 >= 5 && x12:0 > 1 && x13:0 > 4 f74_0_loop_aux_LE(x12, x13, x12) -> f74_0_loop_aux_LE(x12 + -1, x13 + 1, x12 + -1) :|: TRUE && x13 <= 4 && x12 + -1 * x13 >= 6 && x12 >= 2 && x13 >= 4 f74_0_loop_aux_LE(x32:0:0, x33:0:0, x32:0:0) -> f74_0_loop_aux_LE(x32:0:0 - 1, x33:0:0 + 2, x32:0:0 - 1) :|: x33:0:0 > -1 && x32:0:0 - 1 - (x33:0:0 + 1) <= 2 && x33:0:0 < 5 && x32:0:0 > 0 && x33:0:0 <= x32:0:0 f74_0_loop_aux_LE(x16, x17, x16) -> f74_0_loop_aux_LE(x16 + -1, x17 + 3, x16 + -1) :|: TRUE && x17 >= 0 && x16 + -1 * x17 >= 5 && x16 >= 1 && x16 + -1 * x17 <= 5 && x17 <= 3 f74_0_loop_aux_LE(x4:0, x5:0, x4:0) -> f74_0_loop_aux_LE(x4:0 - 2, x5:0 + 1, x4:0 - 2) :|: x5:0 < 6 && x4:0 + -1 * x5:0 <= 4 && x4:0 + -1 * x5:0 >= 0 && x4:0 > 1 && x5:0 > 4 f74_0_loop_aux_LE(x20, x21, x20) -> f74_0_loop_aux_LE(x20 + -2, x21 + 2, x20 + -2) :|: TRUE && x20 + -1 * x21 >= 5 && x21 <= 4 && x20 + -1 * x21 <= 5 && x20 >= 2 && x21 >= 4 ---------------------------------------- (17) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f74_0_loop_aux_LE(x, x1, x) -> f74_0_loop_aux_LE(x, x1 + 2, x) :|: TRUE && x1 >= 0 && x >= 1 && x + -1 * x1 >= 6 && x1 <= 3 (2) f74_0_loop_aux_LE(x:0, x1:0, x:0) -> f74_0_loop_aux_LE(x:0 - 2, x1:0 - 2, x:0 - 2) :|: x:0 > 2 && x:0 + -1 * x1:0 >= 0 && x1:0 > 5 (3) f74_0_loop_aux_LE(x16:0:0, x17:0:0, x16:0:0) -> f74_0_loop_aux_LE(x16:0:0 + 1, x17:0:0 - 1, x16:0:0 + 1) :|: x17:0:0 - 1 >= x16:0:0 && x17:0:0 >= x16:0:0 + 1 && x17:0:0 > 1 && x16:0:0 > 0 && x16:0:0 + 1 <= 2 * x17:0:0 - 1 (4) f74_0_loop_aux_LE(x12:0, x13:0, x12:0) -> f74_0_loop_aux_LE(x12:0 - 1, x13:0, x12:0 - 1) :|: x13:0 < 6 && x12:0 + -1 * x13:0 >= 5 && x12:0 > 1 && x13:0 > 4 (5) f74_0_loop_aux_LE(x12, x13, x12) -> f74_0_loop_aux_LE(x12 + -1, x13 + 1, x12 + -1) :|: TRUE && x13 <= 4 && x12 + -1 * x13 >= 6 && x12 >= 2 && x13 >= 4 (6) f74_0_loop_aux_LE(x32:0:0, x33:0:0, x32:0:0) -> f74_0_loop_aux_LE(x32:0:0 - 1, x33:0:0 + 2, x32:0:0 - 1) :|: x33:0:0 > -1 && x32:0:0 - 1 - (x33:0:0 + 1) <= 2 && x33:0:0 < 5 && x32:0:0 > 0 && x33:0:0 <= x32:0:0 (7) f74_0_loop_aux_LE(x16, x17, x16) -> f74_0_loop_aux_LE(x16 + -1, x17 + 3, x16 + -1) :|: TRUE && x17 >= 0 && x16 + -1 * x17 >= 5 && x16 >= 1 && x16 + -1 * x17 <= 5 && x17 <= 3 (8) f74_0_loop_aux_LE(x4:0, x5:0, x4:0) -> f74_0_loop_aux_LE(x4:0 - 2, x5:0 + 1, x4:0 - 2) :|: x5:0 < 6 && x4:0 + -1 * x5:0 <= 4 && x4:0 + -1 * x5:0 >= 0 && x4:0 > 1 && x5:0 > 4 (9) f74_0_loop_aux_LE(x20, x21, x20) -> f74_0_loop_aux_LE(x20 + -2, x21 + 2, x20 + -2) :|: TRUE && x20 + -1 * x21 >= 5 && x21 <= 4 && x20 + -1 * x21 <= 5 && x20 >= 2 && x21 >= 4 Arcs: (1) -> (1), (4), (5), (6), (7), (8), (9) (2) -> (2), (4), (5), (6), (8), (9) (3) -> (2), (3), (6), (8) (4) -> (4), (8) (5) -> (4), (8) (6) -> (2), (3), (6), (8) (7) -> (2), (6), (8) (8) -> (2), (3) (9) -> (2) This digraph is fully evaluated! ---------------------------------------- (18) Complex Obligation (AND) ---------------------------------------- (19) Obligation: Termination digraph: Nodes: (1) f74_0_loop_aux_LE(x, x1, x) -> f74_0_loop_aux_LE(x, x1 + 2, x) :|: TRUE && x1 >= 0 && x >= 1 && x + -1 * x1 >= 6 && x1 <= 3 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (20) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (21) Obligation: Rules: f74_0_loop_aux_LE(x:0, x1:0, x:0) -> f74_0_loop_aux_LE(x:0, x1:0 + 2, x:0) :|: x:0 + -1 * x1:0 >= 6 && x1:0 < 4 && x1:0 > -1 && x:0 > 0 ---------------------------------------- (22) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f74_0_loop_aux_LE(INTEGER, INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (23) Obligation: Rules: f74_0_loop_aux_LE(x:0, x1:0, x:0) -> f74_0_loop_aux_LE(x:0, c, x:0) :|: c = x1:0 + 2 && (x:0 + -1 * x1:0 >= 6 && x1:0 < 4 && x1:0 > -1 && x:0 > 0) ---------------------------------------- (24) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f74_0_loop_aux_LE(x, x1, x2)] = -x1 + x2 The following rules are decreasing: f74_0_loop_aux_LE(x:0, x1:0, x:0) -> f74_0_loop_aux_LE(x:0, c, x:0) :|: c = x1:0 + 2 && (x:0 + -1 * x1:0 >= 6 && x1:0 < 4 && x1:0 > -1 && x:0 > 0) The following rules are bounded: f74_0_loop_aux_LE(x:0, x1:0, x:0) -> f74_0_loop_aux_LE(x:0, c, x:0) :|: c = x1:0 + 2 && (x:0 + -1 * x1:0 >= 6 && x1:0 < 4 && x1:0 > -1 && x:0 > 0) ---------------------------------------- (25) YES ---------------------------------------- (26) Obligation: Termination digraph: Nodes: (1) f74_0_loop_aux_LE(x12:0, x13:0, x12:0) -> f74_0_loop_aux_LE(x12:0 - 1, x13:0, x12:0 - 1) :|: x13:0 < 6 && x12:0 + -1 * x13:0 >= 5 && x12:0 > 1 && x13:0 > 4 (2) f74_0_loop_aux_LE(x:0, x1:0, x:0) -> f74_0_loop_aux_LE(x:0 - 2, x1:0 - 2, x:0 - 2) :|: x:0 > 2 && x:0 + -1 * x1:0 >= 0 && x1:0 > 5 (3) f74_0_loop_aux_LE(x20, x21, x20) -> f74_0_loop_aux_LE(x20 + -2, x21 + 2, x20 + -2) :|: TRUE && x20 + -1 * x21 >= 5 && x21 <= 4 && x20 + -1 * x21 <= 5 && x20 >= 2 && x21 >= 4 (4) f74_0_loop_aux_LE(x16:0:0, x17:0:0, x16:0:0) -> f74_0_loop_aux_LE(x16:0:0 + 1, x17:0:0 - 1, x16:0:0 + 1) :|: x17:0:0 - 1 >= x16:0:0 && x17:0:0 >= x16:0:0 + 1 && x17:0:0 > 1 && x16:0:0 > 0 && x16:0:0 + 1 <= 2 * x17:0:0 - 1 (5) f74_0_loop_aux_LE(x4:0, x5:0, x4:0) -> f74_0_loop_aux_LE(x4:0 - 2, x5:0 + 1, x4:0 - 2) :|: x5:0 < 6 && x4:0 + -1 * x5:0 <= 4 && x4:0 + -1 * x5:0 >= 0 && x4:0 > 1 && x5:0 > 4 (6) f74_0_loop_aux_LE(x12, x13, x12) -> f74_0_loop_aux_LE(x12 + -1, x13 + 1, x12 + -1) :|: TRUE && x13 <= 4 && x12 + -1 * x13 >= 6 && x12 >= 2 && x13 >= 4 (7) f74_0_loop_aux_LE(x32:0:0, x33:0:0, x32:0:0) -> f74_0_loop_aux_LE(x32:0:0 - 1, x33:0:0 + 2, x32:0:0 - 1) :|: x33:0:0 > -1 && x32:0:0 - 1 - (x33:0:0 + 1) <= 2 && x33:0:0 < 5 && x32:0:0 > 0 && x33:0:0 <= x32:0:0 Arcs: (1) -> (1), (5) (2) -> (1), (2), (3), (5), (6), (7) (3) -> (2) (4) -> (2), (4), (5), (7) (5) -> (2), (4) (6) -> (1), (5) (7) -> (2), (4), (5), (7) This digraph is fully evaluated! ---------------------------------------- (27) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (28) Obligation: Rules: f74_0_loop_aux_LE(x32:0:0:0, x33:0:0:0, x32:0:0:0) -> f74_0_loop_aux_LE(x32:0:0:0 - 1, x33:0:0:0 + 2, x32:0:0:0 - 1) :|: x32:0:0:0 > 0 && x33:0:0:0 <= x32:0:0:0 && x33:0:0:0 < 5 && x32:0:0:0 - 1 - (x33:0:0:0 + 1) <= 2 && x33:0:0:0 > -1 f74_0_loop_aux_LE(x12:0:0, x13:0:0, x12:0:0) -> f74_0_loop_aux_LE(x12:0:0 - 1, x13:0:0, x12:0:0 - 1) :|: x12:0:0 > 1 && x13:0:0 > 4 && x12:0:0 + -1 * x13:0:0 >= 5 && x13:0:0 < 6 f74_0_loop_aux_LE(x20:0, x21:0, x20:0) -> f74_0_loop_aux_LE(x20:0 - 2, x21:0 + 2, x20:0 - 2) :|: x20:0 > 1 && x21:0 > 3 && x20:0 + -1 * x21:0 = 5 && x21:0 < 5 f74_0_loop_aux_LE(x16:0:0:0, x17:0:0:0, x16:0:0:0) -> f74_0_loop_aux_LE(x16:0:0:0 + 1, x17:0:0:0 - 1, x16:0:0:0 + 1) :|: x16:0:0:0 > 0 && x16:0:0:0 + 1 <= 2 * x17:0:0:0 - 1 && x17:0:0:0 > 1 && x17:0:0:0 >= x16:0:0:0 + 1 && x17:0:0:0 - 1 >= x16:0:0:0 f74_0_loop_aux_LE(x:0:0, x1:0:0, x:0:0) -> f74_0_loop_aux_LE(x:0:0 - 2, x1:0:0 - 2, x:0:0 - 2) :|: x:0:0 > 2 && x:0:0 + -1 * x1:0:0 >= 0 && x1:0:0 > 5 f74_0_loop_aux_LE(x4:0:0, x5:0:0, x4:0:0) -> f74_0_loop_aux_LE(x4:0:0 - 2, x5:0:0 + 1, x4:0:0 - 2) :|: x4:0:0 > 1 && x5:0:0 > 4 && x4:0:0 + -1 * x5:0:0 >= 0 && x4:0:0 + -1 * x5:0:0 <= 4 && x5:0:0 < 6 f74_0_loop_aux_LE(x12:0, x13:0, x12:0) -> f74_0_loop_aux_LE(x12:0 - 1, x13:0 + 1, x12:0 - 1) :|: x12:0 > 1 && x13:0 > 3 && x13:0 < 5 && x12:0 + -1 * x13:0 >= 6 ---------------------------------------- (29) IRSwTChainingProof (EQUIVALENT) Chaining! ---------------------------------------- (30) Obligation: Rules: f74_0_loop_aux_LE(x, x1, x) -> f74_0_loop_aux_LE(x + -2, x1 + 4, x + -2) :|: TRUE && x + -1 * x1 <= 4 && x1 >= 0 && x >= 2 && x1 + -1 * x <= -3 && x1 <= 2 f74_0_loop_aux_LE(x12:0:0, x13:0:0, x12:0:0) -> f74_0_loop_aux_LE(x12:0:0 - 1, x13:0:0, x12:0:0 - 1) :|: x12:0:0 > 1 && x13:0:0 > 4 && x12:0:0 + -1 * x13:0:0 >= 5 && x13:0:0 < 6 f74_0_loop_aux_LE(x20:0, x21:0, x20:0) -> f74_0_loop_aux_LE(x20:0 - 2, x21:0 + 2, x20:0 - 2) :|: x20:0 > 1 && x21:0 > 3 && x20:0 + -1 * x21:0 = 5 && x21:0 < 5 f74_0_loop_aux_LE(x16:0:0:0, x17:0:0:0, x16:0:0:0) -> f74_0_loop_aux_LE(x16:0:0:0 + 1, x17:0:0:0 - 1, x16:0:0:0 + 1) :|: x16:0:0:0 > 0 && x16:0:0:0 + 1 <= 2 * x17:0:0:0 - 1 && x17:0:0:0 > 1 && x17:0:0:0 >= x16:0:0:0 + 1 && x17:0:0:0 - 1 >= x16:0:0:0 f74_0_loop_aux_LE(x12, x13, x12) -> f74_0_loop_aux_LE(x12, x13 + 1, x12) :|: TRUE && x13 + -1 * x12 <= 0 && x13 <= 4 && x13 >= 0 && x12 >= 2 && x12 + -2 * x13 <= 3 && x13 + -1 * x12 >= -2 f74_0_loop_aux_LE(x:0:0, x1:0:0, x:0:0) -> f74_0_loop_aux_LE(x:0:0 - 2, x1:0:0 - 2, x:0:0 - 2) :|: x:0:0 > 2 && x:0:0 + -1 * x1:0:0 >= 0 && x1:0:0 > 5 f74_0_loop_aux_LE(x16, x17, x16) -> f74_0_loop_aux_LE(x16 + -3, x17, x16 + -3) :|: TRUE && x17 <= 4 && x16 + -1 * x17 <= 4 && x16 >= 4 && x16 + -1 * x17 >= 3 && x17 >= 4 f74_0_loop_aux_LE(x4:0:0, x5:0:0, x4:0:0) -> f74_0_loop_aux_LE(x4:0:0 - 2, x5:0:0 + 1, x4:0:0 - 2) :|: x4:0:0 > 1 && x5:0:0 > 4 && x4:0:0 + -1 * x5:0:0 >= 0 && x4:0:0 + -1 * x5:0:0 <= 4 && x5:0:0 < 6 f74_0_loop_aux_LE(x20, x21, x20) -> f74_0_loop_aux_LE(x20 + -3, x21 + 3, x20 + -3) :|: TRUE && x20 + -1 * x21 <= 4 && x20 >= 3 && x21 >= 3 && x20 + -1 * x21 >= 3 && x21 <= 3 f74_0_loop_aux_LE(x12:0, x13:0, x12:0) -> f74_0_loop_aux_LE(x12:0 - 1, x13:0 + 1, x12:0 - 1) :|: x12:0 > 1 && x13:0 > 3 && x13:0 < 5 && x12:0 + -1 * x13:0 >= 6 ---------------------------------------- (31) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f74_0_loop_aux_LE(x, x1, x) -> f74_0_loop_aux_LE(x + -2, x1 + 4, x + -2) :|: TRUE && x + -1 * x1 <= 4 && x1 >= 0 && x >= 2 && x1 + -1 * x <= -3 && x1 <= 2 (2) f74_0_loop_aux_LE(x12:0:0, x13:0:0, x12:0:0) -> f74_0_loop_aux_LE(x12:0:0 - 1, x13:0:0, x12:0:0 - 1) :|: x12:0:0 > 1 && x13:0:0 > 4 && x12:0:0 + -1 * x13:0:0 >= 5 && x13:0:0 < 6 (3) f74_0_loop_aux_LE(x20:0, x21:0, x20:0) -> f74_0_loop_aux_LE(x20:0 - 2, x21:0 + 2, x20:0 - 2) :|: x20:0 > 1 && x21:0 > 3 && x20:0 + -1 * x21:0 = 5 && x21:0 < 5 (4) f74_0_loop_aux_LE(x16:0:0:0, x17:0:0:0, x16:0:0:0) -> f74_0_loop_aux_LE(x16:0:0:0 + 1, x17:0:0:0 - 1, x16:0:0:0 + 1) :|: x16:0:0:0 > 0 && x16:0:0:0 + 1 <= 2 * x17:0:0:0 - 1 && x17:0:0:0 > 1 && x17:0:0:0 >= x16:0:0:0 + 1 && x17:0:0:0 - 1 >= x16:0:0:0 (5) f74_0_loop_aux_LE(x12, x13, x12) -> f74_0_loop_aux_LE(x12, x13 + 1, x12) :|: TRUE && x13 + -1 * x12 <= 0 && x13 <= 4 && x13 >= 0 && x12 >= 2 && x12 + -2 * x13 <= 3 && x13 + -1 * x12 >= -2 (6) f74_0_loop_aux_LE(x:0:0, x1:0:0, x:0:0) -> f74_0_loop_aux_LE(x:0:0 - 2, x1:0:0 - 2, x:0:0 - 2) :|: x:0:0 > 2 && x:0:0 + -1 * x1:0:0 >= 0 && x1:0:0 > 5 (7) f74_0_loop_aux_LE(x16, x17, x16) -> f74_0_loop_aux_LE(x16 + -3, x17, x16 + -3) :|: TRUE && x17 <= 4 && x16 + -1 * x17 <= 4 && x16 >= 4 && x16 + -1 * x17 >= 3 && x17 >= 4 (8) f74_0_loop_aux_LE(x4:0:0, x5:0:0, x4:0:0) -> f74_0_loop_aux_LE(x4:0:0 - 2, x5:0:0 + 1, x4:0:0 - 2) :|: x4:0:0 > 1 && x5:0:0 > 4 && x4:0:0 + -1 * x5:0:0 >= 0 && x4:0:0 + -1 * x5:0:0 <= 4 && x5:0:0 < 6 (9) f74_0_loop_aux_LE(x20, x21, x20) -> f74_0_loop_aux_LE(x20 + -3, x21 + 3, x20 + -3) :|: TRUE && x20 + -1 * x21 <= 4 && x20 >= 3 && x21 >= 3 && x20 + -1 * x21 >= 3 && x21 <= 3 (10) f74_0_loop_aux_LE(x12:0, x13:0, x12:0) -> f74_0_loop_aux_LE(x12:0 - 1, x13:0 + 1, x12:0 - 1) :|: x12:0 > 1 && x13:0 > 3 && x13:0 < 5 && x12:0 + -1 * x13:0 >= 6 Arcs: (1) -> (4) (2) -> (2), (8) (3) -> (6) (4) -> (4), (5), (6), (8) (5) -> (4), (5), (8) (6) -> (2), (3), (5), (6), (7), (8), (10) (7) -> (5) (8) -> (4), (6) (9) -> (4) (10) -> (2), (8) This digraph is fully evaluated! ---------------------------------------- (32) Obligation: Termination digraph: Nodes: (1) f74_0_loop_aux_LE(x16:0:0:0, x17:0:0:0, x16:0:0:0) -> f74_0_loop_aux_LE(x16:0:0:0 + 1, x17:0:0:0 - 1, x16:0:0:0 + 1) :|: x16:0:0:0 > 0 && x16:0:0:0 + 1 <= 2 * x17:0:0:0 - 1 && x17:0:0:0 > 1 && x17:0:0:0 >= x16:0:0:0 + 1 && x17:0:0:0 - 1 >= x16:0:0:0 (2) f74_0_loop_aux_LE(x12, x13, x12) -> f74_0_loop_aux_LE(x12, x13 + 1, x12) :|: TRUE && x13 + -1 * x12 <= 0 && x13 <= 4 && x13 >= 0 && x12 >= 2 && x12 + -2 * x13 <= 3 && x13 + -1 * x12 >= -2 (3) f74_0_loop_aux_LE(x16, x17, x16) -> f74_0_loop_aux_LE(x16 + -3, x17, x16 + -3) :|: TRUE && x17 <= 4 && x16 + -1 * x17 <= 4 && x16 >= 4 && x16 + -1 * x17 >= 3 && x17 >= 4 (4) f74_0_loop_aux_LE(x:0:0, x1:0:0, x:0:0) -> f74_0_loop_aux_LE(x:0:0 - 2, x1:0:0 - 2, x:0:0 - 2) :|: x:0:0 > 2 && x:0:0 + -1 * x1:0:0 >= 0 && x1:0:0 > 5 (5) f74_0_loop_aux_LE(x4:0:0, x5:0:0, x4:0:0) -> f74_0_loop_aux_LE(x4:0:0 - 2, x5:0:0 + 1, x4:0:0 - 2) :|: x4:0:0 > 1 && x5:0:0 > 4 && x4:0:0 + -1 * x5:0:0 >= 0 && x4:0:0 + -1 * x5:0:0 <= 4 && x5:0:0 < 6 (6) f74_0_loop_aux_LE(x12:0:0, x13:0:0, x12:0:0) -> f74_0_loop_aux_LE(x12:0:0 - 1, x13:0:0, x12:0:0 - 1) :|: x12:0:0 > 1 && x13:0:0 > 4 && x12:0:0 + -1 * x13:0:0 >= 5 && x13:0:0 < 6 (7) f74_0_loop_aux_LE(x12:0, x13:0, x12:0) -> f74_0_loop_aux_LE(x12:0 - 1, x13:0 + 1, x12:0 - 1) :|: x12:0 > 1 && x13:0 > 3 && x13:0 < 5 && x12:0 + -1 * x13:0 >= 6 (8) f74_0_loop_aux_LE(x20:0, x21:0, x20:0) -> f74_0_loop_aux_LE(x20:0 - 2, x21:0 + 2, x20:0 - 2) :|: x20:0 > 1 && x21:0 > 3 && x20:0 + -1 * x21:0 = 5 && x21:0 < 5 Arcs: (1) -> (1), (2), (4), (5) (2) -> (1), (2), (5) (3) -> (2) (4) -> (2), (3), (4), (5), (6), (7), (8) (5) -> (1), (4) (6) -> (5), (6) (7) -> (5), (6) (8) -> (4) This digraph is fully evaluated! ---------------------------------------- (33) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (34) Obligation: Rules: f74_0_loop_aux_LE(x4:0:0:0, x5:0:0:0, x4:0:0:0) -> f74_0_loop_aux_LE(x4:0:0:0 - 2, x5:0:0:0 + 1, x4:0:0:0 - 2) :|: x4:0:0:0 + -1 * x5:0:0:0 <= 4 && x5:0:0:0 < 6 && x4:0:0:0 + -1 * x5:0:0:0 >= 0 && x5:0:0:0 > 4 && x4:0:0:0 > 1 f74_0_loop_aux_LE(x12:0:0:0, x13:0:0:0, x12:0:0:0) -> f74_0_loop_aux_LE(x12:0:0:0 - 1, x13:0:0:0, x12:0:0:0 - 1) :|: x12:0:0:0 + -1 * x13:0:0:0 >= 5 && x13:0:0:0 < 6 && x13:0:0:0 > 4 && x12:0:0:0 > 1 f74_0_loop_aux_LE(x16:0:0:0:0, x17:0:0:0:0, x16:0:0:0:0) -> f74_0_loop_aux_LE(x16:0:0:0:0 + 1, x17:0:0:0:0 - 1, x16:0:0:0:0 + 1) :|: x17:0:0:0:0 >= x16:0:0:0:0 + 1 && x17:0:0:0:0 - 1 >= x16:0:0:0:0 && x17:0:0:0:0 > 1 && x16:0:0:0:0 + 1 <= 2 * x17:0:0:0:0 - 1 && x16:0:0:0:0 > 0 f74_0_loop_aux_LE(x20:0:0, x21:0:0, x20:0:0) -> f74_0_loop_aux_LE(x20:0:0 - 2, x21:0:0 + 2, x20:0:0 - 2) :|: x20:0:0 + -1 * x21:0:0 = 5 && x21:0:0 < 5 && x21:0:0 > 3 && x20:0:0 > 1 f74_0_loop_aux_LE(x12:0:0, x13:0:0, x12:0:0) -> f74_0_loop_aux_LE(x12:0:0 - 1, x13:0:0 + 1, x12:0:0 - 1) :|: x13:0:0 < 5 && x12:0:0 + -1 * x13:0:0 >= 6 && x13:0:0 > 3 && x12:0:0 > 1 f74_0_loop_aux_LE(x:0:0:0, x1:0:0:0, x:0:0:0) -> f74_0_loop_aux_LE(x:0:0:0 - 2, x1:0:0:0 - 2, x:0:0:0 - 2) :|: x:0:0:0 > 2 && x:0:0:0 + -1 * x1:0:0:0 >= 0 && x1:0:0:0 > 5 f74_0_loop_aux_LE(x12:0, x13:0, x12:0) -> f74_0_loop_aux_LE(x12:0, x13:0 + 1, x12:0) :|: x12:0 + -2 * x13:0 <= 3 && x13:0 + -1 * x12:0 >= -2 && x12:0 > 1 && x13:0 > -1 && x13:0 + -1 * x12:0 <= 0 && x13:0 < 5 f74_0_loop_aux_LE(x16:0, x17:0, x16:0) -> f74_0_loop_aux_LE(x16:0 - 3, x17:0, x16:0 - 3) :|: x16:0 + -1 * x17:0 >= 3 && x17:0 > 3 && x16:0 > 3 && x17:0 < 5 && x16:0 + -1 * x17:0 <= 4 ---------------------------------------- (35) IRSwTChainingProof (EQUIVALENT) Chaining! ---------------------------------------- (36) Obligation: Rules: f74_0_loop_aux_LE(x12:0:0:0, x13:0:0:0, x12:0:0:0) -> f74_0_loop_aux_LE(x12:0:0:0 - 1, x13:0:0:0, x12:0:0:0 - 1) :|: x12:0:0:0 + -1 * x13:0:0:0 >= 5 && x13:0:0:0 < 6 && x13:0:0:0 > 4 && x12:0:0:0 > 1 f74_0_loop_aux_LE(x16:0:0:0:0, x17:0:0:0:0, x16:0:0:0:0) -> f74_0_loop_aux_LE(x16:0:0:0:0 + 1, x17:0:0:0:0 - 1, x16:0:0:0:0 + 1) :|: x17:0:0:0:0 >= x16:0:0:0:0 + 1 && x17:0:0:0:0 - 1 >= x16:0:0:0:0 && x17:0:0:0:0 > 1 && x16:0:0:0:0 + 1 <= 2 * x17:0:0:0:0 - 1 && x16:0:0:0:0 > 0 f74_0_loop_aux_LE(x8, x9, x8) -> f74_0_loop_aux_LE(x8 + -1, x9, x8 + -1) :|: TRUE && x9 <= 5 && x8 + -1 * x9 >= 0 && x9 >= 5 && x9 + -1 * x8 >= -2 && x8 + -2 * x9 <= 2 && x8 >= 3 f74_0_loop_aux_LE(x20:0:0, x21:0:0, x20:0:0) -> f74_0_loop_aux_LE(x20:0:0 - 2, x21:0:0 + 2, x20:0:0 - 2) :|: x20:0:0 + -1 * x21:0:0 = 5 && x21:0:0 < 5 && x21:0:0 > 3 && x20:0:0 > 1 f74_0_loop_aux_LE(x12:0:0, x13:0:0, x12:0:0) -> f74_0_loop_aux_LE(x12:0:0 - 1, x13:0:0 + 1, x12:0:0 - 1) :|: x13:0:0 < 5 && x12:0:0 + -1 * x13:0:0 >= 6 && x13:0:0 > 3 && x12:0:0 > 1 f74_0_loop_aux_LE(x:0:0:0, x1:0:0:0, x:0:0:0) -> f74_0_loop_aux_LE(x:0:0:0 - 2, x1:0:0:0 - 2, x:0:0:0 - 2) :|: x:0:0:0 > 2 && x:0:0:0 + -1 * x1:0:0:0 >= 0 && x1:0:0:0 > 5 f74_0_loop_aux_LE(x20, x21, x20) -> f74_0_loop_aux_LE(x20 + -4, x21 + -1, x20 + -4) :|: TRUE && x20 + -1 * x21 <= 4 && x21 <= 5 && x21 >= 5 && x20 >= 5 && x20 + -1 * x21 >= 3 f74_0_loop_aux_LE(x12:0, x13:0, x12:0) -> f74_0_loop_aux_LE(x12:0, x13:0 + 1, x12:0) :|: x12:0 + -2 * x13:0 <= 3 && x13:0 + -1 * x12:0 >= -2 && x12:0 > 1 && x13:0 > -1 && x13:0 + -1 * x12:0 <= 0 && x13:0 < 5 f74_0_loop_aux_LE(x16:0, x17:0, x16:0) -> f74_0_loop_aux_LE(x16:0 - 3, x17:0, x16:0 - 3) :|: x16:0 + -1 * x17:0 >= 3 && x17:0 > 3 && x16:0 > 3 && x17:0 < 5 && x16:0 + -1 * x17:0 <= 4 ---------------------------------------- (37) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f74_0_loop_aux_LE(x12:0:0:0, x13:0:0:0, x12:0:0:0) -> f74_0_loop_aux_LE(x12:0:0:0 - 1, x13:0:0:0, x12:0:0:0 - 1) :|: x12:0:0:0 + -1 * x13:0:0:0 >= 5 && x13:0:0:0 < 6 && x13:0:0:0 > 4 && x12:0:0:0 > 1 (2) f74_0_loop_aux_LE(x16:0:0:0:0, x17:0:0:0:0, x16:0:0:0:0) -> f74_0_loop_aux_LE(x16:0:0:0:0 + 1, x17:0:0:0:0 - 1, x16:0:0:0:0 + 1) :|: x17:0:0:0:0 >= x16:0:0:0:0 + 1 && x17:0:0:0:0 - 1 >= x16:0:0:0:0 && x17:0:0:0:0 > 1 && x16:0:0:0:0 + 1 <= 2 * x17:0:0:0:0 - 1 && x16:0:0:0:0 > 0 (3) f74_0_loop_aux_LE(x8, x9, x8) -> f74_0_loop_aux_LE(x8 + -1, x9, x8 + -1) :|: TRUE && x9 <= 5 && x8 + -1 * x9 >= 0 && x9 >= 5 && x9 + -1 * x8 >= -2 && x8 + -2 * x9 <= 2 && x8 >= 3 (4) f74_0_loop_aux_LE(x20:0:0, x21:0:0, x20:0:0) -> f74_0_loop_aux_LE(x20:0:0 - 2, x21:0:0 + 2, x20:0:0 - 2) :|: x20:0:0 + -1 * x21:0:0 = 5 && x21:0:0 < 5 && x21:0:0 > 3 && x20:0:0 > 1 (5) f74_0_loop_aux_LE(x12:0:0, x13:0:0, x12:0:0) -> f74_0_loop_aux_LE(x12:0:0 - 1, x13:0:0 + 1, x12:0:0 - 1) :|: x13:0:0 < 5 && x12:0:0 + -1 * x13:0:0 >= 6 && x13:0:0 > 3 && x12:0:0 > 1 (6) f74_0_loop_aux_LE(x:0:0:0, x1:0:0:0, x:0:0:0) -> f74_0_loop_aux_LE(x:0:0:0 - 2, x1:0:0:0 - 2, x:0:0:0 - 2) :|: x:0:0:0 > 2 && x:0:0:0 + -1 * x1:0:0:0 >= 0 && x1:0:0:0 > 5 (7) f74_0_loop_aux_LE(x20, x21, x20) -> f74_0_loop_aux_LE(x20 + -4, x21 + -1, x20 + -4) :|: TRUE && x20 + -1 * x21 <= 4 && x21 <= 5 && x21 >= 5 && x20 >= 5 && x20 + -1 * x21 >= 3 (8) f74_0_loop_aux_LE(x12:0, x13:0, x12:0) -> f74_0_loop_aux_LE(x12:0, x13:0 + 1, x12:0) :|: x12:0 + -2 * x13:0 <= 3 && x13:0 + -1 * x12:0 >= -2 && x12:0 > 1 && x13:0 > -1 && x13:0 + -1 * x12:0 <= 0 && x13:0 < 5 (9) f74_0_loop_aux_LE(x16:0, x17:0, x16:0) -> f74_0_loop_aux_LE(x16:0 - 3, x17:0, x16:0 - 3) :|: x16:0 + -1 * x17:0 >= 3 && x17:0 > 3 && x16:0 > 3 && x17:0 < 5 && x16:0 + -1 * x17:0 <= 4 Arcs: (1) -> (1), (7) (2) -> (2), (3), (6), (8) (3) -> (2), (3) (4) -> (6) (5) -> (1), (7) (6) -> (1), (3), (4), (5), (6), (7), (8), (9) (7) -> (8) (8) -> (2), (3), (8) (9) -> (8) This digraph is fully evaluated! ---------------------------------------- (38) Obligation: Termination digraph: Nodes: (1) f74_0_loop_aux_LE(x12:0:0:0, x13:0:0:0, x12:0:0:0) -> f74_0_loop_aux_LE(x12:0:0:0 - 1, x13:0:0:0, x12:0:0:0 - 1) :|: x12:0:0:0 + -1 * x13:0:0:0 >= 5 && x13:0:0:0 < 6 && x13:0:0:0 > 4 && x12:0:0:0 > 1 (2) f74_0_loop_aux_LE(x12:0:0, x13:0:0, x12:0:0) -> f74_0_loop_aux_LE(x12:0:0 - 1, x13:0:0 + 1, x12:0:0 - 1) :|: x13:0:0 < 5 && x12:0:0 + -1 * x13:0:0 >= 6 && x13:0:0 > 3 && x12:0:0 > 1 (3) f74_0_loop_aux_LE(x:0:0:0, x1:0:0:0, x:0:0:0) -> f74_0_loop_aux_LE(x:0:0:0 - 2, x1:0:0:0 - 2, x:0:0:0 - 2) :|: x:0:0:0 > 2 && x:0:0:0 + -1 * x1:0:0:0 >= 0 && x1:0:0:0 > 5 (4) f74_0_loop_aux_LE(x20:0:0, x21:0:0, x20:0:0) -> f74_0_loop_aux_LE(x20:0:0 - 2, x21:0:0 + 2, x20:0:0 - 2) :|: x20:0:0 + -1 * x21:0:0 = 5 && x21:0:0 < 5 && x21:0:0 > 3 && x20:0:0 > 1 (5) f74_0_loop_aux_LE(x16:0:0:0:0, x17:0:0:0:0, x16:0:0:0:0) -> f74_0_loop_aux_LE(x16:0:0:0:0 + 1, x17:0:0:0:0 - 1, x16:0:0:0:0 + 1) :|: x17:0:0:0:0 >= x16:0:0:0:0 + 1 && x17:0:0:0:0 - 1 >= x16:0:0:0:0 && x17:0:0:0:0 > 1 && x16:0:0:0:0 + 1 <= 2 * x17:0:0:0:0 - 1 && x16:0:0:0:0 > 0 (6) f74_0_loop_aux_LE(x8, x9, x8) -> f74_0_loop_aux_LE(x8 + -1, x9, x8 + -1) :|: TRUE && x9 <= 5 && x8 + -1 * x9 >= 0 && x9 >= 5 && x9 + -1 * x8 >= -2 && x8 + -2 * x9 <= 2 && x8 >= 3 (7) f74_0_loop_aux_LE(x12:0, x13:0, x12:0) -> f74_0_loop_aux_LE(x12:0, x13:0 + 1, x12:0) :|: x12:0 + -2 * x13:0 <= 3 && x13:0 + -1 * x12:0 >= -2 && x12:0 > 1 && x13:0 > -1 && x13:0 + -1 * x12:0 <= 0 && x13:0 < 5 (8) f74_0_loop_aux_LE(x16:0, x17:0, x16:0) -> f74_0_loop_aux_LE(x16:0 - 3, x17:0, x16:0 - 3) :|: x16:0 + -1 * x17:0 >= 3 && x17:0 > 3 && x16:0 > 3 && x17:0 < 5 && x16:0 + -1 * x17:0 <= 4 (9) f74_0_loop_aux_LE(x20, x21, x20) -> f74_0_loop_aux_LE(x20 + -4, x21 + -1, x20 + -4) :|: TRUE && x20 + -1 * x21 <= 4 && x21 <= 5 && x21 >= 5 && x20 >= 5 && x20 + -1 * x21 >= 3 Arcs: (1) -> (1), (9) (2) -> (1), (9) (3) -> (1), (2), (3), (4), (6), (7), (8), (9) (4) -> (3) (5) -> (3), (5), (6), (7) (6) -> (5), (6) (7) -> (5), (6), (7) (8) -> (7) (9) -> (7) This digraph is fully evaluated! ---------------------------------------- (39) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (40) Obligation: Rules: f74_0_loop_aux_LE(x16:0:0:0:0:0, x17:0:0:0:0:0, x16:0:0:0:0:0) -> f74_0_loop_aux_LE(x16:0:0:0:0:0 + 1, x17:0:0:0:0:0 - 1, x16:0:0:0:0:0 + 1) :|: x16:0:0:0:0:0 + 1 <= 2 * x17:0:0:0:0:0 - 1 && x16:0:0:0:0:0 > 0 && x17:0:0:0:0:0 > 1 && x17:0:0:0:0:0 - 1 >= x16:0:0:0:0:0 && x17:0:0:0:0:0 >= x16:0:0:0:0:0 + 1 f74_0_loop_aux_LE(x12:0:0, x13:0:0, x12:0:0) -> f74_0_loop_aux_LE(x12:0:0, x13:0:0 + 1, x12:0:0) :|: x13:0:0 + -1 * x12:0:0 <= 0 && x13:0:0 < 5 && x13:0:0 > -1 && x12:0:0 > 1 && x13:0:0 + -1 * x12:0:0 >= -2 && x12:0:0 + -2 * x13:0:0 <= 3 f74_0_loop_aux_LE(x12:0:0:0:0, x13:0:0:0:0, x12:0:0:0:0) -> f74_0_loop_aux_LE(x12:0:0:0:0 - 1, x13:0:0:0:0, x12:0:0:0:0 - 1) :|: x13:0:0:0:0 > 4 && x12:0:0:0:0 > 1 && x13:0:0:0:0 < 6 && x12:0:0:0:0 + -1 * x13:0:0:0:0 >= 5 f74_0_loop_aux_LE(x20:0:0:0, x21:0:0:0, x20:0:0:0) -> f74_0_loop_aux_LE(x20:0:0:0 - 2, x21:0:0:0 + 2, x20:0:0:0 - 2) :|: x21:0:0:0 > 3 && x20:0:0:0 > 1 && x21:0:0:0 < 5 && x20:0:0:0 + -1 * x21:0:0:0 = 5 f74_0_loop_aux_LE(x8:0, x9:0, x8:0) -> f74_0_loop_aux_LE(x8:0 - 1, x9:0, x8:0 - 1) :|: x8:0 + -2 * x9:0 <= 2 && x8:0 > 2 && x9:0 + -1 * x8:0 >= -2 && x9:0 > 4 && x9:0 < 6 && x8:0 + -1 * x9:0 >= 0 f74_0_loop_aux_LE(x:0:0:0:0, x1:0:0:0:0, x:0:0:0:0) -> f74_0_loop_aux_LE(x:0:0:0:0 - 2, x1:0:0:0:0 - 2, x:0:0:0:0 - 2) :|: x:0:0:0:0 > 2 && x:0:0:0:0 + -1 * x1:0:0:0:0 >= 0 && x1:0:0:0:0 > 5 f74_0_loop_aux_LE(x16:0:0, x17:0:0, x16:0:0) -> f74_0_loop_aux_LE(x16:0:0 - 3, x17:0:0, x16:0:0 - 3) :|: x17:0:0 < 5 && x16:0:0 + -1 * x17:0:0 <= 4 && x16:0:0 > 3 && x17:0:0 > 3 && x16:0:0 + -1 * x17:0:0 >= 3 f74_0_loop_aux_LE(x12:0:0:0, x13:0:0:0, x12:0:0:0) -> f74_0_loop_aux_LE(x12:0:0:0 - 1, x13:0:0:0 + 1, x12:0:0:0 - 1) :|: x13:0:0:0 > 3 && x12:0:0:0 > 1 && x12:0:0:0 + -1 * x13:0:0:0 >= 6 && x13:0:0:0 < 5 f74_0_loop_aux_LE(x20:0, x21:0, x20:0) -> f74_0_loop_aux_LE(x20:0 - 4, x21:0 - 1, x20:0 - 4) :|: x20:0 > 4 && x20:0 + -1 * x21:0 >= 3 && x21:0 > 4 && x20:0 + -1 * x21:0 <= 4 && x21:0 < 6 ---------------------------------------- (41) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f74_0_loop_aux_LE(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 - RankingReductionPairProof Rules: f74_0_loop_aux_LE(x16:0:0:0:0:0, x17:0:0:0:0:0, x16:0:0:0:0:0) -> f74_0_loop_aux_LE(c, c1, c2) :|: c2 = x16:0:0:0:0:0 + 1 && (c1 = x17:0:0:0:0:0 - 1 && c = x16:0:0:0:0:0 + 1) && (x16:0:0:0:0:0 + 1 <= 2 * x17:0:0:0:0:0 - 1 && x16:0:0:0:0:0 > 0 && x17:0:0:0:0:0 > 1 && x17:0:0:0:0:0 - 1 >= x16:0:0:0:0:0 && x17:0:0:0:0:0 >= x16:0:0:0:0:0 + 1) f74_0_loop_aux_LE(x12:0:0, x13:0:0, x12:0:0) -> f74_0_loop_aux_LE(x12:0:0, c3, x12:0:0) :|: c3 = x13:0:0 + 1 && (x13:0:0 + -1 * x12:0:0 <= 0 && x13:0:0 < 5 && x13:0:0 > -1 && x12:0:0 > 1 && x13:0:0 + -1 * x12:0:0 >= -2 && x12:0:0 + -2 * x13:0:0 <= 3) f74_0_loop_aux_LE(x12:0:0:0:0, x13:0:0:0:0, x12:0:0:0:0) -> f74_0_loop_aux_LE(c4, x13:0:0:0:0, c5) :|: c5 = x12:0:0:0:0 - 1 && c4 = x12:0:0:0:0 - 1 && (x13:0:0:0:0 > 4 && x12:0:0:0:0 > 1 && x13:0:0:0:0 < 6 && x12:0:0:0:0 + -1 * x13:0:0:0:0 >= 5) f74_0_loop_aux_LE(x20:0:0:0, x21:0:0:0, x20:0:0:0) -> f74_0_loop_aux_LE(c6, c7, c8) :|: c8 = x20:0:0:0 - 2 && (c7 = x21:0:0:0 + 2 && c6 = x20:0:0:0 - 2) && (x21:0:0:0 > 3 && x20:0:0:0 > 1 && x21:0:0:0 < 5 && x20:0:0:0 + -1 * x21:0:0:0 = 5) f74_0_loop_aux_LE(x8:0, x9:0, x8:0) -> f74_0_loop_aux_LE(c9, x9:0, c10) :|: c10 = x8:0 - 1 && c9 = x8:0 - 1 && (x8:0 + -2 * x9:0 <= 2 && x8:0 > 2 && x9:0 + -1 * x8:0 >= -2 && x9:0 > 4 && x9:0 < 6 && x8:0 + -1 * x9:0 >= 0) f74_0_loop_aux_LE(x:0:0:0:0, x1:0:0:0:0, x:0:0:0:0) -> f74_0_loop_aux_LE(c11, c12, c13) :|: c13 = x:0:0:0:0 - 2 && (c12 = x1:0:0:0:0 - 2 && c11 = x:0:0:0:0 - 2) && (x:0:0:0:0 > 2 && x:0:0:0:0 + -1 * x1:0:0:0:0 >= 0 && x1:0:0:0:0 > 5) f74_0_loop_aux_LE(x16:0:0, x17:0:0, x16:0:0) -> f74_0_loop_aux_LE(c14, x17:0:0, c15) :|: c15 = x16:0:0 - 3 && c14 = x16:0:0 - 3 && (x17:0:0 < 5 && x16:0:0 + -1 * x17:0:0 <= 4 && x16:0:0 > 3 && x17:0:0 > 3 && x16:0:0 + -1 * x17:0:0 >= 3) f74_0_loop_aux_LE(x12:0:0:0, x13:0:0:0, x12:0:0:0) -> f74_0_loop_aux_LE(c16, c17, c18) :|: c18 = x12:0:0:0 - 1 && (c17 = x13:0:0:0 + 1 && c16 = x12:0:0:0 - 1) && (x13:0:0:0 > 3 && x12:0:0:0 > 1 && x12:0:0:0 + -1 * x13:0:0:0 >= 6 && x13:0:0:0 < 5) f74_0_loop_aux_LE(x20:0, x21:0, x20:0) -> f74_0_loop_aux_LE(c19, c20, c21) :|: c21 = x20:0 - 4 && (c20 = x21:0 - 1 && c19 = x20:0 - 4) && (x20:0 > 4 && x20:0 + -1 * x21:0 >= 3 && x21:0 > 4 && x20:0 + -1 * x21:0 <= 4 && x21:0 < 6) Interpretation: [ f74_0_loop_aux_LE ] = -219/2*f74_0_loop_aux_LE_3 + -219/2*f74_0_loop_aux_LE_2 + 73/6*f74_0_loop_aux_LE_3^2 + 73/6*f74_0_loop_aux_LE_2^2 The following rules are decreasing: f74_0_loop_aux_LE(x12:0:0:0:0, x13:0:0:0:0, x12:0:0:0:0) -> f74_0_loop_aux_LE(c4, x13:0:0:0:0, c5) :|: c5 = x12:0:0:0:0 - 1 && c4 = x12:0:0:0:0 - 1 && (x13:0:0:0:0 > 4 && x12:0:0:0:0 > 1 && x13:0:0:0:0 < 6 && x12:0:0:0:0 + -1 * x13:0:0:0:0 >= 5) f74_0_loop_aux_LE(x20:0:0:0, x21:0:0:0, x20:0:0:0) -> f74_0_loop_aux_LE(c6, c7, c8) :|: c8 = x20:0:0:0 - 2 && (c7 = x21:0:0:0 + 2 && c6 = x20:0:0:0 - 2) && (x21:0:0:0 > 3 && x20:0:0:0 > 1 && x21:0:0:0 < 5 && x20:0:0:0 + -1 * x21:0:0:0 = 5) f74_0_loop_aux_LE(x:0:0:0:0, x1:0:0:0:0, x:0:0:0:0) -> f74_0_loop_aux_LE(c11, c12, c13) :|: c13 = x:0:0:0:0 - 2 && (c12 = x1:0:0:0:0 - 2 && c11 = x:0:0:0:0 - 2) && (x:0:0:0:0 > 2 && x:0:0:0:0 + -1 * x1:0:0:0:0 >= 0 && x1:0:0:0:0 > 5) f74_0_loop_aux_LE(x16:0:0, x17:0:0, x16:0:0) -> f74_0_loop_aux_LE(c14, x17:0:0, c15) :|: c15 = x16:0:0 - 3 && c14 = x16:0:0 - 3 && (x17:0:0 < 5 && x16:0:0 + -1 * x17:0:0 <= 4 && x16:0:0 > 3 && x17:0:0 > 3 && x16:0:0 + -1 * x17:0:0 >= 3) f74_0_loop_aux_LE(x12:0:0:0, x13:0:0:0, x12:0:0:0) -> f74_0_loop_aux_LE(c16, c17, c18) :|: c18 = x12:0:0:0 - 1 && (c17 = x13:0:0:0 + 1 && c16 = x12:0:0:0 - 1) && (x13:0:0:0 > 3 && x12:0:0:0 > 1 && x12:0:0:0 + -1 * x13:0:0:0 >= 6 && x13:0:0:0 < 5) f74_0_loop_aux_LE(x20:0, x21:0, x20:0) -> f74_0_loop_aux_LE(c19, c20, c21) :|: c21 = x20:0 - 4 && (c20 = x21:0 - 1 && c19 = x20:0 - 4) && (x20:0 > 4 && x20:0 + -1 * x21:0 >= 3 && x21:0 > 4 && x20:0 + -1 * x21:0 <= 4 && x21:0 < 6) The following rules are bounded: f74_0_loop_aux_LE(x8:0, x9:0, x8:0) -> f74_0_loop_aux_LE(c9, x9:0, c10) :|: c10 = x8:0 - 1 && c9 = x8:0 - 1 && (x8:0 + -2 * x9:0 <= 2 && x8:0 > 2 && x9:0 + -1 * x8:0 >= -2 && x9:0 > 4 && x9:0 < 6 && x8:0 + -1 * x9:0 >= 0) f74_0_loop_aux_LE(x16:0:0, x17:0:0, x16:0:0) -> f74_0_loop_aux_LE(c14, x17:0:0, c15) :|: c15 = x16:0:0 - 3 && c14 = x16:0:0 - 3 && (x17:0:0 < 5 && x16:0:0 + -1 * x17:0:0 <= 4 && x16:0:0 > 3 && x17:0:0 > 3 && x16:0:0 + -1 * x17:0:0 >= 3) f74_0_loop_aux_LE(x12:0:0:0, x13:0:0:0, x12:0:0:0) -> f74_0_loop_aux_LE(c16, c17, c18) :|: c18 = x12:0:0:0 - 1 && (c17 = x13:0:0:0 + 1 && c16 = x12:0:0:0 - 1) && (x13:0:0:0 > 3 && x12:0:0:0 > 1 && x12:0:0:0 + -1 * x13:0:0:0 >= 6 && x13:0:0:0 < 5) - IntTRS - RankingReductionPairProof - AND - IntTRS - IntTRS - IntTRS Rules: f74_0_loop_aux_LE(x16:0:0:0:0:0, x17:0:0:0:0:0, x16:0:0:0:0:0) -> f74_0_loop_aux_LE(c, c1, c2) :|: c2 = x16:0:0:0:0:0 + 1 && (c1 = x17:0:0:0:0:0 - 1 && c = x16:0:0:0:0:0 + 1) && (x16:0:0:0:0:0 + 1 <= 2 * x17:0:0:0:0:0 - 1 && x16:0:0:0:0:0 > 0 && x17:0:0:0:0:0 > 1 && x17:0:0:0:0:0 - 1 >= x16:0:0:0:0:0 && x17:0:0:0:0:0 >= x16:0:0:0:0:0 + 1) f74_0_loop_aux_LE(x12:0:0, x13:0:0, x12:0:0) -> f74_0_loop_aux_LE(x12:0:0, c3, x12:0:0) :|: c3 = x13:0:0 + 1 && (x13:0:0 + -1 * x12:0:0 <= 0 && x13:0:0 < 5 && x13:0:0 > -1 && x12:0:0 > 1 && x13:0:0 + -1 * x12:0:0 >= -2 && x12:0:0 + -2 * x13:0:0 <= 3) f74_0_loop_aux_LE(x8:0, x9:0, x8:0) -> f74_0_loop_aux_LE(c9, x9:0, c10) :|: c10 = x8:0 - 1 && c9 = x8:0 - 1 && (x8:0 + -2 * x9:0 <= 2 && x8:0 > 2 && x9:0 + -1 * x8:0 >= -2 && x9:0 > 4 && x9:0 < 6 && x8:0 + -1 * x9:0 >= 0) - IntTRS - RankingReductionPairProof - AND - IntTRS - IntTRS - IntTRS - RankingReductionPairProof Rules: f74_0_loop_aux_LE(x16:0:0:0:0:0, x17:0:0:0:0:0, x16:0:0:0:0:0) -> f74_0_loop_aux_LE(c, c1, c2) :|: c2 = x16:0:0:0:0:0 + 1 && (c1 = x17:0:0:0:0:0 - 1 && c = x16:0:0:0:0:0 + 1) && (x16:0:0:0:0:0 + 1 <= 2 * x17:0:0:0:0:0 - 1 && x16:0:0:0:0:0 > 0 && x17:0:0:0:0:0 > 1 && x17:0:0:0:0:0 - 1 >= x16:0:0:0:0:0 && x17:0:0:0:0:0 >= x16:0:0:0:0:0 + 1) f74_0_loop_aux_LE(x12:0:0, x13:0:0, x12:0:0) -> f74_0_loop_aux_LE(x12:0:0, c3, x12:0:0) :|: c3 = x13:0:0 + 1 && (x13:0:0 + -1 * x12:0:0 <= 0 && x13:0:0 < 5 && x13:0:0 > -1 && x12:0:0 > 1 && x13:0:0 + -1 * x12:0:0 >= -2 && x12:0:0 + -2 * x13:0:0 <= 3) f74_0_loop_aux_LE(x12:0:0:0:0, x13:0:0:0:0, x12:0:0:0:0) -> f74_0_loop_aux_LE(c4, x13:0:0:0:0, c5) :|: c5 = x12:0:0:0:0 - 1 && c4 = x12:0:0:0:0 - 1 && (x13:0:0:0:0 > 4 && x12:0:0:0:0 > 1 && x13:0:0:0:0 < 6 && x12:0:0:0:0 + -1 * x13:0:0:0:0 >= 5) f74_0_loop_aux_LE(x20:0:0:0, x21:0:0:0, x20:0:0:0) -> f74_0_loop_aux_LE(c6, c7, c8) :|: c8 = x20:0:0:0 - 2 && (c7 = x21:0:0:0 + 2 && c6 = x20:0:0:0 - 2) && (x21:0:0:0 > 3 && x20:0:0:0 > 1 && x21:0:0:0 < 5 && x20:0:0:0 + -1 * x21:0:0:0 = 5) f74_0_loop_aux_LE(x:0:0:0:0, x1:0:0:0:0, x:0:0:0:0) -> f74_0_loop_aux_LE(c11, c12, c13) :|: c13 = x:0:0:0:0 - 2 && (c12 = x1:0:0:0:0 - 2 && c11 = x:0:0:0:0 - 2) && (x:0:0:0:0 > 2 && x:0:0:0:0 + -1 * x1:0:0:0:0 >= 0 && x1:0:0:0:0 > 5) f74_0_loop_aux_LE(x20:0, x21:0, x20:0) -> f74_0_loop_aux_LE(c19, c20, c21) :|: c21 = x20:0 - 4 && (c20 = x21:0 - 1 && c19 = x20:0 - 4) && (x20:0 > 4 && x20:0 + -1 * x21:0 >= 3 && x21:0 > 4 && x20:0 + -1 * x21:0 <= 4 && x21:0 < 6) Interpretation: [ f74_0_loop_aux_LE ] = -737/8*f74_0_loop_aux_LE_3 + -729/8*f74_0_loop_aux_LE_2 + 147/16*f74_0_loop_aux_LE_3^2 + 147/16*f74_0_loop_aux_LE_2^2 The following rules are decreasing: f74_0_loop_aux_LE(x16:0:0:0:0:0, x17:0:0:0:0:0, x16:0:0:0:0:0) -> f74_0_loop_aux_LE(c, c1, c2) :|: c2 = x16:0:0:0:0:0 + 1 && (c1 = x17:0:0:0:0:0 - 1 && c = x16:0:0:0:0:0 + 1) && (x16:0:0:0:0:0 + 1 <= 2 * x17:0:0:0:0:0 - 1 && x16:0:0:0:0:0 > 0 && x17:0:0:0:0:0 > 1 && x17:0:0:0:0:0 - 1 >= x16:0:0:0:0:0 && x17:0:0:0:0:0 >= x16:0:0:0:0:0 + 1) f74_0_loop_aux_LE(x12:0:0, x13:0:0, x12:0:0) -> f74_0_loop_aux_LE(x12:0:0, c3, x12:0:0) :|: c3 = x13:0:0 + 1 && (x13:0:0 + -1 * x12:0:0 <= 0 && x13:0:0 < 5 && x13:0:0 > -1 && x12:0:0 > 1 && x13:0:0 + -1 * x12:0:0 >= -2 && x12:0:0 + -2 * x13:0:0 <= 3) f74_0_loop_aux_LE(x12:0:0:0:0, x13:0:0:0:0, x12:0:0:0:0) -> f74_0_loop_aux_LE(c4, x13:0:0:0:0, c5) :|: c5 = x12:0:0:0:0 - 1 && c4 = x12:0:0:0:0 - 1 && (x13:0:0:0:0 > 4 && x12:0:0:0:0 > 1 && x13:0:0:0:0 < 6 && x12:0:0:0:0 + -1 * x13:0:0:0:0 >= 5) f74_0_loop_aux_LE(x20:0:0:0, x21:0:0:0, x20:0:0:0) -> f74_0_loop_aux_LE(c6, c7, c8) :|: c8 = x20:0:0:0 - 2 && (c7 = x21:0:0:0 + 2 && c6 = x20:0:0:0 - 2) && (x21:0:0:0 > 3 && x20:0:0:0 > 1 && x21:0:0:0 < 5 && x20:0:0:0 + -1 * x21:0:0:0 = 5) f74_0_loop_aux_LE(x:0:0:0:0, x1:0:0:0:0, x:0:0:0:0) -> f74_0_loop_aux_LE(c11, c12, c13) :|: c13 = x:0:0:0:0 - 2 && (c12 = x1:0:0:0:0 - 2 && c11 = x:0:0:0:0 - 2) && (x:0:0:0:0 > 2 && x:0:0:0:0 + -1 * x1:0:0:0:0 >= 0 && x1:0:0:0:0 > 5) f74_0_loop_aux_LE(x20:0, x21:0, x20:0) -> f74_0_loop_aux_LE(c19, c20, c21) :|: c21 = x20:0 - 4 && (c20 = x21:0 - 1 && c19 = x20:0 - 4) && (x20:0 > 4 && x20:0 + -1 * x21:0 >= 3 && x21:0 > 4 && x20:0 + -1 * x21:0 <= 4 && x21:0 < 6) The following rules are bounded: f74_0_loop_aux_LE(x12:0:0, x13:0:0, x12:0:0) -> f74_0_loop_aux_LE(x12:0:0, c3, x12:0:0) :|: c3 = x13:0:0 + 1 && (x13:0:0 + -1 * x12:0:0 <= 0 && x13:0:0 < 5 && x13:0:0 > -1 && x12:0:0 > 1 && x13:0:0 + -1 * x12:0:0 >= -2 && x12:0:0 + -2 * x13:0:0 <= 3) - IntTRS - RankingReductionPairProof - AND - IntTRS - IntTRS - IntTRS - RankingReductionPairProof - IntTRS - PolynomialOrderProcessor Rules: f74_0_loop_aux_LE(x16:0:0:0:0:0, x17:0:0:0:0:0, x16:0:0:0:0:0) -> f74_0_loop_aux_LE(c, c1, c2) :|: c2 = x16:0:0:0:0:0 + 1 && (c1 = x17:0:0:0:0:0 - 1 && c = x16:0:0:0:0:0 + 1) && (x16:0:0:0:0:0 + 1 <= 2 * x17:0:0:0:0:0 - 1 && x16:0:0:0:0:0 > 0 && x17:0:0:0:0:0 > 1 && x17:0:0:0:0:0 - 1 >= x16:0:0:0:0:0 && x17:0:0:0:0:0 >= x16:0:0:0:0:0 + 1) f74_0_loop_aux_LE(x12:0:0:0:0, x13:0:0:0:0, x12:0:0:0:0) -> f74_0_loop_aux_LE(c4, x13:0:0:0:0, c5) :|: c5 = x12:0:0:0:0 - 1 && c4 = x12:0:0:0:0 - 1 && (x13:0:0:0:0 > 4 && x12:0:0:0:0 > 1 && x13:0:0:0:0 < 6 && x12:0:0:0:0 + -1 * x13:0:0:0:0 >= 5) f74_0_loop_aux_LE(x20:0:0:0, x21:0:0:0, x20:0:0:0) -> f74_0_loop_aux_LE(c6, c7, c8) :|: c8 = x20:0:0:0 - 2 && (c7 = x21:0:0:0 + 2 && c6 = x20:0:0:0 - 2) && (x21:0:0:0 > 3 && x20:0:0:0 > 1 && x21:0:0:0 < 5 && x20:0:0:0 + -1 * x21:0:0:0 = 5) f74_0_loop_aux_LE(x:0:0:0:0, x1:0:0:0:0, x:0:0:0:0) -> f74_0_loop_aux_LE(c11, c12, c13) :|: c13 = x:0:0:0:0 - 2 && (c12 = x1:0:0:0:0 - 2 && c11 = x:0:0:0:0 - 2) && (x:0:0:0:0 > 2 && x:0:0:0:0 + -1 * x1:0:0:0:0 >= 0 && x1:0:0:0:0 > 5) f74_0_loop_aux_LE(x20:0, x21:0, x20:0) -> f74_0_loop_aux_LE(c19, c20, c21) :|: c21 = x20:0 - 4 && (c20 = x21:0 - 1 && c19 = x20:0 - 4) && (x20:0 > 4 && x20:0 + -1 * x21:0 >= 3 && x21:0 > 4 && x20:0 + -1 * x21:0 <= 4 && x21:0 < 6) Found the following polynomial interpretation: [f74_0_loop_aux_LE(x, x1, x2)] = -14 + x + x1 The following rules are decreasing: f74_0_loop_aux_LE(x12:0:0:0:0, x13:0:0:0:0, x12:0:0:0:0) -> f74_0_loop_aux_LE(c4, x13:0:0:0:0, c5) :|: c5 = x12:0:0:0:0 - 1 && c4 = x12:0:0:0:0 - 1 && (x13:0:0:0:0 > 4 && x12:0:0:0:0 > 1 && x13:0:0:0:0 < 6 && x12:0:0:0:0 + -1 * x13:0:0:0:0 >= 5) f74_0_loop_aux_LE(x:0:0:0:0, x1:0:0:0:0, x:0:0:0:0) -> f74_0_loop_aux_LE(c11, c12, c13) :|: c13 = x:0:0:0:0 - 2 && (c12 = x1:0:0:0:0 - 2 && c11 = x:0:0:0:0 - 2) && (x:0:0:0:0 > 2 && x:0:0:0:0 + -1 * x1:0:0:0:0 >= 0 && x1:0:0:0:0 > 5) f74_0_loop_aux_LE(x20:0, x21:0, x20:0) -> f74_0_loop_aux_LE(c19, c20, c21) :|: c21 = x20:0 - 4 && (c20 = x21:0 - 1 && c19 = x20:0 - 4) && (x20:0 > 4 && x20:0 + -1 * x21:0 >= 3 && x21:0 > 4 && x20:0 + -1 * x21:0 <= 4 && x21:0 < 6) The following rules are bounded: f74_0_loop_aux_LE(x12:0:0:0:0, x13:0:0:0:0, x12:0:0:0:0) -> f74_0_loop_aux_LE(c4, x13:0:0:0:0, c5) :|: c5 = x12:0:0:0:0 - 1 && c4 = x12:0:0:0:0 - 1 && (x13:0:0:0:0 > 4 && x12:0:0:0:0 > 1 && x13:0:0:0:0 < 6 && x12:0:0:0:0 + -1 * x13:0:0:0:0 >= 5) - IntTRS - RankingReductionPairProof - AND - IntTRS - IntTRS - IntTRS - RankingReductionPairProof - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor Rules: f74_0_loop_aux_LE(x16:0:0:0:0:0, x17:0:0:0:0:0, x16:0:0:0:0:0) -> f74_0_loop_aux_LE(c, c1, c2) :|: c2 = x16:0:0:0:0:0 + 1 && (c1 = x17:0:0:0:0:0 - 1 && c = x16:0:0:0:0:0 + 1) && (x16:0:0:0:0:0 + 1 <= 2 * x17:0:0:0:0:0 - 1 && x16:0:0:0:0:0 > 0 && x17:0:0:0:0:0 > 1 && x17:0:0:0:0:0 - 1 >= x16:0:0:0:0:0 && x17:0:0:0:0:0 >= x16:0:0:0:0:0 + 1) f74_0_loop_aux_LE(x20:0:0:0, x21:0:0:0, x20:0:0:0) -> f74_0_loop_aux_LE(c6, c7, c8) :|: c8 = x20:0:0:0 - 2 && (c7 = x21:0:0:0 + 2 && c6 = x20:0:0:0 - 2) && (x21:0:0:0 > 3 && x20:0:0:0 > 1 && x21:0:0:0 < 5 && x20:0:0:0 + -1 * x21:0:0:0 = 5) f74_0_loop_aux_LE(x:0:0:0:0, x1:0:0:0:0, x:0:0:0:0) -> f74_0_loop_aux_LE(c11, c12, c13) :|: c13 = x:0:0:0:0 - 2 && (c12 = x1:0:0:0:0 - 2 && c11 = x:0:0:0:0 - 2) && (x:0:0:0:0 > 2 && x:0:0:0:0 + -1 * x1:0:0:0:0 >= 0 && x1:0:0:0:0 > 5) f74_0_loop_aux_LE(x20:0, x21:0, x20:0) -> f74_0_loop_aux_LE(c19, c20, c21) :|: c21 = x20:0 - 4 && (c20 = x21:0 - 1 && c19 = x20:0 - 4) && (x20:0 > 4 && x20:0 + -1 * x21:0 >= 3 && x21:0 > 4 && x20:0 + -1 * x21:0 <= 4 && x21:0 < 6) Found the following polynomial interpretation: [f74_0_loop_aux_LE(x, x1, x2)] = -12 + x + x1 The following rules are decreasing: f74_0_loop_aux_LE(x:0:0:0:0, x1:0:0:0:0, x:0:0:0:0) -> f74_0_loop_aux_LE(c11, c12, c13) :|: c13 = x:0:0:0:0 - 2 && (c12 = x1:0:0:0:0 - 2 && c11 = x:0:0:0:0 - 2) && (x:0:0:0:0 > 2 && x:0:0:0:0 + -1 * x1:0:0:0:0 >= 0 && x1:0:0:0:0 > 5) f74_0_loop_aux_LE(x20:0, x21:0, x20:0) -> f74_0_loop_aux_LE(c19, c20, c21) :|: c21 = x20:0 - 4 && (c20 = x21:0 - 1 && c19 = x20:0 - 4) && (x20:0 > 4 && x20:0 + -1 * x21:0 >= 3 && x21:0 > 4 && x20:0 + -1 * x21:0 <= 4 && x21:0 < 6) The following rules are bounded: f74_0_loop_aux_LE(x20:0:0:0, x21:0:0:0, x20:0:0:0) -> f74_0_loop_aux_LE(c6, c7, c8) :|: c8 = x20:0:0:0 - 2 && (c7 = x21:0:0:0 + 2 && c6 = x20:0:0:0 - 2) && (x21:0:0:0 > 3 && x20:0:0:0 > 1 && x21:0:0:0 < 5 && x20:0:0:0 + -1 * x21:0:0:0 = 5) f74_0_loop_aux_LE(x:0:0:0:0, x1:0:0:0:0, x:0:0:0:0) -> f74_0_loop_aux_LE(c11, c12, c13) :|: c13 = x:0:0:0:0 - 2 && (c12 = x1:0:0:0:0 - 2 && c11 = x:0:0:0:0 - 2) && (x:0:0:0:0 > 2 && x:0:0:0:0 + -1 * x1:0:0:0:0 >= 0 && x1:0:0:0:0 > 5) f74_0_loop_aux_LE(x20:0, x21:0, x20:0) -> f74_0_loop_aux_LE(c19, c20, c21) :|: c21 = x20:0 - 4 && (c20 = x21:0 - 1 && c19 = x20:0 - 4) && (x20:0 > 4 && x20:0 + -1 * x21:0 >= 3 && x21:0 > 4 && x20:0 + -1 * x21:0 <= 4 && x21:0 < 6) - IntTRS - RankingReductionPairProof - AND - IntTRS - IntTRS - IntTRS - RankingReductionPairProof - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor Rules: f74_0_loop_aux_LE(x16:0:0:0:0:0, x17:0:0:0:0:0, x16:0:0:0:0:0) -> f74_0_loop_aux_LE(c, c1, c2) :|: c2 = x16:0:0:0:0:0 + 1 && (c1 = x17:0:0:0:0:0 - 1 && c = x16:0:0:0:0:0 + 1) && (x16:0:0:0:0:0 + 1 <= 2 * x17:0:0:0:0:0 - 1 && x16:0:0:0:0:0 > 0 && x17:0:0:0:0:0 > 1 && x17:0:0:0:0:0 - 1 >= x16:0:0:0:0:0 && x17:0:0:0:0:0 >= x16:0:0:0:0:0 + 1) f74_0_loop_aux_LE(x20:0:0:0, x21:0:0:0, x20:0:0:0) -> f74_0_loop_aux_LE(c6, c7, c8) :|: c8 = x20:0:0:0 - 2 && (c7 = x21:0:0:0 + 2 && c6 = x20:0:0:0 - 2) && (x21:0:0:0 > 3 && x20:0:0:0 > 1 && x21:0:0:0 < 5 && x20:0:0:0 + -1 * x21:0:0:0 = 5) Found the following polynomial interpretation: [f74_0_loop_aux_LE(x, x1, x2)] = -7 - 6*x - x*x1 + x*x2 + 6*x1 - x1*x2 + x1^2 The following rules are decreasing: f74_0_loop_aux_LE(x16:0:0:0:0:0, x17:0:0:0:0:0, x16:0:0:0:0:0) -> f74_0_loop_aux_LE(c, c1, c2) :|: c2 = x16:0:0:0:0:0 + 1 && (c1 = x17:0:0:0:0:0 - 1 && c = x16:0:0:0:0:0 + 1) && (x16:0:0:0:0:0 + 1 <= 2 * x17:0:0:0:0:0 - 1 && x16:0:0:0:0:0 > 0 && x17:0:0:0:0:0 > 1 && x17:0:0:0:0:0 - 1 >= x16:0:0:0:0:0 && x17:0:0:0:0:0 >= x16:0:0:0:0:0 + 1) The following rules are bounded: f74_0_loop_aux_LE(x16:0:0:0:0:0, x17:0:0:0:0:0, x16:0:0:0:0:0) -> f74_0_loop_aux_LE(c, c1, c2) :|: c2 = x16:0:0:0:0:0 + 1 && (c1 = x17:0:0:0:0:0 - 1 && c = x16:0:0:0:0:0 + 1) && (x16:0:0:0:0:0 + 1 <= 2 * x17:0:0:0:0:0 - 1 && x16:0:0:0:0:0 > 0 && x17:0:0:0:0:0 > 1 && x17:0:0:0:0:0 - 1 >= x16:0:0:0:0:0 && x17:0:0:0:0:0 >= x16:0:0:0:0:0 + 1) - IntTRS - RankingReductionPairProof - AND - IntTRS - IntTRS - IntTRS - RankingReductionPairProof - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor Rules: f74_0_loop_aux_LE(x20:0:0:0, x21:0:0:0, x20:0:0:0) -> f74_0_loop_aux_LE(c6, c7, c8) :|: c8 = x20:0:0:0 - 2 && (c7 = x21:0:0:0 + 2 && c6 = x20:0:0:0 - 2) && (x21:0:0:0 > 3 && x20:0:0:0 > 1 && x21:0:0:0 < 5 && x20:0:0:0 + -1 * x21:0:0:0 = 5) Found the following polynomial interpretation: [f74_0_loop_aux_LE(x, x1, x2)] = 4 - x - x1 + x2 The following rules are decreasing: f74_0_loop_aux_LE(x20:0:0:0, x21:0:0:0, x20:0:0:0) -> f74_0_loop_aux_LE(c6, c7, c8) :|: c8 = x20:0:0:0 - 2 && (c7 = x21:0:0:0 + 2 && c6 = x20:0:0:0 - 2) && (x21:0:0:0 > 3 && x20:0:0:0 > 1 && x21:0:0:0 < 5 && x20:0:0:0 + -1 * x21:0:0:0 = 5) The following rules are bounded: f74_0_loop_aux_LE(x20:0:0:0, x21:0:0:0, x20:0:0:0) -> f74_0_loop_aux_LE(c6, c7, c8) :|: c8 = x20:0:0:0 - 2 && (c7 = x21:0:0:0 + 2 && c6 = x20:0:0:0 - 2) && (x21:0:0:0 > 3 && x20:0:0:0 > 1 && x21:0:0:0 < 5 && x20:0:0:0 + -1 * x21:0:0:0 = 5) ---------------------------------------- (42) Obligation: Rules: f74_0_loop_aux_LE(x16:0:0:0:0:0, x17:0:0:0:0:0, x16:0:0:0:0:0) -> f74_0_loop_aux_LE(x16:0:0:0:0:0 + 1, x17:0:0:0:0:0 - 1, x16:0:0:0:0:0 + 1) :|: x16:0:0:0:0:0 + 1 <= 2 * x17:0:0:0:0:0 - 1 && x16:0:0:0:0:0 > 0 && x17:0:0:0:0:0 > 1 && x17:0:0:0:0:0 - 1 >= x16:0:0:0:0:0 && x17:0:0:0:0:0 >= x16:0:0:0:0:0 + 1 f74_0_loop_aux_LE(x12:0:0, x13:0:0, x12:0:0) -> f74_0_loop_aux_LE(x12:0:0, x13:0:0 + 1, x12:0:0) :|: x13:0:0 + -1 * x12:0:0 <= 0 && x13:0:0 < 5 && x13:0:0 > -1 && x12:0:0 > 1 && x13:0:0 + -1 * x12:0:0 >= -2 && x12:0:0 + -2 * x13:0:0 <= 3 f74_0_loop_aux_LE(x8:0, x9:0, x8:0) -> f74_0_loop_aux_LE(x8:0 - 1, x9:0, x8:0 - 1) :|: x8:0 + -2 * x9:0 <= 2 && x8:0 > 2 && x9:0 + -1 * x8:0 >= -2 && x9:0 > 4 && x9:0 < 6 && x8:0 + -1 * x9:0 >= 0 ---------------------------------------- (43) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f74_0_loop_aux_LE(x16:0:0:0:0:0, x17:0:0:0:0:0, x16:0:0:0:0:0) -> f74_0_loop_aux_LE(x16:0:0:0:0:0 + 1, x17:0:0:0:0:0 - 1, x16:0:0:0:0:0 + 1) :|: x16:0:0:0:0:0 + 1 <= 2 * x17:0:0:0:0:0 - 1 && x16:0:0:0:0:0 > 0 && x17:0:0:0:0:0 > 1 && x17:0:0:0:0:0 - 1 >= x16:0:0:0:0:0 && x17:0:0:0:0:0 >= x16:0:0:0:0:0 + 1 (2) f74_0_loop_aux_LE(x12:0:0, x13:0:0, x12:0:0) -> f74_0_loop_aux_LE(x12:0:0, x13:0:0 + 1, x12:0:0) :|: x13:0:0 + -1 * x12:0:0 <= 0 && x13:0:0 < 5 && x13:0:0 > -1 && x12:0:0 > 1 && x13:0:0 + -1 * x12:0:0 >= -2 && x12:0:0 + -2 * x13:0:0 <= 3 (3) f74_0_loop_aux_LE(x8:0, x9:0, x8:0) -> f74_0_loop_aux_LE(x8:0 - 1, x9:0, x8:0 - 1) :|: x8:0 + -2 * x9:0 <= 2 && x8:0 > 2 && x9:0 + -1 * x8:0 >= -2 && x9:0 > 4 && x9:0 < 6 && x8:0 + -1 * x9:0 >= 0 Arcs: (1) -> (1), (2), (3) (2) -> (1), (2), (3) (3) -> (1), (3) This digraph is fully evaluated! ---------------------------------------- (44) Obligation: Termination digraph: Nodes: (1) f74_0_loop_aux_LE(x16:0:0:0:0:0, x17:0:0:0:0:0, x16:0:0:0:0:0) -> f74_0_loop_aux_LE(x16:0:0:0:0:0 + 1, x17:0:0:0:0:0 - 1, x16:0:0:0:0:0 + 1) :|: x16:0:0:0:0:0 + 1 <= 2 * x17:0:0:0:0:0 - 1 && x16:0:0:0:0:0 > 0 && x17:0:0:0:0:0 > 1 && x17:0:0:0:0:0 - 1 >= x16:0:0:0:0:0 && x17:0:0:0:0:0 >= x16:0:0:0:0:0 + 1 (2) f74_0_loop_aux_LE(x8:0, x9:0, x8:0) -> f74_0_loop_aux_LE(x8:0 - 1, x9:0, x8:0 - 1) :|: x8:0 + -2 * x9:0 <= 2 && x8:0 > 2 && x9:0 + -1 * x8:0 >= -2 && x9:0 > 4 && x9:0 < 6 && x8:0 + -1 * x9:0 >= 0 (3) f74_0_loop_aux_LE(x12:0:0, x13:0:0, x12:0:0) -> f74_0_loop_aux_LE(x12:0:0, x13:0:0 + 1, x12:0:0) :|: x13:0:0 + -1 * x12:0:0 <= 0 && x13:0:0 < 5 && x13:0:0 > -1 && x12:0:0 > 1 && x13:0:0 + -1 * x12:0:0 >= -2 && x12:0:0 + -2 * x13:0:0 <= 3 Arcs: (1) -> (1), (2), (3) (2) -> (1), (2) (3) -> (1), (2), (3) This digraph is fully evaluated! ---------------------------------------- (45) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (46) Obligation: Rules: f74_0_loop_aux_LE(x16:0:0:0:0:0:0, x17:0:0:0:0:0:0, x16:0:0:0:0:0:0) -> f74_0_loop_aux_LE(x16:0:0:0:0:0:0 + 1, x17:0:0:0:0:0:0 - 1, x16:0:0:0:0:0:0 + 1) :|: x17:0:0:0:0:0:0 - 1 >= x16:0:0:0:0:0:0 && x17:0:0:0:0:0:0 >= x16:0:0:0:0:0:0 + 1 && x17:0:0:0:0:0:0 > 1 && x16:0:0:0:0:0:0 > 0 && x16:0:0:0:0:0:0 + 1 <= 2 * x17:0:0:0:0:0:0 - 1 f74_0_loop_aux_LE(x8:0:0, x9:0:0, x8:0:0) -> f74_0_loop_aux_LE(x8:0:0 - 1, x9:0:0, x8:0:0 - 1) :|: x9:0:0 < 6 && x8:0:0 + -1 * x9:0:0 >= 0 && x9:0:0 > 4 && x9:0:0 + -1 * x8:0:0 >= -2 && x8:0:0 > 2 && x8:0:0 + -2 * x9:0:0 <= 2 f74_0_loop_aux_LE(x12:0:0:0, x13:0:0:0, x12:0:0:0) -> f74_0_loop_aux_LE(x12:0:0:0, x13:0:0:0 + 1, x12:0:0:0) :|: x13:0:0:0 + -1 * x12:0:0:0 >= -2 && x12:0:0:0 + -2 * x13:0:0:0 <= 3 && x12:0:0:0 > 1 && x13:0:0:0 > -1 && x13:0:0:0 < 5 && x13:0:0:0 + -1 * x12:0:0:0 <= 0