MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 341 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 21 ms] (6) IRSwT (7) IRSwTChainingProof [EQUIVALENT, 0 ms] (8) IRSwT (9) IRSwTTerminationDigraphProof [EQUIVALENT, 112 ms] (10) AND (11) IRSwT (12) IntTRSCompressionProof [EQUIVALENT, 0 ms] (13) IRSwT (14) IRSwTChainingProof [EQUIVALENT, 0 ms] (15) IRSwT (16) IRSwTTerminationDigraphProof [EQUIVALENT, 141 ms] (17) IRSwT (18) IntTRSCompressionProof [EQUIVALENT, 0 ms] (19) IRSwT (20) TempFilterProof [SOUND, 358 ms] (21) IRSwT (22) IRSwTTerminationDigraphProof [EQUIVALENT, 15 ms] (23) IRSwT (24) IntTRSCompressionProof [EQUIVALENT, 0 ms] (25) IRSwT (26) IRSwT (27) IntTRSCompressionProof [EQUIVALENT, 0 ms] (28) IRSwT (29) IRSwTChainingProof [EQUIVALENT, 0 ms] (30) IRSwT (31) IRSwTTerminationDigraphProof [EQUIVALENT, 53 ms] (32) IRSwT (33) IntTRSCompressionProof [EQUIVALENT, 0 ms] (34) IRSwT (35) IRSwTChainingProof [EQUIVALENT, 0 ms] (36) IRSwT ---------------------------------------- (0) Obligation: Rules: f1_0_main_Load(arg1, arg2, arg3) -> f213_0_increase_LE(arg1P, arg2P, arg3P) :|: arg1P + arg2P = arg3P && 0 <= arg1 - 1 && -1 <= arg2P - 1 && 1 <= arg2 - 1 && -1 <= arg1P - 1 f213_0_increase_LE(x, x1, x2) -> f213_0_increase_LE'(x3, x4, x5) :|: -2 <= x - 1 && x1 - 2 * x6 <= -1 && 0 <= x2 - 1 && x = x3 && x1 = x4 && x2 = x5 f213_0_increase_LE(x7, x8, x9) -> f213_0_increase_LE'(x10, x11, x12) :|: -2 <= x7 - 1 && 0 <= x8 - 2 * x14 - 1 && 0 <= x9 - 1 && x7 = x10 && x8 = x11 && x9 = x12 f213_0_increase_LE'(x15, x16, x18) -> f213_0_increase_LE(x19, x20, x22) :|: 0 <= x16 - 2 * x23 - 1 && -2 <= x15 - 1 && x16 - 2 * x23 <= 1 && 0 <= x18 - 1 && x15 + 1 = x19 && x16 = x20 && x15 + 1 + x16 = x22 f213_0_increase_LE(x24, x26, x27) -> f213_0_increase_LE'(x28, x30, x31) :|: -2 <= x24 - 1 && x26 - 2 * x32 = 0 && 0 <= x27 - 1 && x24 = x28 && x26 = x30 && x27 = x31 f213_0_increase_LE'(x33, x34, x35) -> f213_0_increase_LE(x36, x37, x38) :|: -2 <= x33 - 1 && 0 <= x35 - 1 && x34 - 2 * x39 = 0 && x34 - 2 * x39 <= 1 && 0 <= x34 - 2 * x39 && x33 + 1 = x36 && x34 - 2 = x37 && x33 + 1 + x34 - 2 = x38 __init(x40, x41, x42) -> f1_0_main_Load(x43, x44, x45) :|: 0 <= 0 Start term: __init(arg1, arg2, arg3) ---------------------------------------- (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) -> f213_0_increase_LE(arg1P, arg2P, arg3P) :|: arg1P + arg2P = arg3P && 0 <= arg1 - 1 && -1 <= arg2P - 1 && 1 <= arg2 - 1 && -1 <= arg1P - 1 f213_0_increase_LE(x, x1, x2) -> f213_0_increase_LE'(x3, x4, x5) :|: -2 <= x - 1 && x1 - 2 * x6 <= -1 && 0 <= x2 - 1 && x = x3 && x1 = x4 && x2 = x5 f213_0_increase_LE(x7, x8, x9) -> f213_0_increase_LE'(x10, x11, x12) :|: -2 <= x7 - 1 && 0 <= x8 - 2 * x14 - 1 && 0 <= x9 - 1 && x7 = x10 && x8 = x11 && x9 = x12 f213_0_increase_LE'(x15, x16, x18) -> f213_0_increase_LE(x19, x20, x22) :|: 0 <= x16 - 2 * x23 - 1 && -2 <= x15 - 1 && x16 - 2 * x23 <= 1 && 0 <= x18 - 1 && x15 + 1 = x19 && x16 = x20 && x15 + 1 + x16 = x22 f213_0_increase_LE(x24, x26, x27) -> f213_0_increase_LE'(x28, x30, x31) :|: -2 <= x24 - 1 && x26 - 2 * x32 = 0 && 0 <= x27 - 1 && x24 = x28 && x26 = x30 && x27 = x31 f213_0_increase_LE'(x33, x34, x35) -> f213_0_increase_LE(x36, x37, x38) :|: -2 <= x33 - 1 && 0 <= x35 - 1 && x34 - 2 * x39 = 0 && x34 - 2 * x39 <= 1 && 0 <= x34 - 2 * x39 && x33 + 1 = x36 && x34 - 2 = x37 && x33 + 1 + x34 - 2 = x38 __init(x40, x41, x42) -> f1_0_main_Load(x43, x44, x45) :|: 0 <= 0 Start term: __init(arg1, arg2, arg3) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f1_0_main_Load(arg1, arg2, arg3) -> f213_0_increase_LE(arg1P, arg2P, arg3P) :|: arg1P + arg2P = arg3P && 0 <= arg1 - 1 && -1 <= arg2P - 1 && 1 <= arg2 - 1 && -1 <= arg1P - 1 (2) f213_0_increase_LE(x, x1, x2) -> f213_0_increase_LE'(x3, x4, x5) :|: -2 <= x - 1 && x1 - 2 * x6 <= -1 && 0 <= x2 - 1 && x = x3 && x1 = x4 && x2 = x5 (3) f213_0_increase_LE(x7, x8, x9) -> f213_0_increase_LE'(x10, x11, x12) :|: -2 <= x7 - 1 && 0 <= x8 - 2 * x14 - 1 && 0 <= x9 - 1 && x7 = x10 && x8 = x11 && x9 = x12 (4) f213_0_increase_LE'(x15, x16, x18) -> f213_0_increase_LE(x19, x20, x22) :|: 0 <= x16 - 2 * x23 - 1 && -2 <= x15 - 1 && x16 - 2 * x23 <= 1 && 0 <= x18 - 1 && x15 + 1 = x19 && x16 = x20 && x15 + 1 + x16 = x22 (5) f213_0_increase_LE(x24, x26, x27) -> f213_0_increase_LE'(x28, x30, x31) :|: -2 <= x24 - 1 && x26 - 2 * x32 = 0 && 0 <= x27 - 1 && x24 = x28 && x26 = x30 && x27 = x31 (6) f213_0_increase_LE'(x33, x34, x35) -> f213_0_increase_LE(x36, x37, x38) :|: -2 <= x33 - 1 && 0 <= x35 - 1 && x34 - 2 * x39 = 0 && x34 - 2 * x39 <= 1 && 0 <= x34 - 2 * x39 && x33 + 1 = x36 && x34 - 2 = x37 && x33 + 1 + x34 - 2 = x38 (7) __init(x40, x41, x42) -> f1_0_main_Load(x43, x44, x45) :|: 0 <= 0 Arcs: (1) -> (2), (3), (5) (2) -> (4), (6) (3) -> (4), (6) (4) -> (2), (3) (5) -> (6) (6) -> (2), (3), (5) (7) -> (1) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) f213_0_increase_LE(x, x1, x2) -> f213_0_increase_LE'(x3, x4, x5) :|: -2 <= x - 1 && x1 - 2 * x6 <= -1 && 0 <= x2 - 1 && x = x3 && x1 = x4 && x2 = x5 (2) f213_0_increase_LE'(x15, x16, x18) -> f213_0_increase_LE(x19, x20, x22) :|: 0 <= x16 - 2 * x23 - 1 && -2 <= x15 - 1 && x16 - 2 * x23 <= 1 && 0 <= x18 - 1 && x15 + 1 = x19 && x16 = x20 && x15 + 1 + x16 = x22 (3) f213_0_increase_LE(x7, x8, x9) -> f213_0_increase_LE'(x10, x11, x12) :|: -2 <= x7 - 1 && 0 <= x8 - 2 * x14 - 1 && 0 <= x9 - 1 && x7 = x10 && x8 = x11 && x9 = x12 (4) f213_0_increase_LE'(x33, x34, x35) -> f213_0_increase_LE(x36, x37, x38) :|: -2 <= x33 - 1 && 0 <= x35 - 1 && x34 - 2 * x39 = 0 && x34 - 2 * x39 <= 1 && 0 <= x34 - 2 * x39 && x33 + 1 = x36 && x34 - 2 = x37 && x33 + 1 + x34 - 2 = x38 (5) f213_0_increase_LE(x24, x26, x27) -> f213_0_increase_LE'(x28, x30, x31) :|: -2 <= x24 - 1 && x26 - 2 * x32 = 0 && 0 <= x27 - 1 && x24 = x28 && x26 = x30 && x27 = x31 Arcs: (1) -> (2), (4) (2) -> (1), (3) (3) -> (2), (4) (4) -> (1), (3), (5) (5) -> (4) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: f213_0_increase_LE'(x15:0, x16:0, x18:0) -> f213_0_increase_LE(x15:0 + 1, x16:0, x15:0 + 1 + x16:0) :|: x15:0 > -2 && x16:0 - 2 * x23:0 = 1 && x18:0 > 0 f213_0_increase_LE(x24:0, x26:0, x27:0) -> f213_0_increase_LE'(x24:0, x26:0, x27:0) :|: x24:0 > -2 && x26:0 - 2 * x32:0 = 0 && x27:0 > 0 f213_0_increase_LE'(x33:0, x34:0, x35:0) -> f213_0_increase_LE(x33:0 + 1, x34:0 - 2, x33:0 + 1 + x34:0 - 2) :|: x34:0 - 2 * x39:0 <= 1 && x34:0 - 2 * x39:0 >= 0 && x34:0 - 2 * x39:0 = 0 && x35:0 > 0 && x33:0 > -2 f213_0_increase_LE(x3:0, x1:0, x2:0) -> f213_0_increase_LE'(x3:0, x1:0, x2:0) :|: x3:0 > -2 && x1:0 - 2 * x6:0 <= -1 && x2:0 > 0 f213_0_increase_LE(x10:0, x11:0, x12:0) -> f213_0_increase_LE'(x10:0, x11:0, x12:0) :|: x10:0 > -2 && x11:0 - 2 * x14:0 >= 1 && x12:0 > 0 ---------------------------------------- (7) IRSwTChainingProof (EQUIVALENT) Chaining! ---------------------------------------- (8) Obligation: Rules: f213_0_increase_LE(x24:0, x26:0, x27:0) -> f213_0_increase_LE'(x24:0, x26:0, x27:0) :|: x24:0 > -2 && x26:0 - 2 * x32:0 = 0 && x27:0 > 0 f213_0_increase_LE'(x8, x9, x10) -> f213_0_increase_LE'(x8 + 1, x9, x8 + 1 + x9) :|: TRUE && x8 >= -1 && x9 + -2 * x11 = 1 && x10 >= 1 && x9 + -2 * x15 = 0 && x8 + x9 >= 0 f213_0_increase_LE'(x33:0, x34:0, x35:0) -> f213_0_increase_LE(x33:0 + 1, x34:0 - 2, x33:0 + 1 + x34:0 - 2) :|: x34:0 - 2 * x39:0 <= 1 && x34:0 - 2 * x39:0 >= 0 && x34:0 - 2 * x39:0 = 0 && x35:0 > 0 && x33:0 > -2 f213_0_increase_LE(x3:0, x1:0, x2:0) -> f213_0_increase_LE'(x3:0, x1:0, x2:0) :|: x3:0 > -2 && x1:0 - 2 * x6:0 <= -1 && x2:0 > 0 f213_0_increase_LE'(x24, x25, x26) -> f213_0_increase_LE'(x24 + 1, x25, x24 + 1 + x25) :|: TRUE && x24 >= -1 && x25 + -2 * x27 = 1 && x26 >= 1 && x25 + -2 * x31 <= -1 && x24 + x25 >= 0 f213_0_increase_LE(x10:0, x11:0, x12:0) -> f213_0_increase_LE'(x10:0, x11:0, x12:0) :|: x10:0 > -2 && x11:0 - 2 * x14:0 >= 1 && x12:0 > 0 f213_0_increase_LE'(x32, x33, x34) -> f213_0_increase_LE'(x32 + 1, x33, x32 + 1 + x33) :|: TRUE && x32 >= -1 && x33 + -2 * x35 = 1 && x34 >= 1 && x33 + -2 * x39 >= 1 && x32 + x33 >= 0 ---------------------------------------- (9) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f213_0_increase_LE(x24:0, x26:0, x27:0) -> f213_0_increase_LE'(x24:0, x26:0, x27:0) :|: x24:0 > -2 && x26:0 - 2 * x32:0 = 0 && x27:0 > 0 (2) f213_0_increase_LE'(x8, x9, x10) -> f213_0_increase_LE'(x8 + 1, x9, x8 + 1 + x9) :|: TRUE && x8 >= -1 && x9 + -2 * x11 = 1 && x10 >= 1 && x9 + -2 * x15 = 0 && x8 + x9 >= 0 (3) f213_0_increase_LE'(x33:0, x34:0, x35:0) -> f213_0_increase_LE(x33:0 + 1, x34:0 - 2, x33:0 + 1 + x34:0 - 2) :|: x34:0 - 2 * x39:0 <= 1 && x34:0 - 2 * x39:0 >= 0 && x34:0 - 2 * x39:0 = 0 && x35:0 > 0 && x33:0 > -2 (4) f213_0_increase_LE(x3:0, x1:0, x2:0) -> f213_0_increase_LE'(x3:0, x1:0, x2:0) :|: x3:0 > -2 && x1:0 - 2 * x6:0 <= -1 && x2:0 > 0 (5) f213_0_increase_LE'(x24, x25, x26) -> f213_0_increase_LE'(x24 + 1, x25, x24 + 1 + x25) :|: TRUE && x24 >= -1 && x25 + -2 * x27 = 1 && x26 >= 1 && x25 + -2 * x31 <= -1 && x24 + x25 >= 0 (6) f213_0_increase_LE(x10:0, x11:0, x12:0) -> f213_0_increase_LE'(x10:0, x11:0, x12:0) :|: x10:0 > -2 && x11:0 - 2 * x14:0 >= 1 && x12:0 > 0 (7) f213_0_increase_LE'(x32, x33, x34) -> f213_0_increase_LE'(x32 + 1, x33, x32 + 1 + x33) :|: TRUE && x32 >= -1 && x33 + -2 * x35 = 1 && x34 >= 1 && x33 + -2 * x39 >= 1 && x32 + x33 >= 0 Arcs: (1) -> (3) (3) -> (1), (4), (6) (4) -> (3), (5), (7) (5) -> (5), (7) (6) -> (3), (5), (7) (7) -> (5), (7) This digraph is fully evaluated! ---------------------------------------- (10) Complex Obligation (AND) ---------------------------------------- (11) Obligation: Termination digraph: Nodes: (1) f213_0_increase_LE(x24:0, x26:0, x27:0) -> f213_0_increase_LE'(x24:0, x26:0, x27:0) :|: x24:0 > -2 && x26:0 - 2 * x32:0 = 0 && x27:0 > 0 (2) f213_0_increase_LE'(x33:0, x34:0, x35:0) -> f213_0_increase_LE(x33:0 + 1, x34:0 - 2, x33:0 + 1 + x34:0 - 2) :|: x34:0 - 2 * x39:0 <= 1 && x34:0 - 2 * x39:0 >= 0 && x34:0 - 2 * x39:0 = 0 && x35:0 > 0 && x33:0 > -2 (3) f213_0_increase_LE(x10:0, x11:0, x12:0) -> f213_0_increase_LE'(x10:0, x11:0, x12:0) :|: x10:0 > -2 && x11:0 - 2 * x14:0 >= 1 && x12:0 > 0 (4) f213_0_increase_LE(x3:0, x1:0, x2:0) -> f213_0_increase_LE'(x3:0, x1:0, x2:0) :|: x3:0 > -2 && x1:0 - 2 * x6:0 <= -1 && x2:0 > 0 Arcs: (1) -> (2) (2) -> (1), (3), (4) (3) -> (2) (4) -> (2) This digraph is fully evaluated! ---------------------------------------- (12) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (13) Obligation: Rules: f213_0_increase_LE(x10:0:0, x11:0:0, x12:0:0) -> f213_0_increase_LE(x10:0:0 + 1, x11:0:0 - 2, x10:0:0 + 1 + x11:0:0 - 2) :|: x10:0:0 > -2 && x11:0:0 - 2 * x14:0:0 >= 1 && x12:0:0 > 0 && x11:0:0 - 2 * x39:0:0 = 0 && x11:0:0 - 2 * x39:0:0 >= 0 && x11:0:0 - 2 * x39:0:0 <= 1 f213_0_increase_LE(x, x1, x2) -> f213_0_increase_LE(x + 1, x1 - 2, x + 1 + x1 - 2) :|: x > -2 && x1 - 2 * x3 <= -1 && x2 > 0 && x1 - 2 * x4 = 0 && x1 - 2 * x4 >= 0 && x1 - 2 * x4 <= 1 f213_0_increase_LE(x5, x6, x7) -> f213_0_increase_LE(x5 + 1, x6 - 2, x5 + 1 + x6 - 2) :|: x5 > -2 && x6 - 2 * x8 = 0 && x7 > 0 && x6 - 2 * x9 = 0 && x6 - 2 * x9 >= 0 && x6 - 2 * x9 <= 1 ---------------------------------------- (14) IRSwTChainingProof (EQUIVALENT) Chaining! ---------------------------------------- (15) Obligation: Rules: f213_0_increase_LE(x10, x11, x12) -> f213_0_increase_LE(x10 + 2, x11 + -4, x10 + x11 + -2) :|: TRUE && x10 >= -1 && x11 + -2 * x13 >= 1 && x12 >= 1 && x11 + -2 * x14 = 0 && x11 + -2 * x18 >= 3 && x10 + x11 >= 2 && x11 + -2 * x19 = 2 f213_0_increase_LE(x, x1, x2) -> f213_0_increase_LE(x + 1, x1 - 2, x + 1 + x1 - 2) :|: x > -2 && x1 - 2 * x3 <= -1 && x2 > 0 && x1 - 2 * x4 = 0 && x1 - 2 * x4 >= 0 && x1 - 2 * x4 <= 1 f213_0_increase_LE(x20, x21, x22) -> f213_0_increase_LE(x20 + 2, x21 + -4, x20 + x21 + -2) :|: TRUE && x20 >= -1 && x21 + -2 * x23 >= 1 && x22 >= 1 && x21 + -2 * x24 = 0 && x21 + -2 * x28 <= 1 && x20 + x21 >= 2 && x21 + -2 * x29 = 2 f213_0_increase_LE(x5, x6, x7) -> f213_0_increase_LE(x5 + 1, x6 - 2, x5 + 1 + x6 - 2) :|: x5 > -2 && x6 - 2 * x8 = 0 && x7 > 0 && x6 - 2 * x9 = 0 && x6 - 2 * x9 >= 0 && x6 - 2 * x9 <= 1 f213_0_increase_LE(x30, x31, x32) -> f213_0_increase_LE(x30 + 2, x31 + -4, x30 + x31 + -2) :|: TRUE && x30 >= -1 && x31 + -2 * x33 >= 1 && x32 >= 1 && x31 + -2 * x34 = 0 && x31 + -2 * x38 = 2 && x30 + x31 >= 2 && x31 + -2 * x39 = 2 ---------------------------------------- (16) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f213_0_increase_LE(x10, x11, x12) -> f213_0_increase_LE(x10 + 2, x11 + -4, x10 + x11 + -2) :|: TRUE && x10 >= -1 && x11 + -2 * x13 >= 1 && x12 >= 1 && x11 + -2 * x14 = 0 && x11 + -2 * x18 >= 3 && x10 + x11 >= 2 && x11 + -2 * x19 = 2 (2) f213_0_increase_LE(x, x1, x2) -> f213_0_increase_LE(x + 1, x1 - 2, x + 1 + x1 - 2) :|: x > -2 && x1 - 2 * x3 <= -1 && x2 > 0 && x1 - 2 * x4 = 0 && x1 - 2 * x4 >= 0 && x1 - 2 * x4 <= 1 (3) f213_0_increase_LE(x20, x21, x22) -> f213_0_increase_LE(x20 + 2, x21 + -4, x20 + x21 + -2) :|: TRUE && x20 >= -1 && x21 + -2 * x23 >= 1 && x22 >= 1 && x21 + -2 * x24 = 0 && x21 + -2 * x28 <= 1 && x20 + x21 >= 2 && x21 + -2 * x29 = 2 (4) f213_0_increase_LE(x5, x6, x7) -> f213_0_increase_LE(x5 + 1, x6 - 2, x5 + 1 + x6 - 2) :|: x5 > -2 && x6 - 2 * x8 = 0 && x7 > 0 && x6 - 2 * x9 = 0 && x6 - 2 * x9 >= 0 && x6 - 2 * x9 <= 1 (5) f213_0_increase_LE(x30, x31, x32) -> f213_0_increase_LE(x30 + 2, x31 + -4, x30 + x31 + -2) :|: TRUE && x30 >= -1 && x31 + -2 * x33 >= 1 && x32 >= 1 && x31 + -2 * x34 = 0 && x31 + -2 * x38 = 2 && x30 + x31 >= 2 && x31 + -2 * x39 = 2 Arcs: (1) -> (1), (2), (3), (4), (5) (2) -> (1), (2), (3), (4), (5) (3) -> (1), (2), (3), (4), (5) (4) -> (1), (2), (3), (4), (5) (5) -> (1), (2), (3), (4), (5) This digraph is fully evaluated! ---------------------------------------- (17) Obligation: Termination digraph: Nodes: (1) f213_0_increase_LE(x10, x11, x12) -> f213_0_increase_LE(x10 + 2, x11 + -4, x10 + x11 + -2) :|: TRUE && x10 >= -1 && x11 + -2 * x13 >= 1 && x12 >= 1 && x11 + -2 * x14 = 0 && x11 + -2 * x18 >= 3 && x10 + x11 >= 2 && x11 + -2 * x19 = 2 (2) f213_0_increase_LE(x, x1, x2) -> f213_0_increase_LE(x + 1, x1 - 2, x + 1 + x1 - 2) :|: x > -2 && x1 - 2 * x3 <= -1 && x2 > 0 && x1 - 2 * x4 = 0 && x1 - 2 * x4 >= 0 && x1 - 2 * x4 <= 1 (3) f213_0_increase_LE(x20, x21, x22) -> f213_0_increase_LE(x20 + 2, x21 + -4, x20 + x21 + -2) :|: TRUE && x20 >= -1 && x21 + -2 * x23 >= 1 && x22 >= 1 && x21 + -2 * x24 = 0 && x21 + -2 * x28 <= 1 && x20 + x21 >= 2 && x21 + -2 * x29 = 2 (4) f213_0_increase_LE(x5, x6, x7) -> f213_0_increase_LE(x5 + 1, x6 - 2, x5 + 1 + x6 - 2) :|: x5 > -2 && x6 - 2 * x8 = 0 && x7 > 0 && x6 - 2 * x9 = 0 && x6 - 2 * x9 >= 0 && x6 - 2 * x9 <= 1 (5) f213_0_increase_LE(x30, x31, x32) -> f213_0_increase_LE(x30 + 2, x31 + -4, x30 + x31 + -2) :|: TRUE && x30 >= -1 && x31 + -2 * x33 >= 1 && x32 >= 1 && x31 + -2 * x34 = 0 && x31 + -2 * x38 = 2 && x30 + x31 >= 2 && x31 + -2 * x39 = 2 Arcs: (1) -> (1), (2), (3), (4), (5) (2) -> (1), (2), (3), (4), (5) (3) -> (1), (2), (3), (4), (5) (4) -> (1), (2), (3), (4), (5) (5) -> (1), (2), (3), (4), (5) This digraph is fully evaluated! ---------------------------------------- (18) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (19) Obligation: Rules: f213_0_increase_LE(x10:0, x11:0, x12:0) -> f213_0_increase_LE(x10:0 + 2, x11:0 - 4, x10:0 + x11:0 - 2) :|: x10:0 + x11:0 >= 2 && x11:0 + -2 * x19:0 = 2 && x11:0 + -2 * x18:0 >= 3 && x11:0 + -2 * x14:0 = 0 && x12:0 > 0 && x10:0 > -2 && x11:0 + -2 * x13:0 >= 1 f213_0_increase_LE(x20:0, x21:0, x22:0) -> f213_0_increase_LE(x20:0 + 2, x21:0 - 4, x20:0 + x21:0 - 2) :|: x20:0 + x21:0 >= 2 && x21:0 + -2 * x29:0 = 2 && x21:0 + -2 * x28:0 <= 1 && x21:0 + -2 * x24:0 = 0 && x22:0 > 0 && x20:0 > -2 && x21:0 + -2 * x23:0 >= 1 f213_0_increase_LE(x:0, x1:0, x2:0) -> f213_0_increase_LE(x:0 + 1, x1:0 - 2, x:0 + 1 + x1:0 - 2) :|: x1:0 - 2 * x4:0 >= 0 && x1:0 - 2 * x4:0 <= 1 && x1:0 - 2 * x4:0 = 0 && x2:0 > 0 && x1:0 - 2 * x3:0 <= -1 && x:0 > -2 f213_0_increase_LE(x30:0, x31:0, x32:0) -> f213_0_increase_LE(x30:0 + 2, x31:0 - 4, x30:0 + x31:0 - 2) :|: x30:0 + x31:0 >= 2 && x31:0 + -2 * x39:0 = 2 && x31:0 + -2 * x38:0 = 2 && x31:0 + -2 * x34:0 = 0 && x32:0 > 0 && x30:0 > -2 && x31:0 + -2 * x33:0 >= 1 f213_0_increase_LE(x5:0, x6:0, x7:0) -> f213_0_increase_LE(x5:0 + 1, x6:0 - 2, x5:0 + 1 + x6:0 - 2) :|: x6:0 - 2 * x9:0 >= 0 && x6:0 - 2 * x9:0 <= 1 && x6:0 - 2 * x9:0 = 0 && x7:0 > 0 && x6:0 - 2 * x8:0 = 0 && x5:0 > -2 ---------------------------------------- (20) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f213_0_increase_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: f213_0_increase_LE(x10:0, x11:0, x12:0) -> f213_0_increase_LE(c, c1, c2) :|: c2 = x10:0 + x11:0 - 2 && (c1 = x11:0 - 4 && c = x10:0 + 2) && (x10:0 + x11:0 >= 2 && x11:0 + -2 * x19:0 = 2 && x11:0 + -2 * x18:0 >= 3 && x11:0 + -2 * x14:0 = 0 && x12:0 > 0 && x10:0 > -2 && x11:0 + -2 * x13:0 >= 1) f213_0_increase_LE(x20:0, x21:0, x22:0) -> f213_0_increase_LE(c3, c4, c5) :|: c5 = x20:0 + x21:0 - 2 && (c4 = x21:0 - 4 && c3 = x20:0 + 2) && (x20:0 + x21:0 >= 2 && x21:0 + -2 * x29:0 = 2 && x21:0 + -2 * x28:0 <= 1 && x21:0 + -2 * x24:0 = 0 && x22:0 > 0 && x20:0 > -2 && x21:0 + -2 * x23:0 >= 1) f213_0_increase_LE(x:0, x1:0, x2:0) -> f213_0_increase_LE(c6, c7, c8) :|: c8 = x:0 + 1 + x1:0 - 2 && (c7 = x1:0 - 2 && c6 = x:0 + 1) && (x1:0 - 2 * x4:0 >= 0 && x1:0 - 2 * x4:0 <= 1 && x1:0 - 2 * x4:0 = 0 && x2:0 > 0 && x1:0 - 2 * x3:0 <= -1 && x:0 > -2) f213_0_increase_LE(x30:0, x31:0, x32:0) -> f213_0_increase_LE(c9, c10, c11) :|: c11 = x30:0 + x31:0 - 2 && (c10 = x31:0 - 4 && c9 = x30:0 + 2) && (x30:0 + x31:0 >= 2 && x31:0 + -2 * x39:0 = 2 && x31:0 + -2 * x38:0 = 2 && x31:0 + -2 * x34:0 = 0 && x32:0 > 0 && x30:0 > -2 && x31:0 + -2 * x33:0 >= 1) f213_0_increase_LE(x5:0, x6:0, x7:0) -> f213_0_increase_LE(c12, c13, c14) :|: c14 = x5:0 + 1 + x6:0 - 2 && (c13 = x6:0 - 2 && c12 = x5:0 + 1) && (x6:0 - 2 * x9:0 >= 0 && x6:0 - 2 * x9:0 <= 1 && x6:0 - 2 * x9:0 = 0 && x7:0 > 0 && x6:0 - 2 * x8:0 = 0 && x5:0 > -2) Interpretation: [ f213_0_increase_LE ] = f213_0_increase_LE_1 + f213_0_increase_LE_2 + 1 The following rules are decreasing: f213_0_increase_LE(x10:0, x11:0, x12:0) -> f213_0_increase_LE(c, c1, c2) :|: c2 = x10:0 + x11:0 - 2 && (c1 = x11:0 - 4 && c = x10:0 + 2) && (x10:0 + x11:0 >= 2 && x11:0 + -2 * x19:0 = 2 && x11:0 + -2 * x18:0 >= 3 && x11:0 + -2 * x14:0 = 0 && x12:0 > 0 && x10:0 > -2 && x11:0 + -2 * x13:0 >= 1) f213_0_increase_LE(x20:0, x21:0, x22:0) -> f213_0_increase_LE(c3, c4, c5) :|: c5 = x20:0 + x21:0 - 2 && (c4 = x21:0 - 4 && c3 = x20:0 + 2) && (x20:0 + x21:0 >= 2 && x21:0 + -2 * x29:0 = 2 && x21:0 + -2 * x28:0 <= 1 && x21:0 + -2 * x24:0 = 0 && x22:0 > 0 && x20:0 > -2 && x21:0 + -2 * x23:0 >= 1) f213_0_increase_LE(x:0, x1:0, x2:0) -> f213_0_increase_LE(c6, c7, c8) :|: c8 = x:0 + 1 + x1:0 - 2 && (c7 = x1:0 - 2 && c6 = x:0 + 1) && (x1:0 - 2 * x4:0 >= 0 && x1:0 - 2 * x4:0 <= 1 && x1:0 - 2 * x4:0 = 0 && x2:0 > 0 && x1:0 - 2 * x3:0 <= -1 && x:0 > -2) f213_0_increase_LE(x30:0, x31:0, x32:0) -> f213_0_increase_LE(c9, c10, c11) :|: c11 = x30:0 + x31:0 - 2 && (c10 = x31:0 - 4 && c9 = x30:0 + 2) && (x30:0 + x31:0 >= 2 && x31:0 + -2 * x39:0 = 2 && x31:0 + -2 * x38:0 = 2 && x31:0 + -2 * x34:0 = 0 && x32:0 > 0 && x30:0 > -2 && x31:0 + -2 * x33:0 >= 1) f213_0_increase_LE(x5:0, x6:0, x7:0) -> f213_0_increase_LE(c12, c13, c14) :|: c14 = x5:0 + 1 + x6:0 - 2 && (c13 = x6:0 - 2 && c12 = x5:0 + 1) && (x6:0 - 2 * x9:0 >= 0 && x6:0 - 2 * x9:0 <= 1 && x6:0 - 2 * x9:0 = 0 && x7:0 > 0 && x6:0 - 2 * x8:0 = 0 && x5:0 > -2) The following rules are bounded: f213_0_increase_LE(x20:0, x21:0, x22:0) -> f213_0_increase_LE(c3, c4, c5) :|: c5 = x20:0 + x21:0 - 2 && (c4 = x21:0 - 4 && c3 = x20:0 + 2) && (x20:0 + x21:0 >= 2 && x21:0 + -2 * x29:0 = 2 && x21:0 + -2 * x28:0 <= 1 && x21:0 + -2 * x24:0 = 0 && x22:0 > 0 && x20:0 > -2 && x21:0 + -2 * x23:0 >= 1) f213_0_increase_LE(x30:0, x31:0, x32:0) -> f213_0_increase_LE(c9, c10, c11) :|: c11 = x30:0 + x31:0 - 2 && (c10 = x31:0 - 4 && c9 = x30:0 + 2) && (x30:0 + x31:0 >= 2 && x31:0 + -2 * x39:0 = 2 && x31:0 + -2 * x38:0 = 2 && x31:0 + -2 * x34:0 = 0 && x32:0 > 0 && x30:0 > -2 && x31:0 + -2 * x33:0 >= 1) - IntTRS - RankingReductionPairProof - IntTRS - RankingReductionPairProof Rules: f213_0_increase_LE(x10:0, x11:0, x12:0) -> f213_0_increase_LE(c, c1, c2) :|: c2 = x10:0 + x11:0 - 2 && (c1 = x11:0 - 4 && c = x10:0 + 2) && (x10:0 + x11:0 >= 2 && x11:0 + -2 * x19:0 = 2 && x11:0 + -2 * x18:0 >= 3 && x11:0 + -2 * x14:0 = 0 && x12:0 > 0 && x10:0 > -2 && x11:0 + -2 * x13:0 >= 1) f213_0_increase_LE(x:0, x1:0, x2:0) -> f213_0_increase_LE(c6, c7, c8) :|: c8 = x:0 + 1 + x1:0 - 2 && (c7 = x1:0 - 2 && c6 = x:0 + 1) && (x1:0 - 2 * x4:0 >= 0 && x1:0 - 2 * x4:0 <= 1 && x1:0 - 2 * x4:0 = 0 && x2:0 > 0 && x1:0 - 2 * x3:0 <= -1 && x:0 > -2) f213_0_increase_LE(x5:0, x6:0, x7:0) -> f213_0_increase_LE(c12, c13, c14) :|: c14 = x5:0 + 1 + x6:0 - 2 && (c13 = x6:0 - 2 && c12 = x5:0 + 1) && (x6:0 - 2 * x9:0 >= 0 && x6:0 - 2 * x9:0 <= 1 && x6:0 - 2 * x9:0 = 0 && x7:0 > 0 && x6:0 - 2 * x8:0 = 0 && x5:0 > -2) Interpretation: [ f213_0_increase_LE ] = 4*f213_0_increase_LE_1 + 4*f213_0_increase_LE_2 + 1 The following rules are decreasing: f213_0_increase_LE(x10:0, x11:0, x12:0) -> f213_0_increase_LE(c, c1, c2) :|: c2 = x10:0 + x11:0 - 2 && (c1 = x11:0 - 4 && c = x10:0 + 2) && (x10:0 + x11:0 >= 2 && x11:0 + -2 * x19:0 = 2 && x11:0 + -2 * x18:0 >= 3 && x11:0 + -2 * x14:0 = 0 && x12:0 > 0 && x10:0 > -2 && x11:0 + -2 * x13:0 >= 1) f213_0_increase_LE(x:0, x1:0, x2:0) -> f213_0_increase_LE(c6, c7, c8) :|: c8 = x:0 + 1 + x1:0 - 2 && (c7 = x1:0 - 2 && c6 = x:0 + 1) && (x1:0 - 2 * x4:0 >= 0 && x1:0 - 2 * x4:0 <= 1 && x1:0 - 2 * x4:0 = 0 && x2:0 > 0 && x1:0 - 2 * x3:0 <= -1 && x:0 > -2) f213_0_increase_LE(x5:0, x6:0, x7:0) -> f213_0_increase_LE(c12, c13, c14) :|: c14 = x5:0 + 1 + x6:0 - 2 && (c13 = x6:0 - 2 && c12 = x5:0 + 1) && (x6:0 - 2 * x9:0 >= 0 && x6:0 - 2 * x9:0 <= 1 && x6:0 - 2 * x9:0 = 0 && x7:0 > 0 && x6:0 - 2 * x8:0 = 0 && x5:0 > -2) The following rules are bounded: f213_0_increase_LE(x10:0, x11:0, x12:0) -> f213_0_increase_LE(c, c1, c2) :|: c2 = x10:0 + x11:0 - 2 && (c1 = x11:0 - 4 && c = x10:0 + 2) && (x10:0 + x11:0 >= 2 && x11:0 + -2 * x19:0 = 2 && x11:0 + -2 * x18:0 >= 3 && x11:0 + -2 * x14:0 = 0 && x12:0 > 0 && x10:0 > -2 && x11:0 + -2 * x13:0 >= 1) - IntTRS - RankingReductionPairProof - IntTRS - RankingReductionPairProof - IntTRS Rules: f213_0_increase_LE(x:0, x1:0, x2:0) -> f213_0_increase_LE(c6, c7, c8) :|: c8 = x:0 + 1 + x1:0 - 2 && (c7 = x1:0 - 2 && c6 = x:0 + 1) && (x1:0 - 2 * x4:0 >= 0 && x1:0 - 2 * x4:0 <= 1 && x1:0 - 2 * x4:0 = 0 && x2:0 > 0 && x1:0 - 2 * x3:0 <= -1 && x:0 > -2) f213_0_increase_LE(x5:0, x6:0, x7:0) -> f213_0_increase_LE(c12, c13, c14) :|: c14 = x5:0 + 1 + x6:0 - 2 && (c13 = x6:0 - 2 && c12 = x5:0 + 1) && (x6:0 - 2 * x9:0 >= 0 && x6:0 - 2 * x9:0 <= 1 && x6:0 - 2 * x9:0 = 0 && x7:0 > 0 && x6:0 - 2 * x8:0 = 0 && x5:0 > -2) ---------------------------------------- (21) Obligation: Rules: f213_0_increase_LE(x:0, x1:0, x2:0) -> f213_0_increase_LE(x:0 + 1, x1:0 - 2, x:0 + 1 + x1:0 - 2) :|: x1:0 - 2 * x4:0 >= 0 && x1:0 - 2 * x4:0 <= 1 && x1:0 - 2 * x4:0 = 0 && x2:0 > 0 && x1:0 - 2 * x3:0 <= -1 && x:0 > -2 f213_0_increase_LE(x5:0, x6:0, x7:0) -> f213_0_increase_LE(x5:0 + 1, x6:0 - 2, x5:0 + 1 + x6:0 - 2) :|: x6:0 - 2 * x9:0 >= 0 && x6:0 - 2 * x9:0 <= 1 && x6:0 - 2 * x9:0 = 0 && x7:0 > 0 && x6:0 - 2 * x8:0 = 0 && x5:0 > -2 ---------------------------------------- (22) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f213_0_increase_LE(x:0, x1:0, x2:0) -> f213_0_increase_LE(x:0 + 1, x1:0 - 2, x:0 + 1 + x1:0 - 2) :|: x1:0 - 2 * x4:0 >= 0 && x1:0 - 2 * x4:0 <= 1 && x1:0 - 2 * x4:0 = 0 && x2:0 > 0 && x1:0 - 2 * x3:0 <= -1 && x:0 > -2 (2) f213_0_increase_LE(x5:0, x6:0, x7:0) -> f213_0_increase_LE(x5:0 + 1, x6:0 - 2, x5:0 + 1 + x6:0 - 2) :|: x6:0 - 2 * x9:0 >= 0 && x6:0 - 2 * x9:0 <= 1 && x6:0 - 2 * x9:0 = 0 && x7:0 > 0 && x6:0 - 2 * x8:0 = 0 && x5:0 > -2 Arcs: (1) -> (1), (2) (2) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (23) Obligation: Termination digraph: Nodes: (1) f213_0_increase_LE(x:0, x1:0, x2:0) -> f213_0_increase_LE(x:0 + 1, x1:0 - 2, x:0 + 1 + x1:0 - 2) :|: x1:0 - 2 * x4:0 >= 0 && x1:0 - 2 * x4:0 <= 1 && x1:0 - 2 * x4:0 = 0 && x2:0 > 0 && x1:0 - 2 * x3:0 <= -1 && x:0 > -2 (2) f213_0_increase_LE(x5:0, x6:0, x7:0) -> f213_0_increase_LE(x5:0 + 1, x6:0 - 2, x5:0 + 1 + x6:0 - 2) :|: x6:0 - 2 * x9:0 >= 0 && x6:0 - 2 * x9:0 <= 1 && x6:0 - 2 * x9:0 = 0 && x7:0 > 0 && x6:0 - 2 * x8:0 = 0 && x5:0 > -2 Arcs: (1) -> (1), (2) (2) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (24) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (25) Obligation: Rules: f213_0_increase_LE(x:0:0, x1:0:0, x2:0:0) -> f213_0_increase_LE(x:0:0 + 1, x1:0:0 - 2, x:0:0 + 1 + x1:0:0 - 2) :|: x1:0:0 - 2 * x3:0:0 <= -1 && x:0:0 > -2 && x2:0:0 > 0 && x1:0:0 - 2 * x4:0:0 = 0 && x1:0:0 - 2 * x4:0:0 <= 1 && x1:0:0 - 2 * x4:0:0 >= 0 f213_0_increase_LE(x5:0:0, x6:0:0, x7:0:0) -> f213_0_increase_LE(x5:0:0 + 1, x6:0:0 - 2, x5:0:0 + 1 + x6:0:0 - 2) :|: x6:0:0 - 2 * x8:0:0 = 0 && x5:0:0 > -2 && x7:0:0 > 0 && x6:0:0 - 2 * x9:0:0 = 0 && x6:0:0 - 2 * x9:0:0 <= 1 && x6:0:0 - 2 * x9:0:0 >= 0 ---------------------------------------- (26) Obligation: Termination digraph: Nodes: (1) f213_0_increase_LE'(x24, x25, x26) -> f213_0_increase_LE'(x24 + 1, x25, x24 + 1 + x25) :|: TRUE && x24 >= -1 && x25 + -2 * x27 = 1 && x26 >= 1 && x25 + -2 * x31 <= -1 && x24 + x25 >= 0 (2) f213_0_increase_LE'(x32, x33, x34) -> f213_0_increase_LE'(x32 + 1, x33, x32 + 1 + x33) :|: TRUE && x32 >= -1 && x33 + -2 * x35 = 1 && x34 >= 1 && x33 + -2 * x39 >= 1 && x32 + x33 >= 0 Arcs: (1) -> (1), (2) (2) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (27) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (28) Obligation: Rules: f213_0_increase_LE'(x32:0, x33:0, x34:0) -> f213_0_increase_LE'(x32:0 + 1, x33:0, x32:0 + 1 + x33:0) :|: x33:0 + -2 * x39:0 >= 1 && x32:0 + x33:0 >= 0 && x34:0 > 0 && x32:0 > -2 && x33:0 + -2 * x35:0 = 1 f213_0_increase_LE'(x24:0, x25:0, x26:0) -> f213_0_increase_LE'(x24:0 + 1, x25:0, x24:0 + 1 + x25:0) :|: x25:0 + -2 * x31:0 <= -1 && x24:0 + x25:0 >= 0 && x26:0 > 0 && x24:0 > -2 && x25:0 + -2 * x27:0 = 1 ---------------------------------------- (29) IRSwTChainingProof (EQUIVALENT) Chaining! ---------------------------------------- (30) Obligation: Rules: f213_0_increase_LE'(x, x1, x2) -> f213_0_increase_LE'(x + 2, x1, x + 2 + x1) :|: TRUE && x1 + -2 * x3 >= 1 && x + x1 >= 0 && x2 >= 1 && x >= -1 && x1 + -2 * x4 = 1 && x1 + -2 * x8 >= 1 && x1 + -2 * x9 = 1 f213_0_increase_LE'(x24:0, x25:0, x26:0) -> f213_0_increase_LE'(x24:0 + 1, x25:0, x24:0 + 1 + x25:0) :|: x25:0 + -2 * x31:0 <= -1 && x24:0 + x25:0 >= 0 && x26:0 > 0 && x24:0 > -2 && x25:0 + -2 * x27:0 = 1 f213_0_increase_LE'(x10, x11, x12) -> f213_0_increase_LE'(x10 + 2, x11, x10 + 2 + x11) :|: TRUE && x11 + -2 * x13 >= 1 && x10 + x11 >= 0 && x12 >= 1 && x10 >= -1 && x11 + -2 * x14 = 1 && x11 + -2 * x18 <= -1 && x11 + -2 * x19 = 1 ---------------------------------------- (31) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f213_0_increase_LE'(x, x1, x2) -> f213_0_increase_LE'(x + 2, x1, x + 2 + x1) :|: TRUE && x1 + -2 * x3 >= 1 && x + x1 >= 0 && x2 >= 1 && x >= -1 && x1 + -2 * x4 = 1 && x1 + -2 * x8 >= 1 && x1 + -2 * x9 = 1 (2) f213_0_increase_LE'(x24:0, x25:0, x26:0) -> f213_0_increase_LE'(x24:0 + 1, x25:0, x24:0 + 1 + x25:0) :|: x25:0 + -2 * x31:0 <= -1 && x24:0 + x25:0 >= 0 && x26:0 > 0 && x24:0 > -2 && x25:0 + -2 * x27:0 = 1 (3) f213_0_increase_LE'(x10, x11, x12) -> f213_0_increase_LE'(x10 + 2, x11, x10 + 2 + x11) :|: TRUE && x11 + -2 * x13 >= 1 && x10 + x11 >= 0 && x12 >= 1 && x10 >= -1 && x11 + -2 * x14 = 1 && x11 + -2 * x18 <= -1 && x11 + -2 * x19 = 1 Arcs: (1) -> (1), (2), (3) (2) -> (1), (2), (3) (3) -> (1), (2), (3) This digraph is fully evaluated! ---------------------------------------- (32) Obligation: Termination digraph: Nodes: (1) f213_0_increase_LE'(x, x1, x2) -> f213_0_increase_LE'(x + 2, x1, x + 2 + x1) :|: TRUE && x1 + -2 * x3 >= 1 && x + x1 >= 0 && x2 >= 1 && x >= -1 && x1 + -2 * x4 = 1 && x1 + -2 * x8 >= 1 && x1 + -2 * x9 = 1 (2) f213_0_increase_LE'(x24:0, x25:0, x26:0) -> f213_0_increase_LE'(x24:0 + 1, x25:0, x24:0 + 1 + x25:0) :|: x25:0 + -2 * x31:0 <= -1 && x24:0 + x25:0 >= 0 && x26:0 > 0 && x24:0 > -2 && x25:0 + -2 * x27:0 = 1 (3) f213_0_increase_LE'(x10, x11, x12) -> f213_0_increase_LE'(x10 + 2, x11, x10 + 2 + x11) :|: TRUE && x11 + -2 * x13 >= 1 && x10 + x11 >= 0 && x12 >= 1 && x10 >= -1 && x11 + -2 * x14 = 1 && x11 + -2 * x18 <= -1 && x11 + -2 * x19 = 1 Arcs: (1) -> (1), (2), (3) (2) -> (1), (2), (3) (3) -> (1), (2), (3) This digraph is fully evaluated! ---------------------------------------- (33) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (34) Obligation: Rules: f213_0_increase_LE'(x10:0, x11:0, x12:0) -> f213_0_increase_LE'(x10:0 + 2, x11:0, x10:0 + 2 + x11:0) :|: x11:0 + -2 * x18:0 <= -1 && x11:0 + -2 * x19:0 = 1 && x11:0 + -2 * x14:0 = 1 && x10:0 > -2 && x12:0 > 0 && x11:0 + -2 * x13:0 >= 1 && x10:0 + x11:0 >= 0 f213_0_increase_LE'(x24:0:0, x25:0:0, x26:0:0) -> f213_0_increase_LE'(x24:0:0 + 1, x25:0:0, x24:0:0 + 1 + x25:0:0) :|: x24:0:0 > -2 && x25:0:0 + -2 * x27:0:0 = 1 && x26:0:0 > 0 && x24:0:0 + x25:0:0 >= 0 && x25:0:0 + -2 * x31:0:0 <= -1 f213_0_increase_LE'(x:0, x1:0, x2:0) -> f213_0_increase_LE'(x:0 + 2, x1:0, x:0 + 2 + x1:0) :|: x1:0 + -2 * x8:0 >= 1 && x1:0 + -2 * x9:0 = 1 && x1:0 + -2 * x4:0 = 1 && x:0 > -2 && x2:0 > 0 && x1:0 + -2 * x3:0 >= 1 && x:0 + x1:0 >= 0 ---------------------------------------- (35) IRSwTChainingProof (EQUIVALENT) Chaining! ---------------------------------------- (36) Obligation: Rules: f213_0_increase_LE'(x, x1, x2) -> f213_0_increase_LE'(x + 4, x1, x + 4 + x1) :|: TRUE && x1 + -2 * x3 <= -1 && x1 + -2 * x4 = 1 && x1 + -2 * x5 = 1 && x >= -1 && x2 >= 1 && x1 + -2 * x6 >= 1 && x + x1 >= 0 && x1 + -2 * x10 <= -1 && x1 + -2 * x11 = 1 && x1 + -2 * x12 = 1 && x1 + -2 * x13 >= 1 f213_0_increase_LE'(x24:0:0, x25:0:0, x26:0:0) -> f213_0_increase_LE'(x24:0:0 + 1, x25:0:0, x24:0:0 + 1 + x25:0:0) :|: x24:0:0 > -2 && x25:0:0 + -2 * x27:0:0 = 1 && x26:0:0 > 0 && x24:0:0 + x25:0:0 >= 0 && x25:0:0 + -2 * x31:0:0 <= -1 f213_0_increase_LE'(x14, x15, x16) -> f213_0_increase_LE'(x14 + 3, x15, x14 + 3 + x15) :|: TRUE && x15 + -2 * x17 <= -1 && x15 + -2 * x18 = 1 && x15 + -2 * x19 = 1 && x14 >= -1 && x16 >= 1 && x15 + -2 * x20 >= 1 && x14 + x15 >= 0 && x15 + -2 * x24 = 1 && x15 + -2 * x25 <= -1 f213_0_increase_LE'(x:0, x1:0, x2:0) -> f213_0_increase_LE'(x:0 + 2, x1:0, x:0 + 2 + x1:0) :|: x1:0 + -2 * x8:0 >= 1 && x1:0 + -2 * x9:0 = 1 && x1:0 + -2 * x4:0 = 1 && x:0 > -2 && x2:0 > 0 && x1:0 + -2 * x3:0 >= 1 && x:0 + x1:0 >= 0 f213_0_increase_LE'(x26, x27, x28) -> f213_0_increase_LE'(x26 + 4, x27, x26 + 4 + x27) :|: TRUE && x27 + -2 * x29 <= -1 && x27 + -2 * x30 = 1 && x27 + -2 * x31 = 1 && x26 >= -1 && x28 >= 1 && x27 + -2 * x32 >= 1 && x26 + x27 >= 0 && x27 + -2 * x36 >= 1 && x27 + -2 * x37 = 1 && x27 + -2 * x38 = 1 && x27 + -2 * x39 >= 1