MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 219 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 28 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 70 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] (12) IRSwT ---------------------------------------- (0) Obligation: Rules: l0(__const_10HAT0, iHAT0, jHAT0, tempHAT0) -> l1(__const_10HATpost, iHATpost, jHATpost, tempHATpost) :|: tempHAT0 = tempHATpost && jHAT0 = jHATpost && iHAT0 = iHATpost && __const_10HAT0 = __const_10HATpost l2(x, x1, x2, x3) -> l3(x4, x5, x6, x7) :|: x3 = x7 && x2 = x6 && x1 = x5 && x = x4 l3(x8, x9, x10, x11) -> l2(x12, x13, x14, x15) :|: x9 = x13 && x8 = x12 && x14 = -1 + x10 && x15 = x15 l3(x16, x17, x18, x19) -> l0(x20, x21, x22, x23) :|: x19 = x23 && x18 = x22 && x16 = x20 && x21 = 1 + x17 l1(x24, x25, x26, x27) -> l4(x28, x29, x30, x31) :|: x27 = x31 && x26 = x30 && x25 = x29 && x24 = x28 && 1 + x24 <= x25 l1(x32, x33, x34, x35) -> l2(x36, x37, x38, x39) :|: x35 = x39 && x33 = x37 && x32 = x36 && x38 = x33 && x33 <= x32 l5(x40, x41, x42, x43) -> l0(x44, x45, x46, x47) :|: x43 = x47 && x42 = x46 && x40 = x44 && x45 = 2 l6(x48, x49, x50, x51) -> l5(x52, x53, x54, x55) :|: x51 = x55 && x50 = x54 && x49 = x53 && x48 = x52 Start term: l6(__const_10HAT0, iHAT0, jHAT0, tempHAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(__const_10HAT0, iHAT0, jHAT0, tempHAT0) -> l1(__const_10HATpost, iHATpost, jHATpost, tempHATpost) :|: tempHAT0 = tempHATpost && jHAT0 = jHATpost && iHAT0 = iHATpost && __const_10HAT0 = __const_10HATpost l2(x, x1, x2, x3) -> l3(x4, x5, x6, x7) :|: x3 = x7 && x2 = x6 && x1 = x5 && x = x4 l3(x8, x9, x10, x11) -> l2(x12, x13, x14, x15) :|: x9 = x13 && x8 = x12 && x14 = -1 + x10 && x15 = x15 l3(x16, x17, x18, x19) -> l0(x20, x21, x22, x23) :|: x19 = x23 && x18 = x22 && x16 = x20 && x21 = 1 + x17 l1(x24, x25, x26, x27) -> l4(x28, x29, x30, x31) :|: x27 = x31 && x26 = x30 && x25 = x29 && x24 = x28 && 1 + x24 <= x25 l1(x32, x33, x34, x35) -> l2(x36, x37, x38, x39) :|: x35 = x39 && x33 = x37 && x32 = x36 && x38 = x33 && x33 <= x32 l5(x40, x41, x42, x43) -> l0(x44, x45, x46, x47) :|: x43 = x47 && x42 = x46 && x40 = x44 && x45 = 2 l6(x48, x49, x50, x51) -> l5(x52, x53, x54, x55) :|: x51 = x55 && x50 = x54 && x49 = x53 && x48 = x52 Start term: l6(__const_10HAT0, iHAT0, jHAT0, tempHAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(__const_10HAT0, iHAT0, jHAT0, tempHAT0) -> l1(__const_10HATpost, iHATpost, jHATpost, tempHATpost) :|: tempHAT0 = tempHATpost && jHAT0 = jHATpost && iHAT0 = iHATpost && __const_10HAT0 = __const_10HATpost (2) l2(x, x1, x2, x3) -> l3(x4, x5, x6, x7) :|: x3 = x7 && x2 = x6 && x1 = x5 && x = x4 (3) l3(x8, x9, x10, x11) -> l2(x12, x13, x14, x15) :|: x9 = x13 && x8 = x12 && x14 = -1 + x10 && x15 = x15 (4) l3(x16, x17, x18, x19) -> l0(x20, x21, x22, x23) :|: x19 = x23 && x18 = x22 && x16 = x20 && x21 = 1 + x17 (5) l1(x24, x25, x26, x27) -> l4(x28, x29, x30, x31) :|: x27 = x31 && x26 = x30 && x25 = x29 && x24 = x28 && 1 + x24 <= x25 (6) l1(x32, x33, x34, x35) -> l2(x36, x37, x38, x39) :|: x35 = x39 && x33 = x37 && x32 = x36 && x38 = x33 && x33 <= x32 (7) l5(x40, x41, x42, x43) -> l0(x44, x45, x46, x47) :|: x43 = x47 && x42 = x46 && x40 = x44 && x45 = 2 (8) l6(x48, x49, x50, x51) -> l5(x52, x53, x54, x55) :|: x51 = x55 && x50 = x54 && x49 = x53 && x48 = x52 Arcs: (1) -> (5), (6) (2) -> (3), (4) (3) -> (2) (4) -> (1) (6) -> (2) (7) -> (1) (8) -> (7) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l0(__const_10HAT0, iHAT0, jHAT0, tempHAT0) -> l1(__const_10HATpost, iHATpost, jHATpost, tempHATpost) :|: tempHAT0 = tempHATpost && jHAT0 = jHATpost && iHAT0 = iHATpost && __const_10HAT0 = __const_10HATpost (2) l3(x16, x17, x18, x19) -> l0(x20, x21, x22, x23) :|: x19 = x23 && x18 = x22 && x16 = x20 && x21 = 1 + x17 (3) l2(x, x1, x2, x3) -> l3(x4, x5, x6, x7) :|: x3 = x7 && x2 = x6 && x1 = x5 && x = x4 (4) l1(x32, x33, x34, x35) -> l2(x36, x37, x38, x39) :|: x35 = x39 && x33 = x37 && x32 = x36 && x38 = x33 && x33 <= x32 (5) l3(x8, x9, x10, x11) -> l2(x12, x13, x14, x15) :|: x9 = x13 && x8 = x12 && x14 = -1 + x10 && x15 = x15 Arcs: (1) -> (4) (2) -> (1) (3) -> (2), (5) (4) -> (3) (5) -> (3) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l2(__const_10HATpost:0, x1:0, jHATpost:0, tempHATpost:0) -> l2(__const_10HATpost:0, 1 + x1:0, 1 + x1:0, tempHATpost:0) :|: __const_10HATpost:0 >= 1 + x1:0 l2(x12:0, x13:0, x2:0, x3:0) -> l2(x12:0, x13:0, -1 + x2:0, x15:0) :|: TRUE ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l2(x1, x2, x3, x4) -> l2(x1, x2) ---------------------------------------- (8) Obligation: Rules: l2(__const_10HATpost:0, x1:0) -> l2(__const_10HATpost:0, 1 + x1:0) :|: __const_10HATpost:0 >= 1 + x1:0 l2(x12:0, x13:0) -> l2(x12:0, x13:0) :|: TRUE ---------------------------------------- (9) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l2(VARIABLE, VARIABLE) Replaced non-predefined constructor symbols by 0.The following proof was generated: # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IntTRS could not be shown: - IntTRS - PolynomialOrderProcessor Rules: l2(__const_10HATpost:0, x1:0) -> l2(__const_10HATpost:0, c) :|: c = 1 + x1:0 && __const_10HATpost:0 >= 1 + x1:0 l2(x12:0, x13:0) -> l2(x12:0, x13:0) :|: TRUE Found the following polynomial interpretation: [l2(x, x1)] = -1 + x - x1 The following rules are decreasing: l2(__const_10HATpost:0, x1:0) -> l2(__const_10HATpost:0, c) :|: c = 1 + x1:0 && __const_10HATpost:0 >= 1 + x1:0 The following rules are bounded: l2(__const_10HATpost:0, x1:0) -> l2(__const_10HATpost:0, c) :|: c = 1 + x1:0 && __const_10HATpost:0 >= 1 + x1:0 - IntTRS - PolynomialOrderProcessor - IntTRS Rules: l2(x12:0, x13:0) -> l2(x12:0, x13:0) :|: TRUE ---------------------------------------- (10) Obligation: Rules: l2(x12:0, x13:0) -> l2(x12:0, x13:0) :|: TRUE ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l2(x12:0, x13:0) -> l2(x12:0, x13:0) :|: TRUE Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) l2(x12:0, x13:0) -> l2(x12:0, x13:0) :|: TRUE Arcs: (1) -> (1) This digraph is fully evaluated!