8.18/2.96 YES 8.18/2.97 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 8.18/2.97 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 8.18/2.97 8.18/2.97 8.18/2.97 Termination of the given C Problem could be proven: 8.18/2.97 8.18/2.97 (0) C Problem 8.18/2.97 (1) CToIRSProof [EQUIVALENT, 0 ms] 8.18/2.97 (2) IntTRS 8.18/2.97 (3) TerminationGraphProcessor [SOUND, 84 ms] 8.18/2.97 (4) IntTRS 8.18/2.97 (5) IntTRSCompressionProof [EQUIVALENT, 42 ms] 8.18/2.97 (6) IntTRS 8.18/2.97 (7) PolynomialOrderProcessor [EQUIVALENT, 13 ms] 8.18/2.97 (8) IntTRS 8.18/2.97 (9) PolynomialOrderProcessor [EQUIVALENT, 3 ms] 8.18/2.97 (10) YES 8.18/2.97 8.18/2.97 8.18/2.97 ---------------------------------------- 8.18/2.97 8.18/2.97 (0) 8.18/2.97 Obligation: 8.18/2.97 c file /export/starexec/sandbox/benchmark/theBenchmark.c 8.18/2.97 ---------------------------------------- 8.18/2.97 8.18/2.97 (1) CToIRSProof (EQUIVALENT) 8.18/2.97 Parsed C Integer Program as IRS. 8.18/2.97 ---------------------------------------- 8.18/2.97 8.18/2.97 (2) 8.18/2.97 Obligation: 8.18/2.97 Rules: 8.18/2.97 f1(x, y) -> f2(x_1, y) :|: TRUE 8.18/2.97 f2(x1, x2) -> f3(x1, x3) :|: TRUE 8.18/2.97 f4(x4, x5) -> f5(arith, x5) :|: TRUE && arith = x4 - 1 8.18/2.97 f5(x28, x29) -> f6(x28, x30) :|: TRUE && x30 = x29 + x28 8.18/2.97 f7(x31, x32) -> f8(x31, x33) :|: TRUE && x33 = x32 - 1 8.18/2.97 f6(x10, x11) -> f7(x10, x11) :|: x11 >= x10 && x12 < 0 8.18/2.97 f6(x34, x35) -> f7(x34, x35) :|: x35 >= x34 && x36 > 0 8.18/2.97 f8(x13, x14) -> f6(x13, x14) :|: TRUE 8.18/2.97 f6(x15, x16) -> f9(x15, x16) :|: x16 < x15 8.18/2.97 f6(x37, x38) -> f9(x37, x38) :|: x39 = 0 8.18/2.97 f9(x40, x41) -> f10(x42, x41) :|: TRUE && x42 = x40 - 1 8.18/2.97 f10(x43, x44) -> f11(x43, x45) :|: TRUE && x45 = x44 - x43 8.18/2.97 f3(x22, x23) -> f4(x22, x23) :|: x22 >= 2 8.18/2.97 f11(x24, x25) -> f3(x24, x25) :|: TRUE 8.18/2.97 f3(x26, x27) -> f12(x26, x27) :|: x26 < 2 8.18/2.97 Start term: f1(x, y) 8.18/2.97 8.18/2.97 ---------------------------------------- 8.18/2.97 8.18/2.97 (3) TerminationGraphProcessor (SOUND) 8.18/2.97 Constructed the termination graph and obtained one non-trivial SCC. 8.18/2.97 8.18/2.97 ---------------------------------------- 8.18/2.97 8.18/2.97 (4) 8.18/2.97 Obligation: 8.18/2.97 Rules: 8.18/2.97 f3(x22, x23) -> f4(x22, x23) :|: x22 >= 2 8.18/2.97 f11(x24, x25) -> f3(x24, x25) :|: TRUE 8.18/2.97 f10(x43, x44) -> f11(x43, x45) :|: TRUE && x45 = x44 - x43 8.18/2.97 f9(x40, x41) -> f10(x42, x41) :|: TRUE && x42 = x40 - 1 8.18/2.97 f6(x15, x16) -> f9(x15, x16) :|: x16 < x15 8.18/2.97 f5(x28, x29) -> f6(x28, x30) :|: TRUE && x30 = x29 + x28 8.18/2.97 f4(x4, x5) -> f5(arith, x5) :|: TRUE && arith = x4 - 1 8.18/2.97 f8(x13, x14) -> f6(x13, x14) :|: TRUE 8.18/2.97 f7(x31, x32) -> f8(x31, x33) :|: TRUE && x33 = x32 - 1 8.18/2.97 f6(x10, x11) -> f7(x10, x11) :|: x11 >= x10 && x12 < 0 8.18/2.97 f6(x34, x35) -> f7(x34, x35) :|: x35 >= x34 && x36 > 0 8.18/2.97 f6(x37, x38) -> f9(x37, x38) :|: x39 = 0 8.18/2.97 8.18/2.97 ---------------------------------------- 8.18/2.97 8.18/2.97 (5) IntTRSCompressionProof (EQUIVALENT) 8.18/2.97 Compressed rules. 8.18/2.97 ---------------------------------------- 8.18/2.97 8.18/2.97 (6) 8.18/2.97 Obligation: 8.18/2.97 Rules: 8.18/2.97 f6(x10:0, x11:0) -> f6(x10:0, x11:0 - 1) :|: x11:0 >= x10:0 && x12:0 < 0 8.18/2.97 f6(x15:0, x16:0) -> f6(x15:0 - 2, x16:0 - (x15:0 - 1) + (x15:0 - 2)) :|: x16:0 < x15:0 && x15:0 > 2 8.18/2.97 f6(x37:0, x38:0) -> f6(x37:0 - 2, x38:0 - (x37:0 - 1) + (x37:0 - 2)) :|: x37:0 > 2 8.18/2.97 f6(x34:0, x35:0) -> f6(x34:0, x35:0 - 1) :|: x35:0 >= x34:0 && x36:0 > 0 8.18/2.97 8.18/2.97 ---------------------------------------- 8.18/2.97 8.18/2.97 (7) PolynomialOrderProcessor (EQUIVALENT) 8.18/2.97 Found the following polynomial interpretation: 8.18/2.97 [f6(x, x1)] = -1 + x 8.18/2.97 8.18/2.97 The following rules are decreasing: 8.18/2.97 f6(x15:0, x16:0) -> f6(x15:0 - 2, x16:0 - (x15:0 - 1) + (x15:0 - 2)) :|: x16:0 < x15:0 && x15:0 > 2 8.18/2.97 f6(x37:0, x38:0) -> f6(x37:0 - 2, x38:0 - (x37:0 - 1) + (x37:0 - 2)) :|: x37:0 > 2 8.18/2.97 The following rules are bounded: 8.18/2.97 f6(x15:0, x16:0) -> f6(x15:0 - 2, x16:0 - (x15:0 - 1) + (x15:0 - 2)) :|: x16:0 < x15:0 && x15:0 > 2 8.18/2.97 f6(x37:0, x38:0) -> f6(x37:0 - 2, x38:0 - (x37:0 - 1) + (x37:0 - 2)) :|: x37:0 > 2 8.18/2.97 8.18/2.97 ---------------------------------------- 8.18/2.97 8.18/2.97 (8) 8.18/2.97 Obligation: 8.18/2.97 Rules: 8.18/2.97 f6(x10:0, x11:0) -> f6(x10:0, x11:0 - 1) :|: x11:0 >= x10:0 && x12:0 < 0 8.18/2.97 f6(x34:0, x35:0) -> f6(x34:0, x35:0 - 1) :|: x35:0 >= x34:0 && x36:0 > 0 8.18/2.97 8.18/2.97 ---------------------------------------- 8.18/2.97 8.18/2.97 (9) PolynomialOrderProcessor (EQUIVALENT) 8.18/2.97 Found the following polynomial interpretation: 8.18/2.97 [f6(x, x1)] = -x + x1 8.18/2.97 8.18/2.97 The following rules are decreasing: 8.18/2.97 f6(x10:0, x11:0) -> f6(x10:0, x11:0 - 1) :|: x11:0 >= x10:0 && x12:0 < 0 8.18/2.97 f6(x34:0, x35:0) -> f6(x34:0, x35:0 - 1) :|: x35:0 >= x34:0 && x36:0 > 0 8.18/2.97 The following rules are bounded: 8.18/2.97 f6(x10:0, x11:0) -> f6(x10:0, x11:0 - 1) :|: x11:0 >= x10:0 && x12:0 < 0 8.18/2.97 f6(x34:0, x35:0) -> f6(x34:0, x35:0 - 1) :|: x35:0 >= x34:0 && x36:0 > 0 8.18/2.97 8.18/2.97 ---------------------------------------- 8.18/2.97 8.18/2.97 (10) 8.18/2.97 YES 8.18/3.00 EOF