9.50/3.23 YES 9.50/3.24 proof of /export/starexec/sandbox2/benchmark/theBenchmark.c 9.50/3.24 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.50/3.24 9.50/3.24 9.50/3.24 Termination of the given C Problem could be proven: 9.50/3.24 9.50/3.24 (0) C Problem 9.50/3.24 (1) CToIRSProof [EQUIVALENT, 0 ms] 9.50/3.24 (2) IntTRS 9.50/3.24 (3) IRS2T2 [EQUIVALENT, 0 ms] 9.50/3.24 (4) T2IntSys 9.50/3.24 (5) T2 [EQUIVALENT, 1394 ms] 9.50/3.24 (6) YES 9.50/3.24 9.50/3.24 9.50/3.24 ---------------------------------------- 9.50/3.24 9.50/3.24 (0) 9.50/3.24 Obligation: 9.50/3.24 c file /export/starexec/sandbox2/benchmark/theBenchmark.c 9.50/3.24 ---------------------------------------- 9.50/3.24 9.50/3.24 (1) CToIRSProof (EQUIVALENT) 9.50/3.24 Parsed C Integer Program as IRS. 9.50/3.24 ---------------------------------------- 9.50/3.24 9.50/3.24 (2) 9.50/3.24 Obligation: 9.50/3.24 Rules: 9.50/3.24 f1(x, y, m) -> f2(x, 0, m) :|: TRUE 9.50/3.24 f2(x1, x2, x3) -> f3(x1, x2, x4) :|: TRUE 9.50/3.24 f3(x5, x6, x7) -> f4(x7, x6, x7) :|: TRUE 9.50/3.24 f9(x8, x9, x10) -> f10(x8, arith, x10) :|: TRUE && arith = x9 + 1 9.50/3.24 f6(x11, x12, x13) -> f9(x11, x12, x13) :|: x12 <= x13 && x14 < 0 9.50/3.24 f6(x51, x52, x53) -> f9(x51, x52, x53) :|: x52 <= x53 && x54 > 0 9.50/3.24 f10(x15, x16, x17) -> f6(x15, x16, x17) :|: TRUE 9.50/3.24 f6(x18, x19, x20) -> f11(x18, x19, x20) :|: x19 > x20 9.50/3.24 f6(x55, x56, x57) -> f11(x55, x56, x57) :|: x58 = 0 9.50/3.24 f11(x59, x60, x61) -> f12(x62, x60, x61) :|: TRUE && x62 = x59 - 1 9.50/3.24 f5(x25, x26, x27) -> f6(x25, x26, x27) :|: x28 < 0 9.50/3.24 f5(x63, x64, x65) -> f6(x63, x64, x65) :|: x66 > 0 9.50/3.24 f5(x29, x30, x31) -> f7(x29, x30, x31) :|: x32 = 0 9.50/3.24 f12(x33, x34, x35) -> f8(x33, x34, x35) :|: TRUE 9.50/3.24 f7(x36, x37, x38) -> f8(x36, x37, x38) :|: TRUE 9.50/3.24 f8(x67, x68, x69) -> f13(x67, x70, x69) :|: TRUE && x70 = x68 - 1 9.50/3.24 f4(x42, x43, x44) -> f5(x42, x43, x44) :|: x42 >= 0 && x43 >= 0 9.50/3.24 f13(x45, x46, x47) -> f4(x45, x46, x47) :|: TRUE 9.50/3.24 f4(x48, x49, x50) -> f14(x48, x49, x50) :|: x48 < 0 9.50/3.24 f4(x71, x72, x73) -> f14(x71, x72, x73) :|: x72 < 0 9.50/3.24 Start term: f1(x, y, m) 9.50/3.24 9.50/3.24 ---------------------------------------- 9.50/3.24 9.50/3.24 (3) IRS2T2 (EQUIVALENT) 9.50/3.24 Transformed input IRS into an integer transition system.Used the following mapping from defined symbols to location IDs: 9.50/3.24 9.50/3.24 (f1_3,1) 9.50/3.24 (f2_3,2) 9.50/3.24 (f3_3,3) 9.50/3.24 (f4_3,4) 9.50/3.24 (f9_3,5) 9.50/3.24 (f10_3,6) 9.50/3.24 (f6_3,7) 9.50/3.24 (f11_3,8) 9.50/3.24 (f12_3,9) 9.50/3.24 (f5_3,10) 9.50/3.24 (f7_3,11) 9.50/3.24 (f8_3,12) 9.50/3.24 (f13_3,13) 9.50/3.24 (f14_3,14) 9.50/3.24 9.50/3.24 ---------------------------------------- 9.50/3.24 9.50/3.24 (4) 9.50/3.24 Obligation: 9.50/3.24 START: 1; 9.50/3.24 9.50/3.24 FROM: 1; 9.50/3.24 oldX0 := x0; 9.50/3.24 oldX1 := x1; 9.50/3.24 oldX2 := x2; 9.50/3.24 assume(0 = 0); 9.50/3.24 x0 := oldX0; 9.50/3.24 x1 := 0; 9.50/3.24 x2 := oldX2; 9.50/3.24 TO: 2; 9.50/3.24 9.50/3.24 FROM: 2; 9.50/3.24 oldX0 := x0; 9.50/3.24 oldX1 := x1; 9.50/3.24 oldX2 := x2; 9.50/3.24 oldX3 := nondet(); 9.50/3.24 assume(0 = 0); 9.50/3.24 x0 := oldX0; 9.50/3.24 x1 := oldX1; 9.50/3.24 x2 := oldX3; 9.50/3.24 TO: 3; 9.50/3.24 9.50/3.24 FROM: 3; 9.50/3.24 oldX0 := x0; 9.50/3.24 oldX1 := x1; 9.50/3.24 oldX2 := x2; 9.50/3.24 assume(0 = 0); 9.50/3.24 x0 := oldX2; 9.50/3.24 x1 := oldX1; 9.50/3.24 x2 := oldX2; 9.50/3.24 TO: 4; 9.50/3.24 9.50/3.24 FROM: 5; 9.50/3.24 oldX0 := x0; 9.50/3.24 oldX1 := x1; 9.50/3.24 oldX2 := x2; 9.50/3.24 oldX3 := -(-(oldX1 + 1)); 9.50/3.24 assume(0 = 0 && oldX3 = oldX1 + 1); 9.50/3.24 x0 := oldX0; 9.50/3.24 x1 := -(-(oldX1 + 1)); 9.50/3.24 x2 := oldX2; 9.50/3.24 TO: 6; 9.50/3.24 9.50/3.24 FROM: 7; 9.50/3.24 oldX0 := x0; 9.50/3.24 oldX1 := x1; 9.50/3.24 oldX2 := x2; 9.50/3.24 oldX3 := nondet(); 9.50/3.24 assume(oldX1 <= oldX2 && oldX3 < 0); 9.50/3.24 x0 := oldX0; 9.50/3.24 x1 := oldX1; 9.50/3.24 x2 := oldX2; 9.50/3.24 TO: 5; 9.50/3.24 9.50/3.24 FROM: 7; 9.50/3.24 oldX0 := x0; 9.50/3.24 oldX1 := x1; 9.50/3.24 oldX2 := x2; 9.50/3.24 oldX3 := nondet(); 9.50/3.24 assume(oldX1 <= oldX2 && oldX3 > 0); 9.50/3.24 x0 := oldX0; 9.50/3.24 x1 := oldX1; 9.50/3.24 x2 := oldX2; 9.50/3.24 TO: 5; 9.50/3.24 9.50/3.24 FROM: 6; 9.50/3.24 oldX0 := x0; 9.50/3.24 oldX1 := x1; 9.50/3.24 oldX2 := x2; 9.50/3.24 assume(0 = 0); 9.50/3.24 x0 := oldX0; 9.50/3.24 x1 := oldX1; 9.50/3.24 x2 := oldX2; 9.50/3.24 TO: 7; 9.50/3.24 9.50/3.24 FROM: 7; 9.50/3.24 oldX0 := x0; 9.50/3.24 oldX1 := x1; 9.50/3.24 oldX2 := x2; 9.50/3.24 assume(oldX1 > oldX2); 9.50/3.24 x0 := oldX0; 9.50/3.24 x1 := oldX1; 9.50/3.24 x2 := oldX2; 9.50/3.24 TO: 8; 9.50/3.24 9.50/3.24 FROM: 7; 9.50/3.24 oldX0 := x0; 9.50/3.24 oldX1 := x1; 9.50/3.24 oldX2 := x2; 9.50/3.24 oldX3 := -(0); 9.50/3.24 assume(oldX3 = 0); 9.50/3.24 x0 := oldX0; 9.50/3.24 x1 := oldX1; 9.50/3.24 x2 := oldX2; 9.50/3.24 TO: 8; 9.50/3.24 9.50/3.24 FROM: 8; 9.50/3.24 oldX0 := x0; 9.50/3.24 oldX1 := x1; 9.50/3.24 oldX2 := x2; 9.50/3.24 oldX3 := -(1 - oldX0); 9.50/3.24 assume(0 = 0 && oldX3 = oldX0 - 1); 9.50/3.24 x0 := -(1 - oldX0); 9.50/3.24 x1 := oldX1; 9.50/3.24 x2 := oldX2; 9.50/3.24 TO: 9; 9.50/3.24 9.50/3.24 FROM: 10; 9.50/3.24 oldX0 := x0; 9.50/3.24 oldX1 := x1; 9.50/3.24 oldX2 := x2; 9.50/3.24 oldX3 := nondet(); 9.50/3.24 assume(oldX3 < 0); 9.50/3.24 x0 := oldX0; 9.50/3.24 x1 := oldX1; 9.50/3.24 x2 := oldX2; 9.50/3.24 TO: 7; 9.50/3.24 9.50/3.24 FROM: 10; 9.50/3.24 oldX0 := x0; 9.50/3.24 oldX1 := x1; 9.50/3.24 oldX2 := x2; 9.50/3.24 oldX3 := nondet(); 9.50/3.24 assume(oldX3 > 0); 9.50/3.24 x0 := oldX0; 9.50/3.24 x1 := oldX1; 9.50/3.24 x2 := oldX2; 9.50/3.24 TO: 7; 9.50/3.24 9.50/3.24 FROM: 10; 9.50/3.24 oldX0 := x0; 9.50/3.24 oldX1 := x1; 9.50/3.24 oldX2 := x2; 9.50/3.24 oldX3 := -(0); 9.50/3.24 assume(oldX3 = 0); 9.50/3.24 x0 := oldX0; 9.50/3.24 x1 := oldX1; 9.50/3.24 x2 := oldX2; 9.50/3.24 TO: 11; 9.50/3.24 9.50/3.24 FROM: 9; 9.50/3.24 oldX0 := x0; 9.50/3.24 oldX1 := x1; 9.50/3.24 oldX2 := x2; 9.50/3.24 assume(0 = 0); 9.50/3.24 x0 := oldX0; 9.50/3.24 x1 := oldX1; 9.50/3.24 x2 := oldX2; 9.50/3.24 TO: 12; 9.50/3.24 9.50/3.24 FROM: 11; 9.50/3.24 oldX0 := x0; 9.50/3.24 oldX1 := x1; 9.50/3.24 oldX2 := x2; 9.50/3.24 assume(0 = 0); 9.50/3.24 x0 := oldX0; 9.50/3.24 x1 := oldX1; 9.50/3.24 x2 := oldX2; 9.50/3.24 TO: 12; 9.50/3.24 9.50/3.24 FROM: 12; 9.50/3.24 oldX0 := x0; 9.50/3.24 oldX1 := x1; 9.50/3.24 oldX2 := x2; 9.50/3.24 oldX3 := -(1 - oldX1); 9.50/3.24 assume(0 = 0 && oldX3 = oldX1 - 1); 9.50/3.24 x0 := oldX0; 9.50/3.24 x1 := -(1 - oldX1); 9.50/3.24 x2 := oldX2; 9.50/3.24 TO: 13; 9.50/3.24 9.50/3.24 FROM: 4; 9.50/3.24 oldX0 := x0; 9.50/3.24 oldX1 := x1; 9.50/3.24 oldX2 := x2; 9.50/3.24 assume(oldX0 >= 0 && oldX1 >= 0); 9.50/3.24 x0 := oldX0; 9.50/3.24 x1 := oldX1; 9.50/3.24 x2 := oldX2; 9.50/3.24 TO: 10; 9.50/3.24 9.50/3.24 FROM: 13; 9.50/3.24 oldX0 := x0; 9.50/3.24 oldX1 := x1; 9.50/3.24 oldX2 := x2; 9.50/3.24 assume(0 = 0); 9.50/3.24 x0 := oldX0; 9.50/3.24 x1 := oldX1; 9.50/3.24 x2 := oldX2; 9.50/3.24 TO: 4; 9.50/3.24 9.50/3.24 FROM: 4; 9.50/3.24 oldX0 := x0; 9.50/3.24 oldX1 := x1; 9.50/3.24 oldX2 := x2; 9.50/3.24 assume(oldX0 < 0); 9.50/3.24 x0 := oldX0; 9.50/3.24 x1 := oldX1; 9.50/3.24 x2 := oldX2; 9.50/3.24 TO: 14; 9.50/3.24 9.50/3.24 FROM: 4; 9.50/3.24 oldX0 := x0; 9.50/3.24 oldX1 := x1; 9.50/3.24 oldX2 := x2; 9.50/3.24 assume(oldX1 < 0); 9.50/3.24 x0 := oldX0; 9.50/3.24 x1 := oldX1; 9.50/3.24 x2 := oldX2; 9.50/3.24 TO: 14; 9.50/3.24 9.50/3.24 9.50/3.24 ---------------------------------------- 9.50/3.24 9.50/3.24 (5) T2 (EQUIVALENT) 9.50/3.24 Initially, performed program simplifications using lexicographic rank functions: 9.50/3.24 * Removed transitions 11, 12, 15, 16, 17, 18, 30, 31, 32, 33, 34, 35, 39, 40 using the following rank functions: 9.50/3.24 - Rank function 1: 9.50/3.24 RF for loc. 12: -1+3*x0 9.50/3.24 RF for loc. 13: -1+3*x0 9.50/3.24 RF for loc. 14: -2+3*x0 9.50/3.24 RF for loc. 15: 3*x0 9.50/3.24 RF for loc. 16: 3*x0 9.50/3.24 RF for loc. 17: -1+3*x0 9.50/3.24 RF for loc. 21: 3*x0 9.50/3.24 Bound for (chained) transitions 17: -1 9.50/3.24 Bound for (chained) transitions 18: -1 9.50/3.24 Bound for (chained) transitions 30: -2 9.50/3.24 Bound for (chained) transitions 31: 0 9.50/3.24 Bound for (chained) transitions 32: 0 9.50/3.24 - Rank function 2: 9.50/3.24 RF for loc. 12: -1-3*x1+3*x2 9.50/3.24 RF for loc. 13: 1-3*x1+3*x2 9.50/3.24 RF for loc. 15: -2+3*x1 9.50/3.24 RF for loc. 16: -1+3*x1 9.50/3.24 RF for loc. 17: -3*x1+3*x2 9.50/3.24 RF for loc. 21: 3*x1 9.50/3.24 Bound for (chained) transitions 15: 0 9.50/3.24 Bound for (chained) transitions 16: 0 9.50/3.24 Bound for (chained) transitions 33: -1 9.50/3.24 Bound for (chained) transitions 34, 35: -2 9.50/3.24 Bound for (chained) transitions 39: 0 9.50/3.24 Bound for (chained) transitions 40: 0 9.50/3.24 - Rank function 3: 9.50/3.24 RF for loc. 12: 0 9.50/3.24 RF for loc. 13: -1 9.50/3.24 RF for loc. 17: -2 9.50/3.24 Bound for (chained) transitions 11: 0 9.50/3.24 Bound for (chained) transitions 12: -1 9.50/3.24 9.50/3.24 ---------------------------------------- 9.50/3.24 9.50/3.24 (6) 9.50/3.24 YES 9.50/3.26 EOF