8.99/3.05 YES 8.99/3.05 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 8.99/3.05 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 8.99/3.05 8.99/3.05 8.99/3.05 Termination of the given C Problem could be proven: 8.99/3.05 8.99/3.05 (0) C Problem 8.99/3.05 (1) CToIRSProof [EQUIVALENT, 0 ms] 8.99/3.05 (2) IntTRS 8.99/3.05 (3) IRS2T2 [EQUIVALENT, 0 ms] 8.99/3.05 (4) T2IntSys 8.99/3.05 (5) T2 [EQUIVALENT, 1344 ms] 8.99/3.05 (6) YES 8.99/3.05 8.99/3.05 8.99/3.05 ---------------------------------------- 8.99/3.05 8.99/3.05 (0) 8.99/3.05 Obligation: 8.99/3.05 c file /export/starexec/sandbox/benchmark/theBenchmark.c 8.99/3.05 ---------------------------------------- 8.99/3.05 8.99/3.05 (1) CToIRSProof (EQUIVALENT) 8.99/3.05 Parsed C Integer Program as IRS. 8.99/3.05 ---------------------------------------- 8.99/3.05 8.99/3.05 (2) 8.99/3.05 Obligation: 8.99/3.05 Rules: 8.99/3.05 f1(x, y) -> f2(x_1, y) :|: TRUE 8.99/3.05 f2(x1, x2) -> f3(x1, x3) :|: TRUE 8.99/3.05 f8(x4, x5) -> f9(arith, x5) :|: TRUE && arith = x4 - 1 8.99/3.05 f5(x6, x7) -> f8(x6, x7) :|: x6 > 0 8.99/3.05 f9(x8, x9) -> f5(x8, x9) :|: TRUE 8.99/3.05 f5(x10, x11) -> f10(x10, x11) :|: x10 <= 0 8.99/3.05 f11(x34, x35) -> f12(x34, x36) :|: TRUE && x36 = x35 - 1 8.99/3.05 f6(x14, x15) -> f11(x14, x15) :|: x15 > 0 8.99/3.05 f12(x16, x17) -> f6(x16, x17) :|: TRUE 8.99/3.05 f6(x18, x19) -> f13(x18, x19) :|: x19 <= 0 8.99/3.05 f4(x20, x21) -> f5(x20, x21) :|: x20 > x21 8.99/3.05 f4(x22, x23) -> f6(x22, x23) :|: x22 <= x23 8.99/3.05 f10(x24, x25) -> f7(x24, x25) :|: TRUE 8.99/3.05 f13(x26, x27) -> f7(x26, x27) :|: TRUE 8.99/3.05 f3(x28, x29) -> f4(x28, x29) :|: x28 > 0 && x29 > 0 8.99/3.05 f7(x30, x31) -> f3(x30, x31) :|: TRUE 8.99/3.05 f3(x32, x33) -> f14(x32, x33) :|: x32 <= 0 8.99/3.05 f3(x37, x38) -> f14(x37, x38) :|: x38 <= 0 8.99/3.05 Start term: f1(x, y) 8.99/3.05 8.99/3.05 ---------------------------------------- 8.99/3.05 8.99/3.05 (3) IRS2T2 (EQUIVALENT) 8.99/3.05 Transformed input IRS into an integer transition system.Used the following mapping from defined symbols to location IDs: 8.99/3.05 8.99/3.05 (f1_2,1) 8.99/3.05 (f2_2,2) 8.99/3.05 (f3_2,3) 8.99/3.05 (f8_2,4) 8.99/3.05 (f9_2,5) 8.99/3.05 (f5_2,6) 8.99/3.05 (f10_2,7) 8.99/3.05 (f11_2,8) 8.99/3.05 (f12_2,9) 8.99/3.05 (f6_2,10) 8.99/3.05 (f13_2,11) 8.99/3.05 (f4_2,12) 8.99/3.05 (f7_2,13) 8.99/3.05 (f14_2,14) 8.99/3.05 8.99/3.05 ---------------------------------------- 8.99/3.05 8.99/3.05 (4) 8.99/3.05 Obligation: 8.99/3.05 START: 1; 8.99/3.05 8.99/3.05 FROM: 1; 8.99/3.05 oldX0 := x0; 8.99/3.05 oldX1 := x1; 8.99/3.05 oldX2 := nondet(); 8.99/3.05 assume(0 = 0); 8.99/3.05 x0 := oldX2; 8.99/3.05 x1 := oldX1; 8.99/3.05 TO: 2; 8.99/3.05 8.99/3.05 FROM: 2; 8.99/3.05 oldX0 := x0; 8.99/3.05 oldX1 := x1; 8.99/3.05 oldX2 := nondet(); 8.99/3.05 assume(0 = 0); 8.99/3.05 x0 := oldX0; 8.99/3.05 x1 := oldX2; 8.99/3.05 TO: 3; 8.99/3.05 8.99/3.05 FROM: 4; 8.99/3.05 oldX0 := x0; 8.99/3.05 oldX1 := x1; 8.99/3.05 oldX2 := -(1 - oldX0); 8.99/3.05 assume(0 = 0 && oldX2 = oldX0 - 1); 8.99/3.05 x0 := -(1 - oldX0); 8.99/3.05 x1 := oldX1; 8.99/3.05 TO: 5; 8.99/3.05 8.99/3.05 FROM: 6; 8.99/3.05 oldX0 := x0; 8.99/3.05 oldX1 := x1; 8.99/3.05 assume(oldX0 > 0); 8.99/3.05 x0 := oldX0; 8.99/3.05 x1 := oldX1; 8.99/3.05 TO: 4; 8.99/3.05 8.99/3.05 FROM: 5; 8.99/3.05 oldX0 := x0; 8.99/3.05 oldX1 := x1; 8.99/3.05 assume(0 = 0); 8.99/3.05 x0 := oldX0; 8.99/3.05 x1 := oldX1; 8.99/3.05 TO: 6; 8.99/3.05 8.99/3.05 FROM: 6; 8.99/3.05 oldX0 := x0; 8.99/3.05 oldX1 := x1; 8.99/3.05 assume(oldX0 <= 0); 8.99/3.05 x0 := oldX0; 8.99/3.05 x1 := oldX1; 8.99/3.05 TO: 7; 8.99/3.05 8.99/3.05 FROM: 8; 8.99/3.05 oldX0 := x0; 8.99/3.05 oldX1 := x1; 8.99/3.05 oldX2 := -(1 - oldX1); 8.99/3.05 assume(0 = 0 && oldX2 = oldX1 - 1); 8.99/3.05 x0 := oldX0; 8.99/3.05 x1 := -(1 - oldX1); 8.99/3.05 TO: 9; 8.99/3.05 8.99/3.05 FROM: 10; 8.99/3.05 oldX0 := x0; 8.99/3.05 oldX1 := x1; 8.99/3.05 assume(oldX1 > 0); 8.99/3.05 x0 := oldX0; 8.99/3.05 x1 := oldX1; 8.99/3.05 TO: 8; 8.99/3.05 8.99/3.05 FROM: 9; 8.99/3.05 oldX0 := x0; 8.99/3.05 oldX1 := x1; 8.99/3.05 assume(0 = 0); 8.99/3.05 x0 := oldX0; 8.99/3.05 x1 := oldX1; 8.99/3.05 TO: 10; 8.99/3.05 8.99/3.05 FROM: 10; 8.99/3.05 oldX0 := x0; 8.99/3.05 oldX1 := x1; 8.99/3.05 assume(oldX1 <= 0); 8.99/3.05 x0 := oldX0; 8.99/3.05 x1 := oldX1; 8.99/3.05 TO: 11; 8.99/3.05 8.99/3.05 FROM: 12; 8.99/3.05 oldX0 := x0; 8.99/3.05 oldX1 := x1; 8.99/3.05 assume(oldX0 > oldX1); 8.99/3.05 x0 := oldX0; 8.99/3.05 x1 := oldX1; 8.99/3.05 TO: 6; 8.99/3.05 8.99/3.05 FROM: 12; 8.99/3.05 oldX0 := x0; 8.99/3.05 oldX1 := x1; 8.99/3.05 assume(oldX0 <= oldX1); 8.99/3.05 x0 := oldX0; 8.99/3.05 x1 := oldX1; 8.99/3.05 TO: 10; 8.99/3.05 8.99/3.05 FROM: 7; 8.99/3.05 oldX0 := x0; 8.99/3.05 oldX1 := x1; 8.99/3.05 assume(0 = 0); 8.99/3.05 x0 := oldX0; 8.99/3.05 x1 := oldX1; 8.99/3.05 TO: 13; 8.99/3.05 8.99/3.05 FROM: 11; 8.99/3.05 oldX0 := x0; 8.99/3.05 oldX1 := x1; 8.99/3.05 assume(0 = 0); 8.99/3.05 x0 := oldX0; 8.99/3.05 x1 := oldX1; 8.99/3.05 TO: 13; 8.99/3.05 8.99/3.05 FROM: 3; 8.99/3.05 oldX0 := x0; 8.99/3.05 oldX1 := x1; 8.99/3.05 assume(oldX0 > 0 && oldX1 > 0); 8.99/3.05 x0 := oldX0; 8.99/3.05 x1 := oldX1; 8.99/3.05 TO: 12; 8.99/3.05 8.99/3.05 FROM: 13; 8.99/3.05 oldX0 := x0; 8.99/3.05 oldX1 := x1; 8.99/3.05 assume(0 = 0); 8.99/3.05 x0 := oldX0; 8.99/3.05 x1 := oldX1; 8.99/3.05 TO: 3; 8.99/3.05 8.99/3.05 FROM: 3; 8.99/3.05 oldX0 := x0; 8.99/3.05 oldX1 := x1; 8.99/3.05 assume(oldX0 <= 0); 8.99/3.05 x0 := oldX0; 8.99/3.05 x1 := oldX1; 8.99/3.05 TO: 14; 8.99/3.05 8.99/3.05 FROM: 3; 8.99/3.05 oldX0 := x0; 8.99/3.05 oldX1 := x1; 8.99/3.05 assume(oldX1 <= 0); 8.99/3.05 x0 := oldX0; 8.99/3.05 x1 := oldX1; 8.99/3.05 TO: 14; 8.99/3.05 8.99/3.05 8.99/3.05 ---------------------------------------- 8.99/3.05 8.99/3.05 (5) T2 (EQUIVALENT) 8.99/3.05 Initially, performed program simplifications using lexicographic rank functions: 8.99/3.05 * Removed transitions 14, 16, 17, 18, 21, 23, 24, 25, 28, 29, 30, 34, 35, 38 using the following rank functions: 8.99/3.05 - Rank function 1: 8.99/3.05 RF for loc. 11: 3*x0+5*x1 8.99/3.05 RF for loc. 12: -1+6*x0+5*x1 8.99/3.05 RF for loc. 13: 6*x0+2*x1 8.99/3.05 RF for loc. 14: 1+3*x0+5*x1 8.99/3.05 RF for loc. 15: -1+3*x0+5*x1 8.99/3.05 RF for loc. 19: -1+6*x0+2*x1 8.99/3.05 RF for loc. 23: -1+6*x0+5*x1 8.99/3.05 Bound for (chained) transitions 18: 7 8.99/3.05 Bound for (chained) transitions 25: 7 8.99/3.05 Bound for (chained) transitions 29: 9 8.99/3.05 Bound for (chained) transitions 34: 10 8.99/3.05 Bound for (chained) transitions 35: 10 8.99/3.05 - Rank function 2: 8.99/3.05 RF for loc. 11: 0 8.99/3.05 RF for loc. 12: -1 8.99/3.05 RF for loc. 13: 0 8.99/3.05 RF for loc. 14: 1 8.99/3.05 RF for loc. 15: 0 8.99/3.05 RF for loc. 19: 0 8.99/3.05 RF for loc. 23: -2 8.99/3.05 Bound for (chained) transitions 16: 0 8.99/3.05 Bound for (chained) transitions 23: 0 8.99/3.05 Bound for (chained) transitions 28: 1 8.99/3.05 Bound for (chained) transitions 30, 38: -1 8.99/3.05 - Rank function 3: 8.99/3.05 RF for loc. 11: 2*x0 8.99/3.05 RF for loc. 13: 2*x1 8.99/3.05 RF for loc. 15: -1+2*x0 8.99/3.05 RF for loc. 19: -1+2*x1 8.99/3.05 Bound for (chained) transitions 24: 1 8.99/3.05 - Rank function 4: 8.99/3.05 RF for loc. 11: 1+2*x0 8.99/3.05 RF for loc. 13: 1 8.99/3.05 RF for loc. 15: 2*x0 8.99/3.05 RF for loc. 19: 0 8.99/3.05 Bound for (chained) transitions 17: 2 8.99/3.05 Bound for (chained) transitions 21: 1 8.99/3.05 - Rank function 5: 8.99/3.05 RF for loc. 11: 0 8.99/3.05 RF for loc. 15: -1 8.99/3.05 Bound for (chained) transitions 14: 0 8.99/3.05 8.99/3.05 ---------------------------------------- 8.99/3.05 8.99/3.05 (6) 8.99/3.05 YES 8.99/3.09 EOF