/export/starexec/sandbox2/solver/bin/starexec_run_c /export/starexec/sandbox2/benchmark/theBenchmark.c /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.c
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination of the given C Problem could be proven:

(0) C Problem
(1) CToIRSProof [EQUIVALENT, 0 ms]
(2) IntTRS
(3) IRS2T2 [EQUIVALENT, 0 ms]
(4) T2IntSys
(5) T2 [EQUIVALENT, 1108 ms]
(6) YES


----------------------------------------

(0)
Obligation:
c file /export/starexec/sandbox2/benchmark/theBenchmark.c
----------------------------------------

(1) CToIRSProof (EQUIVALENT)
Parsed C Integer Program as IRS.
----------------------------------------

(2)
Obligation:
Rules:
f1(x, y, n) -> f2(x, y, x_1) :|: TRUE
f2(x1, x2, x3) -> f3(x4, x2, x3) :|: TRUE
f3(x5, x6, x7) -> f4(x5, x8, x7) :|: TRUE
f6(x9, x10, x11) -> f7(x9, arith, x11) :|: TRUE && arith = x10 - 1
f5(x12, x13, x14) -> f6(x12, x13, x14) :|: x13 >= 0 && x15 < 0
f5(x49, x50, x51) -> f6(x49, x50, x51) :|: x50 >= 0 && x52 > 0
f7(x16, x17, x18) -> f5(x16, x17, x18) :|: TRUE
f5(x19, x20, x21) -> f8(x19, x20, x21) :|: x20 < 0
f5(x53, x54, x55) -> f8(x53, x54, x55) :|: x56 = 0
f8(x57, x58, x59) -> f9(x60, x58, x59) :|: TRUE && x60 = x57 - 1
f10(x61, x62, x63) -> f11(x61, x64, x63) :|: TRUE && x64 = x62 + 1
f9(x29, x30, x31) -> f10(x29, x30, x31) :|: x30 <= x31 && x32 < 0
f9(x65, x66, x67) -> f10(x65, x66, x67) :|: x66 <= x67 && x68 > 0
f11(x33, x34, x35) -> f9(x33, x34, x35) :|: TRUE
f9(x36, x37, x38) -> f12(x36, x37, x38) :|: x37 > x38
f9(x69, x70, x71) -> f12(x69, x70, x71) :|: x72 = 0
f4(x40, x41, x42) -> f5(x40, x41, x42) :|: x40 >= 0
f12(x43, x44, x45) -> f4(x43, x44, x45) :|: TRUE
f4(x46, x47, x48) -> f13(x46, x47, x48) :|: x46 < 0
Start term: f1(x, y, n)

----------------------------------------

(3) IRS2T2 (EQUIVALENT)
Transformed input IRS into an integer transition system.Used the following mapping from defined symbols to location IDs:

   (f1_3,1)
   (f2_3,2)
   (f3_3,3)
   (f4_3,4)
   (f6_3,5)
   (f7_3,6)
   (f5_3,7)
   (f8_3,8)
   (f9_3,9)
   (f10_3,10)
   (f11_3,11)
   (f12_3,12)
   (f13_3,13)

----------------------------------------

(4)
Obligation:
START: 1;

FROM: 1;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := nondet();
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX3;
TO: 2;

FROM: 2;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := nondet();
assume(0 = 0);
x0 := oldX3;
x1 := oldX1;
x2 := oldX2;
TO: 3;

FROM: 3;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := nondet();
assume(0 = 0);
x0 := oldX0;
x1 := oldX3;
x2 := oldX2;
TO: 4;

FROM: 5;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := -(1 - oldX1);
assume(0 = 0 && oldX3 = oldX1 - 1);
x0 := oldX0;
x1 := -(1 - oldX1);
x2 := oldX2;
TO: 6;

FROM: 7;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := nondet();
assume(oldX1 >= 0 && oldX3 < 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 5;

FROM: 7;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := nondet();
assume(oldX1 >= 0 && oldX3 > 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 5;

FROM: 6;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 7;

FROM: 7;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX1 < 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 8;

FROM: 7;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := -(0);
assume(oldX3 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 8;

FROM: 8;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := -(1 - oldX0);
assume(0 = 0 && oldX3 = oldX0 - 1);
x0 := -(1 - oldX0);
x1 := oldX1;
x2 := oldX2;
TO: 9;

FROM: 10;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := -(-(oldX1 + 1));
assume(0 = 0 && oldX3 = oldX1 + 1);
x0 := oldX0;
x1 := -(-(oldX1 + 1));
x2 := oldX2;
TO: 11;

FROM: 9;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := nondet();
assume(oldX1 <= oldX2 && oldX3 < 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 10;

FROM: 9;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := nondet();
assume(oldX1 <= oldX2 && oldX3 > 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 10;

FROM: 11;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 9;

FROM: 9;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX1 > oldX2);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 12;

FROM: 9;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := -(0);
assume(oldX3 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 12;

FROM: 4;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX0 >= 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 7;

FROM: 12;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 4;

FROM: 4;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX0 < 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 13;


----------------------------------------

(5) T2 (EQUIVALENT)
Initially, performed program simplifications using lexicographic rank functions:
 * Removed transitions 8, 9, 12, 13, 14, 15, 27, 28, 29, 32, 33, 34, 35, 47, 50, 51, 54 using the following rank functions:
    - Rank function 1:
      RF for loc. 13: 5*x0
      RF for loc. 14: 5*x0
      RF for loc. 15: -1+5*x0
      RF for loc. 16: 3+5*x0
      RF for loc. 17: 3+5*x0
      RF for loc. 18: 2+5*x0
      RF for loc. 19: 5*x0
      RF for loc. 23: 3+5*x0
      RF for loc. 27: 1+5*x0
      Bound for (chained) transitions 14: 0
      Bound for (chained) transitions 15: 0
      Bound for (chained) transitions 27: -1
      Bound for (chained) transitions 34: -2
      Bound for (chained) transitions 35: -2
      Bound for (chained) transitions 47, 54: -3
      Bound for (chained) transitions 50: 1
      Bound for (chained) transitions 51: 1
    - Rank function 2:
      RF for loc. 13: -1+3*x1
      RF for loc. 14: 1+3*x1
      RF for loc. 16: 1-3*x1+3*x2
      RF for loc. 17: -1-3*x1+3*x2
      RF for loc. 19: 3*x1
      RF for loc. 23: -3*x1+3*x2
      Bound for (chained) transitions 8: -1
      Bound for (chained) transitions 12: 0
      Bound for (chained) transitions 32: 0
      Bound for (chained) transitions 33: 0
    - Rank function 3:
      RF for loc. 13: -1
      RF for loc. 14: 1
      RF for loc. 16: 0
      RF for loc. 17: 1
      RF for loc. 19: 0
      RF for loc. 23: -1
      Bound for (chained) transitions 9: 1
      Bound for (chained) transitions 13: 0
      Bound for (chained) transitions 28: 1
      Bound for (chained) transitions 29: 0

----------------------------------------

(6)
YES