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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 1323 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(i, j, k, t) -> f2(x_1, j, k, t) :|: TRUE
f2(x, x1, x2, x3) -> f3(x, x4, x2, x3) :|: TRUE
f3(x5, x6, x7, x8) -> f4(x5, x6, x9, x8) :|: TRUE
f5(x10, x11, x12, x13) -> f6(x11, x11, x12, x13) :|: TRUE
f6(x14, x15, x16, x17) -> f7(x14, arith, x16, x17) :|: TRUE && arith = x14 + 1
f7(x34, x35, x36, x37) -> f8(x34, x35, x38, x37) :|: TRUE && x38 = x36 - 1
f4(x22, x23, x24, x25) -> f5(x22, x23, x24, x25) :|: x22 <= 100 && x23 <= x24
f8(x26, x27, x28, x29) -> f4(x26, x27, x28, x29) :|: TRUE
f4(x30, x31, x32, x33) -> f9(x30, x31, x32, x33) :|: x30 > 100
f4(x39, x40, x41, x42) -> f9(x39, x40, x41, x42) :|: x40 > x41
Start term: f1(i, j, k, t)

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

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

   (f1_4,1)
   (f2_4,2)
   (f3_4,3)
   (f4_4,4)
   (f5_4,5)
   (f6_4,6)
   (f7_4,7)
   (f8_4,8)
   (f9_4,9)

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

(4)
Obligation:
START: 1;

FROM: 1;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := nondet();
assume(0 = 0);
x0 := oldX4;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 2;

FROM: 2;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := nondet();
assume(0 = 0);
x0 := oldX0;
x1 := oldX4;
x2 := oldX2;
x3 := oldX3;
TO: 3;

FROM: 3;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := nondet();
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX4;
x3 := oldX3;
TO: 4;

FROM: 5;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(0 = 0);
x0 := oldX1;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 6;

FROM: 6;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := -(-(oldX0 + 1));
assume(0 = 0 && oldX4 = oldX0 + 1);
x0 := oldX0;
x1 := -(-(oldX0 + 1));
x2 := oldX2;
x3 := oldX3;
TO: 7;

FROM: 7;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := -(1 - oldX2);
assume(0 = 0 && oldX4 = oldX2 - 1);
x0 := oldX0;
x1 := oldX1;
x2 := -(1 - oldX2);
x3 := oldX3;
TO: 8;

FROM: 4;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX0 <= 100 && oldX1 <= oldX2);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 5;

FROM: 8;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 4;

FROM: 4;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX0 > 100);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 9;

FROM: 4;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX1 > oldX2);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 9;


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

(5) T2 (EQUIVALENT)
Initially, performed program simplifications using lexicographic rank functions:
 * Removed transitions 5, 9, 10 using the following rank functions:
    - Rank function 1:
      RF for loc. 6: 2-2*x1+2*x2
      RF for loc. 7: -2*x1+2*x2
      Bound for (chained) transitions 9: 0
      Bound for (chained) transitions 10: 0
    - Rank function 2:
      RF for loc. 6: 0
      RF for loc. 7: -1
      Bound for (chained) transitions 5: 0

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

(6)
YES