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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 3 ms]
(4) T2IntSys
(5) T2 [EQUIVALENT, 1267 ms]
(6) YES


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(0)
Obligation:
c file /export/starexec/sandbox2/benchmark/theBenchmark.c
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(1) CToIRSProof (EQUIVALENT)
Parsed C Integer Program as IRS.
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(2)
Obligation:
Rules:
f1(c, i, j) -> f2(c, x_1, j) :|: TRUE
f2(x, x1, x2) -> f3(x, x1, x3) :|: TRUE
f3(x4, x5, x6) -> f4(0, x5, x6) :|: TRUE
f5(x7, x8, x9) -> f6(x7, x8, 0) :|: TRUE
f7(x10, x11, x12) -> f8(x10, x11, arith) :|: TRUE && arith = x12 + 1
f8(x37, x38, x39) -> f9(x40, x38, x39) :|: TRUE && x40 = x37 + 1
f6(x16, x17, x18) -> f7(x16, x17, x18) :|: x18 <= x17 - 1
f9(x19, x20, x21) -> f6(x19, x20, x21) :|: TRUE
f6(x22, x23, x24) -> f10(x22, x23, x24) :|: x24 > x23 - 1
f10(x41, x42, x43) -> f11(x41, x44, x43) :|: TRUE && x44 = x42 - 1
f4(x28, x29, x30) -> f5(x28, x29, x30) :|: x29 >= 0
f11(x31, x32, x33) -> f4(x31, x32, x33) :|: TRUE
f4(x34, x35, x36) -> f12(x34, x35, x36) :|: x35 < 0
Start term: f1(c, i, j)

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(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)
   (f5_3,5)
   (f6_3,6)
   (f7_3,7)
   (f8_3,8)
   (f9_3,9)
   (f10_3,10)
   (f11_3,11)
   (f12_3,12)

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(4)
Obligation:
START: 1;

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

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

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

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

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

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

FROM: 6;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX2 <= oldX1 - 1);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 7;

FROM: 9;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 6;

FROM: 6;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX2 > oldX1 - 1);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 10;

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

FROM: 4;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX1 >= 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 5;

FROM: 11;
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(oldX1 < 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 12;


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(5) T2 (EQUIVALENT)
Initially, performed program simplifications using lexicographic rank functions:
 * Removed transitions 7, 9, 10, 11, 14, 17, 18 using the following rank functions:
    - Rank function 1:
      RF for loc. 8: 2*x1
      RF for loc. 9: 2*x1
      RF for loc. 13: 1+2*x1
      Bound for (chained) transitions 17: 1
      Bound for (chained) transitions 18: 1
    - Rank function 2:
      RF for loc. 8: 2*x1-2*x2
      RF for loc. 9: -1+2*x1-2*x2
      RF for loc. 13: 2+2*oldX1-2*x2
      Bound for (chained) transitions 10: 1
      Bound for (chained) transitions 11: 1
    - Rank function 3:
      RF for loc. 8: 1
      RF for loc. 9: 0
      RF for loc. 13: 0
      Bound for (chained) transitions 7: 1
      Bound for (chained) transitions 9, 14: 1

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(6)
YES