YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.c
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 1207 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(x, y, z) -> f2(0, y, z) :|: TRUE
f2(x1, x2, x3) -> f3(x1, 100, x3) :|: TRUE
f3(x4, x5, x6) -> f4(x4, x5, x7) :|: TRUE
f6(x8, x9, x10) -> f9(arith, x9, x10) :|: TRUE && arith = x8 + 1
f7(x35, x36, x37) -> f10(x38, x36, x37) :|: TRUE && x38 = x35 + 2
f5(x14, x15, x16) -> f6(x14, x15, x16) :|: x16 = 0
f5(x17, x18, x19) -> f7(x17, x18, x19) :|: x19 < 0
f5(x39, x40, x41) -> f7(x39, x40, x41) :|: x41 > 0
f9(x20, x21, x22) -> f8(x20, x21, x22) :|: TRUE
f10(x23, x24, x25) -> f8(x23, x24, x25) :|: TRUE
f4(x26, x27, x28) -> f5(x26, x27, x28) :|: x26 < 40
f8(x29, x30, x31) -> f4(x29, x30, x31) :|: TRUE
f4(x32, x33, x34) -> f11(x32, x33, x34) :|: x32 >= 40
Start term: f1(x, y, z)

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

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(4)
Obligation:
START: 1;

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

FROM: 2;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(0 = 0);
x0 := oldX0;
x1 := 100;
x2 := oldX2;
TO: 3;

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

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

FROM: 7;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := -(-(oldX0 + 2));
assume(0 = 0 && oldX3 = oldX0 + 2);
x0 := -(-(oldX0 + 2));
x1 := oldX1;
x2 := oldX2;
TO: 8;

FROM: 9;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX2 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 5;

FROM: 9;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX2 < 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 7;

FROM: 9;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX2 > 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 7;

FROM: 6;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 10;

FROM: 8;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 10;

FROM: 4;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX0 < 40);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 9;

FROM: 10;
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 >= 40);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 11;


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(5) T2 (EQUIVALENT)
Initially, performed program simplifications using lexicographic rank functions:
 * Removed transitions 9, 10, 11, 12, 13, 16, 17, 20 using the following rank functions:
    - Rank function 1:
      RF for loc. 10: -1-76*x0
      RF for loc. 11: 76-77*x0
      RF for loc. 12: -76*x0
      RF for loc. 13: 40-77*x0
      Bound for (chained) transitions 16: -2963
      Bound for (chained) transitions 17: -2963
    - Rank function 2:
      RF for loc. 10: -1
      RF for loc. 11: -2
      RF for loc. 12: 0
      RF for loc. 13: -3*oldX0
      Bound for (chained) transitions 9: -1
      Bound for (chained) transitions 10: 0
      Bound for (chained) transitions 11: 0
      Bound for (chained) transitions 12: 0
      Bound for (chained) transitions 13, 20: -2

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(6)
YES