YES
proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 1318 ms]
(6) YES


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(0)
Obligation:
c file /export/starexec/sandbox/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, x, y) -> f2(c, x_1, y) :|: TRUE
f2(x1, x2, x3) -> f3(x1, x2, x4) :|: TRUE
f3(x5, x6, x7) -> f4(0, x6, x7) :|: TRUE
f6(x8, x9, x10) -> f9(x8, arith, x10) :|: TRUE && arith = x9 - 1
f10(x53, x54, x55) -> f13(x53, x56, x55) :|: TRUE && x56 = x54 - 1
f11(x57, x58, x59) -> f14(x57, x58, x60) :|: TRUE && x60 = x59 - 1
f7(x17, x18, x19) -> f10(x17, x18, x19) :|: x18 = x19
f7(x20, x21, x22) -> f11(x20, x21, x22) :|: x21 < x22
f7(x61, x62, x63) -> f11(x61, x62, x63) :|: x62 > x63
f13(x23, x24, x25) -> f12(x23, x24, x25) :|: TRUE
f14(x26, x27, x28) -> f12(x26, x27, x28) :|: TRUE
f5(x29, x30, x31) -> f6(x29, x30, x31) :|: x30 > x31
f5(x32, x33, x34) -> f7(x32, x33, x34) :|: x33 <= x34
f9(x35, x36, x37) -> f8(x35, x36, x37) :|: TRUE
f12(x38, x39, x40) -> f8(x38, x39, x40) :|: TRUE
f8(x64, x65, x66) -> f15(x67, x65, x66) :|: TRUE && x67 = x64 + 1
f4(x44, x45, x46) -> f5(x44, x45, x46) :|: x45 + x46 > 0
f15(x47, x48, x49) -> f4(x47, x48, x49) :|: TRUE
f4(x50, x51, x52) -> f16(x50, x51, x52) :|: x51 + x52 <= 0
Start term: f1(c, x, y)

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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)
   (f10_3,7)
   (f13_3,8)
   (f11_3,9)
   (f14_3,10)
   (f7_3,11)
   (f12_3,12)
   (f5_3,13)
   (f8_3,14)
   (f15_3,15)
   (f16_3,16)

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

FROM: 9;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := -(1 - oldX2);
assume(0 = 0 && oldX3 = oldX2 - 1);
x0 := oldX0;
x1 := oldX1;
x2 := -(1 - oldX2);
TO: 10;

FROM: 11;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX1 = oldX2);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 7;

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

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

FROM: 8;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 12;

FROM: 10;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 12;

FROM: 13;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX1 > oldX2);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 5;

FROM: 13;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX1 <= oldX2);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 11;

FROM: 6;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 14;

FROM: 12;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 14;

FROM: 14;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := -(-(oldX0 + 1));
assume(0 = 0 && oldX3 = oldX0 + 1);
x0 := -(-(oldX0 + 1));
x1 := oldX1;
x2 := oldX2;
TO: 15;

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

FROM: 15;
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 + oldX2 <= 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 16;


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(5) T2 (EQUIVALENT)
Initially, performed program simplifications using lexicographic rank functions:
 * Removed transitions 12, 13, 14, 15, 16, 17, 18, 19, 20, 23, 24 using the following rank functions:
    - Rank function 1:
      RF for loc. 12: -2+6*x1+6*x2
      RF for loc. 13: 3+6*x1+6*x2
      RF for loc. 14: -1+6*x1+6*x2
      RF for loc. 15: 6*x1+6*x2
      RF for loc. 16: 2+6*x1+6*x2
      RF for loc. 17: 1+6*x1+6*x2
      Bound for (chained) transitions 23: 7
      Bound for (chained) transitions 24: 7
    - Rank function 2:
      RF for loc. 12: 2
      RF for loc. 13: 1
      RF for loc. 14: 3
      RF for loc. 15: 4
      RF for loc. 16: 0
      RF for loc. 17: -1
      Bound for (chained) transitions 12: 2
      Bound for (chained) transitions 13: 3
      Bound for (chained) transitions 14: 3
      Bound for (chained) transitions 15: 3
      Bound for (chained) transitions 16: 4
      Bound for (chained) transitions 17: 4
      Bound for (chained) transitions 18: 1
      Bound for (chained) transitions 19, 20: 0

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(6)
YES