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


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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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 1327 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(i, m, n) -> f2(i, m, x_1) :|: TRUE
f2(x, x1, x2) -> f3(x, x3, x2) :|: TRUE
f4(x4, x5, x6) -> f7(x6, x5, x6) :|: TRUE
f9(x7, x8, x9) -> f12(arith, x8, x9) :|: TRUE && arith = x7 - 1
f10(x46, x47, x48) -> f13(x49, x47, x48) :|: TRUE && x49 = x46 - x47
f8(x13, x14, x15) -> f9(x13, x14, x15) :|: x13 < x14
f8(x16, x17, x18) -> f10(x16, x17, x18) :|: x16 >= x17
f12(x19, x20, x21) -> f11(x19, x20, x21) :|: TRUE
f13(x22, x23, x24) -> f11(x22, x23, x24) :|: TRUE
f7(x25, x26, x27) -> f8(x25, x26, x27) :|: x25 > 0
f11(x28, x29, x30) -> f7(x28, x29, x30) :|: TRUE
f7(x31, x32, x33) -> f14(x31, x32, x33) :|: x31 <= 0
f3(x34, x35, x36) -> f4(x34, x35, x36) :|: x35 > 0 && x36 > x35
f3(x37, x38, x39) -> f5(x37, x38, x39) :|: x38 <= 0
f3(x50, x51, x52) -> f5(x50, x51, x52) :|: x52 <= x51
f14(x40, x41, x42) -> f6(x40, x41, x42) :|: TRUE
f5(x43, x44, x45) -> f6(x43, x44, x45) :|: TRUE
Start term: f1(i, m, n)

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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)
   (f7_3,5)
   (f9_3,6)
   (f12_3,7)
   (f10_3,8)
   (f13_3,9)
   (f8_3,10)
   (f11_3,11)
   (f14_3,12)
   (f5_3,13)
   (f6_3,14)

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(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 := oldX0;
x1 := oldX3;
x2 := oldX2;
TO: 3;

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

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

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

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

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

FROM: 7;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 11;

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

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

FROM: 5;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX0 <= 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 12;

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

FROM: 3;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX1 <= 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 13;

FROM: 3;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX2 <= oldX1);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 13;

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

FROM: 13;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 14;


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(5) T2 (EQUIVALENT)
Initially, performed program simplifications using lexicographic rank functions:
 * Removed transitions 11, 12, 13, 16, 17, 20 using the following rank functions:
    - Rank function 1:
      RF for loc. 10: 3*x0
      RF for loc. 11: 2+3*x0
      RF for loc. 13: 1+3*x0
      Bound for (chained) transitions 11: 3
      Bound for (chained) transitions 16: 4
      Bound for (chained) transitions 17: 4
    - Rank function 2:
      RF for loc. 10: 2*x0
      RF for loc. 11: oldX1
      RF for loc. 13: 0
      Bound for (chained) transitions 13, 20: 1
    - Rank function 3:
      RF for loc. 10: oldX1
      RF for loc. 11: 0
      Bound for (chained) transitions 12: 1

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(6)
YES