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


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YES
proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 1077 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(x, y) -> f2(x_1, y) :|: TRUE
f2(x1, x2) -> f3(x1, x3) :|: TRUE
f8(x4, x5) -> f9(arith, x5) :|: TRUE && arith = x4 - 1
f5(x6, x7) -> f8(x6, x7) :|: x6 > 0
f9(x8, x9) -> f5(x8, x9) :|: TRUE
f5(x10, x11) -> f10(x10, x11) :|: x10 <= 0
f11(x34, x35) -> f12(x34, x36) :|: TRUE && x36 = x35 - 1
f6(x14, x15) -> f11(x14, x15) :|: x15 > 0
f12(x16, x17) -> f6(x16, x17) :|: TRUE
f6(x18, x19) -> f13(x18, x19) :|: x19 <= 0
f4(x20, x21) -> f5(x20, x21) :|: x20 > x21
f4(x22, x23) -> f6(x22, x23) :|: x22 <= x23
f10(x24, x25) -> f7(x24, x25) :|: TRUE
f13(x26, x27) -> f7(x26, x27) :|: TRUE
f3(x28, x29) -> f4(x28, x29) :|: x28 > 0 && x29 > 0
f7(x30, x31) -> f3(x30, x31) :|: TRUE
f3(x32, x33) -> f14(x32, x33) :|: x32 <= 0
f3(x37, x38) -> f14(x37, x38) :|: x38 <= 0
Start term: f1(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_2,1)
   (f2_2,2)
   (f3_2,3)
   (f8_2,4)
   (f9_2,5)
   (f5_2,6)
   (f10_2,7)
   (f11_2,8)
   (f12_2,9)
   (f6_2,10)
   (f13_2,11)
   (f4_2,12)
   (f7_2,13)
   (f14_2,14)

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(4)
Obligation:
START: 1;

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

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

FROM: 4;
oldX0 := x0;
oldX1 := x1;
oldX2 := -(1 - oldX0);
assume(0 = 0 && oldX2 = oldX0 - 1);
x0 := -(1 - oldX0);
x1 := oldX1;
TO: 5;

FROM: 6;
oldX0 := x0;
oldX1 := x1;
assume(oldX0 > 0);
x0 := oldX0;
x1 := oldX1;
TO: 4;

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

FROM: 6;
oldX0 := x0;
oldX1 := x1;
assume(oldX0 <= 0);
x0 := oldX0;
x1 := oldX1;
TO: 7;

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

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

FROM: 9;
oldX0 := x0;
oldX1 := x1;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
TO: 10;

FROM: 10;
oldX0 := x0;
oldX1 := x1;
assume(oldX1 <= 0);
x0 := oldX0;
x1 := oldX1;
TO: 11;

FROM: 12;
oldX0 := x0;
oldX1 := x1;
assume(oldX0 > oldX1);
x0 := oldX0;
x1 := oldX1;
TO: 6;

FROM: 12;
oldX0 := x0;
oldX1 := x1;
assume(oldX0 <= oldX1);
x0 := oldX0;
x1 := oldX1;
TO: 10;

FROM: 7;
oldX0 := x0;
oldX1 := x1;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
TO: 13;

FROM: 11;
oldX0 := x0;
oldX1 := x1;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
TO: 13;

FROM: 3;
oldX0 := x0;
oldX1 := x1;
assume(oldX0 > 0 && oldX1 > 0);
x0 := oldX0;
x1 := oldX1;
TO: 12;

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

FROM: 3;
oldX0 := x0;
oldX1 := x1;
assume(oldX0 <= 0);
x0 := oldX0;
x1 := oldX1;
TO: 14;

FROM: 3;
oldX0 := x0;
oldX1 := x1;
assume(oldX1 <= 0);
x0 := oldX0;
x1 := oldX1;
TO: 14;


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(5) T2 (EQUIVALENT)
Initially, performed program simplifications using lexicographic rank functions:
 * Removed transitions 14, 16, 17, 18, 21, 23, 24, 25, 28, 29, 30, 34, 35, 38 using the following rank functions:
    - Rank function 1:
      RF for loc. 11: 3*x0+5*x1
      RF for loc. 12: -1+6*x0+5*x1
      RF for loc. 13: 6*x0+2*x1
      RF for loc. 14: 1+3*x0+5*x1
      RF for loc. 15: -1+3*x0+5*x1
      RF for loc. 19: -1+6*x0+2*x1
      RF for loc. 23: -1+6*x0+5*x1
      Bound for (chained) transitions 18: 7
      Bound for (chained) transitions 25: 7
      Bound for (chained) transitions 29: 9
      Bound for (chained) transitions 34: 10
      Bound for (chained) transitions 35: 10
    - Rank function 2:
      RF for loc. 11: 0
      RF for loc. 12: -1
      RF for loc. 13: 0
      RF for loc. 14: 1
      RF for loc. 15: 0
      RF for loc. 19: 0
      RF for loc. 23: -2
      Bound for (chained) transitions 16: 0
      Bound for (chained) transitions 23: 0
      Bound for (chained) transitions 28: 1
      Bound for (chained) transitions 30, 38: -1
    - Rank function 3:
      RF for loc. 11: 2*x0
      RF for loc. 13: 2*x1
      RF for loc. 15: -1+2*x0
      RF for loc. 19: -1+2*x1
      Bound for (chained) transitions 24: 1
    - Rank function 4:
      RF for loc. 11: 1+2*x0
      RF for loc. 13: 1
      RF for loc. 15: 2*x0
      RF for loc. 19: 0
      Bound for (chained) transitions 17: 2
      Bound for (chained) transitions 21: 1
    - Rank function 5:
      RF for loc. 11: 0
      RF for loc. 15: -1
      Bound for (chained) transitions 14: 0

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(6)
YES