/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 5 ms]
(4) T2IntSys
(5) T2 [EQUIVALENT, 1227 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, res) -> f2(x_1, y, res) :|: TRUE
f2(x1, x2, x3) -> f3(x1, x4, x3) :|: TRUE
f3(x5, x6, x7) -> f4(x5, x6, 0) :|: TRUE
f5(x8, x9, x10) -> f6(arith, x9, x10) :|: TRUE && arith = x8 - 1
f6(x53, x54, x55) -> f7(x53, x56, x55) :|: TRUE && x56 = x54 - 1
f4(x14, x15, x16) -> f5(x14, x15, x16) :|: x14 > 0 && x15 > 0
f7(x17, x18, x19) -> f4(x17, x18, x19) :|: TRUE
f4(x20, x21, x22) -> f8(x20, x21, x22) :|: x20 <= 0
f4(x57, x58, x59) -> f8(x57, x58, x59) :|: x58 <= 0
f9(x60, x61, x62) -> f10(x60, x63, x62) :|: TRUE && x63 = x61 + 1
f10(x64, x65, x66) -> f11(x64, x65, x67) :|: TRUE && x67 = x66 + 1
f12(x68, x69, x70) -> f13(x71, x69, x70) :|: TRUE && x71 = x68 - 1
f13(x72, x73, x74) -> f14(x72, x75, x74) :|: TRUE && x75 = x73 - 1
f11(x35, x36, x37) -> f12(x35, x36, x37) :|: x35 > 0 && x36 > 0
f14(x38, x39, x40) -> f11(x38, x39, x40) :|: TRUE
f11(x41, x42, x43) -> f15(x41, x42, x43) :|: x41 <= 0
f11(x76, x77, x78) -> f15(x76, x77, x78) :|: x77 <= 0
f8(x44, x45, x46) -> f9(x44, x45, x46) :|: x44 > 0
f15(x47, x48, x49) -> f8(x47, x48, x49) :|: TRUE
f8(x50, x51, x52) -> f16(x50, x51, x52) :|: x50 <= 0
Start term: f1(x, y, res)

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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)
   (f13_3,13)
   (f14_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 := oldX3;
x1 := oldX1;
x2 := oldX2;
TO: 2;

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

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

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

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

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

FROM: 7;
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 <= 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 8;

FROM: 4;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX1 <= 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 8;

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

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

FROM: 12;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := -(1 - oldX0);
assume(0 = 0 && oldX3 = oldX0 - 1);
x0 := -(1 - oldX0);
x1 := oldX1;
x2 := oldX2;
TO: 13;

FROM: 13;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := -(1 - oldX1);
assume(0 = 0 && oldX3 = oldX1 - 1);
x0 := oldX0;
x1 := -(1 - oldX1);
x2 := oldX2;
TO: 14;

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

FROM: 14;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 11;

FROM: 11;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX0 <= 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 15;

FROM: 11;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX1 <= 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 15;

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

FROM: 15;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 8;

FROM: 8;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX0 <= 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 17, 20, 21, 22, 32, 35, 36, 39 using the following rank functions:
    - Rank function 1:
      RF for loc. 11: 3*x0
      RF for loc. 12: 3*x0
      RF for loc. 17: 3*x0
      RF for loc. 21: 3*x0
      Bound for (chained) transitions 20: 3
    - Rank function 2:
      RF for loc. 11: 3-4*x1
      RF for loc. 12: 1-4*x1
      RF for loc. 17: 2-4*x1
      RF for loc. 21: -4*x1
      Bound for (chained) transitions 22: 2
    - Rank function 3:
      RF for loc. 11: 3
      RF for loc. 12: 1+4*x0
      RF for loc. 17: 2
      RF for loc. 21: 4*x0
      Bound for (chained) transitions 17: 3
      Bound for (chained) transitions 21: 2
      Bound for (chained) transitions 35: 4
      Bound for (chained) transitions 36: 4
    - Rank function 4:
      RF for loc. 12: oldX2
      RF for loc. 21: 0
      Bound for (chained) transitions 32, 39: 1
 * Removed transitions 5, 9, 10 using the following rank functions:
    - Rank function 1:
      RF for loc. 9: 1+x0+x1
      RF for loc. 13: x0+x1
      Bound for (chained) transitions 9: 2
      Bound for (chained) transitions 10: 2
    - Rank function 2:
      RF for loc. 9: 0
      RF for loc. 13: -1
      Bound for (chained) transitions 5: 0

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(6)
YES