/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 1137 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(a, b, c, i, j, M, N) -> f2(a, b, c, x_1, j, M, N) :|: TRUE
f2(x, x1, x2, x3, x4, x5, x6) -> f3(x, x1, x2, x3, x7, x5, x6) :|: TRUE
f3(x8, x9, x10, x11, x12, x13, x14) -> f4(x8, x9, x10, x11, x12, x15, x14) :|: TRUE
f4(x16, x17, x18, x19, x20, x21, x22) -> f5(x16, x17, x18, x19, x20, x21, x23) :|: TRUE
f5(x24, x25, x26, x27, x28, x29, x30) -> f6(x27, x25, x26, x27, x28, x29, x30) :|: TRUE
f6(x31, x32, x33, x34, x35, x36, x37) -> f7(x31, x35, x33, x34, x35, x36, x37) :|: TRUE
f7(x38, x39, x40, x41, x42, x43, x44) -> f8(x38, x39, 0, x41, x42, x43, x44) :|: TRUE
f9(x45, x46, x47, x48, x49, x50, x51) -> f10(x45, x46, x47, arith, x49, x50, x51) :|: TRUE && arith = x48 + 1
f10(x87, x88, x89, x90, x91, x92, x93) -> f11(x87, x88, x89, x90, x94, x92, x93) :|: TRUE && x94 = x91 + 1
f11(x95, x96, x97, x98, x99, x100, x101) -> f12(x95, x96, x102, x98, x99, x100, x101) :|: TRUE && x102 = x97 + 1
f8(x66, x67, x68, x69, x70, x71, x72) -> f9(x66, x67, x68, x69, x70, x71, x72) :|: x69 < x71
f8(x103, x104, x105, x106, x107, x108, x109) -> f9(x103, x104, x105, x106, x107, x108, x109) :|: x107 < x109
f12(x73, x74, x75, x76, x77, x78, x79) -> f8(x73, x74, x75, x76, x77, x78, x79) :|: TRUE
f8(x80, x81, x82, x83, x84, x85, x86) -> f13(x80, x81, x82, x83, x84, x85, x86) :|: x83 >= x85 && x84 >= x86
Start term: f1(a, b, c, i, j, 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_7,1)
   (f2_7,2)
   (f3_7,3)
   (f4_7,4)
   (f5_7,5)
   (f6_7,6)
   (f7_7,7)
   (f8_7,8)
   (f9_7,9)
   (f10_7,10)
   (f11_7,11)
   (f12_7,12)
   (f13_7,13)

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(4)
Obligation:
START: 1;

FROM: 1;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
oldX6 := x6;
oldX7 := nondet();
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX7;
x4 := oldX4;
x5 := oldX5;
x6 := oldX6;
TO: 2;

FROM: 2;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
oldX6 := x6;
oldX7 := nondet();
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX7;
x5 := oldX5;
x6 := oldX6;
TO: 3;

FROM: 3;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
oldX6 := x6;
oldX7 := nondet();
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
x5 := oldX7;
x6 := oldX6;
TO: 4;

FROM: 4;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
oldX6 := x6;
oldX7 := nondet();
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
x5 := oldX5;
x6 := oldX7;
TO: 5;

FROM: 5;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
oldX6 := x6;
assume(0 = 0);
x0 := oldX3;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
x5 := oldX5;
x6 := oldX6;
TO: 6;

FROM: 6;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
oldX6 := x6;
assume(0 = 0);
x0 := oldX0;
x1 := oldX4;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
x5 := oldX5;
x6 := oldX6;
TO: 7;

FROM: 7;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
oldX6 := x6;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := 0;
x3 := oldX3;
x4 := oldX4;
x5 := oldX5;
x6 := oldX6;
TO: 8;

FROM: 9;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
oldX6 := x6;
oldX7 := -(-(oldX3 + 1));
assume(0 = 0 && oldX7 = oldX3 + 1);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := -(-(oldX3 + 1));
x4 := oldX4;
x5 := oldX5;
x6 := oldX6;
TO: 10;

FROM: 10;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
oldX6 := x6;
oldX7 := -(-(oldX4 + 1));
assume(0 = 0 && oldX7 = oldX4 + 1);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := -(-(oldX4 + 1));
x5 := oldX5;
x6 := oldX6;
TO: 11;

FROM: 11;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
oldX6 := x6;
oldX7 := -(-(oldX2 + 1));
assume(0 = 0 && oldX7 = oldX2 + 1);
x0 := oldX0;
x1 := oldX1;
x2 := -(-(oldX2 + 1));
x3 := oldX3;
x4 := oldX4;
x5 := oldX5;
x6 := oldX6;
TO: 12;

FROM: 8;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
oldX6 := x6;
assume(oldX3 < oldX5);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
x5 := oldX5;
x6 := oldX6;
TO: 9;

FROM: 8;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
oldX6 := x6;
assume(oldX4 < oldX6);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
x5 := oldX5;
x6 := oldX6;
TO: 9;

FROM: 12;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
oldX6 := x6;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
x5 := oldX5;
x6 := oldX6;
TO: 8;

FROM: 8;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
oldX6 := x6;
assume(oldX3 >= oldX5 && oldX4 >= oldX6);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
x5 := oldX5;
x6 := oldX6;
TO: 13;


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(5) T2 (EQUIVALENT)
Initially, performed program simplifications using lexicographic rank functions:
 * Removed transitions 6, 7, 11, 12 using the following rank functions:
    - Rank function 1:
      RF for loc. 8: -2-2*x4+2*x6
      RF for loc. 9: -2*x4+2*x6
      Bound for (chained) transitions 12: 2
    - Rank function 2:
      RF for loc. 8: -1-2*x3+2*x5
      RF for loc. 9: -2*x3+2*x5
      Bound for (chained) transitions 11: 2
    - Rank function 3:
      RF for loc. 8: 1
      RF for loc. 9: 0
      Bound for (chained) transitions 6, 7: 1

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(6)
YES