YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 9 ms]
(4) T2IntSys
(5) T2 [EQUIVALENT, 1369 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(x, tx, y, ty, n) -> f2(x_1, tx, y, ty, n) :|: TRUE
f2(x1, x2, x3, x4, x5) -> f3(x1, x6, x3, x4, x5) :|: TRUE
f3(x7, x8, x9, x10, x11) -> f4(x7, x8, x12, x10, x11) :|: TRUE
f4(x13, x14, x15, x16, x17) -> f5(x13, x14, x15, x18, x17) :|: TRUE
f5(x19, x20, x21, x22, x23) -> f6(x19, x20, x21, x22, x24) :|: TRUE
f11(x25, x26, x27, x28, x29) -> f14(x25, x25, x27, x28, x29) :|: TRUE
f14(x30, x31, x32, x33, x34) -> f15(x30, x31, x32, x32, x34) :|: TRUE
f15(x35, x36, x37, x38, x39) -> f16(x40, x36, x37, x38, x39) :|: TRUE
f16(x41, x42, x43, x44, x45) -> f17(x41, x42, x46, x44, x45) :|: TRUE
f12(x47, x48, x49, x50, x51) -> f18(x47, x47, x49, x50, x51) :|: TRUE
f18(x52, x53, x54, x55, x56) -> f19(x57, x53, x54, x55, x56) :|: TRUE
f10(x58, x59, x60, x61, x62) -> f11(x58, x59, x60, x61, x62) :|: x63 < 0
f10(x115, x116, x117, x118, x119) -> f11(x115, x116, x117, x118, x119) :|: x120 > 0
f10(x64, x65, x66, x67, x68) -> f12(x64, x65, x66, x67, x68) :|: x69 = 0
f17(x70, x71, x72, x73, x74) -> f13(x70, x71, x72, x73, x74) :|: TRUE
f19(x75, x76, x77, x78, x79) -> f13(x75, x76, x77, x78, x79) :|: TRUE
f7(x80, x81, x82, x83, x84) -> f10(x80, x81, x82, x83, x84) :|: x80 <= x84 && x80 >= 2 * x81 + x82 && x82 >= x83 + 1 && x80 >= x81 + 1
f13(x85, x86, x87, x88, x89) -> f7(x85, x86, x87, x88, x89) :|: TRUE
f7(x90, x91, x92, x93, x94) -> f20(x90, x91, x92, x93, x94) :|: x90 < x91 + 1
f7(x121, x122, x123, x124, x125) -> f20(x121, x122, x123, x124, x125) :|: x123 < x124 + 1
f7(x126, x127, x128, x129, x130) -> f20(x126, x127, x128, x129, x130) :|: x126 > x130
f7(x131, x132, x133, x134, x135) -> f20(x131, x132, x133, x134, x135) :|: x131 < 2 * x132 + x133
f6(x95, x96, x97, x98, x99) -> f7(x95, x96, x97, x98, x99) :|: x95 + x97 >= 0
f6(x100, x101, x102, x103, x104) -> f8(x100, x101, x102, x103, x104) :|: x100 + x102 < 0
f20(x105, x106, x107, x108, x109) -> f9(x105, x106, x107, x108, x109) :|: TRUE
f8(x110, x111, x112, x113, x114) -> f9(x110, x111, x112, x113, x114) :|: TRUE
Start term: f1(x, tx, y, ty, 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_5,1)
   (f2_5,2)
   (f3_5,3)
   (f4_5,4)
   (f5_5,5)
   (f6_5,6)
   (f11_5,7)
   (f14_5,8)
   (f15_5,9)
   (f16_5,10)
   (f17_5,11)
   (f12_5,12)
   (f18_5,13)
   (f19_5,14)
   (f10_5,15)
   (f13_5,16)
   (f7_5,17)
   (f20_5,18)
   (f8_5,19)
   (f9_5,20)

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(4)
Obligation:
START: 1;

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

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

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

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

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

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

FROM: 8;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX2;
x4 := oldX4;
TO: 9;

FROM: 9;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := nondet();
assume(0 = 0);
x0 := oldX5;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
TO: 10;

FROM: 10;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := nondet();
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX5;
x3 := oldX3;
x4 := oldX4;
TO: 11;

FROM: 12;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
assume(0 = 0);
x0 := oldX0;
x1 := oldX0;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
TO: 13;

FROM: 13;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := nondet();
assume(0 = 0);
x0 := oldX5;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
TO: 14;

FROM: 15;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := nondet();
assume(oldX5 < 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
TO: 7;

FROM: 15;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := nondet();
assume(oldX5 > 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
TO: 7;

FROM: 15;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := -(0);
assume(oldX5 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
TO: 12;

FROM: 11;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
TO: 16;

FROM: 14;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
TO: 16;

FROM: 17;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
assume(oldX0 <= oldX4 && oldX0 >= 2 * oldX1 + oldX2 && oldX2 >= oldX3 + 1 && oldX0 >= oldX1 + 1);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
TO: 15;

FROM: 16;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
TO: 17;

FROM: 17;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
assume(oldX0 < oldX1 + 1);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
TO: 18;

FROM: 17;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
assume(oldX2 < oldX3 + 1);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
TO: 18;

FROM: 17;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
assume(oldX0 > oldX4);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
TO: 18;

FROM: 17;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
assume(oldX0 < 2 * oldX1 + oldX2);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
TO: 18;

FROM: 6;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
assume(oldX0 + oldX2 >= 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
TO: 17;

FROM: 6;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
assume(oldX0 + oldX2 < 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
TO: 19;

FROM: 18;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
TO: 20;

FROM: 19;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
TO: 20;


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(5) T2 (EQUIVALENT)
Initially, performed program simplifications using lexicographic rank functions:
 * Removed transitions 15, 16, 17, 18, 19, 25, 26, 29 using the following rank functions:
    - Rank function 1:
      RF for loc. 11: -1-4*x0+4*x4
      RF for loc. 12: -2-4*x1+4*x4
      RF for loc. 13: -4*x0+4*x4
      RF for loc. 15: -3-4*x1+4*x4
      Bound for (chained) transitions 25: 1
      Bound for (chained) transitions 26: 1
    - Rank function 2:
      RF for loc. 11: 1
      RF for loc. 12: 0
      RF for loc. 13: 2
      RF for loc. 15: -1
      Bound for (chained) transitions 15: 1
      Bound for (chained) transitions 16: 2
      Bound for (chained) transitions 17: 2
      Bound for (chained) transitions 18: 2
      Bound for (chained) transitions 19, 29: 0

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(6)
YES