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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 70 ms]
(2) IntTRS
(3) IRS2T2 [EQUIVALENT, 0 ms]
(4) T2IntSys
(5) T2 [EQUIVALENT, 1609 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, j, k, m, n, N) -> f2(x_1, j, k, m, n, N) :|: TRUE
f2(x, x1, x2, x3, x4, x5) -> f3(x, x6, x2, x3, x4, x5) :|: TRUE
f3(x7, x8, x9, x10, x11, x12) -> f4(x7, x8, x13, x10, x11, x12) :|: TRUE
f4(x14, x15, x16, x17, x18, x19) -> f5(x14, x15, x16, x17, x20, x19) :|: TRUE
f5(x21, x22, x23, x24, x25, x26) -> f6(x21, x22, x23, x27, x25, x26) :|: TRUE
f6(x28, x29, x30, x31, x32, x33) -> f7(x28, x29, x30, x31, x32, x34) :|: TRUE
f8(x35, x36, x37, x38, x39, x40) -> f11(0, x36, x37, x38, x39, x40) :|: TRUE
f12(x41, x42, x43, x44, x45, x46) -> f13(x41, 0, x43, x44, x45, x46) :|: TRUE
f14(x47, x48, x49, x50, x51, x52) -> f15(x47, arith, x49, x50, x51, x52) :|: TRUE && arith = x48 + 1
f15(x53, x54, x55, x56, x57, x58) -> f16(x53, x54, x53, x56, x57, x58) :|: TRUE
f17(x155, x156, x157, x158, x159, x160) -> f18(x155, x156, x161, x158, x159, x160) :|: TRUE && x161 = x157 + 1
f16(x65, x66, x67, x68, x69, x70) -> f17(x65, x66, x67, x68, x69, x70) :|: x67 < x70
f18(x71, x72, x73, x74, x75, x76) -> f16(x71, x72, x73, x74, x75, x76) :|: TRUE
f16(x77, x78, x79, x80, x81, x82) -> f19(x77, x78, x79, x80, x81, x82) :|: x79 >= x82
f19(x83, x84, x85, x86, x87, x88) -> f20(x85, x84, x85, x86, x87, x88) :|: TRUE
f13(x89, x90, x91, x92, x93, x94) -> f14(x89, x90, x91, x92, x93, x94) :|: x90 < x92
f20(x95, x96, x97, x98, x99, x100) -> f13(x95, x96, x97, x98, x99, x100) :|: TRUE
f13(x101, x102, x103, x104, x105, x106) -> f21(x101, x102, x103, x104, x105, x106) :|: x102 >= x104
f21(x162, x163, x164, x165, x166, x167) -> f22(x168, x163, x164, x165, x166, x167) :|: TRUE && x168 = x162 + 1
f11(x113, x114, x115, x116, x117, x118) -> f12(x113, x114, x115, x116, x117, x118) :|: x113 < x117
f22(x119, x120, x121, x122, x123, x124) -> f11(x119, x120, x121, x122, x123, x124) :|: TRUE
f11(x125, x126, x127, x128, x129, x130) -> f23(x125, x126, x127, x128, x129, x130) :|: x125 >= x129
f7(x131, x132, x133, x134, x135, x136) -> f8(x131, x132, x133, x134, x135, x136) :|: 0 <= x135 && 0 <= x134 && 0 <= x136
f7(x137, x138, x139, x140, x141, x142) -> f9(x137, x138, x139, x140, x141, x142) :|: 0 > x142
f7(x169, x170, x171, x172, x173, x174) -> f9(x169, x170, x171, x172, x173, x174) :|: 0 > x173
f7(x175, x176, x177, x178, x179, x180) -> f9(x175, x176, x177, x178, x179, x180) :|: 0 > x178
f23(x143, x144, x145, x146, x147, x148) -> f10(x143, x144, x145, x146, x147, x148) :|: TRUE
f9(x149, x150, x151, x152, x153, x154) -> f10(x149, x150, x151, x152, x153, x154) :|: TRUE
Start term: f1(i, j, k, m, n, 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_6,1)
   (f2_6,2)
   (f3_6,3)
   (f4_6,4)
   (f5_6,5)
   (f6_6,6)
   (f7_6,7)
   (f8_6,8)
   (f11_6,9)
   (f12_6,10)
   (f13_6,11)
   (f14_6,12)
   (f15_6,13)
   (f16_6,14)
   (f17_6,15)
   (f18_6,16)
   (f19_6,17)
   (f20_6,18)
   (f21_6,19)
   (f22_6,20)
   (f23_6,21)
   (f9_6,22)
   (f10_6,23)

----------------------------------------

(4)
Obligation:
START: 1;

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

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

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

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

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

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

FROM: 8;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
assume(0 = 0);
x0 := 0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
x5 := oldX5;
TO: 9;

FROM: 10;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
assume(0 = 0);
x0 := oldX0;
x1 := 0;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
x5 := oldX5;
TO: 11;

FROM: 12;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
oldX6 := -(-(oldX1 + 1));
assume(0 = 0 && oldX6 = oldX1 + 1);
x0 := oldX0;
x1 := -(-(oldX1 + 1));
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
x5 := oldX5;
TO: 13;

FROM: 13;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX0;
x3 := oldX3;
x4 := oldX4;
x5 := oldX5;
TO: 14;

FROM: 15;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
oldX6 := -(-(oldX2 + 1));
assume(0 = 0 && oldX6 = oldX2 + 1);
x0 := oldX0;
x1 := oldX1;
x2 := -(-(oldX2 + 1));
x3 := oldX3;
x4 := oldX4;
x5 := oldX5;
TO: 16;

FROM: 14;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
assume(oldX2 < oldX5);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
x5 := oldX5;
TO: 15;

FROM: 16;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
x5 := oldX5;
TO: 14;

FROM: 14;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
assume(oldX2 >= oldX5);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
x5 := oldX5;
TO: 17;

FROM: 17;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
assume(0 = 0);
x0 := oldX2;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
x5 := oldX5;
TO: 18;

FROM: 11;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
assume(oldX1 < oldX3);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
x5 := oldX5;
TO: 12;

FROM: 18;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
x5 := oldX5;
TO: 11;

FROM: 11;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
assume(oldX1 >= oldX3);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
x5 := oldX5;
TO: 19;

FROM: 19;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
oldX6 := -(-(oldX0 + 1));
assume(0 = 0 && oldX6 = oldX0 + 1);
x0 := -(-(oldX0 + 1));
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
x5 := oldX5;
TO: 20;

FROM: 9;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
assume(oldX0 < oldX4);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
x5 := oldX5;
TO: 10;

FROM: 20;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
x5 := oldX5;
TO: 9;

FROM: 9;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
assume(oldX0 >= oldX4);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
x5 := oldX5;
TO: 21;

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

FROM: 7;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
assume(0 > oldX5);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
x5 := oldX5;
TO: 22;

FROM: 7;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
assume(0 > oldX4);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
x5 := oldX5;
TO: 22;

FROM: 7;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
assume(0 > oldX3);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
x5 := oldX5;
TO: 22;

FROM: 21;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
x5 := oldX5;
TO: 23;

FROM: 22;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := x4;
oldX5 := x5;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
x4 := oldX4;
x5 := oldX5;
TO: 23;


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(5) T2 (EQUIVALENT)
Initially, performed program simplifications using lexicographic rank functions:
 * Removed transitions 15, 17, 18, 19, 22, 24, 25, 26, 29, 32, 33 using the following rank functions:
    - Rank function 1:
      RF for loc. 10: -6*x2+6*x4
      RF for loc. 11: -6*x0+6*x4
      RF for loc. 13: -1-6*x2+6*x4
      RF for loc. 17: -6*x0+6*x4
      RF for loc. 21: 5-6*x0+6*x4
      Bound for (chained) transitions 32: 11
      Bound for (chained) transitions 33: 11
    - Rank function 2:
      RF for loc. 10: -3*x1+3*x3
      RF for loc. 11: -1-3*x1+3*x3
      RF for loc. 13: -3*x1+3*x3
      RF for loc. 17: -2-3*x1+3*x3
      RF for loc. 21: -2+3*oldX3-3*x1
      Bound for (chained) transitions 25: 1
      Bound for (chained) transitions 26: 1
    - Rank function 3:
      RF for loc. 10: 0
      RF for loc. 11: 0
      RF for loc. 13: 0
      RF for loc. 17: -1
      RF for loc. 21: -1
      Bound for (chained) transitions 22: 0
      Bound for (chained) transitions 24, 29: 0
    - Rank function 4:
      RF for loc. 10: -2*x2+2*x5
      RF for loc. 11: -1-2*oldX0+2*oldX5
      RF for loc. 13: -1-2*x2+2*x5
      Bound for (chained) transitions 18: 1
      Bound for (chained) transitions 19: 1
    - Rank function 5:
      RF for loc. 10: 0
      RF for loc. 11: -1
      RF for loc. 13: -1
      Bound for (chained) transitions 15: 0
      Bound for (chained) transitions 17: 0

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(6)
YES