/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 4 ms]
(4) T2IntSys
(5) T2 [EQUIVALENT, 2668 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, tmp, xtmp) -> f2(x_1, y, tmp, xtmp) :|: TRUE
f2(x1, x2, x3, x4) -> f3(x1, x5, x3, x4) :|: TRUE
f4(x6, x7, x8, x9) -> f5(x6, x7, x7, x9) :|: TRUE
f5(x10, x11, x12, x13) -> f6(x10, x11, x12, x10) :|: TRUE
f7(x14, x15, x16, x17) -> f10(x14, x15, x16, x17) :|: TRUE
f11(x18, x19, x20, x21) -> f14(x18, x19, x20, arith) :|: TRUE && arith = 0 - x21
f8(x22, x23, x24, x25) -> f11(x22, x23, x24, x25) :|: x23 < 0
f8(x26, x27, x28, x29) -> f12(x26, x27, x28, x29) :|: x27 >= 0
f14(x30, x31, x32, x33) -> f13(x30, x31, x32, x33) :|: TRUE
f12(x34, x35, x36, x37) -> f13(x34, x35, x36, x37) :|: TRUE
f6(x38, x39, x40, x41) -> f7(x38, x39, x40, x41) :|: x39 = 0
f6(x42, x43, x44, x45) -> f8(x42, x43, x44, x45) :|: x43 < 0
f6(x126, x127, x128, x129) -> f8(x126, x127, x128, x129) :|: x127 > 0
f10(x46, x47, x48, x49) -> f9(x46, x47, x48, x49) :|: TRUE
f13(x50, x51, x52, x53) -> f9(x50, x51, x52, x53) :|: TRUE
f18(x130, x131, x132, x133) -> f19(x130, x131, x132, x134) :|: TRUE && x134 = x133 - x131
f15(x58, x59, x60, x61) -> f18(x58, x59, x60, x61) :|: x61 >= x59
f19(x62, x63, x64, x65) -> f15(x62, x63, x64, x65) :|: TRUE
f15(x66, x67, x68, x69) -> f20(x66, x67, x68, x69) :|: x69 < x67
f20(x70, x71, x72, x73) -> f21(x70, x73, x72, x73) :|: TRUE
f22(x135, x136, x137, x138) -> f23(x135, x136, x137, x139) :|: TRUE && x139 = x138 - x136
f16(x78, x79, x80, x81) -> f22(x78, x79, x80, x81) :|: x81 < 0
f23(x82, x83, x84, x85) -> f16(x82, x83, x84, x85) :|: TRUE
f16(x86, x87, x88, x89) -> f24(x86, x87, x88, x89) :|: x89 >= 0
f24(x90, x91, x92, x93) -> f25(x90, x93, x92, x93) :|: TRUE
f9(x94, x95, x96, x97) -> f15(x94, x95, x96, x97) :|: x97 > 0
f9(x98, x99, x100, x101) -> f16(x98, x99, x100, x101) :|: x101 <= 0
f21(x102, x103, x104, x105) -> f17(x102, x103, x104, x105) :|: TRUE
f25(x106, x107, x108, x109) -> f17(x106, x107, x108, x109) :|: TRUE
f17(x110, x111, x112, x113) -> f26(x112, x111, x112, x113) :|: TRUE
f3(x114, x115, x116, x117) -> f4(x114, x115, x116, x117) :|: x115 > 0 && x114 > 0
f26(x118, x119, x120, x121) -> f3(x118, x119, x120, x121) :|: TRUE
f3(x122, x123, x124, x125) -> f27(x122, x123, x124, x125) :|: x123 <= 0
f3(x140, x141, x142, x143) -> f27(x140, x141, x142, x143) :|: x140 <= 0
Start term: f1(x, y, tmp, xtmp)

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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_4,1)
   (f2_4,2)
   (f3_4,3)
   (f4_4,4)
   (f5_4,5)
   (f6_4,6)
   (f7_4,7)
   (f10_4,8)
   (f11_4,9)
   (f14_4,10)
   (f8_4,11)
   (f12_4,12)
   (f13_4,13)
   (f9_4,14)
   (f18_4,15)
   (f19_4,16)
   (f15_4,17)
   (f20_4,18)
   (f21_4,19)
   (f22_4,20)
   (f23_4,21)
   (f16_4,22)
   (f24_4,23)
   (f25_4,24)
   (f17_4,25)
   (f26_4,26)
   (f27_4,27)

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(4)
Obligation:
START: 1;

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

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

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

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

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

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

FROM: 11;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX1 < 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 9;

FROM: 11;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX1 >= 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 12;

FROM: 10;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 13;

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

FROM: 6;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX1 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 7;

FROM: 6;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX1 < 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 11;

FROM: 6;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX1 > 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 11;

FROM: 8;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 14;

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

FROM: 15;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := -(oldX1 - oldX3);
assume(0 = 0 && oldX4 = oldX3 - oldX1);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := -(oldX1 - oldX3);
TO: 16;

FROM: 17;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX3 >= oldX1);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 15;

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

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

FROM: 18;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(0 = 0);
x0 := oldX0;
x1 := oldX3;
x2 := oldX2;
x3 := oldX3;
TO: 19;

FROM: 20;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := -(oldX1 - oldX3);
assume(0 = 0 && oldX4 = oldX3 - oldX1);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := -(oldX1 - oldX3);
TO: 21;

FROM: 22;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX3 < 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 20;

FROM: 21;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 22;

FROM: 22;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX3 >= 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 23;

FROM: 23;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(0 = 0);
x0 := oldX0;
x1 := oldX3;
x2 := oldX2;
x3 := oldX3;
TO: 24;

FROM: 14;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX3 > 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 17;

FROM: 14;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX3 <= 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 22;

FROM: 19;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 25;

FROM: 24;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 25;

FROM: 25;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(0 = 0);
x0 := oldX2;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 26;

FROM: 3;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX1 > 0 && oldX0 > 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 4;

FROM: 26;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 3;

FROM: 3;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX1 <= 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 27;

FROM: 3;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX0 <= 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 27;


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(5) T2 (EQUIVALENT)
Initially, performed program simplifications using lexicographic rank functions:
 * Removed transitions 20, 22, 23 using the following rank functions:
    - Rank function 1:
      RF for loc. 14: 0
      RF for loc. 15: 0
      RF for loc. 16: 0
      RF for loc. 17: 0
      RF for loc. 18: 0
      RF for loc. 19: 0
      RF for loc. 20: 0
      RF for loc. 21: 0
      RF for loc. 25: 0
      RF for loc. 29: 0
      Bound for (chained) transitions 20: 0
      Bound for (chained) transitions 22: 0
      Bound for (chained) transitions 23: 0
Used the following cutpoint-specific lexicographic rank functions:
 * For cutpoint 13, used the following rank functions/bounds (in descending priority order):
    - RF x1, bound 0
 * For cutpoint 18, used the following rank functions/bounds (in descending priority order):
    - RF x3, bound 1

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(6)
YES