/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 1244 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(c, x, y, z) -> f2(c, x_1, y, z) :|: TRUE
f2(x1, x2, x3, x4) -> f3(x1, x2, x5, x4) :|: TRUE
f3(x6, x7, x8, x9) -> f4(x6, x7, x8, x10) :|: TRUE
f4(x11, x12, x13, x14) -> f5(0, x12, x13, x14) :|: TRUE
f7(x15, x16, x17, x18) -> f10(x15, arith, x17, x18) :|: TRUE && arith = x16 - 1
f11(x71, x72, x73, x74) -> f14(x71, x72, x75, x74) :|: TRUE && x75 = x73 - 1
f8(x23, x24, x25, x26) -> f11(x23, x24, x25, x26) :|: x25 > x26
f8(x27, x28, x29, x30) -> f12(x27, x28, x29, x30) :|: x29 <= x30
f14(x31, x32, x33, x34) -> f13(x31, x32, x33, x34) :|: TRUE
f12(x35, x36, x37, x38) -> f13(x35, x36, x37, x38) :|: TRUE
f6(x39, x40, x41, x42) -> f7(x39, x40, x41, x42) :|: x40 > x42
f6(x43, x44, x45, x46) -> f8(x43, x44, x45, x46) :|: x44 <= x46
f10(x47, x48, x49, x50) -> f9(x47, x48, x49, x50) :|: TRUE
f13(x51, x52, x53, x54) -> f9(x51, x52, x53, x54) :|: TRUE
f9(x76, x77, x78, x79) -> f15(x80, x77, x78, x79) :|: TRUE && x80 = x76 + 1
f5(x59, x60, x61, x62) -> f6(x59, x60, x61, x62) :|: x60 > x62
f5(x81, x82, x83, x84) -> f6(x81, x82, x83, x84) :|: x83 > x84
f15(x63, x64, x65, x66) -> f5(x63, x64, x65, x66) :|: TRUE
f5(x67, x68, x69, x70) -> f16(x67, x68, x69, x70) :|: x68 <= x70 && x69 <= x70
Start term: f1(c, x, y, z)

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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)
   (f7_4,6)
   (f10_4,7)
   (f11_4,8)
   (f14_4,9)
   (f8_4,10)
   (f12_4,11)
   (f13_4,12)
   (f6_4,13)
   (f9_4,14)
   (f15_4,15)
   (f16_4,16)

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(4)
Obligation:
START: 1;

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

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

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

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

FROM: 6;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := -(1 - oldX1);
assume(0 = 0 && oldX4 = oldX1 - 1);
x0 := oldX0;
x1 := -(1 - oldX1);
x2 := oldX2;
x3 := oldX3;
TO: 7;

FROM: 8;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := -(1 - oldX2);
assume(0 = 0 && oldX4 = oldX2 - 1);
x0 := oldX0;
x1 := oldX1;
x2 := -(1 - oldX2);
x3 := oldX3;
TO: 9;

FROM: 10;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX2 > oldX3);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 8;

FROM: 10;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX2 <= oldX3);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 11;

FROM: 9;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 12;

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

FROM: 13;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX1 > oldX3);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 6;

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

FROM: 7;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 14;

FROM: 12;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 14;

FROM: 14;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := -(-(oldX0 + 1));
assume(0 = 0 && oldX4 = oldX0 + 1);
x0 := -(-(oldX0 + 1));
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 15;

FROM: 5;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX1 > oldX3);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 13;

FROM: 5;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX2 > oldX3);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 13;

FROM: 15;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 5;

FROM: 5;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX1 <= oldX3 && oldX2 <= oldX3);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 16;


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(5) T2 (EQUIVALENT)
Initially, performed program simplifications using lexicographic rank functions:
 * Removed transitions 11, 13 using the following rank functions:
    - Rank function 1:
      RF for loc. 11: 2*x1-2*x3
      RF for loc. 12: 2*x1-2*x3
      RF for loc. 13: 2*x1-2*x3
      RF for loc. 14: 2*x1-2*x3
      RF for loc. 15: 2*x1-2*x3
      Bound for (chained) transitions 13: 2
    - Rank function 2:
      RF for loc. 11: x2-x3
      RF for loc. 12: x2-x3
      RF for loc. 13: x2-x3
      RF for loc. 14: x2-x3
      RF for loc. 15: x2-x3
      Bound for (chained) transitions 11: 1

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(6)
YES