/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 0 ms]
(4) T2IntSys
(5) T2 [EQUIVALENT, 1238 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, z) -> f2(x_1, y, z) :|: TRUE
f2(x1, x2, x3) -> f3(x1, x4, x3) :|: TRUE
f3(x5, x6, x7) -> f4(x5, x6, x8) :|: TRUE
f6(x9, x10, x11) -> f9(arith, x10, x11) :|: TRUE && arith = x9 - 1
f10(x63, x64, x65) -> f13(x63, x66, x65) :|: TRUE && x66 = x64 - 1
f13(x15, x16, x17) -> f14(x15, x16, x18) :|: TRUE
f11(x67, x68, x69) -> f15(x67, x68, x70) :|: TRUE && x70 = x69 - 1
f15(x22, x23, x24) -> f16(x25, x23, x24) :|: TRUE
f7(x26, x27, x28) -> f10(x26, x27, x28) :|: x29 < 0
f7(x71, x72, x73) -> f10(x71, x72, x73) :|: x74 > 0
f7(x30, x31, x32) -> f11(x30, x31, x32) :|: x33 = 0
f14(x34, x35, x36) -> f12(x34, x35, x36) :|: TRUE
f16(x37, x38, x39) -> f12(x37, x38, x39) :|: TRUE
f5(x40, x41, x42) -> f6(x40, x41, x42) :|: x43 < 0
f5(x75, x76, x77) -> f6(x75, x76, x77) :|: x78 > 0
f5(x44, x45, x46) -> f7(x44, x45, x46) :|: x47 = 0
f9(x48, x49, x50) -> f8(x48, x49, x50) :|: TRUE
f12(x51, x52, x53) -> f8(x51, x52, x53) :|: TRUE
f4(x54, x55, x56) -> f5(x54, x55, x56) :|: x54 > 0 && x55 > 0 && x56 > 0
f8(x57, x58, x59) -> f4(x57, x58, x59) :|: TRUE
f4(x60, x61, x62) -> f17(x60, x61, x62) :|: x62 <= 0
f4(x79, x80, x81) -> f17(x79, x80, x81) :|: x79 <= 0
f4(x82, x83, x84) -> f17(x82, x83, x84) :|: x83 <= 0
Start term: f1(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_3,1)
   (f2_3,2)
   (f3_3,3)
   (f4_3,4)
   (f6_3,5)
   (f9_3,6)
   (f10_3,7)
   (f13_3,8)
   (f14_3,9)
   (f11_3,10)
   (f15_3,11)
   (f16_3,12)
   (f7_3,13)
   (f12_3,14)
   (f5_3,15)
   (f8_3,16)
   (f17_3,17)

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(4)
Obligation:
START: 1;

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

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

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

FROM: 5;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := -(1 - oldX0);
assume(0 = 0 && oldX3 = oldX0 - 1);
x0 := -(1 - oldX0);
x1 := oldX1;
x2 := oldX2;
TO: 6;

FROM: 7;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := -(1 - oldX1);
assume(0 = 0 && oldX3 = oldX1 - 1);
x0 := oldX0;
x1 := -(1 - oldX1);
x2 := oldX2;
TO: 8;

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

FROM: 10;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := -(1 - oldX2);
assume(0 = 0 && oldX3 = oldX2 - 1);
x0 := oldX0;
x1 := oldX1;
x2 := -(1 - oldX2);
TO: 11;

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

FROM: 13;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := nondet();
assume(oldX3 < 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 7;

FROM: 13;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := nondet();
assume(oldX3 > 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 7;

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

FROM: 9;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 14;

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

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

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

FROM: 15;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := -(0);
assume(oldX3 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 13;

FROM: 6;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 16;

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

FROM: 4;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX0 > 0 && oldX1 > 0 && oldX2 > 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 15;

FROM: 16;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 4;

FROM: 4;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX2 <= 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 17;

FROM: 4;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX0 <= 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 17;

FROM: 4;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX1 <= 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 17;


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(5) T2 (EQUIVALENT)
Initially, performed program simplifications using lexicographic rank functions:
 * Removed transitions 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 30, 31, 34 using the following rank functions:
    - Rank function 1:
      RF for loc. 13: 3*x1
      RF for loc. 14: 3*x1
      RF for loc. 15: -1+3*x1
      RF for loc. 16: 3*x1
      RF for loc. 17: 3*x1
      RF for loc. 18: 3*x1
      RF for loc. 19: 3*x1
      Bound for (chained) transitions 17: 2
      Bound for (chained) transitions 18: 3
      Bound for (chained) transitions 19: 3
    - Rank function 2:
      RF for loc. 13: 3*x2
      RF for loc. 14: 3*x2
      RF for loc. 16: 1+3*x2
      RF for loc. 17: -1+3*x2
      RF for loc. 18: 3*x2
      RF for loc. 19: 3*x2
      Bound for (chained) transitions 20: 2
      Bound for (chained) transitions 23: 3
    - Rank function 3:
      RF for loc. 13: -1+4*x0
      RF for loc. 14: 2+4*x0
      RF for loc. 16: 3+4*x0
      RF for loc. 18: 4*x0
      RF for loc. 19: 1+4*x0
      Bound for (chained) transitions 16: 3
      Bound for (chained) transitions 21: 4
      Bound for (chained) transitions 22: 4
      Bound for (chained) transitions 30: 5
      Bound for (chained) transitions 31: 5
    - Rank function 4:
      RF for loc. 14: -1
      RF for loc. 16: 0
      RF for loc. 19: -2
      Bound for (chained) transitions 24: 0
    - Rank function 5:
      RF for loc. 14: 0
      RF for loc. 19: -1
      Bound for (chained) transitions 25, 34: 0

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(6)
YES