YES
proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 3 ms]
(4) T2IntSys
(5) T2 [EQUIVALENT, 1228 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, m) -> f2(x, 0, m) :|: TRUE
f2(x1, x2, x3) -> f3(x1, x2, x4) :|: TRUE
f3(x5, x6, x7) -> f4(x7, x6, x7) :|: TRUE
f9(x8, x9, x10) -> f10(x8, arith, x10) :|: TRUE && arith = x9 + 1
f6(x11, x12, x13) -> f9(x11, x12, x13) :|: x12 <= x13 && x14 < 0
f6(x51, x52, x53) -> f9(x51, x52, x53) :|: x52 <= x53 && x54 > 0
f10(x15, x16, x17) -> f6(x15, x16, x17) :|: TRUE
f6(x18, x19, x20) -> f11(x18, x19, x20) :|: x19 > x20
f6(x55, x56, x57) -> f11(x55, x56, x57) :|: x58 = 0
f11(x59, x60, x61) -> f12(x62, x60, x61) :|: TRUE && x62 = x59 - 1
f5(x25, x26, x27) -> f6(x25, x26, x27) :|: x28 < 0
f5(x63, x64, x65) -> f6(x63, x64, x65) :|: x66 > 0
f5(x29, x30, x31) -> f7(x29, x30, x31) :|: x32 = 0
f12(x33, x34, x35) -> f8(x33, x34, x35) :|: TRUE
f7(x36, x37, x38) -> f8(x36, x37, x38) :|: TRUE
f8(x67, x68, x69) -> f13(x67, x70, x69) :|: TRUE && x70 = x68 - 1
f4(x42, x43, x44) -> f5(x42, x43, x44) :|: x42 >= 0 && x43 >= 0
f13(x45, x46, x47) -> f4(x45, x46, x47) :|: TRUE
f4(x48, x49, x50) -> f14(x48, x49, x50) :|: x48 < 0
f4(x71, x72, x73) -> f14(x71, x72, x73) :|: x72 < 0
Start term: f1(x, y, m)

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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)
   (f9_3,5)
   (f10_3,6)
   (f6_3,7)
   (f11_3,8)
   (f12_3,9)
   (f5_3,10)
   (f7_3,11)
   (f8_3,12)
   (f13_3,13)
   (f14_3,14)

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(4)
Obligation:
START: 1;

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

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

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

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

FROM: 7;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := nondet();
assume(oldX1 <= oldX2 && oldX3 < 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 5;

FROM: 7;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := nondet();
assume(oldX1 <= oldX2 && oldX3 > 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 5;

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

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

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

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

FROM: 10;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := nondet();
assume(oldX3 < 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 7;

FROM: 10;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := nondet();
assume(oldX3 > 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 7;

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

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

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

FROM: 12;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := -(1 - oldX1);
assume(0 = 0 && oldX3 = oldX1 - 1);
x0 := oldX0;
x1 := -(1 - oldX1);
x2 := oldX2;
TO: 13;

FROM: 4;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX0 >= 0 && oldX1 >= 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 10;

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

FROM: 4;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX1 < 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 14;


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(5) T2 (EQUIVALENT)
Initially, performed program simplifications using lexicographic rank functions:
 * Removed transitions 11, 12, 15, 16, 17, 18, 30, 31, 32, 33, 34, 35, 39, 40 using the following rank functions:
    - Rank function 1:
      RF for loc. 12: -1+3*x0
      RF for loc. 13: -1+3*x0
      RF for loc. 14: -2+3*x0
      RF for loc. 15: 3*x0
      RF for loc. 16: 3*x0
      RF for loc. 17: -1+3*x0
      RF for loc. 21: 3*x0
      Bound for (chained) transitions 17: -1
      Bound for (chained) transitions 18: -1
      Bound for (chained) transitions 30: -2
      Bound for (chained) transitions 31: 0
      Bound for (chained) transitions 32: 0
    - Rank function 2:
      RF for loc. 12: -1-3*x1+3*x2
      RF for loc. 13: 1-3*x1+3*x2
      RF for loc. 15: -2+3*x1
      RF for loc. 16: -1+3*x1
      RF for loc. 17: -3*x1+3*x2
      RF for loc. 21: 3*x1
      Bound for (chained) transitions 15: 0
      Bound for (chained) transitions 16: 0
      Bound for (chained) transitions 33: -1
      Bound for (chained) transitions 34, 35: -2
      Bound for (chained) transitions 39: 0
      Bound for (chained) transitions 40: 0
    - Rank function 3:
      RF for loc. 12: 0
      RF for loc. 13: -1
      RF for loc. 17: -2
      Bound for (chained) transitions 11: 0
      Bound for (chained) transitions 12: -1

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(6)
YES