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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 0 ms]
(4) T2IntSys
(5) T2 [EQUIVALENT, 1667 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(a, b) -> f2(x_1, b) :|: TRUE
f2(x, x1) -> f3(x, x2) :|: TRUE
f6(x3, x4) -> f9(x3, arith) :|: TRUE && arith = x4 + 7
f7(x43, x44) -> f10(x43, x45) :|: TRUE && x45 = x44 + 2
f5(x7, x8) -> f6(x7, x8) :|: x8 > 5
f5(x9, x10) -> f7(x9, x10) :|: x10 <= 5
f9(x11, x12) -> f8(x11, x12) :|: TRUE
f10(x13, x14) -> f8(x13, x14) :|: TRUE
f11(x46, x47) -> f14(x48, x47) :|: TRUE && x48 = x46 + 10
f12(x49, x50) -> f15(x51, x50) :|: TRUE && x51 = x49 + 1
f8(x19, x20) -> f11(x19, x20) :|: x20 >= 10 && x20 <= 12
f8(x21, x22) -> f12(x21, x22) :|: x22 < 10
f8(x52, x53) -> f12(x52, x53) :|: x53 > 12
f14(x23, x24) -> f13(x23, x24) :|: TRUE
f15(x25, x26) -> f13(x25, x26) :|: TRUE
f4(x27, x28) -> f5(x27, x28) :|: x28 < x27
f13(x29, x30) -> f4(x29, x30) :|: TRUE
f4(x31, x32) -> f16(x31, x32) :|: x32 >= x31
f16(x54, x55) -> f17(x56, x55) :|: TRUE && x56 = x54 + 2
f17(x57, x58) -> f18(x57, x59) :|: TRUE && x59 = x58 - 10
f3(x37, x38) -> f4(x37, x38) :|: x37 < 30
f18(x39, x40) -> f3(x39, x40) :|: TRUE
f3(x41, x42) -> f19(x41, x42) :|: x41 >= 30
Start term: f1(a, b)

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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_2,1)
   (f2_2,2)
   (f3_2,3)
   (f6_2,4)
   (f9_2,5)
   (f7_2,6)
   (f10_2,7)
   (f5_2,8)
   (f8_2,9)
   (f11_2,10)
   (f14_2,11)
   (f12_2,12)
   (f15_2,13)
   (f13_2,14)
   (f4_2,15)
   (f16_2,16)
   (f17_2,17)
   (f18_2,18)
   (f19_2,19)

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(4)
Obligation:
START: 1;

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

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

FROM: 4;
oldX0 := x0;
oldX1 := x1;
oldX2 := -(-(oldX1 + 7));
assume(0 = 0 && oldX2 = oldX1 + 7);
x0 := oldX0;
x1 := -(-(oldX1 + 7));
TO: 5;

FROM: 6;
oldX0 := x0;
oldX1 := x1;
oldX2 := -(-(oldX1 + 2));
assume(0 = 0 && oldX2 = oldX1 + 2);
x0 := oldX0;
x1 := -(-(oldX1 + 2));
TO: 7;

FROM: 8;
oldX0 := x0;
oldX1 := x1;
assume(oldX1 > 5);
x0 := oldX0;
x1 := oldX1;
TO: 4;

FROM: 8;
oldX0 := x0;
oldX1 := x1;
assume(oldX1 <= 5);
x0 := oldX0;
x1 := oldX1;
TO: 6;

FROM: 5;
oldX0 := x0;
oldX1 := x1;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
TO: 9;

FROM: 7;
oldX0 := x0;
oldX1 := x1;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
TO: 9;

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

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

FROM: 9;
oldX0 := x0;
oldX1 := x1;
assume(oldX1 >= 10 && oldX1 <= 12);
x0 := oldX0;
x1 := oldX1;
TO: 10;

FROM: 9;
oldX0 := x0;
oldX1 := x1;
assume(oldX1 < 10);
x0 := oldX0;
x1 := oldX1;
TO: 12;

FROM: 9;
oldX0 := x0;
oldX1 := x1;
assume(oldX1 > 12);
x0 := oldX0;
x1 := oldX1;
TO: 12;

FROM: 11;
oldX0 := x0;
oldX1 := x1;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
TO: 14;

FROM: 13;
oldX0 := x0;
oldX1 := x1;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
TO: 14;

FROM: 15;
oldX0 := x0;
oldX1 := x1;
assume(oldX1 < oldX0);
x0 := oldX0;
x1 := oldX1;
TO: 8;

FROM: 14;
oldX0 := x0;
oldX1 := x1;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
TO: 15;

FROM: 15;
oldX0 := x0;
oldX1 := x1;
assume(oldX1 >= oldX0);
x0 := oldX0;
x1 := oldX1;
TO: 16;

FROM: 16;
oldX0 := x0;
oldX1 := x1;
oldX2 := -(-(oldX0 + 2));
assume(0 = 0 && oldX2 = oldX0 + 2);
x0 := -(-(oldX0 + 2));
x1 := oldX1;
TO: 17;

FROM: 17;
oldX0 := x0;
oldX1 := x1;
oldX2 := -(10 - oldX1);
assume(0 = 0 && oldX2 = oldX1 - 10);
x0 := oldX0;
x1 := -(10 - oldX1);
TO: 18;

FROM: 3;
oldX0 := x0;
oldX1 := x1;
assume(oldX0 < 30);
x0 := oldX0;
x1 := oldX1;
TO: 15;

FROM: 18;
oldX0 := x0;
oldX1 := x1;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
TO: 3;

FROM: 3;
oldX0 := x0;
oldX1 := x1;
assume(oldX0 >= 30);
x0 := oldX0;
x1 := oldX1;
TO: 19;


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(5) T2 (EQUIVALENT)
Initially, performed program simplifications using lexicographic rank functions:
 * Removed transitions 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 27, 28, 31, 32 using the following rank functions:
    - Rank function 1:
      RF for loc. 12: -6*x0
      RF for loc. 13: -1-6*x0
      RF for loc. 14: -2-6*x0
      RF for loc. 15: 3-6*x0
      RF for loc. 16: 2-6*x0
      RF for loc. 17: 1-6*x0
      RF for loc. 21: 3-6*x0
      Bound for (chained) transitions 31: -171
      Bound for (chained) transitions 32: -171
    - Rank function 2:
      RF for loc. 12: -3-6*x1
      RF for loc. 13: 8-6*x1
      RF for loc. 14: 1-6*x1
      RF for loc. 15: -6*x1
      RF for loc. 16: -1-6*x1
      RF for loc. 17: -2-6*x1
      RF for loc. 21: -61-6*oldX2
      Bound for (chained) transitions 15: -33
      Bound for (chained) transitions 18: -46
    - Rank function 3:
      RF for loc. 12: -21-5*x1
      RF for loc. 13: 7-5*x1
      RF for loc. 14: 7-5*x1
      RF for loc. 15: -5*x1
      RF for loc. 16: -7-5*x1
      RF for loc. 17: -14-5*x1
      RF for loc. 21: -58-5*x1
      Bound for (chained) transitions 17: -53
    - Rank function 4:
      RF for loc. 12: -2+2*x0-2*x1
      RF for loc. 13: 11+2*x0-2*x1
      RF for loc. 14: 4+2*x0-2*x1
      RF for loc. 15: 1+2*x0-2*x1
      RF for loc. 16: 2*x0-2*x1
      RF for loc. 17: -1+2*x0-2*x1
      RF for loc. 21: -25+2*oldX0-2*oldX1
      Bound for (chained) transitions 23: 1
      Bound for (chained) transitions 24: 1
    - Rank function 5:
      RF for loc. 12: 14*x1
      RF for loc. 13: 6*x1
      RF for loc. 14: 0
      RF for loc. 15: -1
      RF for loc. 16: -2
      RF for loc. 17: -3
      RF for loc. 21: -3
      Bound for (chained) transitions 14: 84
      Bound for (chained) transitions 16: 0
      Bound for (chained) transitions 19: 78
      Bound for (chained) transitions 20: -2
      Bound for (chained) transitions 22, 28: -2
      Bound for (chained) transitions 27: -1

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(6)
YES