YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 1737 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(x, y, n) -> f2(x, y, x_1) :|: TRUE
f2(x1, x2, x3) -> f3(x1, x4, x3) :|: TRUE
f3(x5, x6, x7) -> f4(x7, x6, x7) :|: TRUE
f8(x8, x9, x10) -> f9(x8, 1, x10) :|: TRUE
f13(x11, x12, x13) -> f14(x11, arith, x13) :|: TRUE && arith = 2 * x12
f10(x14, x15, x16) -> f13(x14, x15, x16) :|: x15 < x14
f14(x17, x18, x19) -> f10(x17, x18, x19) :|: TRUE
f10(x20, x21, x22) -> f15(x20, x21, x22) :|: x21 >= x20
f9(x23, x24, x25) -> f10(x23, x24, x25) :|: x24 < x23
f9(x26, x27, x28) -> f11(x26, x27, x28) :|: x27 >= x26
f15(x29, x30, x31) -> f12(x29, x30, x31) :|: TRUE
f11(x32, x33, x34) -> f12(x32, x33, x34) :|: TRUE
f12(x59, x60, x61) -> f16(x62, x60, x61) :|: TRUE && x62 = x59 - 1
f5(x38, x39, x40) -> f8(x38, x39, x40) :|: x38 >= 0
f16(x41, x42, x43) -> f5(x41, x42, x43) :|: TRUE
f5(x44, x45, x46) -> f17(x44, x45, x46) :|: x44 < 0
f4(x47, x48, x49) -> f5(x47, x48, x49) :|: x47 >= 0
f4(x50, x51, x52) -> f6(x50, x51, x52) :|: x50 < 0
f17(x53, x54, x55) -> f7(x53, x54, x55) :|: TRUE
f6(x56, x57, x58) -> f7(x56, x57, x58) :|: TRUE
Start term: f1(x, y, n)

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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)
   (f8_3,5)
   (f9_3,6)
   (f13_3,7)
   (f14_3,8)
   (f10_3,9)
   (f15_3,10)
   (f11_3,11)
   (f12_3,12)
   (f16_3,13)
   (f5_3,14)
   (f17_3,15)
   (f6_3,16)
   (f7_3,17)

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(4)
Obligation:
START: 1;

FROM: 1;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := nondet();
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX3;
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;
assume(0 = 0);
x0 := oldX2;
x1 := oldX1;
x2 := oldX2;
TO: 4;

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

FROM: 7;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := nondet();
assume(0 = 0 && oldX3 = 2 * oldX1);
x0 := oldX0;
x1 := oldX3;
x2 := oldX2;
TO: 8;

FROM: 9;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX1 < oldX0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 7;

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

FROM: 9;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX1 >= oldX0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 10;

FROM: 6;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX1 < oldX0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 9;

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

FROM: 10;
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 - oldX0);
assume(0 = 0 && oldX3 = oldX0 - 1);
x0 := -(1 - oldX0);
x1 := oldX1;
x2 := oldX2;
TO: 13;

FROM: 14;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX0 >= 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 5;

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

FROM: 14;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX0 < 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 15;

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(oldX0 < 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 16;

FROM: 15;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 17;

FROM: 16;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(0 = 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 14, 19, 20, 21, 22, 25, 26 using the following rank functions:
    - Rank function 1:
      RF for loc. 10: -3+6*x0
      RF for loc. 11: -4+6*x0
      RF for loc. 12: 6*x0
      RF for loc. 14: -3+6*x0
      RF for loc. 18: 1+6*x0
      Bound for (chained) transitions 19: 0
      Bound for (chained) transitions 20: 0
      Bound for (chained) transitions 21, 22: -4
      Bound for (chained) transitions 25: 1
      Bound for (chained) transitions 26: 1
    - Rank function 2:
      RF for loc. 10: 0
      RF for loc. 11: -1
      RF for loc. 14: 0
      Bound for (chained) transitions 14: 0
Used the following cutpoint-specific lexicographic rank functions:
 * For cutpoint 10, used the following rank functions/bounds (in descending priority order):
    - RF -2*x1+2*oldX2, bound 2

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(6)
YES