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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 1769 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, ytmp, res) -> f2(x_1, y, ytmp, res) :|: TRUE
f2(x1, x2, x3, x4) -> f3(x1, x5, x3, x4) :|: TRUE
f3(x6, x7, x8, x9) -> f4(x6, x7, x8, 0) :|: TRUE
f5(x10, x11, x12, x13) -> f6(x10, x11, x11, x13) :|: TRUE
f8(x14, x15, x16, x17) -> f11(x14, x15, arith, x17) :|: TRUE && arith = x16 - 1
f11(x74, x75, x76, x77) -> f12(x78, x75, x76, x77) :|: TRUE && x78 = x74 - 1
f9(x79, x80, x81, x82) -> f13(x79, x80, x83, x82) :|: TRUE && x83 = x81 + 1
f13(x84, x85, x86, x87) -> f14(x88, x85, x86, x87) :|: TRUE && x88 = x84 + 1
f7(x30, x31, x32, x33) -> f8(x30, x31, x32, x33) :|: x32 > 0
f7(x34, x35, x36, x37) -> f9(x34, x35, x36, x37) :|: x36 <= 0
f12(x38, x39, x40, x41) -> f10(x38, x39, x40, x41) :|: TRUE
f14(x42, x43, x44, x45) -> f10(x42, x43, x44, x45) :|: TRUE
f6(x46, x47, x48, x49) -> f7(x46, x47, x48, x49) :|: x48 < 0
f6(x89, x90, x91, x92) -> f7(x89, x90, x91, x92) :|: x91 > 0
f10(x50, x51, x52, x53) -> f6(x50, x51, x52, x53) :|: TRUE
f6(x54, x55, x56, x57) -> f15(x54, x55, x56, x57) :|: x56 = 0
f15(x93, x94, x95, x96) -> f16(x93, x94, x95, x97) :|: TRUE && x97 = x96 + 1
f4(x62, x63, x64, x65) -> f5(x62, x63, x64, x65) :|: x62 >= x63 && x63 > 0
f16(x66, x67, x68, x69) -> f4(x66, x67, x68, x69) :|: TRUE
f4(x70, x71, x72, x73) -> f17(x70, x71, x72, x73) :|: x70 < x71
f4(x98, x99, x100, x101) -> f17(x98, x99, x100, x101) :|: x99 <= 0
Start term: f1(x, y, ytmp, res)

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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)
   (f6_4,6)
   (f8_4,7)
   (f11_4,8)
   (f12_4,9)
   (f9_4,10)
   (f13_4,11)
   (f14_4,12)
   (f7_4,13)
   (f10_4,14)
   (f15_4,15)
   (f16_4,16)
   (f17_4,17)

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(4)
Obligation:
START: 1;

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

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

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

FROM: 5;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX1;
x3 := oldX3;
TO: 6;

FROM: 7;
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: 8;

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

FROM: 10;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := -(-(oldX2 + 1));
assume(0 = 0 && oldX4 = oldX2 + 1);
x0 := oldX0;
x1 := oldX1;
x2 := -(-(oldX2 + 1));
x3 := oldX3;
TO: 11;

FROM: 11;
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: 12;

FROM: 13;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX2 > 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 7;

FROM: 13;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX2 <= 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 10;

FROM: 9;
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: 6;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX2 < 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 13;

FROM: 6;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX2 > 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 13;

FROM: 14;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 6;

FROM: 6;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX2 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 15;

FROM: 15;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := -(-(oldX3 + 1));
assume(0 = 0 && oldX4 = oldX3 + 1);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := -(-(oldX3 + 1));
TO: 16;

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

FROM: 16;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 4;

FROM: 4;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX0 < oldX1);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 17;

FROM: 4;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX1 <= 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 17;


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(5) T2 (EQUIVALENT)
Initially, performed program simplifications using lexicographic rank functions:
 * Removed transitions 16, 25, 29, 30 using the following rank functions:
    - Rank function 1:
      RF for loc. 10: 1+2*x0-2*x2
      RF for loc. 11: 1+2*x0-2*x2
      RF for loc. 12: 1+2*x0-2*x2
      RF for loc. 13: 1+2*x0-2*x2
      RF for loc. 17: 2*x0
      Bound for (chained) transitions 29: 2
      Bound for (chained) transitions 30: 2
    - Rank function 2:
      RF for loc. 10: 0
      RF for loc. 11: 0
      RF for loc. 12: 0
      RF for loc. 13: 0
      RF for loc. 17: -1
      Bound for (chained) transitions 16, 25: 0
Used the following cutpoint-specific lexicographic rank functions:
 * For cutpoint 12, used the following rank functions/bounds (in descending priority order):
    - RF x2, bound 1

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(6)
YES