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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 1374 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(m, n, v1, v2) -> f2(m, x_1, v1, v2) :|: TRUE
f2(x, x1, x2, x3) -> f3(x4, x1, x2, x3) :|: TRUE
f4(x5, x6, x7, x8) -> f7(x5, x6, x6, x8) :|: TRUE
f7(x9, x10, x11, x12) -> f8(x9, x10, x11, 0) :|: TRUE
f10(x13, x14, x15, x16) -> f13(x13, x14, x15, arith) :|: TRUE && arith = x16 + 1
f13(x69, x70, x71, x72) -> f14(x69, x70, x73, x72) :|: TRUE && x73 = x71 - 1
f11(x21, x22, x23, x24) -> f15(x21, x22, x23, 0) :|: TRUE
f9(x25, x26, x27, x28) -> f10(x25, x26, x27, x28) :|: x28 < x25
f9(x29, x30, x31, x32) -> f11(x29, x30, x31, x32) :|: x32 >= x29
f14(x33, x34, x35, x36) -> f12(x33, x34, x35, x36) :|: TRUE
f15(x37, x38, x39, x40) -> f12(x37, x38, x39, x40) :|: TRUE
f8(x41, x42, x43, x44) -> f9(x41, x42, x43, x44) :|: x43 > 0
f12(x45, x46, x47, x48) -> f8(x45, x46, x47, x48) :|: TRUE
f8(x49, x50, x51, x52) -> f16(x49, x50, x51, x52) :|: x51 <= 0
f3(x53, x54, x55, x56) -> f4(x53, x54, x55, x56) :|: x54 >= 0 && x53 > 0
f3(x57, x58, x59, x60) -> f5(x57, x58, x59, x60) :|: x58 < 0
f3(x74, x75, x76, x77) -> f5(x74, x75, x76, x77) :|: x74 <= 0
f16(x61, x62, x63, x64) -> f6(x61, x62, x63, x64) :|: TRUE
f5(x65, x66, x67, x68) -> f6(x65, x66, x67, x68) :|: TRUE
Start term: f1(m, n, v1, v2)

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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)
   (f7_4,5)
   (f8_4,6)
   (f10_4,7)
   (f13_4,8)
   (f14_4,9)
   (f11_4,10)
   (f15_4,11)
   (f9_4,12)
   (f12_4,13)
   (f16_4,14)
   (f5_4,15)
   (f6_4,16)

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(4)
Obligation:
START: 1;

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

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

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

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

FROM: 7;
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: 8;

FROM: 8;
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: 9;

FROM: 10;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := 0;
TO: 11;

FROM: 12;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX3 < oldX0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 7;

FROM: 12;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX3 >= oldX0);
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: 13;

FROM: 11;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(0 = 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: 12;

FROM: 13;
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: 14;

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

FROM: 3;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX1 < 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 15;

FROM: 3;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX0 <= 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 15;

FROM: 14;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 16;

FROM: 15;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 16;


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(5) T2 (EQUIVALENT)
Initially, performed program simplifications using lexicographic rank functions:
 * Removed transitions 11, 12, 13, 16, 17, 20 using the following rank functions:
    - Rank function 1:
      RF for loc. 10: 6*x2+3*x3
      RF for loc. 11: 2+6*x2+3*x3
      RF for loc. 13: 1+6*x2+3*x3
      Bound for (chained) transitions 12: 9
    - Rank function 2:
      RF for loc. 10: -2+3*x2
      RF for loc. 11: 3*x2
      RF for loc. 13: -1+3*x2
      Bound for (chained) transitions 11: 1
      Bound for (chained) transitions 13, 20: 0
      Bound for (chained) transitions 16: 2
      Bound for (chained) transitions 17: -1

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(6)
YES