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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 5637 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, z) -> f2(x_1, y, z) :|: TRUE
f2(x1, x2, x3) -> f3(x1, x4, x3) :|: TRUE
f3(x5, x6, x7) -> f4(x5, x6, x8) :|: TRUE
f6(x9, x10, x11) -> f9(arith, x10, x11) :|: TRUE && arith = x9 + x10
f7(x44, x45, x46) -> f10(x47, x45, x46) :|: TRUE && x47 = x44 + x46
f5(x15, x16, x17) -> f6(x15, x16, x17) :|: x18 < 0
f5(x48, x49, x50) -> f6(x48, x49, x50) :|: x51 > 0
f5(x19, x20, x21) -> f7(x19, x20, x21) :|: x22 = 0
f9(x23, x24, x25) -> f8(x23, x24, x25) :|: TRUE
f10(x26, x27, x28) -> f8(x26, x27, x28) :|: TRUE
f8(x52, x53, x54) -> f11(x52, x55, x54) :|: TRUE && x55 = x53 + x54
f11(x56, x57, x58) -> f12(x56, x57, x59) :|: TRUE && x59 = x58 - 1
f4(x35, x36, x37) -> f5(x35, x36, x37) :|: x35 >= 0
f12(x38, x39, x40) -> f4(x38, x39, x40) :|: TRUE
f4(x41, x42, x43) -> f13(x41, x42, x43) :|: x41 < 0
Start term: f1(x, y, z)

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

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(4)
Obligation:
START: 1;

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

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

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

FROM: 9;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := nondet();
assume(oldX3 < 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 5;

FROM: 9;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := nondet();
assume(oldX3 > 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 5;

FROM: 9;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := -(0);
assume(oldX3 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 7;

FROM: 6;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 10;

FROM: 8;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 10;

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

FROM: 11;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := -(1 - oldX2);
assume(0 = 0 && oldX3 = oldX2 - 1);
x0 := oldX0;
x1 := oldX1;
x2 := -(1 - oldX2);
TO: 12;

FROM: 4;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX0 >= 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 9;

FROM: 12;
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: 13;


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(5) T2 (EQUIVALENT)
No proof given by T2
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(6)
YES