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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 1869 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, d1, d2, d1old) -> f2(x_1, d1, d2, d1old) :|: TRUE
f2(x1, x2, x3, x4) -> f3(x1, x5, x3, x4) :|: TRUE
f3(x6, x7, x8, x9) -> f4(x6, x7, x10, x9) :|: TRUE
f5(x11, x12, x13, x14) -> f6(arith, x12, x13, x14) :|: TRUE && arith = x11 - x12
f6(x15, x16, x17, x18) -> f7(x15, x16, x17, x16) :|: TRUE
f7(x39, x40, x41, x42) -> f8(x39, x43, x41, x42) :|: TRUE && x43 = x41 + 1
f8(x44, x45, x46, x47) -> f9(x44, x45, x48, x47) :|: TRUE && x48 = x47 + 1
f4(x27, x28, x29, x30) -> f5(x27, x28, x29, x30) :|: x27 >= 0
f9(x31, x32, x33, x34) -> f4(x31, x32, x33, x34) :|: TRUE
f4(x35, x36, x37, x38) -> f10(x35, x36, x37, x38) :|: x35 < 0
Start term: f1(x, d1, d2, d1old)

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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)
   (f7_4,7)
   (f8_4,8)
   (f9_4,9)
   (f10_4,10)

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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;
oldX4 := nondet();
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX4;
x3 := oldX3;
TO: 4;

FROM: 5;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := -(oldX1 - oldX0);
assume(0 = 0 && oldX4 = oldX0 - oldX1);
x0 := -(oldX1 - oldX0);
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 6;

FROM: 6;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX1;
TO: 7;

FROM: 7;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := -(-(oldX2 + 1));
assume(0 = 0 && oldX4 = oldX2 + 1);
x0 := oldX0;
x1 := -(-(oldX2 + 1));
x2 := oldX2;
x3 := oldX3;
TO: 8;

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

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

FROM: 9;
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 < 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 10;


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