/export/starexec/sandbox/solver/bin/starexec_run_c /export/starexec/sandbox/benchmark/theBenchmark.c /export/starexec/sandbox/output/output_files


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YES
proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 8 ms]
(4) T2IntSys
(5) T2 [EQUIVALENT, 1186 ms]
(6) YES


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(0)
Obligation:
c file /export/starexec/sandbox/benchmark/theBenchmark.c
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(1) CToIRSProof (EQUIVALENT)
Parsed C Integer Program as IRS.
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(2)
Obligation:
Rules:
f1(i, x, y) -> f2(0, x, y) :|: TRUE
f2(x1, x2, x3) -> f3(x1, x4, x3) :|: TRUE
f3(x5, x6, x7) -> f4(x5, x6, x8) :|: TRUE
f8(x9, x10, x11) -> f9(arith, x10, x11) :|: TRUE && arith = x9 + 1
f9(x36, x37, x38) -> f10(x36, x39, x38) :|: TRUE && x39 = x37 - 1 - (x38 - 1)
f5(x15, x16, x17) -> f8(x15, x16, x17) :|: x16 > 0 && x17 > 0
f10(x18, x19, x20) -> f5(x18, x19, x20) :|: TRUE
f5(x21, x22, x23) -> f11(x21, x22, x23) :|: x22 <= 0
f5(x40, x41, x42) -> f11(x40, x41, x42) :|: x42 <= 0
f4(x24, x25, x26) -> f5(x24, x25, x26) :|: x25 < 0
f4(x43, x44, x45) -> f5(x43, x44, x45) :|: x44 > 0
f4(x27, x28, x29) -> f6(x27, x28, x29) :|: x28 = 0
f11(x30, x31, x32) -> f7(x30, x31, x32) :|: TRUE
f6(x33, x34, x35) -> f7(x33, x34, x35) :|: TRUE
Start term: f1(i, x, y)

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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)
   (f10_3,7)
   (f5_3,8)
   (f11_3,9)
   (f6_3,10)
   (f7_3,11)

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(4)
Obligation:
START: 1;

FROM: 1;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(0 = 0);
x0 := 0;
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 + 1));
assume(0 = 0 && oldX3 = oldX0 + 1);
x0 := -(-(oldX0 + 1));
x1 := oldX1;
x2 := oldX2;
TO: 6;

FROM: 6;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := -(oldX2 - 1 - (oldX1 - 1));
assume(0 = 0 && oldX3 = oldX1 - 1 - (oldX2 - 1));
x0 := oldX0;
x1 := -(oldX2 - 1 - (oldX1 - 1));
x2 := oldX2;
TO: 7;

FROM: 8;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX1 > 0 && oldX2 > 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 5;

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

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

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

FROM: 4;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX1 < 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 8;

FROM: 4;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX1 > 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 8;

FROM: 4;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX1 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 10;

FROM: 9;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(0 = 0);
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: 11;


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(5) T2 (EQUIVALENT)
Initially, performed program simplifications using lexicographic rank functions:
 * Removed transitions 9, 13, 14 using the following rank functions:
    - Rank function 1:
      RF for loc. 8: 1+2*x1
      RF for loc. 9: 2*x1
      Bound for (chained) transitions 13: 2
      Bound for (chained) transitions 14: 2
    - Rank function 2:
      RF for loc. 8: 1
      RF for loc. 9: 0
      Bound for (chained) transitions 9: 1

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(6)
YES