/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination of the given C Problem could be proven:

(0) C Problem
(1) CToIRSProof [EQUIVALENT, 0 ms]
(2) IntTRS
(3) IRS2T2 [EQUIVALENT, 7 ms]
(4) T2IntSys
(5) T2 [EQUIVALENT, 1178 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(c, x, y) -> f2(c, x_1, y) :|: TRUE
f2(x1, x2, x3) -> f3(x1, x2, x4) :|: TRUE
f3(x5, x6, x7) -> f4(0, x6, x7) :|: TRUE
f6(x8, x9, x10) -> f9(x8, arith, x10) :|: TRUE && arith = x9 - 1
f10(x50, x51, x52) -> f13(x50, x51, x53) :|: TRUE && x53 = x52 - 1
f7(x14, x15, x16) -> f10(x14, x15, x16) :|: x16 > 0
f7(x17, x18, x19) -> f11(x17, x18, x19) :|: x19 <= 0
f13(x20, x21, x22) -> f12(x20, x21, x22) :|: TRUE
f11(x23, x24, x25) -> f12(x23, x24, x25) :|: TRUE
f5(x26, x27, x28) -> f6(x26, x27, x28) :|: x27 > 0
f5(x29, x30, x31) -> f7(x29, x30, x31) :|: x30 <= 0
f9(x32, x33, x34) -> f8(x32, x33, x34) :|: TRUE
f12(x35, x36, x37) -> f8(x35, x36, x37) :|: TRUE
f8(x54, x55, x56) -> f14(x57, x55, x56) :|: TRUE && x57 = x54 + 1
f4(x41, x42, x43) -> f5(x41, x42, x43) :|: x42 > 0
f4(x58, x59, x60) -> f5(x58, x59, x60) :|: x60 > 0
f14(x44, x45, x46) -> f4(x44, x45, x46) :|: TRUE
f4(x47, x48, x49) -> f15(x47, x48, x49) :|: x48 <= 0 && x49 <= 0
Start term: f1(c, 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)
   (f6_3,5)
   (f9_3,6)
   (f10_3,7)
   (f13_3,8)
   (f7_3,9)
   (f11_3,10)
   (f12_3,11)
   (f5_3,12)
   (f8_3,13)
   (f14_3,14)
   (f15_3,15)

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(4)
Obligation:
START: 1;

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

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

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

FROM: 5;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := -(1 - oldX1);
assume(0 = 0 && oldX3 = oldX1 - 1);
x0 := oldX0;
x1 := -(1 - oldX1);
x2 := oldX2;
TO: 6;

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

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

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

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

FROM: 12;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX1 > 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 5;

FROM: 12;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX1 <= 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 9;

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

FROM: 11;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 13;

FROM: 13;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := -(-(oldX0 + 1));
assume(0 = 0 && oldX3 = oldX0 + 1);
x0 := -(-(oldX0 + 1));
x1 := oldX1;
x2 := oldX2;
TO: 14;

FROM: 4;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX1 > 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 12;

FROM: 4;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
assume(oldX2 > 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 12;

FROM: 14;
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(oldX1 <= 0 && oldX2 <= 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
TO: 15;


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(5) T2 (EQUIVALENT)
Initially, performed program simplifications using lexicographic rank functions:
 * Removed transitions 11, 13 using the following rank functions:
    - Rank function 1:
      RF for loc. 11: x2
      RF for loc. 12: x2
      RF for loc. 13: x2
      RF for loc. 14: x2
      RF for loc. 15: x2
      Bound for (chained) transitions 11: 1
    - Rank function 2:
      RF for loc. 11: 2*x1
      RF for loc. 12: 2*x1
      RF for loc. 13: 2*x1
      RF for loc. 14: 2*x1
      RF for loc. 15: 2*x1
      Bound for (chained) transitions 13: 2

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(6)
YES