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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 3274 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(r, da, db, temp) -> f2(x_1, da, db, temp) :|: TRUE
f3(x, x1, x2, x3) -> f6(x, arith, x2, x3) :|: TRUE && arith = 2 * x
f6(x70, x71, x72, x73) -> f7(x70, x71, x74, x73) :|: TRUE && x74 = 2 * x70
f9(x75, x76, x77, x78) -> f12(x75, x79, x77, x78) :|: TRUE && x79 = x76 - 1
f10(x12, x13, x14, x15) -> f13(x12, x13, x14, x13) :|: TRUE
f13(x80, x81, x82, x83) -> f14(x80, x84, x82, x83) :|: TRUE && x84 = x82 - 1
f14(x20, x21, x22, x23) -> f15(x20, x21, x21, x23) :|: TRUE
f8(x24, x25, x26, x27) -> f9(x24, x25, x26, x27) :|: x28 < 0
f8(x85, x86, x87, x88) -> f9(x85, x86, x87, x88) :|: x89 > 0
f8(x29, x30, x31, x32) -> f10(x29, x30, x31, x32) :|: x33 = 0
f12(x34, x35, x36, x37) -> f11(x34, x35, x36, x37) :|: TRUE
f15(x38, x39, x40, x41) -> f11(x38, x39, x40, x41) :|: TRUE
f7(x42, x43, x44, x45) -> f8(x42, x43, x44, x45) :|: x43 >= x42
f11(x46, x47, x48, x49) -> f7(x46, x47, x48, x49) :|: TRUE
f7(x50, x51, x52, x53) -> f16(x50, x51, x52, x53) :|: x51 < x50
f2(x54, x55, x56, x57) -> f3(x54, x55, x56, x57) :|: x54 >= 0
f2(x58, x59, x60, x61) -> f4(x58, x59, x60, x61) :|: x58 < 0
f16(x62, x63, x64, x65) -> f5(x62, x63, x64, x65) :|: TRUE
f4(x66, x67, x68, x69) -> f5(x66, x67, x68, x69) :|: TRUE
Start term: f1(r, da, db, temp)

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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)
   (f6_4,4)
   (f7_4,5)
   (f9_4,6)
   (f12_4,7)
   (f10_4,8)
   (f13_4,9)
   (f14_4,10)
   (f15_4,11)
   (f8_4,12)
   (f11_4,13)
   (f16_4,14)
   (f4_4,15)
   (f5_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 := oldX4;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 2;

FROM: 3;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := nondet();
assume(0 = 0 && oldX4 = 2 * oldX0);
x0 := oldX0;
x1 := oldX4;
x2 := oldX2;
x3 := oldX3;
TO: 4;

FROM: 4;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := nondet();
assume(0 = 0 && oldX4 = 2 * oldX0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX4;
x3 := oldX3;
TO: 5;

FROM: 6;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := -(1 - oldX1);
assume(0 = 0 && oldX4 = oldX1 - 1);
x0 := oldX0;
x1 := -(1 - oldX1);
x2 := oldX2;
x3 := oldX3;
TO: 7;

FROM: 8;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(0 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX1;
TO: 9;

FROM: 9;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := -(1 - oldX2);
assume(0 = 0 && oldX4 = oldX2 - 1);
x0 := oldX0;
x1 := -(1 - oldX2);
x2 := oldX2;
x3 := oldX3;
TO: 10;

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

FROM: 12;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := nondet();
assume(oldX4 < 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 6;

FROM: 12;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := nondet();
assume(oldX4 > 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 6;

FROM: 12;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
oldX4 := -(0);
assume(oldX4 = 0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 8;

FROM: 7;
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: 5;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX1 >= oldX0);
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: 5;

FROM: 5;
oldX0 := x0;
oldX1 := x1;
oldX2 := x2;
oldX3 := x3;
assume(oldX1 < oldX0);
x0 := oldX0;
x1 := oldX1;
x2 := oldX2;
x3 := oldX3;
TO: 14;

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

FROM: 2;
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)
Used the following cutpoint-specific lexicographic rank functions:
 * For cutpoint 13, used the following rank functions/bounds (in descending priority order):
    - RF x1, bound 0

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(6)
YES