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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) TerminationGraphProcessor [SOUND, 49 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 45 ms]
(6) IntTRS
(7) TerminationGraphProcessor [EQUIVALENT, 0 ms]
(8) IntTRS
(9) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(10) IntTRS
(11) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(12) 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
f5(x9, x10, x11) -> f6(arith, x10, x11) :|: TRUE && arith = 2 * x9 + x10
f6(x24, x25, x26) -> f7(x24, x27, x26) :|: TRUE && x27 = x25 + 1
f4(x15, x16, x17) -> f5(x15, x16, x17) :|: x15 >= 0 && x15 <= x17
f7(x18, x19, x20) -> f4(x18, x19, x20) :|: TRUE
f4(x21, x22, x23) -> f8(x21, x22, x23) :|: x21 < 0
f4(x28, x29, x30) -> f8(x28, x29, x30) :|: x28 > x30
Start term: f1(x, y, z)

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(3) TerminationGraphProcessor (SOUND)
Constructed the termination graph and obtained one non-trivial SCC.

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(4)
Obligation:
Rules:
f4(x15, x16, x17) -> f5(x15, x16, x17) :|: x15 >= 0 && x15 <= x17
f7(x18, x19, x20) -> f4(x18, x19, x20) :|: TRUE
f6(x24, x25, x26) -> f7(x24, x27, x26) :|: TRUE && x27 = x25 + 1
f5(x9, x10, x11) -> f6(arith, x10, x11) :|: TRUE && arith = 2 * x9 + x10

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f6(x24:0, x25:0, x26:0) -> f6(2 * x24:0 + (x25:0 + 1), x25:0 + 1, x26:0) :|: x24:0 > -1 && x26:0 >= x24:0

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(7) TerminationGraphProcessor (EQUIVALENT)
Constructed the termination graph and obtained one non-trivial SCC.

f6(x24:0, x25:0, x26:0) -> f6(2 * x24:0 + (x25:0 + 1), x25:0 + 1, x26:0) :|: x24:0 > -1 && x26:0 >= x24:0
has been transformed into
f6(x24:0, x25:0, x26:0) -> f6(2 * x24:0 + (x25:0 + 1), x25:0 + 1, x26:0) :|: x26:0 = x8 && (x24:0 > -1 && x26:0 >= x24:0) && x6 > -1 && x8 >= x6.


f6(x24:0, x25:0, x26:0) -> f6(2 * x24:0 + (x25:0 + 1), x25:0 + 1, x26:0) :|: x26:0 = x8 && (x24:0 > -1 && x26:0 >= x24:0) && x6 > -1 && x8 >= x6 and 
f6(x24:0, x25:0, x26:0) -> f6(2 * x24:0 + (x25:0 + 1), x25:0 + 1, x26:0) :|: x26:0 = x8 && (x24:0 > -1 && x26:0 >= x24:0) && x6 > -1 && x8 >= x6
have been merged into the new rule
f6(x19, x20, x21) -> f6(2 * (2 * x19 + (x20 + 1)) + (x20 + 1 + 1), x20 + 1 + 1, x21) :|: x21 = x22 && (x19 > -1 && x21 >= x19) && x23 > -1 && x22 >= x23 && (x21 = x24 && (2 * x19 + (x20 + 1) > -1 && x21 >= 2 * x19 + (x20 + 1)) && x25 > -1 && x24 >= x25)


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(8)
Obligation:
Rules:
f6(x26, x27, x28) -> f6(4 * x26 + 3 * x27 + 4, x27 + 2, x28) :|: TRUE && x28 + -1 * x29 = 0 && x26 >= 0 && x28 + -1 * x26 >= 0 && x30 >= 0 && x29 + -1 * x30 >= 0 && x28 + -1 * x31 = 0 && 2 * x26 + x27 >= -1 && x28 + -2 * x26 + -1 * x27 >= 1 && x32 >= 0 && x31 + -1 * x32 >= 0

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(9) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(10)
Obligation:
Rules:
f6(x26:0, x27:0, x28:0) -> f6(4 * x26:0 + 3 * x27:0 + 4, x27:0 + 2, x28:0) :|: x32:0 > -1 && x31:0 + -1 * x32:0 >= 0 && x28:0 + -2 * x26:0 + -1 * x27:0 >= 1 && 2 * x26:0 + x27:0 >= -1 && x28:0 + -1 * x31:0 = 0 && x29:0 + -1 * x30:0 >= 0 && x30:0 > -1 && x28:0 + -1 * x26:0 >= 0 && x28:0 + -1 * x29:0 = 0 && x26:0 > -1

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(11) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f6(x, x1, x2)] = -1 - x1 + x2

The following rules are decreasing:
f6(x26:0, x27:0, x28:0) -> f6(4 * x26:0 + 3 * x27:0 + 4, x27:0 + 2, x28:0) :|: x32:0 > -1 && x31:0 + -1 * x32:0 >= 0 && x28:0 + -2 * x26:0 + -1 * x27:0 >= 1 && 2 * x26:0 + x27:0 >= -1 && x28:0 + -1 * x31:0 = 0 && x29:0 + -1 * x30:0 >= 0 && x30:0 > -1 && x28:0 + -1 * x26:0 >= 0 && x28:0 + -1 * x29:0 = 0 && x26:0 > -1
The following rules are bounded:
f6(x26:0, x27:0, x28:0) -> f6(4 * x26:0 + 3 * x27:0 + 4, x27:0 + 2, x28:0) :|: x32:0 > -1 && x31:0 + -1 * x32:0 >= 0 && x28:0 + -2 * x26:0 + -1 * x27:0 >= 1 && 2 * x26:0 + x27:0 >= -1 && x28:0 + -1 * x31:0 = 0 && x29:0 + -1 * x30:0 >= 0 && x30:0 > -1 && x28:0 + -1 * x26:0 >= 0 && x28:0 + -1 * x29:0 = 0 && x26:0 > -1

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(12)
YES