/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) TerminationGraphProcessor [SOUND, 38 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 30 ms]
(6) IntTRS
(7) TerminationGraphProcessor [EQUIVALENT, 8 ms]
(8) IntTRS
(9) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(10) IntTRS
(11) RankingReductionPairProof [EQUIVALENT, 0 ms]
(12) 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(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 + x16 >= 0 && x15 <= x17
f7(x18, x19, x20) -> f4(x18, x19, x20) :|: TRUE
f4(x21, x22, x23) -> f8(x21, x22, x23) :|: x21 + x22 < 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 + x16 >= 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 + (x25:0 + 1) >= 0 && 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 + (x25:0 + 1) >= 0 && 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 && (x25:0 = x7 + 1 && (x24:0 = 2 * x6 + (x7 + 1) && (x24:0 + (x25:0 + 1) >= 0 && x26:0 >= x24:0))) && x6 + (x7 + 1) >= 0 && x8 >= x6.


f6(x24:0, x25:0, x26:0) -> f6(2 * x24:0 + (x25:0 + 1), x25:0 + 1, x26:0) :|: x26:0 = x8 && (x25:0 = x7 + 1 && (x24:0 = 2 * x6 + (x7 + 1) && (x24:0 + (x25:0 + 1) >= 0 && x26:0 >= x24:0))) && x6 + (x7 + 1) >= 0 && 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 && (x25:0 = x7 + 1 && (x24:0 = 2 * x6 + (x7 + 1) && (x24:0 + (x25:0 + 1) >= 0 && x26:0 >= x24:0))) && x6 + (x7 + 1) >= 0 && x8 >= x6
have been merged into the new rule
f6(x21, x22, x23) -> f6(2 * (2 * x21 + (x22 + 1)) + (x22 + 1 + 1), x22 + 1 + 1, x23) :|: x23 = x24 && (x22 = x25 + 1 && (x21 = 2 * x26 + (x25 + 1) && (x21 + (x22 + 1) >= 0 && x23 >= x21))) && x26 + (x25 + 1) >= 0 && x24 >= x26 && (x23 = x27 && (x22 + 1 = x28 + 1 && (2 * x21 + (x22 + 1) = 2 * x29 + (x28 + 1) && (2 * x21 + (x22 + 1) + (x22 + 1 + 1) >= 0 && x23 >= 2 * x21 + (x22 + 1)))) && x29 + (x28 + 1) >= 0 && x27 >= x29)


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(8)
Obligation:
Rules:
f6(x30, x31, x32) -> f6(4 * x30 + 3 * x31 + 4, x31 + 2, x32) :|: TRUE && x32 + -1 * x33 = 0 && x31 + -1 * x34 = 1 && x30 + -2 * x35 + -1 * x34 = 1 && x30 + x31 >= -1 && x32 + -1 * x30 >= 0 && x35 + x34 >= -1 && x33 + -1 * x35 >= 0 && x32 + -1 * x36 = 0 && x31 + -1 * x37 = 0 && 2 * x30 + x31 + -2 * x38 + -1 * x37 = 0 && x32 + -2 * x30 + -1 * x31 >= 1 && x38 + x37 >= -1 && x36 + -1 * x38 >= 0

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(9) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(10)
Obligation:
Rules:
f6(x30:0, x31:0, x32:0) -> f6(4 * x30:0 + 3 * x31:0 + 4, x31:0 + 2, x32:0) :|: x38:0 + x37:0 >= -1 && x36:0 + -1 * x38:0 >= 0 && x32:0 + -2 * x30:0 + -1 * x31:0 >= 1 && 2 * x30:0 + x31:0 + -2 * x38:0 + -1 * x37:0 = 0 && x31:0 + -1 * x37:0 = 0 && x32:0 + -1 * x36:0 = 0 && x33:0 + -1 * x35:0 >= 0 && x35:0 + x34:0 >= -1 && x32:0 + -1 * x30:0 >= 0 && x30:0 + x31:0 >= -1 && x30:0 + -2 * x35:0 + -1 * x34:0 = 1 && x32:0 + -1 * x33:0 = 0 && x31:0 + -1 * x34:0 = 1

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(11) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f6 ] = 1/4*f6_3 + -1/4*f6_1

The following rules are decreasing:
f6(x30:0, x31:0, x32:0) -> f6(4 * x30:0 + 3 * x31:0 + 4, x31:0 + 2, x32:0) :|: x38:0 + x37:0 >= -1 && x36:0 + -1 * x38:0 >= 0 && x32:0 + -2 * x30:0 + -1 * x31:0 >= 1 && 2 * x30:0 + x31:0 + -2 * x38:0 + -1 * x37:0 = 0 && x31:0 + -1 * x37:0 = 0 && x32:0 + -1 * x36:0 = 0 && x33:0 + -1 * x35:0 >= 0 && x35:0 + x34:0 >= -1 && x32:0 + -1 * x30:0 >= 0 && x30:0 + x31:0 >= -1 && x30:0 + -2 * x35:0 + -1 * x34:0 = 1 && x32:0 + -1 * x33:0 = 0 && x31:0 + -1 * x34:0 = 1

The following rules are bounded:
f6(x30:0, x31:0, x32:0) -> f6(4 * x30:0 + 3 * x31:0 + 4, x31:0 + 2, x32:0) :|: x38:0 + x37:0 >= -1 && x36:0 + -1 * x38:0 >= 0 && x32:0 + -2 * x30:0 + -1 * x31:0 >= 1 && 2 * x30:0 + x31:0 + -2 * x38:0 + -1 * x37:0 = 0 && x31:0 + -1 * x37:0 = 0 && x32:0 + -1 * x36:0 = 0 && x33:0 + -1 * x35:0 >= 0 && x35:0 + x34:0 >= -1 && x32:0 + -1 * x30:0 >= 0 && x30:0 + x31:0 >= -1 && x30:0 + -2 * x35:0 + -1 * x34:0 = 1 && x32:0 + -1 * x33:0 = 0 && x31:0 + -1 * x34:0 = 1


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(12)
YES