/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 46 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IntTRS
(7) TerminationGraphProcessor [EQUIVALENT, 4 ms]
(8) IntTRS
(9) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(10) IntTRS
(11) RankingReductionPairProof [EQUIVALENT, 11 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, n) -> f2(x_1, y, n) :|: 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 = 0 - x9 + x10 - 5
f6(x24, x25, x26) -> f7(x24, x27, x26) :|: TRUE && x27 = 2 * x25
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, n)

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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 = 2 * x25
f5(x9, x10, x11) -> f6(arith, x10, x11) :|: TRUE && arith = 0 - x9 + x10 - 5

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f6(x24:0, x25:0, x26:0) -> f6(0 - x24:0 + 2 * x25:0 - 5, 2 * x25:0, x26:0) :|: x24:0 > 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(0 - x24:0 + 2 * x25:0 - 5, 2 * x25:0, x26:0) :|: x24:0 > 0 && x26:0 > x24:0
has been transformed into
f6(x24:0, x25:0, x26:0) -> f6(0 - x24:0 + 2 * x25:0 - 5, 2 * x25:0, x26:0) :|: x26:0 = x8 && (x24:0 > 0 && x26:0 > x24:0) && x6 > 0 && x8 > x6.


f6(x24:0, x25:0, x26:0) -> f6(0 - x24:0 + 2 * x25:0 - 5, 2 * x25:0, x26:0) :|: x26:0 = x8 && (x24:0 > 0 && x26:0 > x24:0) && x6 > 0 && x8 > x6 and 
f6(x24:0, x25:0, x26:0) -> f6(0 - x24:0 + 2 * x25:0 - 5, 2 * x25:0, x26:0) :|: x26:0 = x8 && (x24:0 > 0 && x26:0 > x24:0) && x6 > 0 && x8 > x6
have been merged into the new rule
f6(x19, x20, x21) -> f6(0 - (0 - x19 + 2 * x20 - 5) + 2 * (2 * x20) - 5, 2 * (2 * x20), x21) :|: x21 = x22 && (x19 > 0 && x21 > x19) && x23 > 0 && x22 > x23 && (x21 = x24 && (0 - x19 + 2 * x20 - 5 > 0 && x21 > 0 - x19 + 2 * x20 - 5) && x25 > 0 && x24 > x25)


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(8)
Obligation:
Rules:
f6(x26, x27, x28) -> f6(x26 + 2 * x27, 4 * x27, x28) :|: TRUE && x28 + -1 * x29 = 0 && x26 >= 1 && x28 + -1 * x26 >= 1 && x30 >= 1 && x29 + -1 * x30 >= 1 && x28 + -1 * x31 = 0 && -1 * x26 + 2 * x27 >= 6 && x28 + x26 + -2 * x27 >= -4 && x32 >= 1 && x31 + -1 * x32 >= 1

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(9) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(10)
Obligation:
Rules:
f6(x26:0, x27:0, x28:0) -> f6(x26:0 + 2 * x27:0, 4 * x27:0, x28:0) :|: x32:0 > 0 && x31:0 + -1 * x32:0 >= 1 && x28:0 + x26:0 + -2 * x27:0 >= -4 && 6 <= -1 * x26:0 + 2 * x27:0 && x28:0 + -1 * x31:0 = 0 && x29:0 + -1 * x30:0 >= 1 && x30:0 > 0 && x28:0 + -1 * x26:0 >= 1 && x28:0 + -1 * x29:0 = 0 && x26:0 > 0

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(11) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f6 ] = 1/14*f6_3 + 1/14*f6_1 + -1/7*f6_2

The following rules are decreasing:
f6(x26:0, x27:0, x28:0) -> f6(x26:0 + 2 * x27:0, 4 * x27:0, x28:0) :|: x32:0 > 0 && x31:0 + -1 * x32:0 >= 1 && x28:0 + x26:0 + -2 * x27:0 >= -4 && 6 <= -1 * x26:0 + 2 * x27:0 && x28:0 + -1 * x31:0 = 0 && x29:0 + -1 * x30:0 >= 1 && x30:0 > 0 && x28:0 + -1 * x26:0 >= 1 && x28:0 + -1 * x29:0 = 0 && x26:0 > 0

The following rules are bounded:
f6(x26:0, x27:0, x28:0) -> f6(x26:0 + 2 * x27:0, 4 * x27:0, x28:0) :|: x32:0 > 0 && x31:0 + -1 * x32:0 >= 1 && x28:0 + x26:0 + -2 * x27:0 >= -4 && 6 <= -1 * x26:0 + 2 * x27:0 && x28:0 + -1 * x31:0 = 0 && x29:0 + -1 * x30:0 >= 1 && x30:0 > 0 && x28:0 + -1 * x26:0 >= 1 && x28:0 + -1 * x29:0 = 0 && x26:0 > 0


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(12)
YES