/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 53 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 33 ms]
(6) IntTRS
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 12 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, i) -> f2(x_1, y, z, i) :|: TRUE
f2(x1, x2, x3, x4) -> f3(x1, x5, x3, x4) :|: TRUE
f3(x6, x7, x8, x9) -> f4(x6, x7, x10, x9) :|: TRUE
f4(x11, x12, x13, x14) -> f5(x11, x12, x13, x15) :|: TRUE
f6(x16, x17, x18, x19) -> f7(x16, x17, x18, arith) :|: TRUE && arith = x19 + 1
f8(x56, x57, x58, x59) -> f11(x60, x57, x58, x59) :|: TRUE && x60 = x56 + 1
f9(x61, x62, x63, x64) -> f12(x61, x62, x65, x64) :|: TRUE && x65 = x63 + 1
f7(x28, x29, x30, x31) -> f8(x28, x29, x30, x31) :|: x30 > x28
f7(x32, x33, x34, x35) -> f9(x32, x33, x34, x35) :|: x34 <= x32
f11(x36, x37, x38, x39) -> f10(x36, x37, x38, x39) :|: TRUE
f12(x40, x41, x42, x43) -> f10(x40, x41, x42, x43) :|: TRUE
f5(x44, x45, x46, x47) -> f6(x44, x45, x46, x47) :|: x44 < x45
f10(x48, x49, x50, x51) -> f5(x48, x49, x50, x51) :|: TRUE
f5(x52, x53, x54, x55) -> f13(x52, x53, x54, x55) :|: x52 >= x53
Start term: f1(x, y, z, i)

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

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(4)
Obligation:
Rules:
f5(x44, x45, x46, x47) -> f6(x44, x45, x46, x47) :|: x44 < x45
f10(x48, x49, x50, x51) -> f5(x48, x49, x50, x51) :|: TRUE
f11(x36, x37, x38, x39) -> f10(x36, x37, x38, x39) :|: TRUE
f8(x56, x57, x58, x59) -> f11(x60, x57, x58, x59) :|: TRUE && x60 = x56 + 1
f7(x28, x29, x30, x31) -> f8(x28, x29, x30, x31) :|: x30 > x28
f6(x16, x17, x18, x19) -> f7(x16, x17, x18, arith) :|: TRUE && arith = x19 + 1
f12(x40, x41, x42, x43) -> f10(x40, x41, x42, x43) :|: TRUE
f9(x61, x62, x63, x64) -> f12(x61, x62, x65, x64) :|: TRUE && x65 = x63 + 1
f7(x32, x33, x34, x35) -> f9(x32, x33, x34, x35) :|: x34 <= x32

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f7(x32:0, x33:0, x34:0, x35:0) -> f7(x32:0, x33:0, x34:0 + 1, x35:0 + 1) :|: x34:0 <= x32:0 && x33:0 > x32:0
f7(x28:0, x29:0, x30:0, x31:0) -> f7(x28:0 + 1, x29:0, x30:0, x31:0 + 1) :|: x30:0 > x28:0 && x29:0 > x28:0 + 1

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(7) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:

   f7(x1, x2, x3, x4) -> f7(x1, x2, x3)

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(8)
Obligation:
Rules:
f7(x32:0, x33:0, x34:0) -> f7(x32:0, x33:0, x34:0 + 1) :|: x34:0 <= x32:0 && x33:0 > x32:0
f7(x28:0, x29:0, x30:0) -> f7(x28:0 + 1, x29:0, x30:0) :|: x30:0 > x28:0 && x29:0 > x28:0 + 1

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f7(x, x1, x2)] = -x + x1

The following rules are decreasing:
f7(x28:0, x29:0, x30:0) -> f7(x28:0 + 1, x29:0, x30:0) :|: x30:0 > x28:0 && x29:0 > x28:0 + 1
The following rules are bounded:
f7(x32:0, x33:0, x34:0) -> f7(x32:0, x33:0, x34:0 + 1) :|: x34:0 <= x32:0 && x33:0 > x32:0
f7(x28:0, x29:0, x30:0) -> f7(x28:0 + 1, x29:0, x30:0) :|: x30:0 > x28:0 && x29:0 > x28:0 + 1

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(10)
Obligation:
Rules:
f7(x32:0, x33:0, x34:0) -> f7(x32:0, x33:0, x34:0 + 1) :|: x34:0 <= x32:0 && x33:0 > x32:0

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(11) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f7 ] = -1*f7_3 + f7_2

The following rules are decreasing:
f7(x32:0, x33:0, x34:0) -> f7(x32:0, x33:0, x34:0 + 1) :|: x34:0 <= x32:0 && x33:0 > x32:0

The following rules are bounded:
f7(x32:0, x33:0, x34:0) -> f7(x32:0, x33:0, x34:0 + 1) :|: x34:0 <= x32:0 && x33:0 > x32:0


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(12)
YES