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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 82 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 21 ms]
(6) IntTRS
(7) PolynomialOrderProcessor [EQUIVALENT, 31 ms]
(8) IntTRS
(9) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(10) IntTRS
(11) PolynomialOrderProcessor [EQUIVALENT, 4 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, d) -> f2(x_1, y, d) :|: TRUE
f2(x1, x2, x3) -> f3(x1, x4, x3) :|: TRUE
f3(x5, x6, x7) -> f4(x5, x6, x8) :|: TRUE
f6(x9, x10, x11) -> f9(arith, x10, x11) :|: TRUE && arith = x9 - 1
f9(x12, x13, x14) -> f10(x12, x13, x15) :|: TRUE
f7(x16, x17, x18) -> f11(x19, x17, x18) :|: TRUE
f11(x49, x50, x51) -> f12(x49, x52, x51) :|: TRUE && x52 = x50 - 1
f12(x53, x54, x55) -> f13(x53, x54, x56) :|: TRUE && x56 = x55 - 1
f5(x26, x27, x28) -> f6(x26, x27, x28) :|: x29 < 0
f5(x57, x58, x59) -> f6(x57, x58, x59) :|: x60 > 0
f5(x30, x31, x32) -> f7(x30, x31, x32) :|: x33 = 0
f10(x34, x35, x36) -> f8(x34, x35, x36) :|: TRUE
f13(x37, x38, x39) -> f8(x37, x38, x39) :|: TRUE
f4(x40, x41, x42) -> f5(x40, x41, x42) :|: x40 > 0 && x41 > 0 && x42 > 0
f8(x43, x44, x45) -> f4(x43, x44, x45) :|: TRUE
f4(x46, x47, x48) -> f14(x46, x47, x48) :|: x48 <= 0
f4(x61, x62, x63) -> f14(x61, x62, x63) :|: x61 <= 0
f4(x64, x65, x66) -> f14(x64, x65, x66) :|: x65 <= 0
Start term: f1(x, y, d)

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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(x40, x41, x42) -> f5(x40, x41, x42) :|: x40 > 0 && x41 > 0 && x42 > 0
f8(x43, x44, x45) -> f4(x43, x44, x45) :|: TRUE
f10(x34, x35, x36) -> f8(x34, x35, x36) :|: TRUE
f9(x12, x13, x14) -> f10(x12, x13, x15) :|: TRUE
f6(x9, x10, x11) -> f9(arith, x10, x11) :|: TRUE && arith = x9 - 1
f5(x26, x27, x28) -> f6(x26, x27, x28) :|: x29 < 0
f5(x57, x58, x59) -> f6(x57, x58, x59) :|: x60 > 0
f13(x37, x38, x39) -> f8(x37, x38, x39) :|: TRUE
f12(x53, x54, x55) -> f13(x53, x54, x56) :|: TRUE && x56 = x55 - 1
f11(x49, x50, x51) -> f12(x49, x52, x51) :|: TRUE && x52 = x50 - 1
f7(x16, x17, x18) -> f11(x19, x17, x18) :|: TRUE
f5(x30, x31, x32) -> f7(x30, x31, x32) :|: x33 = 0

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f8(x43:0, x44:0, x45:0) -> f8(x43:0 - 1, x44:0, x15:0) :|: x45:0 > 0 && x29:0 < 0 && x44:0 > 0 && x43:0 > 0
f8(x, x1, x2) -> f8(x3, x1 - 1, x2 - 1) :|: x > 0 && x1 > 0 && x2 > 0
f8(x4, x5, x6) -> f8(x4 - 1, x5, x7) :|: x6 > 0 && x8 > 0 && x5 > 0 && x4 > 0

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(7) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f8(x, x1, x2)] = -1 + x1

The following rules are decreasing:
f8(x, x1, x2) -> f8(x3, x1 - 1, x2 - 1) :|: x > 0 && x1 > 0 && x2 > 0
The following rules are bounded:
f8(x43:0, x44:0, x45:0) -> f8(x43:0 - 1, x44:0, x15:0) :|: x45:0 > 0 && x29:0 < 0 && x44:0 > 0 && x43:0 > 0
f8(x, x1, x2) -> f8(x3, x1 - 1, x2 - 1) :|: x > 0 && x1 > 0 && x2 > 0
f8(x4, x5, x6) -> f8(x4 - 1, x5, x7) :|: x6 > 0 && x8 > 0 && x5 > 0 && x4 > 0

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(8)
Obligation:
Rules:
f8(x43:0, x44:0, x45:0) -> f8(x43:0 - 1, x44:0, x15:0) :|: x45:0 > 0 && x29:0 < 0 && x44:0 > 0 && x43:0 > 0
f8(x4, x5, x6) -> f8(x4 - 1, x5, x7) :|: x6 > 0 && x8 > 0 && x5 > 0 && x4 > 0

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(9) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(10)
Obligation:
Rules:
f8(x4:0, x5:0, x6:0) -> f8(x4:0 - 1, x5:0, x7:0) :|: x5:0 > 0 && x4:0 > 0 && x8:0 > 0 && x6:0 > 0
f8(x43:0:0, x44:0:0, x45:0:0) -> f8(x43:0:0 - 1, x44:0:0, x15:0:0) :|: x44:0:0 > 0 && x43:0:0 > 0 && x29:0:0 < 0 && x45:0:0 > 0

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(11) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f8(x, x1, x2)] = x

The following rules are decreasing:
f8(x4:0, x5:0, x6:0) -> f8(x4:0 - 1, x5:0, x7:0) :|: x5:0 > 0 && x4:0 > 0 && x8:0 > 0 && x6:0 > 0
f8(x43:0:0, x44:0:0, x45:0:0) -> f8(x43:0:0 - 1, x44:0:0, x15:0:0) :|: x44:0:0 > 0 && x43:0:0 > 0 && x29:0:0 < 0 && x45:0:0 > 0
The following rules are bounded:
f8(x4:0, x5:0, x6:0) -> f8(x4:0 - 1, x5:0, x7:0) :|: x5:0 > 0 && x4:0 > 0 && x8:0 > 0 && x6:0 > 0
f8(x43:0:0, x44:0:0, x45:0:0) -> f8(x43:0:0 - 1, x44:0:0, x15:0:0) :|: x44:0:0 > 0 && x43:0:0 > 0 && x29:0:0 < 0 && x45:0:0 > 0

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(12)
YES