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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 62 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 15 ms]
(6) IntTRS
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 20 ms]
(10) 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(c, x, y, z) -> f2(c, x_1, y, z) :|: TRUE
f2(x1, x2, x3, x4) -> f3(x1, x2, x5, x4) :|: TRUE
f3(x6, x7, x8, x9) -> f4(x6, x7, x8, x10) :|: TRUE
f4(x11, x12, x13, x14) -> f5(0, x12, x13, x14) :|: TRUE
f6(x15, x16, x17, x18) -> f7(x15, arith, x17, x18) :|: TRUE && arith = x16 - 1
f7(x39, x40, x41, x42) -> f8(x39, x40, x43, x42) :|: TRUE && x43 = x41 - 1
f8(x44, x45, x46, x47) -> f9(x48, x45, x46, x47) :|: TRUE && x48 = x44 + 1
f5(x27, x28, x29, x30) -> f6(x27, x28, x29, x30) :|: x28 > x30 && x29 > x30
f9(x31, x32, x33, x34) -> f5(x31, x32, x33, x34) :|: TRUE
f5(x35, x36, x37, x38) -> f10(x35, x36, x37, x38) :|: x36 <= x38
f5(x49, x50, x51, x52) -> f10(x49, x50, x51, x52) :|: x51 <= x52
Start term: f1(c, 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:
f5(x27, x28, x29, x30) -> f6(x27, x28, x29, x30) :|: x28 > x30 && x29 > x30
f9(x31, x32, x33, x34) -> f5(x31, x32, x33, x34) :|: TRUE
f8(x44, x45, x46, x47) -> f9(x48, x45, x46, x47) :|: TRUE && x48 = x44 + 1
f7(x39, x40, x41, x42) -> f8(x39, x40, x43, x42) :|: TRUE && x43 = x41 - 1
f6(x15, x16, x17, x18) -> f7(x15, arith, x17, x18) :|: TRUE && arith = x16 - 1

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f7(x39:0, x40:0, x41:0, x42:0) -> f7(x39:0 + 1, x40:0 - 1, x41:0 - 1, x42:0) :|: x42:0 < x40:0 && x42:0 < x41:0 - 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(x2, x3, x4)

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(8)
Obligation:
Rules:
f7(x40:0, x41:0, x42:0) -> f7(x40:0 - 1, x41:0 - 1, x42:0) :|: x42:0 < x40:0 && x42:0 < x41:0 - 1

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

The following rules are decreasing:
f7(x40:0, x41:0, x42:0) -> f7(x40:0 - 1, x41:0 - 1, x42:0) :|: x42:0 < x40:0 && x42:0 < x41:0 - 1
The following rules are bounded:
f7(x40:0, x41:0, x42:0) -> f7(x40:0 - 1, x41:0 - 1, x42:0) :|: x42:0 < x40:0 && x42:0 < x41:0 - 1

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(10)
YES