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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 47 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 17 ms]
(6) IntTRS
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 18 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(i, j, k, tmp) -> f2(x_1, j, k, tmp) :|: TRUE
f2(x, x1, x2, x3) -> f3(x, x4, x2, x3) :|: TRUE
f3(x5, x6, x7, x8) -> f4(x5, x6, x9, x8) :|: TRUE
f4(x10, x11, x12, x13) -> f5(x10, x11, x12, x14) :|: TRUE
f6(x15, x16, x17, x18) -> f7(x15, x16, x17, x15) :|: TRUE
f7(x19, x20, x21, x22) -> f8(x20, x20, x21, x22) :|: TRUE
f8(x23, x24, x25, x26) -> f9(x23, arith, x25, x26) :|: TRUE && arith = x26 + 1
f9(x43, x44, x45, x46) -> f10(x43, x44, x47, x46) :|: TRUE && x47 = x45 - 1
f5(x31, x32, x33, x34) -> f6(x31, x32, x33, x34) :|: x31 <= 100 && x32 <= x33
f10(x35, x36, x37, x38) -> f5(x35, x36, x37, x38) :|: TRUE
f5(x39, x40, x41, x42) -> f11(x39, x40, x41, x42) :|: x39 > 100
f5(x48, x49, x50, x51) -> f11(x48, x49, x50, x51) :|: x49 > x50
Start term: f1(i, j, k, tmp)

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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(x31, x32, x33, x34) -> f6(x31, x32, x33, x34) :|: x31 <= 100 && x32 <= x33
f10(x35, x36, x37, x38) -> f5(x35, x36, x37, x38) :|: TRUE
f9(x43, x44, x45, x46) -> f10(x43, x44, x47, x46) :|: TRUE && x47 = x45 - 1
f8(x23, x24, x25, x26) -> f9(x23, arith, x25, x26) :|: TRUE && arith = x26 + 1
f7(x19, x20, x21, x22) -> f8(x20, x20, x21, x22) :|: TRUE
f6(x15, x16, x17, x18) -> f7(x15, x16, x17, x15) :|: TRUE

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f7(x19:0, x20:0, x21:0, x22:0) -> f7(x20:0, x22:0 + 1, x21:0 - 1, x20:0) :|: x20:0 < 101 && x22:0 + 1 <= x21:0 - 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(x20:0, x21:0, x22:0) -> f7(x22:0 + 1, x21:0 - 1, x20:0) :|: x20:0 < 101 && x22:0 + 1 <= x21:0 - 1

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f7(x, x1, x2)] = 98 - x + x1 - x2

The following rules are decreasing:
f7(x20:0, x21:0, x22:0) -> f7(x22:0 + 1, x21:0 - 1, x20:0) :|: x20:0 < 101 && x22:0 + 1 <= x21:0 - 1
The following rules are bounded:
f7(x20:0, x21:0, x22:0) -> f7(x22:0 + 1, x21:0 - 1, x20:0) :|: x20:0 < 101 && x22:0 + 1 <= x21:0 - 1

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(10)
YES