YES
proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 61 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 29 ms]
(6) IntTRS
(7) RankingReductionPairProof [EQUIVALENT, 29 ms]
(8) IntTRS
(9) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(10) IntTRS
(11) PolynomialOrderProcessor [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(i, j, N) -> f2(i, x_1, N) :|: TRUE
f2(x, x1, x2) -> f3(x, x1, x3) :|: TRUE
f3(x4, x5, x6) -> f4(x6, x5, x6) :|: TRUE
f6(x7, x8, x9) -> f9(x7, arith, x9) :|: TRUE && arith = x8 - 1
f7(x10, x11, x12) -> f10(x10, x12, x12) :|: TRUE
f10(x37, x38, x39) -> f11(x40, x38, x39) :|: TRUE && x40 = x37 - 1
f5(x16, x17, x18) -> f6(x16, x17, x18) :|: x17 > 0
f5(x19, x20, x21) -> f7(x19, x20, x21) :|: x20 <= 0
f9(x22, x23, x24) -> f8(x22, x23, x24) :|: TRUE
f11(x25, x26, x27) -> f8(x25, x26, x27) :|: TRUE
f4(x28, x29, x30) -> f5(x28, x29, x30) :|: x28 > 0
f8(x31, x32, x33) -> f4(x31, x32, x33) :|: TRUE
f4(x34, x35, x36) -> f12(x34, x35, x36) :|: x34 <= 0
Start term: f1(i, j, 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(x28, x29, x30) -> f5(x28, x29, x30) :|: x28 > 0
f8(x31, x32, x33) -> f4(x31, x32, x33) :|: TRUE
f9(x22, x23, x24) -> f8(x22, x23, x24) :|: TRUE
f6(x7, x8, x9) -> f9(x7, arith, x9) :|: TRUE && arith = x8 - 1
f5(x16, x17, x18) -> f6(x16, x17, x18) :|: x17 > 0
f11(x25, x26, x27) -> f8(x25, x26, x27) :|: TRUE
f10(x37, x38, x39) -> f11(x40, x38, x39) :|: TRUE && x40 = x37 - 1
f7(x10, x11, x12) -> f10(x10, x12, x12) :|: TRUE
f5(x19, x20, x21) -> f7(x19, x20, x21) :|: x20 <= 0

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f8(x31:0, x32:0, x33:0) -> f8(x31:0, x32:0 - 1, x33:0) :|: x31:0 > 0 && x32:0 > 0
f8(x, x1, x2) -> f8(x - 1, x2, x2) :|: x > 0 && x1 < 1

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(7) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f8 ] = f8_1

The following rules are decreasing:
f8(x, x1, x2) -> f8(x - 1, x2, x2) :|: x > 0 && x1 < 1

The following rules are bounded:
f8(x31:0, x32:0, x33:0) -> f8(x31:0, x32:0 - 1, x33:0) :|: x31:0 > 0 && x32:0 > 0
f8(x, x1, x2) -> f8(x - 1, x2, x2) :|: x > 0 && x1 < 1


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(8)
Obligation:
Rules:
f8(x31:0, x32:0, x33:0) -> f8(x31:0, x32:0 - 1, x33:0) :|: x31:0 > 0 && x32:0 > 0

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

   f8(x1, x2, x3) -> f8(x1, x2)

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(10)
Obligation:
Rules:
f8(x31:0, x32:0) -> f8(x31:0, x32:0 - 1) :|: x31:0 > 0 && x32:0 > 0

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

The following rules are decreasing:
f8(x31:0, x32:0) -> f8(x31:0, x32:0 - 1) :|: x31:0 > 0 && x32:0 > 0
The following rules are bounded:
f8(x31:0, x32:0) -> f8(x31:0, x32:0 - 1) :|: x31:0 > 0 && x32:0 > 0

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(12)
YES