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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 42 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 17 ms]
(6) IntTRS
(7) CaseAnalysis [EQUIVALENT, 11 ms]
(8) AND
    (9) IntTRS
        (10) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (11) IntTRS
        (12) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) IntTRS
        (15) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (16) IntTRS
        (17) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (18) 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(c, x) -> f2(c, x_1) :|: TRUE
f2(x1, x2) -> f3(x3, x2) :|: TRUE
f7(x4, x5) -> f8(x4, arith) :|: TRUE && arith = x5 - x4
f8(x22, x23) -> f9(x24, x23) :|: TRUE && x24 = x22 + 1
f4(x8, x9) -> f7(x8, x9) :|: x9 + x8 >= 0
f9(x10, x11) -> f4(x10, x11) :|: TRUE
f4(x12, x13) -> f10(x12, x13) :|: x13 + x12 < 0
f3(x14, x15) -> f4(x14, x15) :|: x14 >= 2
f3(x16, x17) -> f5(x16, x17) :|: x16 < 2
f10(x18, x19) -> f6(x18, x19) :|: TRUE
f5(x20, x21) -> f6(x20, x21) :|: TRUE
Start term: f1(c, x)

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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(x8, x9) -> f7(x8, x9) :|: x9 + x8 >= 0
f9(x10, x11) -> f4(x10, x11) :|: TRUE
f8(x22, x23) -> f9(x24, x23) :|: TRUE && x24 = x22 + 1
f7(x4, x5) -> f8(x4, arith) :|: TRUE && arith = x5 - x4

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f8(x22:0, x23:0) -> f8(x22:0 + 1, x23:0 - (x22:0 + 1)) :|: x23:0 + (x22:0 + 1) >= 0

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(7) CaseAnalysis (EQUIVALENT)
Found the following inductive condition: 
f8(x0, x1): -1 + x0>=0

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(8)
Complex Obligation (AND)

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(9)
Obligation:
Rules:
f8(x22:0, x23:0) -> f8(x22:0 + 1, x23:0 - (x22:0 + 1)) :|: x23:0 + (x22:0 + 1) >= 0 && x22:0 + -1 >= 0

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(10) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(11)
Obligation:
Rules:
f8(x22:0:0, x23:0:0) -> f8(x22:0:0 + 1, x23:0:0 - (x22:0:0 + 1)) :|: x23:0:0 + (x22:0:0 + 1) >= 0 && x22:0:0 > 0

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(12) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f8 ] = f8_2 + f8_1

The following rules are decreasing:
f8(x22:0:0, x23:0:0) -> f8(x22:0:0 + 1, x23:0:0 - (x22:0:0 + 1)) :|: x23:0:0 + (x22:0:0 + 1) >= 0 && x22:0:0 > 0

The following rules are bounded:
f8(x22:0:0, x23:0:0) -> f8(x22:0:0 + 1, x23:0:0 - (x22:0:0 + 1)) :|: x23:0:0 + (x22:0:0 + 1) >= 0 && x22:0:0 > 0


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(13)
YES

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(14)
Obligation:
Rules:
f8(x22:0, x23:0) -> f8(x22:0 + 1, x23:0 - (x22:0 + 1)) :|: x23:0 + (x22:0 + 1) >= 0 && x22:0 + -1 < 0

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(15) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(16)
Obligation:
Rules:
f8(x22:0:0, x23:0:0) -> f8(x22:0:0 + 1, x23:0:0 - (x22:0:0 + 1)) :|: x23:0:0 + (x22:0:0 + 1) >= 0 && x22:0:0 < 1

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(17) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f8 ] = -1*f8_1

The following rules are decreasing:
f8(x22:0:0, x23:0:0) -> f8(x22:0:0 + 1, x23:0:0 - (x22:0:0 + 1)) :|: x23:0:0 + (x22:0:0 + 1) >= 0 && x22:0:0 < 1

The following rules are bounded:
f8(x22:0:0, x23:0:0) -> f8(x22:0:0 + 1, x23:0:0 - (x22:0:0 + 1)) :|: x23:0:0 + (x22:0:0 + 1) >= 0 && x22:0:0 < 1


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(18)
YES