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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 17 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 13 ms]
(6) IntTRS
(7) TerminationGraphProcessor [EQUIVALENT, 2 ms]
(8) IntTRS
(9) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(10) IntTRS
(11) RankingReductionPairProof [EQUIVALENT, 6 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(x, y) -> f2(x_1, y) :|: TRUE
f2(x1, x2) -> f3(x1, x3) :|: TRUE
f4(x4, x5) -> f5(arith, x5) :|: TRUE && arith = x4 + x5
f5(x14, x15) -> f6(x14, x16) :|: TRUE && x16 = (0 - 2) * x15 - 1
f3(x8, x9) -> f4(x8, x9) :|: x8 >= 0
f6(x10, x11) -> f3(x10, x11) :|: TRUE
f3(x12, x13) -> f7(x12, x13) :|: x12 < 0
Start term: f1(x, y)

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(3) TerminationGraphProcessor (SOUND)
Constructed the termination graph and obtained one non-trivial SCC.

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(4)
Obligation:
Rules:
f3(x8, x9) -> f4(x8, x9) :|: x8 >= 0
f6(x10, x11) -> f3(x10, x11) :|: TRUE
f5(x14, x15) -> f6(x14, x16) :|: TRUE && x16 = (0 - 2) * x15 - 1
f4(x4, x5) -> f5(arith, x5) :|: TRUE && arith = x4 + x5

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f5(x14:0, x15:0) -> f5(x14:0 + (-2 * x15:0 - 1), -2 * x15:0 - 1) :|: x14:0 > -1

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(7) TerminationGraphProcessor (EQUIVALENT)
Constructed the termination graph and obtained one non-trivial SCC.

f5(x14:0, x15:0) -> f5(x14:0 + (-2 * x15:0 - 1), -2 * x15:0 - 1) :|: x14:0 > -1
has been transformed into
f5(x14:0, x15:0) -> f5(x14:0 + (-2 * x15:0 - 1), -2 * x15:0 - 1) :|: x14:0 > -1 && x4 > -1.


f5(x14:0, x15:0) -> f5(x14:0 + (-2 * x15:0 - 1), -2 * x15:0 - 1) :|: x14:0 > -1 && x4 > -1 and 
f5(x14:0, x15:0) -> f5(x14:0 + (-2 * x15:0 - 1), -2 * x15:0 - 1) :|: x14:0 > -1 && x4 > -1
have been merged into the new rule
f5(x12, x13) -> f5(x12 + (-2 * x13 - 1) + (-2 * (-2 * x13 - 1) - 1), -2 * (-2 * x13 - 1) - 1) :|: x12 > -1 && x14 > -1 && (x12 + (-2 * x13 - 1) > -1 && x15 > -1)


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(8)
Obligation:
Rules:
f5(x16, x17) -> f5(x16 + 2 * x17, 4 * x17 + 1) :|: TRUE && x16 >= 0 && x18 >= 0 && x16 + -2 * x17 >= 1 && x19 >= 0

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(9) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(10)
Obligation:
Rules:
f5(x16:0, x17:0) -> f5(x16:0 + 2 * x17:0, 4 * x17:0 + 1) :|: x16:0 + -2 * x17:0 >= 1 && x19:0 > -1 && x16:0 > -1 && x18:0 > -1

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(11) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f5 ] = 3/2*f5_1 + -1*f5_2

The following rules are decreasing:
f5(x16:0, x17:0) -> f5(x16:0 + 2 * x17:0, 4 * x17:0 + 1) :|: x16:0 + -2 * x17:0 >= 1 && x19:0 > -1 && x16:0 > -1 && x18:0 > -1

The following rules are bounded:
f5(x16:0, x17:0) -> f5(x16:0 + 2 * x17:0, 4 * x17:0 + 1) :|: x16:0 + -2 * x17:0 >= 1 && x19:0 > -1 && x16:0 > -1 && x18:0 > -1


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(12)
YES