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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 36 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IntTRS
(7) TerminationGraphProcessor [EQUIVALENT, 0 ms]
(8) IntTRS
(9) TerminationGraphProcessor [EQUIVALENT, 0 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(x) -> f2(x_1) :|: TRUE
f3(x1) -> f4(arith) :|: TRUE && arith = 0 - 2 * x1 + 10
f2(x2) -> f3(x2) :|: x2 > 0
f4(x3) -> f2(x3) :|: TRUE
f2(x4) -> f5(x4) :|: x4 <= 0
Start term: f1(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:
f2(x2) -> f3(x2) :|: x2 > 0
f4(x3) -> f2(x3) :|: TRUE
f3(x1) -> f4(arith) :|: TRUE && arith = 0 - 2 * x1 + 10

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f4(x3:0) -> f4(0 - 2 * x3:0 + 10) :|: x3:0 > 0

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

f4(x3:0) -> f4(0 - 2 * x3:0 + 10) :|: x3:0 > 0
has been transformed into
f4(x3:0) -> f4(0 - 2 * x3:0 + 10) :|: x3:0 = 0 - 2 * x2 + 10 && x3:0 > 0 && x2 > 0.


f4(x3:0) -> f4(0 - 2 * x3:0 + 10) :|: x3:0 = 0 - 2 * x2 + 10 && x3:0 > 0 && x2 > 0 and 
f4(x3:0) -> f4(0 - 2 * x3:0 + 10) :|: x3:0 = 0 - 2 * x2 + 10 && x3:0 > 0 && x2 > 0
have been merged into the new rule
f4(x7) -> f4(0 - 2 * (0 - 2 * x7 + 10) + 10) :|: x7 = 0 - 2 * x8 + 10 && x7 > 0 && x8 > 0 && (0 - 2 * x7 + 10 = 0 - 2 * x9 + 10 && 0 - 2 * x7 + 10 > 0 && x9 > 0)


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(8)
Obligation:
Rules:
f4(x10) -> f4(4 * x10 + -10) :|: TRUE && x10 + 2 * x11 = 10 && x10 >= 1 && x11 >= 1 && -1 * x10 + x12 = 0 && -1 * x10 >= -4 && x12 >= 1

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(9) TerminationGraphProcessor (EQUIVALENT)
Constructed the termination graph and obtained no non-trivial SCC(s).

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(10)
YES