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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 71 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 5 ms]
(6) IntTRS
(7) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(10) 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 - 1
f5(x28, x29) -> f6(x28, x30) :|: TRUE && x30 = x29 + x28
f7(x31, x32) -> f8(x31, x33) :|: TRUE && x33 = x32 - 1
f6(x10, x11) -> f7(x10, x11) :|: x11 >= x10 && x12 < 0
f6(x34, x35) -> f7(x34, x35) :|: x35 >= x34 && x36 > 0
f8(x13, x14) -> f6(x13, x14) :|: TRUE
f6(x15, x16) -> f9(x15, x16) :|: x16 < x15
f6(x37, x38) -> f9(x37, x38) :|: x39 = 0
f9(x40, x41) -> f10(x42, x41) :|: TRUE && x42 = x40 - 1
f10(x43, x44) -> f11(x43, x45) :|: TRUE && x45 = x44 - x43
f3(x22, x23) -> f4(x22, x23) :|: x22 >= 2
f11(x24, x25) -> f3(x24, x25) :|: TRUE
f3(x26, x27) -> f12(x26, x27) :|: x26 < 2
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(x22, x23) -> f4(x22, x23) :|: x22 >= 2
f11(x24, x25) -> f3(x24, x25) :|: TRUE
f10(x43, x44) -> f11(x43, x45) :|: TRUE && x45 = x44 - x43
f9(x40, x41) -> f10(x42, x41) :|: TRUE && x42 = x40 - 1
f6(x15, x16) -> f9(x15, x16) :|: x16 < x15
f5(x28, x29) -> f6(x28, x30) :|: TRUE && x30 = x29 + x28
f4(x4, x5) -> f5(arith, x5) :|: TRUE && arith = x4 - 1
f8(x13, x14) -> f6(x13, x14) :|: TRUE
f7(x31, x32) -> f8(x31, x33) :|: TRUE && x33 = x32 - 1
f6(x10, x11) -> f7(x10, x11) :|: x11 >= x10 && x12 < 0
f6(x34, x35) -> f7(x34, x35) :|: x35 >= x34 && x36 > 0
f6(x37, x38) -> f9(x37, x38) :|: x39 = 0

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f6(x10:0, x11:0) -> f6(x10:0, x11:0 - 1) :|: x11:0 >= x10:0 && x12:0 < 0
f6(x15:0, x16:0) -> f6(x15:0 - 2, x16:0 - (x15:0 - 1) + (x15:0 - 2)) :|: x16:0 < x15:0 && x15:0 > 2
f6(x37:0, x38:0) -> f6(x37:0 - 2, x38:0 - (x37:0 - 1) + (x37:0 - 2)) :|: x37:0 > 2
f6(x34:0, x35:0) -> f6(x34:0, x35:0 - 1) :|: x35:0 >= x34:0 && x36:0 > 0

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(7) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f6(x, x1)] = -1 + x

The following rules are decreasing:
f6(x15:0, x16:0) -> f6(x15:0 - 2, x16:0 - (x15:0 - 1) + (x15:0 - 2)) :|: x16:0 < x15:0 && x15:0 > 2
f6(x37:0, x38:0) -> f6(x37:0 - 2, x38:0 - (x37:0 - 1) + (x37:0 - 2)) :|: x37:0 > 2
The following rules are bounded:
f6(x15:0, x16:0) -> f6(x15:0 - 2, x16:0 - (x15:0 - 1) + (x15:0 - 2)) :|: x16:0 < x15:0 && x15:0 > 2
f6(x37:0, x38:0) -> f6(x37:0 - 2, x38:0 - (x37:0 - 1) + (x37:0 - 2)) :|: x37:0 > 2

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(8)
Obligation:
Rules:
f6(x10:0, x11:0) -> f6(x10:0, x11:0 - 1) :|: x11:0 >= x10:0 && x12:0 < 0
f6(x34:0, x35:0) -> f6(x34:0, x35:0 - 1) :|: x35:0 >= x34:0 && x36:0 > 0

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f6(x, x1)] = -x + x1

The following rules are decreasing:
f6(x10:0, x11:0) -> f6(x10:0, x11:0 - 1) :|: x11:0 >= x10:0 && x12:0 < 0
f6(x34:0, x35:0) -> f6(x34:0, x35:0 - 1) :|: x35:0 >= x34:0 && x36:0 > 0
The following rules are bounded:
f6(x10:0, x11:0) -> f6(x10:0, x11:0 - 1) :|: x11:0 >= x10:0 && x12:0 < 0
f6(x34:0, x35:0) -> f6(x34:0, x35:0 - 1) :|: x35:0 >= x34:0 && x36:0 > 0

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(10)
YES