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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 59 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(6) IntTRS
(7) PolynomialOrderProcessor [EQUIVALENT, 2 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 6 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, c) -> f2(x_1, c) :|: TRUE
f2(x1, x2) -> f3(x1, 1) :|: TRUE
f5(x3, x4) -> f8(arith, x4) :|: TRUE && arith = x3 - 10
f8(x25, x26) -> f9(x25, x27) :|: TRUE && x27 = x26 - 1
f6(x28, x29) -> f10(x30, x29) :|: TRUE && x30 = x28 + 11
f10(x31, x32) -> f11(x31, x33) :|: TRUE && x33 = x32 + 1
f4(x11, x12) -> f5(x11, x12) :|: x11 > 100
f4(x13, x14) -> f6(x13, x14) :|: x13 <= 100
f9(x15, x16) -> f7(x15, x16) :|: TRUE
f11(x17, x18) -> f7(x17, x18) :|: TRUE
f3(x19, x20) -> f4(x19, x20) :|: x20 > 0
f7(x21, x22) -> f3(x21, x22) :|: TRUE
f3(x23, x24) -> f12(x23, x24) :|: x24 <= 0
Start term: f1(x, c)

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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(x19, x20) -> f4(x19, x20) :|: x20 > 0
f7(x21, x22) -> f3(x21, x22) :|: TRUE
f9(x15, x16) -> f7(x15, x16) :|: TRUE
f8(x25, x26) -> f9(x25, x27) :|: TRUE && x27 = x26 - 1
f5(x3, x4) -> f8(arith, x4) :|: TRUE && arith = x3 - 10
f4(x11, x12) -> f5(x11, x12) :|: x11 > 100
f11(x17, x18) -> f7(x17, x18) :|: TRUE
f10(x31, x32) -> f11(x31, x33) :|: TRUE && x33 = x32 + 1
f6(x28, x29) -> f10(x30, x29) :|: TRUE && x30 = x28 + 11
f4(x13, x14) -> f6(x13, x14) :|: x13 <= 100

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f7(x21:0, x22:0) -> f7(x21:0 - 10, x22:0 - 1) :|: x22:0 > 0 && x21:0 > 100
f7(x, x1) -> f7(x + 11, x1 + 1) :|: x1 > 0 && x < 101

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(7) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f7(x, x1)] = 27109 - 391*x - x*x1 + x^2 + 2086*x1 + 5*x1^2

The following rules are decreasing:
f7(x, x1) -> f7(x + 11, x1 + 1) :|: x1 > 0 && x < 101
The following rules are bounded:
f7(x, x1) -> f7(x + 11, x1 + 1) :|: x1 > 0 && x < 101

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(8)
Obligation:
Rules:
f7(x21:0, x22:0) -> f7(x21:0 - 10, x22:0 - 1) :|: x22:0 > 0 && x21:0 > 100

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f7(x, x1)] = x1

The following rules are decreasing:
f7(x21:0, x22:0) -> f7(x21:0 - 10, x22:0 - 1) :|: x22:0 > 0 && x21:0 > 100
The following rules are bounded:
f7(x21:0, x22:0) -> f7(x21:0 - 10, x22:0 - 1) :|: x22:0 > 0 && x21:0 > 100

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(10)
YES