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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 53 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 28 ms]
(6) IntTRS
(7) PolynomialOrderProcessor [EQUIVALENT, 14 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 3 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
f5(x4, x5) -> f8(arith, x5) :|: TRUE && arith = x4 - 1
f8(x6, x7) -> f9(x6, x8) :|: TRUE
f6(x27, x28) -> f10(x27, x29) :|: TRUE && x29 = x28 - 1
f4(x11, x12) -> f5(x11, x12) :|: x13 < 0
f4(x30, x31) -> f5(x30, x31) :|: x32 > 0
f4(x14, x15) -> f6(x14, x15) :|: x16 = 0
f9(x17, x18) -> f7(x17, x18) :|: TRUE
f10(x19, x20) -> f7(x19, x20) :|: TRUE
f3(x21, x22) -> f4(x21, x22) :|: x21 > 0 && x22 > 0
f7(x23, x24) -> f3(x23, x24) :|: TRUE
f3(x25, x26) -> f11(x25, x26) :|: x25 <= 0
f3(x33, x34) -> f11(x33, x34) :|: x34 <= 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(x21, x22) -> f4(x21, x22) :|: x21 > 0 && x22 > 0
f7(x23, x24) -> f3(x23, x24) :|: TRUE
f9(x17, x18) -> f7(x17, x18) :|: TRUE
f8(x6, x7) -> f9(x6, x8) :|: TRUE
f5(x4, x5) -> f8(arith, x5) :|: TRUE && arith = x4 - 1
f4(x11, x12) -> f5(x11, x12) :|: x13 < 0
f4(x30, x31) -> f5(x30, x31) :|: x32 > 0
f10(x19, x20) -> f7(x19, x20) :|: TRUE
f6(x27, x28) -> f10(x27, x29) :|: TRUE && x29 = x28 - 1
f4(x14, x15) -> f6(x14, x15) :|: x16 = 0

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f7(x23:0, x24:0) -> f7(x23:0, x24:0 - 1) :|: x23:0 > 0 && x24:0 > 0
f7(x, x1) -> f7(x - 1, x2) :|: x > 0 && x1 > 0 && x3 < 0
f7(x4, x5) -> f7(x4 - 1, x6) :|: x4 > 0 && x5 > 0 && x7 > 0

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(7) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f7(x, x1)] = -1 + x

The following rules are decreasing:
f7(x, x1) -> f7(x - 1, x2) :|: x > 0 && x1 > 0 && x3 < 0
f7(x4, x5) -> f7(x4 - 1, x6) :|: x4 > 0 && x5 > 0 && x7 > 0
The following rules are bounded:
f7(x23:0, x24:0) -> f7(x23:0, x24:0 - 1) :|: x23:0 > 0 && x24:0 > 0
f7(x, x1) -> f7(x - 1, x2) :|: x > 0 && x1 > 0 && x3 < 0
f7(x4, x5) -> f7(x4 - 1, x6) :|: x4 > 0 && x5 > 0 && x7 > 0

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(8)
Obligation:
Rules:
f7(x23:0, x24:0) -> f7(x23:0, x24:0 - 1) :|: x23:0 > 0 && x24:0 > 0

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

The following rules are decreasing:
f7(x23:0, x24:0) -> f7(x23:0, x24:0 - 1) :|: x23:0 > 0 && x24:0 > 0
The following rules are bounded:
f7(x23:0, x24:0) -> f7(x23:0, x24:0 - 1) :|: x23:0 > 0 && x24:0 > 0

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(10)
YES