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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 75 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 31 ms]
(6) IntTRS
(7) PolynomialOrderProcessor [EQUIVALENT, 13 ms]
(8) 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, tx) -> f2(x, y, x_1) :|: TRUE
f2(x1, x2, x3) -> f3(x4, x2, x3) :|: TRUE
f3(x5, x6, x7) -> f4(x5, x8, x7) :|: TRUE
f6(x9, x10, x11) -> f9(arith, x10, x11) :|: TRUE && arith = x9 - 1 - x11
f7(x38, x39, x40) -> f10(x38, x41, x40) :|: TRUE && x41 = x39 + 1 + x40
f5(x15, x16, x17) -> f6(x15, x16, x17) :|: x18 < 0
f5(x42, x43, x44) -> f6(x42, x43, x44) :|: x45 > 0
f5(x19, x20, x21) -> f7(x19, x20, x21) :|: x22 = 0
f9(x23, x24, x25) -> f8(x23, x24, x25) :|: TRUE
f10(x26, x27, x28) -> f8(x26, x27, x28) :|: TRUE
f4(x29, x30, x31) -> f5(x29, x30, x31) :|: x29 >= x30 && x31 >= 0
f8(x32, x33, x34) -> f4(x32, x33, x34) :|: TRUE
f4(x35, x36, x37) -> f11(x35, x36, x37) :|: x35 < x36
f4(x46, x47, x48) -> f11(x46, x47, x48) :|: x48 < 0
Start term: f1(x, y, tx)

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

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(4)
Obligation:
Rules:
f4(x29, x30, x31) -> f5(x29, x30, x31) :|: x29 >= x30 && x31 >= 0
f8(x32, x33, x34) -> f4(x32, x33, x34) :|: TRUE
f9(x23, x24, x25) -> f8(x23, x24, x25) :|: TRUE
f6(x9, x10, x11) -> f9(arith, x10, x11) :|: TRUE && arith = x9 - 1 - x11
f5(x15, x16, x17) -> f6(x15, x16, x17) :|: x18 < 0
f5(x42, x43, x44) -> f6(x42, x43, x44) :|: x45 > 0
f10(x26, x27, x28) -> f8(x26, x27, x28) :|: TRUE
f7(x38, x39, x40) -> f10(x38, x41, x40) :|: TRUE && x41 = x39 + 1 + x40
f5(x19, x20, x21) -> f7(x19, x20, x21) :|: x22 = 0

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f8(x32:0, x33:0, x34:0) -> f8(x32:0 - 1 - x34:0, x33:0, x34:0) :|: x33:0 <= x32:0 && x34:0 > -1 && x45:0 > 0
f8(x, x1, x2) -> f8(x - 1 - x2, x1, x2) :|: x1 <= x && x2 > -1 && x3 < 0
f8(x4, x5, x6) -> f8(x4, x5 + 1 + x6, x6) :|: x5 <= x4 && x6 > -1

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(7) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f8(x, x1, x2)] = x - x1

The following rules are decreasing:
f8(x32:0, x33:0, x34:0) -> f8(x32:0 - 1 - x34:0, x33:0, x34:0) :|: x33:0 <= x32:0 && x34:0 > -1 && x45:0 > 0
f8(x, x1, x2) -> f8(x - 1 - x2, x1, x2) :|: x1 <= x && x2 > -1 && x3 < 0
f8(x4, x5, x6) -> f8(x4, x5 + 1 + x6, x6) :|: x5 <= x4 && x6 > -1
The following rules are bounded:
f8(x32:0, x33:0, x34:0) -> f8(x32:0 - 1 - x34:0, x33:0, x34:0) :|: x33:0 <= x32:0 && x34:0 > -1 && x45:0 > 0
f8(x, x1, x2) -> f8(x - 1 - x2, x1, x2) :|: x1 <= x && x2 > -1 && x3 < 0
f8(x4, x5, x6) -> f8(x4, x5 + 1 + x6, x6) :|: x5 <= x4 && x6 > -1

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(8)
YES