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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 72 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 18 ms]
(6) IntTRS
(7) RankingReductionPairProof [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(i, j, m, n) -> f2(i, j, m, x_1) :|: TRUE
f2(x, x1, x2, x3) -> f3(x, x1, x4, x3) :|: TRUE
f4(x5, x6, x7, x8) -> f7(0, x6, x7, x8) :|: TRUE
f7(x9, x10, x11, x12) -> f8(x9, 0, x11, x12) :|: TRUE
f10(x13, x14, x15, x16) -> f13(x13, arith, x15, x16) :|: TRUE && arith = x14 + 1
f11(x17, x18, x19, x20) -> f14(x17, 0, x19, x20) :|: TRUE
f14(x69, x70, x71, x72) -> f15(x73, x70, x71, x72) :|: TRUE && x73 = x69 + 1
f9(x25, x26, x27, x28) -> f10(x25, x26, x27, x28) :|: x26 < x27
f9(x29, x30, x31, x32) -> f11(x29, x30, x31, x32) :|: x30 >= x31
f13(x33, x34, x35, x36) -> f12(x33, x34, x35, x36) :|: TRUE
f15(x37, x38, x39, x40) -> f12(x37, x38, x39, x40) :|: TRUE
f8(x41, x42, x43, x44) -> f9(x41, x42, x43, x44) :|: x41 < x44
f12(x45, x46, x47, x48) -> f8(x45, x46, x47, x48) :|: TRUE
f8(x49, x50, x51, x52) -> f16(x49, x50, x51, x52) :|: x49 >= x52
f3(x53, x54, x55, x56) -> f4(x53, x54, x55, x56) :|: x55 > 0 && x56 > x55
f3(x57, x58, x59, x60) -> f5(x57, x58, x59, x60) :|: x59 <= 0
f3(x74, x75, x76, x77) -> f5(x74, x75, x76, x77) :|: x77 <= x76
f16(x61, x62, x63, x64) -> f6(x61, x62, x63, x64) :|: TRUE
f5(x65, x66, x67, x68) -> f6(x65, x66, x67, x68) :|: TRUE
Start term: f1(i, j, m, n)

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

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(4)
Obligation:
Rules:
f8(x41, x42, x43, x44) -> f9(x41, x42, x43, x44) :|: x41 < x44
f12(x45, x46, x47, x48) -> f8(x45, x46, x47, x48) :|: TRUE
f13(x33, x34, x35, x36) -> f12(x33, x34, x35, x36) :|: TRUE
f10(x13, x14, x15, x16) -> f13(x13, arith, x15, x16) :|: TRUE && arith = x14 + 1
f9(x25, x26, x27, x28) -> f10(x25, x26, x27, x28) :|: x26 < x27
f15(x37, x38, x39, x40) -> f12(x37, x38, x39, x40) :|: TRUE
f14(x69, x70, x71, x72) -> f15(x73, x70, x71, x72) :|: TRUE && x73 = x69 + 1
f11(x17, x18, x19, x20) -> f14(x17, 0, x19, x20) :|: TRUE
f9(x29, x30, x31, x32) -> f11(x29, x30, x31, x32) :|: x30 >= x31

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f12(x45:0, x46:0, x47:0, x48:0) -> f12(x45:0, x46:0 + 1, x47:0, x48:0) :|: x48:0 > x45:0 && x47:0 > x46:0
f12(x, x1, x2, x3) -> f12(x + 1, 0, x2, x3) :|: x3 > x && x2 <= x1

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(7) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f12 ] = f12_4 + -1*f12_1

The following rules are decreasing:
f12(x, x1, x2, x3) -> f12(x + 1, 0, x2, x3) :|: x3 > x && x2 <= x1

The following rules are bounded:
f12(x45:0, x46:0, x47:0, x48:0) -> f12(x45:0, x46:0 + 1, x47:0, x48:0) :|: x48:0 > x45:0 && x47:0 > x46:0
f12(x, x1, x2, x3) -> f12(x + 1, 0, x2, x3) :|: x3 > x && x2 <= x1


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(8)
Obligation:
Rules:
f12(x45:0, x46:0, x47:0, x48:0) -> f12(x45:0, x46:0 + 1, x47:0, x48:0) :|: x48:0 > x45:0 && x47:0 > x46:0

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f12(x, x1, x2, x3)] = -x1 + x2

The following rules are decreasing:
f12(x45:0, x46:0, x47:0, x48:0) -> f12(x45:0, x46:0 + 1, x47:0, x48:0) :|: x48:0 > x45:0 && x47:0 > x46:0
The following rules are bounded:
f12(x45:0, x46:0, x47:0, x48:0) -> f12(x45:0, x46:0 + 1, x47:0, x48:0) :|: x48:0 > x45:0 && x47:0 > x46:0

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(10)
YES