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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 66 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 21 ms]
(6) IntTRS
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 14 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(a, x, max) -> f2(a, x, x_1) :|: TRUE
f3(x1, x2, x3) -> f6(0, x2, x3) :|: TRUE
f6(x4, x5, x6) -> f7(x4, 1, x6) :|: TRUE
f9(x7, x8, x9) -> f12(arith, x8, x9) :|: TRUE && arith = x7 + 1
f10(x51, x52, x53) -> f13(x54, x52, x53) :|: TRUE && x54 = x51 - 1
f8(x13, x14, x15) -> f9(x13, x14, x15) :|: x16 < 0
f8(x55, x56, x57) -> f9(x55, x56, x57) :|: x58 > 0
f8(x17, x18, x19) -> f10(x17, x18, x19) :|: x20 = 0
f12(x21, x22, x23) -> f11(x21, x22, x23) :|: TRUE
f13(x24, x25, x26) -> f11(x24, x25, x26) :|: TRUE
f11(x59, x60, x61) -> f14(x59, x62, x61) :|: TRUE && x62 = x60 + 1
f7(x30, x31, x32) -> f8(x30, x31, x32) :|: x31 <= x32
f14(x33, x34, x35) -> f7(x33, x34, x35) :|: TRUE
f7(x36, x37, x38) -> f15(x36, x37, x38) :|: x37 > x38
f2(x39, x40, x41) -> f3(x39, x40, x41) :|: x41 > 0
f2(x42, x43, x44) -> f4(x42, x43, x44) :|: x44 <= 0
f15(x45, x46, x47) -> f5(x45, x46, x47) :|: TRUE
f4(x48, x49, x50) -> f5(x48, x49, x50) :|: TRUE
Start term: f1(a, x, max)

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

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(4)
Obligation:
Rules:
f7(x30, x31, x32) -> f8(x30, x31, x32) :|: x31 <= x32
f14(x33, x34, x35) -> f7(x33, x34, x35) :|: TRUE
f11(x59, x60, x61) -> f14(x59, x62, x61) :|: TRUE && x62 = x60 + 1
f12(x21, x22, x23) -> f11(x21, x22, x23) :|: TRUE
f9(x7, x8, x9) -> f12(arith, x8, x9) :|: TRUE && arith = x7 + 1
f8(x13, x14, x15) -> f9(x13, x14, x15) :|: x16 < 0
f8(x55, x56, x57) -> f9(x55, x56, x57) :|: x58 > 0
f13(x24, x25, x26) -> f11(x24, x25, x26) :|: TRUE
f10(x51, x52, x53) -> f13(x54, x52, x53) :|: TRUE && x54 = x51 - 1
f8(x17, x18, x19) -> f10(x17, x18, x19) :|: x20 = 0

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(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(6)
Obligation:
Rules:
f11(x59:0, x60:0, x61:0) -> f11(x59:0 + 1, x60:0 + 1, x61:0) :|: x61:0 >= x60:0 + 1 && x16:0 < 0
f11(x, x1, x2) -> f11(x - 1, x1 + 1, x2) :|: x2 >= x1 + 1
f11(x3, x4, x5) -> f11(x3 + 1, x4 + 1, x5) :|: x5 >= x4 + 1 && x6 > 0

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(7) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:

   f11(x1, x2, x3) -> f11(x2, x3)

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(8)
Obligation:
Rules:
f11(x60:0, x61:0) -> f11(x60:0 + 1, x61:0) :|: x61:0 >= x60:0 + 1 && x16:0 < 0
f11(x1, x2) -> f11(x1 + 1, x2) :|: x2 >= x1 + 1
f11(x4, x5) -> f11(x4 + 1, x5) :|: x5 >= x4 + 1 && x6 > 0

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(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f11(x, x1)] = -x + x1

The following rules are decreasing:
f11(x60:0, x61:0) -> f11(x60:0 + 1, x61:0) :|: x61:0 >= x60:0 + 1 && x16:0 < 0
f11(x1, x2) -> f11(x1 + 1, x2) :|: x2 >= x1 + 1
f11(x4, x5) -> f11(x4 + 1, x5) :|: x5 >= x4 + 1 && x6 > 0
The following rules are bounded:
f11(x60:0, x61:0) -> f11(x60:0 + 1, x61:0) :|: x61:0 >= x60:0 + 1 && x16:0 < 0
f11(x1, x2) -> f11(x1 + 1, x2) :|: x2 >= x1 + 1
f11(x4, x5) -> f11(x4 + 1, x5) :|: x5 >= x4 + 1 && x6 > 0

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(10)
YES