/export/starexec/sandbox/solver/bin/starexec_run_c /export/starexec/sandbox/benchmark/theBenchmark.c /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.c
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination of the given C Problem could be proven:

(0) C Problem
(1) CToIRSProof [EQUIVALENT, 0 ms]
(2) IntTRS
(3) TerminationGraphProcessor [SOUND, 42 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 8 ms]
(6) IntTRS
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IntTRS
(9) PolynomialOrderProcessor [EQUIVALENT, 12 ms]
(10) IntTRS
(11) TerminationGraphProcessor [EQUIVALENT, 8 ms]
(12) AND
    (13) IntTRS
        (14) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (15) YES
    (16) IntTRS
        (17) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (18) IntTRS
        (19) PolynomialOrderProcessor [EQUIVALENT, 4 ms]
        (20) YES


----------------------------------------

(0)
Obligation:
c file /export/starexec/sandbox/benchmark/theBenchmark.c
----------------------------------------

(1) CToIRSProof (EQUIVALENT)
Parsed C Integer Program as IRS.
----------------------------------------

(2)
Obligation:
Rules:
f1(x, y, z) -> f2(0, y, z) :|: TRUE
f2(x1, x2, x3) -> f3(x1, 100, x3) :|: TRUE
f3(x4, x5, x6) -> f4(x4, x5, x7) :|: TRUE
f6(x8, x9, x10) -> f9(arith, x9, x10) :|: TRUE && arith = x8 + 1
f7(x35, x36, x37) -> f10(x38, x36, x37) :|: TRUE && x38 = x35 + 2
f5(x14, x15, x16) -> f6(x14, x15, x16) :|: x16 = 0
f5(x17, x18, x19) -> f7(x17, x18, x19) :|: x19 < 0
f5(x39, x40, x41) -> f7(x39, x40, x41) :|: x41 > 0
f9(x20, x21, x22) -> f8(x20, x21, x22) :|: TRUE
f10(x23, x24, x25) -> f8(x23, x24, x25) :|: TRUE
f4(x26, x27, x28) -> f5(x26, x27, x28) :|: x26 < 40
f8(x29, x30, x31) -> f4(x29, x30, x31) :|: TRUE
f4(x32, x33, x34) -> f11(x32, x33, x34) :|: x32 >= 40
Start term: f1(x, y, z)

----------------------------------------

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

----------------------------------------

(4)
Obligation:
Rules:
f4(x26, x27, x28) -> f5(x26, x27, x28) :|: x26 < 40
f8(x29, x30, x31) -> f4(x29, x30, x31) :|: TRUE
f9(x20, x21, x22) -> f8(x20, x21, x22) :|: TRUE
f6(x8, x9, x10) -> f9(arith, x9, x10) :|: TRUE && arith = x8 + 1
f5(x14, x15, x16) -> f6(x14, x15, x16) :|: x16 = 0
f10(x23, x24, x25) -> f8(x23, x24, x25) :|: TRUE
f7(x35, x36, x37) -> f10(x38, x36, x37) :|: TRUE && x38 = x35 + 2
f5(x17, x18, x19) -> f7(x17, x18, x19) :|: x19 < 0
f5(x39, x40, x41) -> f7(x39, x40, x41) :|: x41 > 0

----------------------------------------

(5) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
----------------------------------------

(6)
Obligation:
Rules:
f8(x29:0, x30:0, x31:0) -> f8(x29:0 + 2, x30:0, x31:0) :|: x29:0 < 40 && x31:0 < 0
f8(x, x1, x2) -> f8(x + 1, x1, 0) :|: x < 40 && x2 = 0
f8(x3, x4, x5) -> f8(x3 + 2, x4, x5) :|: x3 < 40 && x5 > 0

----------------------------------------

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

   f8(x1, x2, x3) -> f8(x1, x3)

----------------------------------------

(8)
Obligation:
Rules:
f8(x29:0, x31:0) -> f8(x29:0 + 2, x31:0) :|: x29:0 < 40 && x31:0 < 0
f8(x, x2) -> f8(x + 1, 0) :|: x < 40 && x2 = 0
f8(x3, x5) -> f8(x3 + 2, x5) :|: x3 < 40 && x5 > 0

----------------------------------------

(9) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f8(x, x1)] = 38 - x + x1

The following rules are decreasing:
f8(x29:0, x31:0) -> f8(x29:0 + 2, x31:0) :|: x29:0 < 40 && x31:0 < 0
f8(x, x2) -> f8(x + 1, 0) :|: x < 40 && x2 = 0
f8(x3, x5) -> f8(x3 + 2, x5) :|: x3 < 40 && x5 > 0
The following rules are bounded:
f8(x3, x5) -> f8(x3 + 2, x5) :|: x3 < 40 && x5 > 0

----------------------------------------

(10)
Obligation:
Rules:
f8(x29:0, x31:0) -> f8(x29:0 + 2, x31:0) :|: x29:0 < 40 && x31:0 < 0
f8(x, x2) -> f8(x + 1, 0) :|: x < 40 && x2 = 0

----------------------------------------

(11) TerminationGraphProcessor (EQUIVALENT)
Constructed the termination graph and obtained 2 non-trivial SCCs.

----------------------------------------

(12)
Complex Obligation (AND)

----------------------------------------

(13)
Obligation:
Rules:
f8(x29:0, x31:0) -> f8(x29:0 + 2, x31:0) :|: x29:0 < 40 && x31:0 < 0

----------------------------------------

(14) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f8(x, x1)] = 39 - x

The following rules are decreasing:
f8(x29:0, x31:0) -> f8(x29:0 + 2, x31:0) :|: x29:0 < 40 && x31:0 < 0
The following rules are bounded:
f8(x29:0, x31:0) -> f8(x29:0 + 2, x31:0) :|: x29:0 < 40 && x31:0 < 0

----------------------------------------

(15)
YES

----------------------------------------

(16)
Obligation:
Rules:
f8(x, x2) -> f8(x + 1, 0) :|: x < 40 && x2 = 0

----------------------------------------

(17) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
----------------------------------------

(18)
Obligation:
Rules:
f8(x:0, cons_0) -> f8(x:0 + 1, 0) :|: x:0 < 40 && cons_0 = 0

----------------------------------------

(19) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f8(x, x1)] = 39 - x + c4*x*x1 + c2*x1 + c3*x1^2

The following rules are decreasing:
f8(x:0, cons_0) -> f8(x:0 + 1, 0) :|: x:0 < 40 && cons_0 = 0
The following rules are bounded:
f8(x:0, cons_0) -> f8(x:0 + 1, 0) :|: x:0 < 40 && cons_0 = 0

----------------------------------------

(20)
YES