/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 54 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 28 ms]
(6) IntTRS
(7) CaseAnalysis [EQUIVALENT, 20 ms]
(8) AND
    (9) IntTRS
        (10) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (11) IntTRS
        (12) TerminationGraphProcessor [EQUIVALENT, 16 ms]
        (13) IntTRS
        (14) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (15) IntTRS
        (16) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (17) IntTRS
        (18) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (19) IntTRS
        (20) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (21) YES
    (22) IntTRS
        (23) TerminationGraphProcessor [EQUIVALENT, 16 ms]
        (24) IntTRS
        (25) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (26) IntTRS
        (27) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (28) 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) -> f2(x_1, y) :|: TRUE
f2(x1, x2) -> f3(x1, x3) :|: TRUE
f5(x4, x5) -> f8(x4, arith) :|: TRUE && arith = x5 + 1
f6(x22, x23) -> f9(x24, x23) :|: TRUE && x24 = x22 + 1
f4(x8, x9) -> f5(x8, x9) :|: x8 > x9
f4(x10, x11) -> f6(x10, x11) :|: x10 <= x11
f8(x12, x13) -> f7(x12, x13) :|: TRUE
f9(x14, x15) -> f7(x14, x15) :|: TRUE
f3(x16, x17) -> f4(x16, x17) :|: x16 < x17
f3(x25, x26) -> f4(x25, x26) :|: x25 > x26
f7(x18, x19) -> f3(x18, x19) :|: TRUE
f3(x20, x21) -> f10(x20, x21) :|: x20 = x21
Start term: f1(x, y)

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

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

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

(4)
Obligation:
Rules:
f3(x16, x17) -> f4(x16, x17) :|: x16 < x17
f7(x18, x19) -> f3(x18, x19) :|: TRUE
f8(x12, x13) -> f7(x12, x13) :|: TRUE
f5(x4, x5) -> f8(x4, arith) :|: TRUE && arith = x5 + 1
f4(x8, x9) -> f5(x8, x9) :|: x8 > x9
f3(x25, x26) -> f4(x25, x26) :|: x25 > x26
f9(x14, x15) -> f7(x14, x15) :|: TRUE
f6(x22, x23) -> f9(x24, x23) :|: TRUE && x24 = x22 + 1
f4(x10, x11) -> f6(x10, x11) :|: x10 <= x11

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

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

(6)
Obligation:
Rules:
f4(x10:0, x11:0) -> f7(x10:0 + 1, x11:0) :|: x11:0 >= x10:0
f7(x18:0, x19:0) -> f4(x18:0, x19:0) :|: x19:0 < x18:0
f4(x8:0, x9:0) -> f7(x8:0, x9:0 + 1) :|: x9:0 < x8:0
f7(x, x1) -> f4(x, x1) :|: x1 > x

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

(7) CaseAnalysis (EQUIVALENT)
Found the following inductive condition: 
f4(x, x1): 3 - 3*x + 3*x1>=0
f7(x2, x3): 3 - 3*x2 + 3*x3>=0

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

(8)
Complex Obligation (AND)

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

(9)
Obligation:
Rules:
f4(x10:0, x11:0) -> f7(x10:0 + 1, x11:0) :|: x11:0 >= x10:0 && 3 + -3 * x10:0 + 3 * x11:0 >= 0
f7(x18:0, x19:0) -> f4(x18:0, x19:0) :|: x19:0 < x18:0 && 3 + -3 * x18:0 + 3 * x19:0 >= 0
f4(x8:0, x9:0) -> f7(x8:0, x9:0 + 1) :|: x9:0 < x8:0 && 3 + -3 * x8:0 + 3 * x9:0 >= 0
f7(x, x1) -> f4(x, x1) :|: x1 > x && 3 + -3 * x + 3 * x1 >= 0

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

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

(11)
Obligation:
Rules:
f7(x18:0:0, x19:0:0) -> f4(x18:0:0, x19:0:0) :|: x19:0:0 < x18:0:0 && 3 + -3 * x18:0:0 + 3 * x19:0:0 >= 0
f4(x8:0:0, x9:0:0) -> f7(x8:0:0, x9:0:0 + 1) :|: x9:0:0 < x8:0:0 && 3 + -3 * x8:0:0 + 3 * x9:0:0 >= 0
f4(x10:0:0, x11:0:0) -> f7(x10:0:0 + 1, x11:0:0) :|: x11:0:0 >= x10:0:0 && 3 + -3 * x10:0:0 + 3 * x11:0:0 >= 0
f7(x:0, x1:0) -> f4(x:0, x1:0) :|: x:0 < x1:0 && 3 + -3 * x:0 + 3 * x1:0 >= 0

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

(12) TerminationGraphProcessor (EQUIVALENT)
Constructed the termination graph and obtained one non-trivial SCC.

f7(x18:0:0, x19:0:0) -> f4(x18:0:0, x19:0:0) :|: x19:0:0 < x18:0:0 && 3 + -3 * x18:0:0 + 3 * x19:0:0 >= 0 and 
f4(x8:0:0, x9:0:0) -> f7(x8:0:0, x9:0:0 + 1) :|: x9:0:0 < x8:0:0 && 3 + -3 * x8:0:0 + 3 * x9:0:0 >= 0
have been merged into the new rule
f7(x12, x13) -> f7(x12, x13 + 1) :|: x13 < x12 && 3 + -3 * x12 + 3 * x13 >= 0 && (x13 < x12 && 3 + -3 * x12 + 3 * x13 >= 0)

f7(x18:0:0, x19:0:0) -> f4(x18:0:0, x19:0:0) :|: x19:0:0 < x18:0:0 && 3 + -3 * x18:0:0 + 3 * x19:0:0 >= 0 and 
f4(x10:0:0, x11:0:0) -> f7(x10:0:0 + 1, x11:0:0) :|: x11:0:0 >= x10:0:0 && 3 + -3 * x10:0:0 + 3 * x11:0:0 >= 0
have been merged into the new rule
f7(x20, x21) -> f7(x20 + 1, x21) :|: x21 < x20 && 3 + -3 * x20 + 3 * x21 >= 0 && (x21 >= x20 && 3 + -3 * x20 + 3 * x21 >= 0)


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

(13)
Obligation:
Rules:
f7(x14, x15) -> f7(x14, x15 + 1) :|: TRUE && x15 + -1 * x14 <= -1 && -1 * x14 + x15 >= -1
f4(x8:0:0, x9:0:0) -> f7(x8:0:0, x9:0:0 + 1) :|: TRUE && x9:0:0 + -1 * x8:0:0 <= -1 && -1 * x8:0:0 + x9:0:0 >= -1
f7(x:0, x1:0) -> f4(x:0, x1:0) :|: TRUE && x:0 + -1 * x1:0 <= -1
f4(x10:0:0, x11:0:0) -> f7(x10:0:0 + 1, x11:0:0) :|: TRUE && x11:0:0 + -1 * x10:0:0 >= 0

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

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

(15)
Obligation:
Rules:
f7(x:0:0, x1:0:0) -> f7(x:0:0 + 1, x1:0:0) :|: x:0:0 + -1 * x1:0:0 <= -1 && x1:0:0 + -1 * x:0:0 >= 0
f7(x, x1) -> f7(x, x1 + 1) :|: -1 * x + x1 >= -1 && x1 + -1 * x <= -1 && x + -1 * x1 <= -1
f7(x14:0, x15:0) -> f7(x14:0, x15:0 + 1) :|: -1 * x14:0 + x15:0 >= -1 && x15:0 + -1 * x14:0 <= -1

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

(16) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f7 ] = 0

The following rules are decreasing:
f7(x, x1) -> f7(x, x1 + 1) :|: -1 * x + x1 >= -1 && x1 + -1 * x <= -1 && x + -1 * x1 <= -1

The following rules are bounded:
f7(x:0:0, x1:0:0) -> f7(x:0:0 + 1, x1:0:0) :|: x:0:0 + -1 * x1:0:0 <= -1 && x1:0:0 + -1 * x:0:0 >= 0
f7(x, x1) -> f7(x, x1 + 1) :|: -1 * x + x1 >= -1 && x1 + -1 * x <= -1 && x + -1 * x1 <= -1
f7(x14:0, x15:0) -> f7(x14:0, x15:0 + 1) :|: -1 * x14:0 + x15:0 >= -1 && x15:0 + -1 * x14:0 <= -1


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

(17)
Obligation:
Rules:
f7(x:0:0, x1:0:0) -> f7(x:0:0 + 1, x1:0:0) :|: x:0:0 + -1 * x1:0:0 <= -1 && x1:0:0 + -1 * x:0:0 >= 0
f7(x14:0, x15:0) -> f7(x14:0, x15:0 + 1) :|: -1 * x14:0 + x15:0 >= -1 && x15:0 + -1 * x14:0 <= -1

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

(18) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f7(x, x1)] = -1 + x - 2*x*x1 + x^2 - x1 + x1^2

The following rules are decreasing:
f7(x14:0, x15:0) -> f7(x14:0, x15:0 + 1) :|: -1 * x14:0 + x15:0 >= -1 && x15:0 + -1 * x14:0 <= -1
The following rules are bounded:
f7(x14:0, x15:0) -> f7(x14:0, x15:0 + 1) :|: -1 * x14:0 + x15:0 >= -1 && x15:0 + -1 * x14:0 <= -1

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

(19)
Obligation:
Rules:
f7(x:0:0, x1:0:0) -> f7(x:0:0 + 1, x1:0:0) :|: x:0:0 + -1 * x1:0:0 <= -1 && x1:0:0 + -1 * x:0:0 >= 0

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

(20) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f7 ] = -1*f7_1 + f7_2

The following rules are decreasing:
f7(x:0:0, x1:0:0) -> f7(x:0:0 + 1, x1:0:0) :|: x:0:0 + -1 * x1:0:0 <= -1 && x1:0:0 + -1 * x:0:0 >= 0

The following rules are bounded:
f7(x:0:0, x1:0:0) -> f7(x:0:0 + 1, x1:0:0) :|: x:0:0 + -1 * x1:0:0 <= -1 && x1:0:0 + -1 * x:0:0 >= 0


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

(21)
YES

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

(22)
Obligation:
Rules:
f4(x10:0, x11:0) -> f7(x10:0 + 1, x11:0) :|: x11:0 >= x10:0 && 3 + -3 * x10:0 + 3 * x11:0 < 0
f7(x18:0, x19:0) -> f4(x18:0, x19:0) :|: x19:0 < x18:0 && 3 + -3 * x18:0 + 3 * x19:0 < 0
f4(x8:0, x9:0) -> f7(x8:0, x9:0 + 1) :|: x9:0 < x8:0 && 3 + -3 * x8:0 + 3 * x9:0 < 0
f7(x, x1) -> f4(x, x1) :|: x1 > x && 3 + -3 * x + 3 * x1 < 0

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

(23) TerminationGraphProcessor (EQUIVALENT)
Constructed the termination graph and obtained one non-trivial SCC.

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

(24)
Obligation:
Rules:
f7(x18:0, x19:0) -> f4(x18:0, x19:0) :|: x19:0 < x18:0 && 3 + -3 * x18:0 + 3 * x19:0 < 0
f4(x8:0, x9:0) -> f7(x8:0, x9:0 + 1) :|: x9:0 < x8:0 && 3 + -3 * x8:0 + 3 * x9:0 < 0

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

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

(26)
Obligation:
Rules:
f7(x18:0:0, x19:0:0) -> f7(x18:0:0, x19:0:0 + 1) :|: 3 + -3 * x18:0:0 + 3 * x19:0:0 < 0 && x19:0:0 < x18:0:0

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

(27) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f7 ] = f7_1 + -1*f7_2

The following rules are decreasing:
f7(x18:0:0, x19:0:0) -> f7(x18:0:0, x19:0:0 + 1) :|: 3 + -3 * x18:0:0 + 3 * x19:0:0 < 0 && x19:0:0 < x18:0:0

The following rules are bounded:
f7(x18:0:0, x19:0:0) -> f7(x18:0:0, x19:0:0 + 1) :|: 3 + -3 * x18:0:0 + 3 * x19:0:0 < 0 && x19:0:0 < x18:0:0


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

(28)
YES