YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 55 ms]
(4) IntTRS
(5) IntTRSCompressionProof [EQUIVALENT, 41 ms]
(6) IntTRS
(7) TerminationGraphProcessor [EQUIVALENT, 18 ms]
(8) IntTRS
(9) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(10) IntTRS
(11) RankingReductionPairProof [EQUIVALENT, 0 ms]
(12) YES


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

(0)
Obligation:
c file /export/starexec/sandbox2/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
f4(x4, x5) -> f5(arith, x5) :|: TRUE && arith = 2 * x4
f5(x14, x15) -> f6(x14, x16) :|: TRUE && x16 = x15 + 1
f3(x8, x9) -> f4(x8, x9) :|: x8 > 0 && x8 < x9
f6(x10, x11) -> f3(x10, x11) :|: TRUE
f3(x12, x13) -> f7(x12, x13) :|: x12 <= 0
f3(x17, x18) -> f7(x17, x18) :|: x17 >= x18
Start term: f1(x, y)

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

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

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

(4)
Obligation:
Rules:
f3(x8, x9) -> f4(x8, x9) :|: x8 > 0 && x8 < x9
f6(x10, x11) -> f3(x10, x11) :|: TRUE
f5(x14, x15) -> f6(x14, x16) :|: TRUE && x16 = x15 + 1
f4(x4, x5) -> f5(arith, x5) :|: TRUE && arith = 2 * x4

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

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

(6)
Obligation:
Rules:
f5(x14:0, x15:0) -> f5(2 * x14:0, x15:0 + 1) :|: x14:0 > 0 && x15:0 + 1 > x14:0

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

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

f5(x14:0, x15:0) -> f5(2 * x14:0, x15:0 + 1) :|: x14:0 > 0 && x15:0 + 1 > x14:0
has been transformed into
f5(x14:0, x15:0) -> f5(2 * x14:0, x15:0 + 1) :|: x15:0 = x5 + 1 && (x14:0 = 2 * x4 && (x14:0 > 0 && x15:0 + 1 > x14:0)) && x4 > 0 && x5 + 1 > x4.


f5(x14:0, x15:0) -> f5(2 * x14:0, x15:0 + 1) :|: x15:0 = x5 + 1 && (x14:0 = 2 * x4 && (x14:0 > 0 && x15:0 + 1 > x14:0)) && x4 > 0 && x5 + 1 > x4 and 
f5(x14:0, x15:0) -> f5(2 * x14:0, x15:0 + 1) :|: x15:0 = x5 + 1 && (x14:0 = 2 * x4 && (x14:0 > 0 && x15:0 + 1 > x14:0)) && x4 > 0 && x5 + 1 > x4
have been merged into the new rule
f5(x14, x15) -> f5(2 * (2 * x14), x15 + 1 + 1) :|: x15 = x16 + 1 && (x14 = 2 * x17 && (x14 > 0 && x15 + 1 > x14)) && x17 > 0 && x16 + 1 > x17 && (x15 + 1 = x18 + 1 && (2 * x14 = 2 * x19 && (2 * x14 > 0 && x15 + 1 + 1 > 2 * x14)) && x19 > 0 && x18 + 1 > x19)


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

(8)
Obligation:
Rules:
f5(x20, x21) -> f5(4 * x20, x21 + 2) :|: TRUE && x21 + -1 * x22 = 1 && x20 + -2 * x23 = 0 && x20 >= 1 && x21 + -1 * x20 >= 0 && x23 >= 1 && x22 + -1 * x23 >= 0 && x21 + -1 * x24 = 0 && x20 + -1 * x25 = 0 && x21 + -2 * x20 >= -1 && x25 >= 1 && x24 + -1 * x25 >= 0

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

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

(10)
Obligation:
Rules:
f5(x20:0, x21:0) -> f5(4 * x20:0, x21:0 + 2) :|: x25:0 > 0 && x24:0 + -1 * x25:0 >= 0 && x21:0 + -2 * x20:0 >= -1 && x20:0 + -1 * x25:0 = 0 && x21:0 + -1 * x24:0 = 0 && x22:0 + -1 * x23:0 >= 0 && x23:0 > 0 && x21:0 + -1 * x20:0 >= 0 && x20:0 > 0 && x21:0 + -1 * x22:0 = 1 && x20:0 + -2 * x23:0 = 0

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

(11) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f5 ] = 1/10*f5_2 + -1/5*f5_1

The following rules are decreasing:
f5(x20:0, x21:0) -> f5(4 * x20:0, x21:0 + 2) :|: x25:0 > 0 && x24:0 + -1 * x25:0 >= 0 && x21:0 + -2 * x20:0 >= -1 && x20:0 + -1 * x25:0 = 0 && x21:0 + -1 * x24:0 = 0 && x22:0 + -1 * x23:0 >= 0 && x23:0 > 0 && x21:0 + -1 * x20:0 >= 0 && x20:0 > 0 && x21:0 + -1 * x22:0 = 1 && x20:0 + -2 * x23:0 = 0

The following rules are bounded:
f5(x20:0, x21:0) -> f5(4 * x20:0, x21:0 + 2) :|: x25:0 > 0 && x24:0 + -1 * x25:0 >= 0 && x21:0 + -2 * x20:0 >= -1 && x20:0 + -1 * x25:0 = 0 && x21:0 + -1 * x24:0 = 0 && x22:0 + -1 * x23:0 >= 0 && x23:0 > 0 && x21:0 + -1 * x20:0 >= 0 && x20:0 > 0 && x21:0 + -1 * x22:0 = 1 && x20:0 + -2 * x23:0 = 0


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

(12)
YES