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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 0 ms]
(6) IntTRS
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IntTRS
(9) RankingReductionPairProof [EQUIVALENT, 27 ms]
(10) YES


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

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

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

(2)
Obligation:
Rules:
f1(c, x, y) -> f2(c, x_1, y) :|: TRUE
f2(x1, x2, x3) -> f3(x1, x2, x4) :|: TRUE
f3(x5, x6, x7) -> f4(0, x6, x7) :|: TRUE
f9(x8, x9, x10) -> f12(x8, x10, x10) :|: TRUE
f10(x11, x12, x13) -> f13(x11, arith, x13) :|: TRUE && arith = x12 - 1
f8(x14, x15, x16) -> f9(x14, x15, x16) :|: x15 > x16
f8(x17, x18, x19) -> f10(x17, x18, x19) :|: x18 <= x19
f12(x20, x21, x22) -> f11(x20, x21, x22) :|: TRUE
f13(x23, x24, x25) -> f11(x23, x24, x25) :|: TRUE
f11(x50, x51, x52) -> f14(x53, x51, x52) :|: TRUE && x53 = x50 + 1
f5(x29, x30, x31) -> f8(x29, x30, x31) :|: x30 > 0
f14(x32, x33, x34) -> f5(x32, x33, x34) :|: TRUE
f5(x35, x36, x37) -> f15(x35, x36, x37) :|: x36 <= 0
f4(x38, x39, x40) -> f5(x38, x39, x40) :|: x40 > 0
f4(x41, x42, x43) -> f6(x41, x42, x43) :|: x43 <= 0
f15(x44, x45, x46) -> f7(x44, x45, x46) :|: TRUE
f6(x47, x48, x49) -> f7(x47, x48, x49) :|: TRUE
Start term: f1(c, x, y)

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

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

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

(4)
Obligation:
Rules:
f5(x29, x30, x31) -> f8(x29, x30, x31) :|: x30 > 0
f14(x32, x33, x34) -> f5(x32, x33, x34) :|: TRUE
f11(x50, x51, x52) -> f14(x53, x51, x52) :|: TRUE && x53 = x50 + 1
f12(x20, x21, x22) -> f11(x20, x21, x22) :|: TRUE
f9(x8, x9, x10) -> f12(x8, x10, x10) :|: TRUE
f8(x14, x15, x16) -> f9(x14, x15, x16) :|: x15 > x16
f13(x23, x24, x25) -> f11(x23, x24, x25) :|: TRUE
f10(x11, x12, x13) -> f13(x11, arith, x13) :|: TRUE && arith = x12 - 1
f8(x17, x18, x19) -> f10(x17, x18, x19) :|: x18 <= x19

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

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

(6)
Obligation:
Rules:
f11(x50:0, x51:0, x52:0) -> f11(x50:0 + 1, x52:0, x52:0) :|: x51:0 > 0 && x52:0 < x51:0
f11(x, x1, x2) -> f11(x + 1, x1 - 1, x2) :|: x1 > 0 && x2 >= x1

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

(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)

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

(8)
Obligation:
Rules:
f11(x51:0, x52:0) -> f11(x52:0, x52:0) :|: x51:0 > 0 && x52:0 < x51:0
f11(x1, x2) -> f11(x1 - 1, x2) :|: x1 > 0 && x2 >= x1

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

(9) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f11 ] = f11_1

The following rules are decreasing:
f11(x51:0, x52:0) -> f11(x52:0, x52:0) :|: x51:0 > 0 && x52:0 < x51:0
f11(x1, x2) -> f11(x1 - 1, x2) :|: x1 > 0 && x2 >= x1

The following rules are bounded:
f11(x51:0, x52:0) -> f11(x52:0, x52:0) :|: x51:0 > 0 && x52:0 < x51:0
f11(x1, x2) -> f11(x1 - 1, x2) :|: x1 > 0 && x2 >= x1


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

(10)
YES