details

property	value
status	complete
benchmark	sumit.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n168.star.cs.uiowa.edu
space	T2

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	4.9791 seconds
cpu usage	8.47599
user time	8.12139
system time	0.354605
max virtual memory	1.8685848E7
max residence set size	213804.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), ?)

output

8.35/4.93 WORST_CASE(Omega(n^1), ?) 8.35/4.94 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 8.35/4.94 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 8.35/4.94 8.35/4.94 8.35/4.94 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, INF). 8.35/4.94 8.35/4.94 (0) CpxIntTrs 8.35/4.94 (1) Loat Proof [FINISHED, 3221 ms] 8.35/4.94 (2) BOUNDS(n^1, INF) 8.35/4.94 8.35/4.94 8.35/4.94 ---------------------------------------- 8.35/4.94 8.35/4.94 (0) 8.35/4.94 Obligation: 8.35/4.94 Complexity Int TRS consisting of the following rules: 8.35/4.94 f6(A, B, C, D) -> Com_1(f7(A, B, C, D)) :|: 0 >= A + 1 8.35/4.94 f6(A, B, C, D) -> Com_1(f7(A, B, C, D)) :|: A >= 1 8.35/4.94 f0(A, B, C, D) -> Com_1(f4(A, B, C, B + 1)) :|: B >= 0 && C >= B 8.35/4.94 f4(A, B, C, D) -> Com_1(f6(E, B, C, D)) :|: B >= D + 1 8.35/4.94 f4(A, B, C, D) -> Com_1(f6(E, B, C, D)) :|: D >= 1 + B 8.35/4.94 f7(A, B, C, D) -> Com_1(f4(A, B, C, D + 1)) :|: C >= D 8.35/4.94 f7(A, B, C, D) -> Com_1(f4(A, B, C, 0)) :|: D >= 1 + C 8.35/4.94 f6(A, B, C, D) -> Com_1(f14(0, B, C, D)) :|: A >= 0 && A <= 0 8.35/4.94 f4(A, B, C, D) -> Com_1(f14(A, B, C, B)) :|: B >= D && B <= D 8.35/4.94 8.35/4.94 The start-symbols are:[f0_4] 8.35/4.94 8.35/4.94 8.35/4.94 ---------------------------------------- 8.35/4.94 8.35/4.94 (1) Loat Proof (FINISHED) 8.35/4.94 8.35/4.94 8.35/4.94 ### Pre-processing the ITS problem ### 8.35/4.94 8.35/4.94 8.35/4.94 8.35/4.94 Initial linear ITS problem 8.35/4.94 8.35/4.94 Start location: f0 8.35/4.94 8.35/4.94 0: f6 -> f7 : [ 0>=1+A ], cost: 1 8.35/4.94 8.35/4.94 1: f6 -> f7 : [ A>=1 ], cost: 1 8.35/4.94 8.35/4.94 7: f6 -> f14 : A'=0, [ A==0 ], cost: 1 8.35/4.94 8.35/4.94 2: f0 -> f4 : D'=1+B, [ B>=0 && C>=B ], cost: 1 8.35/4.94 8.35/4.94 3: f4 -> f6 : A'=free, [ B>=1+D ], cost: 1 8.35/4.94 8.35/4.94 4: f4 -> f6 : A'=free_1, [ D>=1+B ], cost: 1 8.35/4.94 8.35/4.94 8: f4 -> f14 : D'=B, [ B==D ], cost: 1 8.35/4.94 8.35/4.94 5: f7 -> f4 : D'=1+D, [ C>=D ], cost: 1 8.35/4.94 8.35/4.94 6: f7 -> f4 : D'=0, [ D>=1+C ], cost: 1 8.35/4.94 8.35/4.94 8.35/4.94 8.35/4.94 Removed unreachable and leaf rules: 8.35/4.94 8.35/4.94 Start location: f0 8.35/4.94 8.35/4.94 0: f6 -> f7 : [ 0>=1+A ], cost: 1 8.35/4.94 8.35/4.94 1: f6 -> f7 : [ A>=1 ], cost: 1 8.35/4.94 8.35/4.94 2: f0 -> f4 : D'=1+B, [ B>=0 && C>=B ], cost: 1 8.35/4.94 8.35/4.94 3: f4 -> f6 : A'=free, [ B>=1+D ], cost: 1 8.35/4.94 8.35/4.94 4: f4 -> f6 : A'=free_1, [ D>=1+B ], cost: 1 8.35/4.94 8.35/4.94 5: f7 -> f4 : D'=1+D, [ C>=D ], cost: 1 8.35/4.94 8.35/4.94 6: f7 -> f4 : D'=0, [ D>=1+C ], cost: 1 8.35/4.94 8.35/4.94 8.35/4.94 8.35/4.94 ### Simplification by acceleration and chaining ### 8.35/4.94 8.35/4.94 8.35/4.94 8.35/4.94 Eliminated locations (on tree-shaped paths): 8.35/4.94 8.35/4.94 Start location: f0 8.35/4.94 8.35/4.94 2: f0 -> f4 : D'=1+B, [ B>=0 && C>=B ], cost: 1 8.35/4.94 8.35/4.94 9: f4 -> f7 : A'=free, [ B>=1+D && 0>=1+free ], cost: 2 8.35/4.94 8.35/4.94 10: f4 -> f7 : A'=free, [ B>=1+D && free>=1 ], cost: 2 8.35/4.94 8.35/4.94 11: f4 -> f7 : A'=free_1, [ D>=1+B && 0>=1+free_1 ], cost: 2 8.35/4.94 8.35/4.94 12: f4 -> f7 : A'=free_1, [ D>=1+B && free_1>=1 ], cost: 2 popout

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all output return to Complexity_ITS 2019-03-21 04.46