details

property	value
status	complete
benchmark	poly1.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n002.star.cs.uiowa.edu
space	VMCAI05

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	16.6912 seconds
cpu usage	20.8565
user time	20.2764
system time	0.580109
max virtual memory	1.8764096E7
max residence set size	264292.0

stage attributes

key	value
starexec-result	MAYBE

output

20.75/16.42 MAYBE 20.75/16.43 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 20.75/16.43 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 20.75/16.43 20.75/16.43 20.75/16.43 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, INF). 20.75/16.43 20.75/16.43 (0) CpxIntTrs 20.75/16.43 (1) Loat Proof [FINISHED, 14.8 s] 20.75/16.43 (2) BOUNDS(1, INF) 20.75/16.43 20.75/16.43 20.75/16.43 ---------------------------------------- 20.75/16.43 20.75/16.43 (0) 20.75/16.43 Obligation: 20.75/16.43 Complexity Int TRS consisting of the following rules: 20.75/16.43 eval(A, B, C) -> Com_1(eval(A + 1, B + A, C)) :|: A >= B 20.75/16.43 eval(A, B, C) -> Com_1(eval(A - C, B + C * C, C - 1)) :|: A >= B 20.75/16.43 start(A, B, C) -> Com_1(eval(A, B, C)) :|: TRUE 20.75/16.43 20.75/16.43 The start-symbols are:[start_3] 20.75/16.43 20.75/16.43 20.75/16.43 ---------------------------------------- 20.75/16.43 20.75/16.43 (1) Loat Proof (FINISHED) 20.75/16.43 20.75/16.43 20.75/16.43 ### Pre-processing the ITS problem ### 20.75/16.43 20.75/16.43 20.75/16.43 20.75/16.43 Initial linear ITS problem 20.75/16.43 20.75/16.43 Start location: start 20.75/16.43 20.75/16.43 0: eval -> eval : A'=1+A, B'=A+B, [ A>=B ], cost: 1 20.75/16.43 20.75/16.43 1: eval -> eval : A'=-C+A, B'=C^2+B, C'=-1+C, [ A>=B ], cost: 1 20.75/16.43 20.75/16.43 2: start -> eval : [], cost: 1 20.75/16.43 20.75/16.43 20.75/16.43 20.75/16.43 ### Simplification by acceleration and chaining ### 20.75/16.43 20.75/16.43 20.75/16.43 20.75/16.43 Accelerating simple loops of location 0. 20.75/16.43 20.75/16.43 Accelerating the following rules: 20.75/16.43 20.75/16.43 0: eval -> eval : A'=1+A, B'=A+B, [ A>=B ], cost: 1 20.75/16.43 20.75/16.43 1: eval -> eval : A'=-C+A, B'=C^2+B, C'=-1+C, [ A>=B ], cost: 1 20.75/16.43 20.75/16.43 20.75/16.43 20.75/16.43 Found no metering function for rule 0. 20.75/16.43 20.75/16.43 Accelerated rule 1 with backward acceleration, yielding the new rule 3. 20.75/16.43 20.75/16.43 Removing the simple loops: 1. 20.75/16.43 20.75/16.43 20.75/16.43 20.75/16.43 Accelerated all simple loops using metering functions (where possible): 20.75/16.43 20.75/16.43 Start location: start 20.75/16.43 20.75/16.43 0: eval -> eval : A'=1+A, B'=A+B, [ A>=B ], cost: 1 20.75/16.43 20.75/16.43 3: eval -> eval : A'=-1+1/2*k+A-k*C+1/2*k^2, B'=1-k^2*C-11/6*k+2*C+k*C^2+1/3*k^3-k*C+1/2*k^2+B, C'=-k+C, [ A>=B && k>0 && -3/2-(-1+k)*C+1/2*k+1/2*(-1+k)^2+A>=17/6-(-1+k)*C-11/6*k+2*C+(-1+k)*C^2+1/2*(-1+k)^2+1/3*(-1+k)^3-(-1+k)^2*C+B ], cost: k 20.75/16.43 20.75/16.43 2: start -> eval : [], cost: 1 20.75/16.43 20.75/16.43 20.75/16.43 20.75/16.43 Chained accelerated rules (with incoming rules): 20.75/16.43 20.75/16.43 Start location: start 20.75/16.43 20.75/16.43 2: start -> eval : [], cost: 1 20.75/16.43 20.75/16.43 4: start -> eval : A'=1+A, B'=A+B, [ A>=B ], cost: 2 20.75/16.43 20.75/16.43 5: start -> eval : A'=-1+1/2*k+A-k*C+1/2*k^2, B'=1-k^2*C-11/6*k+2*C+k*C^2+1/3*k^3-k*C+1/2*k^2+B, C'=-k+C, [ A>=B && k>0 && -3/2-(-1+k)*C+1/2*k+1/2*(-1+k)^2+A>=17/6-(-1+k)*C-11/6*k+2*C+(-1+k)*C^2+1/2*(-1+k)^2+1/3*(-1+k)^3-(-1+k)^2*C+B ], cost: 1+k 20.75/16.43 20.75/16.43 20.75/16.43 20.75/16.43 Removed unreachable locations (and leaf rules with constant cost): 20.75/16.43 20.75/16.43 Start location: start 20.75/16.43 20.75/16.43 5: start -> eval : A'=-1+1/2*k+A-k*C+1/2*k^2, B'=1-k^2*C-11/6*k+2*C+k*C^2+1/3*k^3-k*C+1/2*k^2+B, C'=-k+C, [ A>=B && k>0 && -3/2-(-1+k)*C+1/2*k+1/2*(-1+k)^2+A>=17/6-(-1+k)*C-11/6*k+2*C+(-1+k)*C^2+1/2*(-1+k)^2+1/3*(-1+k)^3-(-1+k)^2*C+B ], cost: 1+k 20.75/16.43 20.75/16.43 20.75/16.43 20.75/16.43 ### Computing asymptotic complexity ### popout

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actions

all output return to Complexity_ITS 2019-03-21 04.46