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	n045.star.cs.uiowa.edu
space	VMCAI05

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	17.1209728718 seconds
cpu usage	20.471606387
max memory	4.73366528E8

stage attributes

key	value
output-size	3624
starexec-result	MAYBE

output

/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- MAYBE proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, INF). (0) CpxIntTrs (1) Loat Proof [FINISHED, 14.7 s] (2) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval(A, B, C) -> Com_1(eval(A + 1, B + A, C)) :|: A >= B eval(A, B, C) -> Com_1(eval(A - C, B + C * C, C - 1)) :|: A >= B start(A, B, C) -> Com_1(eval(A, B, C)) :|: TRUE The start-symbols are:[start_3] ---------------------------------------- (1) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: start 0: eval -> eval : A'=1+A, B'=A+B, [ A>=B ], cost: 1 1: eval -> eval : A'=-C+A, B'=C^2+B, C'=-1+C, [ A>=B ], cost: 1 2: start -> eval : [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 0. Accelerating the following rules: 0: eval -> eval : A'=1+A, B'=A+B, [ A>=B ], cost: 1 1: eval -> eval : A'=-C+A, B'=C^2+B, C'=-1+C, [ A>=B ], cost: 1 Found no metering function for rule 0. Accelerated rule 1 with backward acceleration, yielding the new rule 3. Removing the simple loops: 1. Accelerated all simple loops using metering functions (where possible): Start location: start 0: eval -> eval : A'=1+A, B'=A+B, [ A>=B ], cost: 1 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 2: start -> eval : [], cost: 1 Chained accelerated rules (with incoming rules): Start location: start 2: start -> eval : [], cost: 1 4: start -> eval : A'=1+A, B'=A+B, [ A>=B ], cost: 2 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 Removed unreachable locations (and leaf rules with constant cost): Start location: start popout

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all output return to Compl Integ Trans Syste 26843