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Compl Integ Trans Syste 26843 pair #381745110
details
property
value
status
complete
benchmark
queue_1000.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n010.star.cs.uiowa.edu
space
T2
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
1.74385690689 seconds
cpu usage
3.893301706
max memory
3.076096E8
stage attributes
key
value
output-size
12992
starexec-result
WORST_CASE(?, O(1))
output
/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(1)) proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 119 ms] (2) BOUNDS(1, 1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: f0(A, B, C) -> Com_1(f8(0, B, C)) :|: TRUE f8(A, B, C) -> Com_1(f14(A, A, C)) :|: 999 >= A && 999 >= D f8(A, B, C) -> Com_1(f14(A, A, C)) :|: 999 >= A f23(A, B, C) -> Com_1(f28(A, B, D)) :|: 999 >= A && 0 >= E + 1 f23(A, B, C) -> Com_1(f28(A, B, D)) :|: 999 >= A f23(A, B, C) -> Com_1(f23(A + 1, B, C)) :|: 999 >= A f28(A, B, C) -> Com_1(f23(A + 1, B, C)) :|: TRUE f28(A, B, C) -> Com_1(f23(A + 1, B, C)) :|: 998 >= D f23(A, B, C) -> Com_1(f38(A, B, C)) :|: A >= 1000 f8(A, B, C) -> Com_1(f8(A + 1, A, C)) :|: 999 >= A f14(A, B, C) -> Com_1(f8(A + 1, B, C)) :|: TRUE f14(A, B, C) -> Com_1(f8(A + 1, B, C)) :|: 998 >= D f8(A, B, C) -> Com_1(f23(0, B, C)) :|: A >= 1000 The start-symbols are:[f0_3] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 14005) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2) -> Com_1(f8(0, ar_1, ar_2)) (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2) -> Com_1(f14(ar_0, ar_0, ar_2)) [ 999 >= ar_0 /\ 999 >= d ] (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2) -> Com_1(f14(ar_0, ar_0, ar_2)) [ 999 >= ar_0 ] (Comp: ?, Cost: 1) f23(ar_0, ar_1, ar_2) -> Com_1(f28(ar_0, ar_1, d)) [ 999 >= ar_0 /\ 0 >= e + 1 ] (Comp: ?, Cost: 1) f23(ar_0, ar_1, ar_2) -> Com_1(f28(ar_0, ar_1, d)) [ 999 >= ar_0 ] (Comp: ?, Cost: 1) f23(ar_0, ar_1, ar_2) -> Com_1(f23(ar_0 + 1, ar_1, ar_2)) [ 999 >= ar_0 ] (Comp: ?, Cost: 1) f28(ar_0, ar_1, ar_2) -> Com_1(f23(ar_0 + 1, ar_1, ar_2)) (Comp: ?, Cost: 1) f28(ar_0, ar_1, ar_2) -> Com_1(f23(ar_0 + 1, ar_1, ar_2)) [ 998 >= d ] (Comp: ?, Cost: 1) f23(ar_0, ar_1, ar_2) -> Com_1(f38(ar_0, ar_1, ar_2)) [ ar_0 >= 1000 ] (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2) -> Com_1(f8(ar_0 + 1, ar_0, ar_2)) [ 999 >= ar_0 ] (Comp: ?, Cost: 1) f14(ar_0, ar_1, ar_2) -> Com_1(f8(ar_0 + 1, ar_1, ar_2)) (Comp: ?, Cost: 1) f14(ar_0, ar_1, ar_2) -> Com_1(f8(ar_0 + 1, ar_1, ar_2)) [ 998 >= d ] (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2) -> Com_1(f23(0, ar_1, ar_2)) [ ar_0 >= 1000 ] (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(f0(ar_0, ar_1, ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [ar_0]. We thus obtain the following problem: 2: T: (Comp: 1, Cost: 0) koat_start(ar_0) -> Com_1(f0(ar_0)) [ 0 <= 0 ] (Comp: ?, Cost: 1) f8(ar_0) -> Com_1(f23(0)) [ ar_0 >= 1000 ] (Comp: ?, Cost: 1) f14(ar_0) -> Com_1(f8(ar_0 + 1)) [ 998 >= d ] (Comp: ?, Cost: 1) f14(ar_0) -> Com_1(f8(ar_0 + 1)) (Comp: ?, Cost: 1) f8(ar_0) -> Com_1(f8(ar_0 + 1)) [ 999 >= ar_0 ]
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