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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313357
details
property
value
status
complete
benchmark
bft_mmult.raml.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n114.star.cs.uiowa.edu
space
raML
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.663 seconds
cpu usage
1103.32
user time
1082.91
system time
20.4106
max virtual memory
3.8189524E7
max residence set size
1.4683236E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1103.09/291.56 WORST_CASE(Omega(n^1), ?) 1103.15/291.56 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1103.15/291.56 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1103.15/291.56 1103.15/291.56 1103.15/291.56 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). 1103.15/291.56 1103.15/291.56 (0) CpxRelTRS 1103.15/291.56 (1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 357 ms] 1103.15/291.56 (2) CpxRelTRS 1103.15/291.56 (3) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1103.15/291.56 (4) TRS for Loop Detection 1103.15/291.56 (5) DecreasingLoopProof [LOWER BOUND(ID), 123 ms] 1103.15/291.56 (6) BEST 1103.15/291.56 (7) proven lower bound 1103.15/291.56 (8) LowerBoundPropagationProof [FINISHED, 0 ms] 1103.15/291.56 (9) BOUNDS(n^1, INF) 1103.15/291.56 (10) TRS for Loop Detection 1103.15/291.56 1103.15/291.56 1103.15/291.56 ---------------------------------------- 1103.15/291.56 1103.15/291.56 (0) 1103.15/291.56 Obligation: 1103.15/291.56 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). 1103.15/291.56 1103.15/291.56 1103.15/291.56 The TRS R consists of the following rules: 1103.15/291.56 1103.15/291.56 *(@x, @y) -> #mult(@x, @y) 1103.15/291.56 +(@x, @y) -> #add(@x, @y) 1103.15/291.56 appendreverse(@toreverse, @sofar) -> appendreverse#1(@toreverse, @sofar) 1103.15/291.56 appendreverse#1(::(@a, @as), @sofar) -> appendreverse(@as, ::(@a, @sofar)) 1103.15/291.56 appendreverse#1(nil, @sofar) -> @sofar 1103.15/291.56 bftMult(@t, @acc) -> bftMult'(tuple#2(::(@t, nil), nil), @acc) 1103.15/291.56 bftMult'(@queue, @acc) -> bftMult'#1(bftMult'#2(@queue), @acc) 1103.15/291.56 bftMult'#1(tuple#2(@elem, @queue), @acc) -> bftMult'#3(@elem, @acc, @queue) 1103.15/291.56 bftMult'#2(tuple#2(@dequeue@1, @dequeue@2)) -> dequeue(@dequeue@1, @dequeue@2) 1103.15/291.56 bftMult'#3(::(@t, @_@3), @acc, @queue) -> bftMult'#4(@t, @acc, @queue) 1103.15/291.56 bftMult'#3(nil, @acc, @queue) -> @acc 1103.15/291.56 bftMult'#4(leaf, @acc, @queue) -> bftMult'(@queue, @acc) 1103.15/291.56 bftMult'#4(node(@y, @t1, @t2), @acc, @queue) -> bftMult'#5(enqueue(@t2, enqueue(@t1, @queue)), @acc, @y) 1103.15/291.56 bftMult'#5(@queue', @acc, @y) -> bftMult'(@queue', matrixMult(@acc, @y)) 1103.15/291.56 computeLine(@line, @m, @acc) -> computeLine#1(@line, @acc, @m) 1103.15/291.56 computeLine#1(::(@x, @xs), @acc, @m) -> computeLine#2(@m, @acc, @x, @xs) 1103.15/291.56 computeLine#1(nil, @acc, @m) -> @acc 1103.15/291.56 computeLine#2(::(@l, @ls), @acc, @x, @xs) -> computeLine(@xs, @ls, lineMult(@x, @l, @acc)) 1103.15/291.56 computeLine#2(nil, @acc, @x, @xs) -> nil 1103.15/291.56 dequeue(@outq, @inq) -> dequeue#1(@outq, @inq) 1103.15/291.56 dequeue#1(::(@t, @ts), @inq) -> tuple#2(::(@t, nil), tuple#2(@ts, @inq)) 1103.15/291.56 dequeue#1(nil, @inq) -> dequeue#2(reverse(@inq)) 1103.15/291.56 dequeue#2(::(@t, @ts)) -> tuple#2(::(@t, nil), tuple#2(@ts, nil)) 1103.15/291.56 dequeue#2(nil) -> tuple#2(nil, tuple#2(nil, nil)) 1103.15/291.56 enqueue(@t, @queue) -> enqueue#1(@queue, @t) 1103.15/291.56 enqueue#1(tuple#2(@outq, @inq), @t) -> tuple#2(@outq, ::(@t, @inq)) 1103.15/291.56 lineMult(@n, @l1, @l2) -> lineMult#1(@l1, @l2, @n) 1103.15/291.56 lineMult#1(::(@x, @xs), @l2, @n) -> lineMult#2(@l2, @n, @x, @xs) 1103.15/291.56 lineMult#1(nil, @l2, @n) -> nil 1103.15/291.56 lineMult#2(::(@y, @ys), @n, @x, @xs) -> ::(+(*(@x, @n), @y), lineMult(@n, @xs, @ys)) 1103.15/291.56 lineMult#2(nil, @n, @x, @xs) -> ::(*(@x, @n), lineMult(@n, @xs, nil)) 1103.15/291.56 matrixMult(@m1, @m2) -> matrixMult#1(@m1, @m2) 1103.15/291.56 matrixMult#1(::(@l, @ls), @m2) -> ::(computeLine(@l, @m2, nil), matrixMult(@ls, @m2)) 1103.15/291.56 matrixMult#1(nil, @m2) -> nil 1103.15/291.56 reverse(@xs) -> appendreverse(@xs, nil) 1103.15/291.56 1103.15/291.56 The (relative) TRS S consists of the following rules: 1103.15/291.56 1103.15/291.56 #add(#0, @y) -> @y 1103.15/291.56 #add(#neg(#s(#0)), @y) -> #pred(@y) 1103.15/291.56 #add(#neg(#s(#s(@x))), @y) -> #pred(#add(#pos(#s(@x)), @y)) 1103.15/291.56 #add(#pos(#s(#0)), @y) -> #succ(@y) 1103.15/291.56 #add(#pos(#s(#s(@x))), @y) -> #succ(#add(#pos(#s(@x)), @y)) 1103.15/291.56 #mult(#0, #0) -> #0 1103.15/291.56 #mult(#0, #neg(@y)) -> #0 1103.15/291.56 #mult(#0, #pos(@y)) -> #0 1103.15/291.56 #mult(#neg(@x), #0) -> #0 1103.15/291.56 #mult(#neg(@x), #neg(@y)) -> #pos(#natmult(@x, @y)) 1103.15/291.56 #mult(#neg(@x), #pos(@y)) -> #neg(#natmult(@x, @y)) 1103.15/291.56 #mult(#pos(@x), #0) -> #0 1103.15/291.56 #mult(#pos(@x), #neg(@y)) -> #neg(#natmult(@x, @y)) 1103.15/291.56 #mult(#pos(@x), #pos(@y)) -> #pos(#natmult(@x, @y)) 1103.15/291.56 #natmult(#0, @y) -> #0 1103.15/291.56 #natmult(#s(@x), @y) -> #add(#pos(@y), #natmult(@x, @y)) 1103.15/291.56 #pred(#0) -> #neg(#s(#0)) 1103.15/291.56 #pred(#neg(#s(@x))) -> #neg(#s(#s(@x))) 1103.15/291.56 #pred(#pos(#s(#0))) -> #0 1103.15/291.56 #pred(#pos(#s(#s(@x)))) -> #pos(#s(@x)) 1103.15/291.56 #succ(#0) -> #pos(#s(#0)) 1103.15/291.56 #succ(#neg(#s(#0))) -> #0 1103.15/291.56 #succ(#neg(#s(#s(@x)))) -> #neg(#s(@x)) 1103.15/291.56 #succ(#pos(#s(@x))) -> #pos(#s(#s(@x))) 1103.15/291.56 1103.15/291.56 Rewrite Strategy: INNERMOST 1103.15/291.56 ---------------------------------------- 1103.15/291.56 1103.15/291.56 (1) STerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) 1103.15/291.56 proved termination of relative rules 1103.15/291.56 ---------------------------------------- 1103.15/291.56 1103.15/291.56 (2)
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return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40