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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313418
details
property
value
status
complete
benchmark
ExAppendixB_AEL03_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n138.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
295.093 seconds
cpu usage
1152.84
user time
1141.86
system time
10.98
max virtual memory
3.7239608E7
max residence set size
1.4916648E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1152.69/295.01 WORST_CASE(Omega(n^1), ?) 1152.69/295.02 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1152.69/295.02 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1152.69/295.02 1152.69/295.02 1152.69/295.02 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1152.69/295.02 1152.69/295.02 (0) CpxTRS 1152.69/295.02 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1152.69/295.02 (2) TRS for Loop Detection 1152.69/295.02 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1152.69/295.02 (4) BEST 1152.69/295.02 (5) proven lower bound 1152.69/295.02 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1152.69/295.02 (7) BOUNDS(n^1, INF) 1152.69/295.02 (8) TRS for Loop Detection 1152.69/295.02 1152.69/295.02 1152.69/295.02 ---------------------------------------- 1152.69/295.02 1152.69/295.02 (0) 1152.69/295.02 Obligation: 1152.69/295.02 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1152.69/295.02 1152.69/295.02 1152.69/295.02 The TRS R consists of the following rules: 1152.69/295.02 1152.69/295.02 a__from(X) -> cons(mark(X), from(s(X))) 1152.69/295.02 a__2ndspos(0, Z) -> rnil 1152.69/295.02 a__2ndspos(s(N), cons(X, Z)) -> a__2ndspos(s(mark(N)), cons2(X, mark(Z))) 1152.69/295.02 a__2ndspos(s(N), cons2(X, cons(Y, Z))) -> rcons(posrecip(mark(Y)), a__2ndsneg(mark(N), mark(Z))) 1152.69/295.02 a__2ndsneg(0, Z) -> rnil 1152.69/295.02 a__2ndsneg(s(N), cons(X, Z)) -> a__2ndsneg(s(mark(N)), cons2(X, mark(Z))) 1152.69/295.02 a__2ndsneg(s(N), cons2(X, cons(Y, Z))) -> rcons(negrecip(mark(Y)), a__2ndspos(mark(N), mark(Z))) 1152.69/295.02 a__pi(X) -> a__2ndspos(mark(X), a__from(0)) 1152.69/295.02 a__plus(0, Y) -> mark(Y) 1152.69/295.02 a__plus(s(X), Y) -> s(a__plus(mark(X), mark(Y))) 1152.69/295.02 a__times(0, Y) -> 0 1152.69/295.02 a__times(s(X), Y) -> a__plus(mark(Y), a__times(mark(X), mark(Y))) 1152.69/295.02 a__square(X) -> a__times(mark(X), mark(X)) 1152.69/295.02 mark(from(X)) -> a__from(mark(X)) 1152.69/295.02 mark(2ndspos(X1, X2)) -> a__2ndspos(mark(X1), mark(X2)) 1152.69/295.02 mark(2ndsneg(X1, X2)) -> a__2ndsneg(mark(X1), mark(X2)) 1152.69/295.02 mark(pi(X)) -> a__pi(mark(X)) 1152.69/295.02 mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1152.69/295.02 mark(times(X1, X2)) -> a__times(mark(X1), mark(X2)) 1152.69/295.02 mark(square(X)) -> a__square(mark(X)) 1152.69/295.02 mark(0) -> 0 1152.69/295.02 mark(s(X)) -> s(mark(X)) 1152.69/295.02 mark(posrecip(X)) -> posrecip(mark(X)) 1152.69/295.02 mark(negrecip(X)) -> negrecip(mark(X)) 1152.69/295.02 mark(nil) -> nil 1152.69/295.02 mark(cons(X1, X2)) -> cons(mark(X1), X2) 1152.69/295.02 mark(cons2(X1, X2)) -> cons2(X1, mark(X2)) 1152.69/295.02 mark(rnil) -> rnil 1152.69/295.02 mark(rcons(X1, X2)) -> rcons(mark(X1), mark(X2)) 1152.69/295.02 a__from(X) -> from(X) 1152.69/295.02 a__2ndspos(X1, X2) -> 2ndspos(X1, X2) 1152.69/295.02 a__2ndsneg(X1, X2) -> 2ndsneg(X1, X2) 1152.69/295.02 a__pi(X) -> pi(X) 1152.69/295.02 a__plus(X1, X2) -> plus(X1, X2) 1152.69/295.02 a__times(X1, X2) -> times(X1, X2) 1152.69/295.02 a__square(X) -> square(X) 1152.69/295.02 1152.69/295.02 S is empty. 1152.69/295.02 Rewrite Strategy: INNERMOST 1152.69/295.02 ---------------------------------------- 1152.69/295.02 1152.69/295.02 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1152.69/295.02 Transformed a relative TRS into a decreasing-loop problem. 1152.69/295.02 ---------------------------------------- 1152.69/295.02 1152.69/295.02 (2) 1152.69/295.02 Obligation: 1152.69/295.02 Analyzing the following TRS for decreasing loops: 1152.69/295.02 1152.69/295.02 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1152.69/295.02 1152.69/295.02 1152.69/295.02 The TRS R consists of the following rules: 1152.69/295.02 1152.69/295.02 a__from(X) -> cons(mark(X), from(s(X))) 1152.69/295.02 a__2ndspos(0, Z) -> rnil 1152.69/295.02 a__2ndspos(s(N), cons(X, Z)) -> a__2ndspos(s(mark(N)), cons2(X, mark(Z))) 1152.69/295.02 a__2ndspos(s(N), cons2(X, cons(Y, Z))) -> rcons(posrecip(mark(Y)), a__2ndsneg(mark(N), mark(Z))) 1152.69/295.02 a__2ndsneg(0, Z) -> rnil 1152.69/295.02 a__2ndsneg(s(N), cons(X, Z)) -> a__2ndsneg(s(mark(N)), cons2(X, mark(Z))) 1152.69/295.02 a__2ndsneg(s(N), cons2(X, cons(Y, Z))) -> rcons(negrecip(mark(Y)), a__2ndspos(mark(N), mark(Z))) 1152.69/295.02 a__pi(X) -> a__2ndspos(mark(X), a__from(0)) 1152.69/295.02 a__plus(0, Y) -> mark(Y) 1152.69/295.02 a__plus(s(X), Y) -> s(a__plus(mark(X), mark(Y))) 1152.69/295.02 a__times(0, Y) -> 0 1152.69/295.02 a__times(s(X), Y) -> a__plus(mark(Y), a__times(mark(X), mark(Y))) 1152.69/295.02 a__square(X) -> a__times(mark(X), mark(X)) 1152.69/295.02 mark(from(X)) -> a__from(mark(X)) 1152.69/295.02 mark(2ndspos(X1, X2)) -> a__2ndspos(mark(X1), mark(X2)) 1152.69/295.02 mark(2ndsneg(X1, X2)) -> a__2ndsneg(mark(X1), mark(X2)) 1152.69/295.02 mark(pi(X)) -> a__pi(mark(X)) 1152.69/295.02 mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1152.69/295.02 mark(times(X1, X2)) -> a__times(mark(X1), mark(X2))
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return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40