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Runtime Complexity: TRS Innermost pair #487111748
details
property
value
status
complete
benchmark
otto04.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n143.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
1.56159 seconds
cpu usage
3.43746
user time
3.28501
system time
0.152456
max virtual memory
1.8275312E7
max residence set size
228652.0
stage attributes
key
value
starexec-result
WORST_CASE(NON_POLY, ?)
output
WORST_CASE(NON_POLY, ?) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). (0) CpxTRS (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (2) TRS for Loop Detection (3) DecreasingLoopProof [FINISHED, 0 ms] (4) BOUNDS(EXP, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). The TRS R consists of the following rules: lt(0, s(x)) -> true lt(x, 0) -> false lt(s(x), s(y)) -> lt(x, y) fibo(0) -> fib(0) fibo(s(0)) -> fib(s(0)) fibo(s(s(x))) -> sum(fibo(s(x)), fibo(x)) fib(0) -> s(0) fib(s(0)) -> s(0) fib(s(s(x))) -> if(true, 0, s(s(x)), 0, 0) if(true, c, s(s(x)), a, b) -> if(lt(s(c), s(s(x))), s(c), s(s(x)), b, c) if(false, c, s(s(x)), a, b) -> sum(fibo(a), fibo(b)) sum(x, 0) -> x sum(x, s(y)) -> s(sum(x, y)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (2) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). The TRS R consists of the following rules: lt(0, s(x)) -> true lt(x, 0) -> false lt(s(x), s(y)) -> lt(x, y) fibo(0) -> fib(0) fibo(s(0)) -> fib(s(0)) fibo(s(s(x))) -> sum(fibo(s(x)), fibo(x)) fib(0) -> s(0) fib(s(0)) -> s(0) fib(s(s(x))) -> if(true, 0, s(s(x)), 0, 0) if(true, c, s(s(x)), a, b) -> if(lt(s(c), s(s(x))), s(c), s(s(x)), b, c) if(false, c, s(s(x)), a, b) -> sum(fibo(a), fibo(b)) sum(x, 0) -> x sum(x, s(y)) -> s(sum(x, y)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) DecreasingLoopProof (FINISHED) The following loop(s) give(s) rise to the lower bound EXP: The rewrite sequence fibo(s(s(x))) ->^+ sum(fibo(s(x)), fibo(x)) gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. The pumping substitution is [x / s(x)]. The result substitution is [ ]. The rewrite sequence fibo(s(s(x))) ->^+ sum(fibo(s(x)), fibo(x)) gives rise to a decreasing loop by considering the right hand sides subterm at position [1]. The pumping substitution is [x / s(s(x))]. The result substitution is [ ].
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