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Runti Compl Inner Rewri 22807 pair #381904599
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
n052.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
1.53146600723 seconds
cpu usage
3.290735883
max memory
2.0881408E8
stage attributes
key
value
output-size
2920
starexec-result
WORST_CASE(NON_POLY, ?)
output
/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(NON_POLY, ?) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).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))].
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