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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313467
details
property
value
status
complete
benchmark
ExProp7_Luc06_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n054.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
1.63787 seconds
cpu usage
3.28431
user time
3.12609
system time
0.158223
max virtual memory
1.8277336E7
max residence set size
217004.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(1))
output
2.98/1.59 WORST_CASE(?, O(1)) 2.98/1.60 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 2.98/1.60 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.98/1.60 2.98/1.60 2.98/1.60 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1). 2.98/1.60 2.98/1.60 (0) CpxTRS 2.98/1.60 (1) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms] 2.98/1.60 (2) BOUNDS(1, 1) 2.98/1.60 2.98/1.60 2.98/1.60 ---------------------------------------- 2.98/1.60 2.98/1.60 (0) 2.98/1.60 Obligation: 2.98/1.60 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, 1). 2.98/1.60 2.98/1.60 2.98/1.60 The TRS R consists of the following rules: 2.98/1.60 2.98/1.60 f(0) -> cons(0, n__f(s(0))) 2.98/1.60 f(s(0)) -> f(p(s(0))) 2.98/1.60 p(s(X)) -> X 2.98/1.60 f(X) -> n__f(X) 2.98/1.60 activate(n__f(X)) -> f(X) 2.98/1.60 activate(X) -> X 2.98/1.60 2.98/1.60 S is empty. 2.98/1.60 Rewrite Strategy: INNERMOST 2.98/1.60 ---------------------------------------- 2.98/1.60 2.98/1.60 (1) NarrowingOnBasicTermsTerminatesProof (FINISHED) 2.98/1.60 Constant runtime complexity proven by termination of constructor-based narrowing. 2.98/1.60 2.98/1.60 The maximal most general narrowing sequences give rise to the following rewrite sequences: 2.98/1.60 2.98/1.60 activate(n__f(x0)) ->^* n__f(x0) 2.98/1.60 2.98/1.60 activate(n__f(s(0))) ->^* n__f(0) 2.98/1.60 2.98/1.60 activate(n__f(s(0))) ->^* cons(0, n__f(s(0))) 2.98/1.60 2.98/1.60 activate(n__f(0)) ->^* cons(0, n__f(s(0))) 2.98/1.60 2.98/1.60 f(x0) ->^* n__f(x0) 2.98/1.60 2.98/1.60 f(s(0)) ->^* n__f(0) 2.98/1.60 2.98/1.60 f(s(0)) ->^* cons(0, n__f(s(0))) 2.98/1.60 2.98/1.60 f(0) ->^* cons(0, n__f(s(0))) 2.98/1.60 2.98/1.60 p(x0) ->^* p(x0) 2.98/1.60 2.98/1.60 2.98/1.60 2.98/1.60 2.98/1.60 ---------------------------------------- 2.98/1.60 2.98/1.60 (2) 2.98/1.60 BOUNDS(1, 1) 3.27/1.63 EOF
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