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Runti Compl Full Rewri 10127 pair #381903619
details
property
value
status
complete
benchmark
Ex9_Luc06_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n045.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
7.11476302147 seconds
cpu usage
22.710388887
max memory
3.880460288E9
stage attributes
key
value
output-size
7272
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) CpxTrsMatchBoundsTAProof [FINISHED, 104 ms] (6) BOUNDS(1, n^1) (7) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (8) TRS for Loop Detection (9) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (10) BEST (11) proven lower bound (12) LowerBoundPropagationProof [FINISHED, 0 ms] (13) BOUNDS(n^1, INF) (14) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: active(f(a, X, X)) -> mark(f(X, b, b)) active(b) -> mark(a) active(f(X1, X2, X3)) -> f(X1, active(X2), X3) f(X1, mark(X2), X3) -> mark(f(X1, X2, X3)) proper(f(X1, X2, X3)) -> f(proper(X1), proper(X2), proper(X3)) proper(a) -> ok(a) proper(b) -> ok(b) f(ok(X1), ok(X2), ok(X3)) -> ok(f(X1, X2, X3)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) The following defined symbols can occur below the 0th argument of top: proper, active The following defined symbols can occur below the 0th argument of proper: proper, active The following defined symbols can occur below the 0th argument of active: proper, active Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: active(f(a, X, X)) -> mark(f(X, b, b)) active(f(X1, X2, X3)) -> f(X1, active(X2), X3) proper(f(X1, X2, X3)) -> f(proper(X1), proper(X2), proper(X3)) ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: active(b) -> mark(a) f(X1, mark(X2), X3) -> mark(f(X1, X2, X3)) proper(a) -> ok(a) proper(b) -> ok(b) f(ok(X1), ok(X2), ok(X3)) -> ok(f(X1, X2, X3)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (3) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (4) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: active(b) -> mark(a) f(X1, mark(X2), X3) -> mark(f(X1, X2, X3)) proper(a) -> ok(a) proper(b) -> ok(b)
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