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Runti Compl Full Rewri 10127 pair #381903501
details
property
value
status
complete
benchmark
Ex1_GM03_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n030.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
8.17494988441 seconds
cpu usage
24.822865019
max memory
4.001722368E9
stage attributes
key
value
output-size
36113
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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, 58 ms] (6) BOUNDS(1, n^1) (7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTRS (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (10) typed CpxTrs (11) OrderProof [LOWER BOUND(ID), 0 ms] (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 470 ms] (14) BEST (15) proven lower bound (16) LowerBoundPropagationProof [FINISHED, 0 ms] (17) BOUNDS(n^1, INF) (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 134 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 89 ms] (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 122 ms] (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 64 ms] (26) typed CpxTrs ---------------------------------------- (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(p(0)) -> mark(0) active(p(s(X))) -> mark(X) active(leq(0, Y)) -> mark(true) active(leq(s(X), 0)) -> mark(false) active(leq(s(X), s(Y))) -> mark(leq(X, Y)) active(if(true, X, Y)) -> mark(X) active(if(false, X, Y)) -> mark(Y) active(diff(X, Y)) -> mark(if(leq(X, Y), 0, s(diff(p(X), Y)))) active(p(X)) -> p(active(X)) active(s(X)) -> s(active(X)) active(leq(X1, X2)) -> leq(active(X1), X2) active(leq(X1, X2)) -> leq(X1, active(X2)) active(if(X1, X2, X3)) -> if(active(X1), X2, X3) active(diff(X1, X2)) -> diff(active(X1), X2) active(diff(X1, X2)) -> diff(X1, active(X2)) p(mark(X)) -> mark(p(X)) s(mark(X)) -> mark(s(X)) leq(mark(X1), X2) -> mark(leq(X1, X2)) leq(X1, mark(X2)) -> mark(leq(X1, X2)) if(mark(X1), X2, X3) -> mark(if(X1, X2, X3)) diff(mark(X1), X2) -> mark(diff(X1, X2)) diff(X1, mark(X2)) -> mark(diff(X1, X2)) proper(p(X)) -> p(proper(X)) proper(0) -> ok(0) proper(s(X)) -> s(proper(X)) proper(leq(X1, X2)) -> leq(proper(X1), proper(X2)) proper(true) -> ok(true) proper(false) -> ok(false) proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3)) proper(diff(X1, X2)) -> diff(proper(X1), proper(X2)) p(ok(X)) -> ok(p(X)) s(ok(X)) -> ok(s(X)) leq(ok(X1), ok(X2)) -> ok(leq(X1, X2)) if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3)) diff(ok(X1), ok(X2)) -> ok(diff(X1, X2)) 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(p(0)) -> mark(0)
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