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Runti Compl Full Rewri 10127 pair #381902065
details
property
value
status
complete
benchmark
Liveness_WRS.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n058.star.cs.uiowa.edu
space
AProVE_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
293.380783081 seconds
cpu usage
1163.08342982
max memory
1.6357146624E10
stage attributes
key
value
output-size
6927
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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, 39 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(x)) -> mark(f(f(x))) chk(no(f(x))) -> f(chk(mat(f(f(f(f(f(f(f(f(f(f(X)))))))))), x))) mat(f(x), f(y)) -> f(mat(x, y)) chk(no(c)) -> active(c) mat(f(x), c) -> no(c) f(active(x)) -> active(f(x)) f(no(x)) -> no(f(x)) f(mark(x)) -> mark(f(x)) tp(mark(x)) -> tp(chk(mat(f(f(f(f(f(f(f(f(f(f(X)))))))))), x))) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) The following defined symbols can occur below the 0th argument of f: chk, f, mat The following defined symbols can occur below the 0th argument of tp: chk, f, mat The following defined symbols can occur below the 0th argument of chk: chk, f, mat The following defined symbols can occur below the 0th argument of mat: chk, f, mat The following defined symbols can occur below the 1th argument of mat: chk, f, mat Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: active(f(x)) -> mark(f(f(x))) f(active(x)) -> active(f(x)) ---------------------------------------- (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: chk(no(f(x))) -> f(chk(mat(f(f(f(f(f(f(f(f(f(f(X)))))))))), x))) mat(f(x), f(y)) -> f(mat(x, y)) chk(no(c)) -> active(c) mat(f(x), c) -> no(c) f(no(x)) -> no(f(x)) f(mark(x)) -> mark(f(x)) tp(mark(x)) -> tp(chk(mat(f(f(f(f(f(f(f(f(f(f(X)))))))))), 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: chk(no(f(x))) -> f(chk(mat(f(f(f(f(f(f(f(f(f(f(X)))))))))), x))) mat(f(x), f(y)) -> f(mat(x, y)) chk(no(c)) -> active(c) mat(f(x), c) -> no(c)
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