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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307669
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
n131.star.cs.uiowa.edu
space
AProVE_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.693 seconds
cpu usage
1149.71
user time
1134.34
system time
15.3612
max virtual memory
3.9282176E7
max residence set size
1.4718568E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
1149.31/291.49 WORST_CASE(Omega(n^1), O(n^1)) 1149.31/291.51 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1149.31/291.51 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1149.31/291.51 1149.31/291.51 1149.31/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 1149.31/291.51 1149.31/291.51 (0) CpxTRS 1149.31/291.51 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 12 ms] 1149.31/291.51 (2) CpxTRS 1149.31/291.51 (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] 1149.31/291.51 (4) CpxTRS 1149.31/291.51 (5) CpxTrsMatchBoundsTAProof [FINISHED, 24 ms] 1149.31/291.51 (6) BOUNDS(1, n^1) 1149.31/291.51 (7) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1149.31/291.51 (8) TRS for Loop Detection 1149.31/291.51 (9) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1149.31/291.51 (10) BEST 1149.31/291.51 (11) proven lower bound 1149.31/291.51 (12) LowerBoundPropagationProof [FINISHED, 0 ms] 1149.31/291.51 (13) BOUNDS(n^1, INF) 1149.31/291.51 (14) TRS for Loop Detection 1149.31/291.51 1149.31/291.51 1149.31/291.51 ---------------------------------------- 1149.31/291.51 1149.31/291.51 (0) 1149.31/291.51 Obligation: 1149.31/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 1149.31/291.51 1149.31/291.51 1149.31/291.51 The TRS R consists of the following rules: 1149.31/291.51 1149.31/291.51 active(f(x)) -> mark(f(f(x))) 1149.31/291.51 chk(no(f(x))) -> f(chk(mat(f(f(f(f(f(f(f(f(f(f(X)))))))))), x))) 1149.31/291.51 mat(f(x), f(y)) -> f(mat(x, y)) 1149.31/291.51 chk(no(c)) -> active(c) 1149.31/291.51 mat(f(x), c) -> no(c) 1149.31/291.51 f(active(x)) -> active(f(x)) 1149.31/291.51 f(no(x)) -> no(f(x)) 1149.31/291.51 f(mark(x)) -> mark(f(x)) 1149.31/291.51 tp(mark(x)) -> tp(chk(mat(f(f(f(f(f(f(f(f(f(f(X)))))))))), x))) 1149.31/291.51 1149.31/291.51 S is empty. 1149.31/291.51 Rewrite Strategy: FULL 1149.31/291.51 ---------------------------------------- 1149.31/291.51 1149.31/291.51 (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) 1149.31/291.51 The following defined symbols can occur below the 0th argument of f: chk, f, mat 1149.31/291.51 The following defined symbols can occur below the 0th argument of tp: chk, f, mat 1149.31/291.51 The following defined symbols can occur below the 0th argument of chk: chk, f, mat 1149.31/291.51 The following defined symbols can occur below the 0th argument of mat: chk, f, mat 1149.31/291.51 The following defined symbols can occur below the 1th argument of mat: chk, f, mat 1149.31/291.51 1149.31/291.51 Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: 1149.31/291.51 active(f(x)) -> mark(f(f(x))) 1149.31/291.51 f(active(x)) -> active(f(x)) 1149.31/291.51 1149.31/291.51 ---------------------------------------- 1149.31/291.51 1149.31/291.51 (2) 1149.31/291.51 Obligation: 1149.31/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 1149.31/291.51 1149.31/291.51 1149.31/291.51 The TRS R consists of the following rules: 1149.31/291.51 1149.31/291.51 chk(no(f(x))) -> f(chk(mat(f(f(f(f(f(f(f(f(f(f(X)))))))))), x))) 1149.31/291.51 mat(f(x), f(y)) -> f(mat(x, y)) 1149.31/291.51 chk(no(c)) -> active(c) 1149.31/291.51 mat(f(x), c) -> no(c) 1149.31/291.51 f(no(x)) -> no(f(x)) 1149.31/291.51 f(mark(x)) -> mark(f(x)) 1149.31/291.51 tp(mark(x)) -> tp(chk(mat(f(f(f(f(f(f(f(f(f(f(X)))))))))), x))) 1149.31/291.51 1149.31/291.51 S is empty. 1149.31/291.51 Rewrite Strategy: FULL 1149.31/291.51 ---------------------------------------- 1149.31/291.51 1149.31/291.51 (3) RelTrsToTrsProof (UPPER BOUND(ID)) 1149.31/291.51 transformed relative TRS to TRS 1149.31/291.51 ---------------------------------------- 1149.31/291.51 1149.31/291.51 (4) 1149.31/291.51 Obligation: 1149.31/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 1149.31/291.51 1149.31/291.51 1149.31/291.51 The TRS R consists of the following rules: 1149.31/291.51 1149.31/291.51 chk(no(f(x))) -> f(chk(mat(f(f(f(f(f(f(f(f(f(f(X)))))))))), x))) 1149.31/291.51 mat(f(x), f(y)) -> f(mat(x, y)) 1149.31/291.51 chk(no(c)) -> active(c) 1149.31/291.51 mat(f(x), c) -> no(c) 1149.31/291.51 f(no(x)) -> no(f(x)) 1149.31/291.51 f(mark(x)) -> mark(f(x)) 1149.31/291.51 tp(mark(x)) -> tp(chk(mat(f(f(f(f(f(f(f(f(f(f(X)))))))))), x))) 1149.31/291.51 1149.31/291.51 S is empty. 1149.31/291.51 Rewrite Strategy: FULL
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