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Runtime Complexity: TRS pair #487111390
details
property
value
status
complete
benchmark
#3.47.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n144.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
5.14104 seconds
cpu usage
16.7017
user time
15.6399
system time
1.06179
max virtual memory
1.8551396E7
max residence set size
3512712.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 9 ms] (2) CpxTRS (3) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (4) CdtProblem (5) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 44 ms] (6) CdtProblem (7) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CdtProblem (9) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CdtProblem (11) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CdtProblem (13) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 0 ms] (14) CdtProblem (15) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (16) BOUNDS(1, 1) (17) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (18) TRS for Loop Detection (19) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (20) BEST (21) proven lower bound (22) LowerBoundPropagationProof [FINISHED, 0 ms] (23) BOUNDS(n^1, INF) (24) 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: f(x, c(y)) -> f(x, s(f(y, y))) f(s(x), y) -> f(x, s(c(y))) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) Converted rc-obligation to irc-obligation. The duplicating contexts are: f(x, c([])) The defined contexts are: f(x0, s([])) f(x0, s(c([]))) As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc. ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: f(x, c(y)) -> f(x, s(f(y, y))) f(s(x), y) -> f(x, s(c(y))) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (4) Obligation: Complexity Dependency Tuples Problem Rules: f(z0, c(z1)) -> f(z0, s(f(z1, z1))) f(s(z0), z1) -> f(z0, s(c(z1))) Tuples: F(z0, c(z1)) -> c1(F(z0, s(f(z1, z1))), F(z1, z1)) F(s(z0), z1) -> c2(F(z0, s(c(z1)))) S tuples: F(z0, c(z1)) -> c1(F(z0, s(f(z1, z1))), F(z1, z1)) F(s(z0), z1) -> c2(F(z0, s(c(z1)))) K tuples:none Defined Rule Symbols: f_2 Defined Pair Symbols: F_2
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