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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308334
details
property
value
status
complete
benchmark
MYNAT_nokinds_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n148.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
10.3742 seconds
cpu usage
32.2028
user time
30.5515
system time
1.6513
max virtual memory
3.7650268E7
max residence set size
4239796.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
31.89/10.29 WORST_CASE(Omega(n^1), O(n^1)) 31.89/10.31 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 31.89/10.31 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 31.89/10.31 31.89/10.31 31.89/10.31 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 31.89/10.31 31.89/10.31 (0) CpxTRS 31.89/10.31 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] 31.89/10.31 (2) CpxTRS 31.89/10.31 (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] 31.89/10.31 (4) CpxTRS 31.89/10.31 (5) CpxTrsMatchBoundsTAProof [FINISHED, 155 ms] 31.89/10.31 (6) BOUNDS(1, n^1) 31.89/10.31 (7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 31.89/10.31 (8) CpxTRS 31.89/10.31 (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 31.89/10.31 (10) typed CpxTrs 31.89/10.31 (11) OrderProof [LOWER BOUND(ID), 0 ms] 31.89/10.31 (12) typed CpxTrs 31.89/10.31 (13) RewriteLemmaProof [LOWER BOUND(ID), 456 ms] 31.89/10.31 (14) BEST 31.89/10.31 (15) proven lower bound 31.89/10.31 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 31.89/10.31 (17) BOUNDS(n^1, INF) 31.89/10.31 (18) typed CpxTrs 31.89/10.31 (19) RewriteLemmaProof [LOWER BOUND(ID), 149 ms] 31.89/10.31 (20) typed CpxTrs 31.89/10.31 (21) RewriteLemmaProof [LOWER BOUND(ID), 148 ms] 31.89/10.31 (22) typed CpxTrs 31.89/10.31 (23) RewriteLemmaProof [LOWER BOUND(ID), 111 ms] 31.89/10.31 (24) typed CpxTrs 31.89/10.31 (25) RewriteLemmaProof [LOWER BOUND(ID), 101 ms] 31.89/10.31 (26) typed CpxTrs 31.89/10.31 (27) RewriteLemmaProof [LOWER BOUND(ID), 144 ms] 31.89/10.31 (28) typed CpxTrs 31.89/10.31 (29) RewriteLemmaProof [LOWER BOUND(ID), 80 ms] 31.89/10.31 (30) typed CpxTrs 31.89/10.31 (31) RewriteLemmaProof [LOWER BOUND(ID), 139 ms] 31.89/10.31 (32) typed CpxTrs 31.89/10.31 31.89/10.31 31.89/10.31 ---------------------------------------- 31.89/10.31 31.89/10.31 (0) 31.89/10.31 Obligation: 31.89/10.31 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 31.89/10.31 31.89/10.31 31.89/10.31 The TRS R consists of the following rules: 31.89/10.31 31.89/10.31 active(U11(tt, N)) -> mark(N) 31.89/10.31 active(U21(tt, M, N)) -> mark(s(plus(N, M))) 31.89/10.31 active(U31(tt)) -> mark(0) 31.89/10.31 active(U41(tt, M, N)) -> mark(plus(x(N, M), N)) 31.89/10.31 active(and(tt, X)) -> mark(X) 31.89/10.31 active(isNat(0)) -> mark(tt) 31.89/10.31 active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))) 31.89/10.31 active(isNat(s(V1))) -> mark(isNat(V1)) 31.89/10.31 active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))) 31.89/10.31 active(plus(N, 0)) -> mark(U11(isNat(N), N)) 31.89/10.31 active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)) 31.89/10.31 active(x(N, 0)) -> mark(U31(isNat(N))) 31.89/10.31 active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)) 31.89/10.31 active(U11(X1, X2)) -> U11(active(X1), X2) 31.89/10.31 active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) 31.89/10.31 active(s(X)) -> s(active(X)) 31.89/10.31 active(plus(X1, X2)) -> plus(active(X1), X2) 31.89/10.31 active(plus(X1, X2)) -> plus(X1, active(X2)) 31.89/10.31 active(U31(X)) -> U31(active(X)) 31.89/10.31 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 31.89/10.31 active(x(X1, X2)) -> x(active(X1), X2) 31.89/10.31 active(x(X1, X2)) -> x(X1, active(X2)) 31.89/10.31 active(and(X1, X2)) -> and(active(X1), X2) 31.89/10.31 U11(mark(X1), X2) -> mark(U11(X1, X2)) 31.89/10.31 U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) 31.89/10.31 s(mark(X)) -> mark(s(X)) 31.89/10.31 plus(mark(X1), X2) -> mark(plus(X1, X2)) 31.89/10.31 plus(X1, mark(X2)) -> mark(plus(X1, X2)) 31.89/10.31 U31(mark(X)) -> mark(U31(X)) 31.89/10.31 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 31.89/10.31 x(mark(X1), X2) -> mark(x(X1, X2)) 31.89/10.31 x(X1, mark(X2)) -> mark(x(X1, X2)) 31.89/10.31 and(mark(X1), X2) -> mark(and(X1, X2)) 31.89/10.31 proper(U11(X1, X2)) -> U11(proper(X1), proper(X2)) 31.89/10.31 proper(tt) -> ok(tt) 31.89/10.31 proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) 31.89/10.31 proper(s(X)) -> s(proper(X)) 31.89/10.31 proper(plus(X1, X2)) -> plus(proper(X1), proper(X2)) 31.89/10.31 proper(U31(X)) -> U31(proper(X)) 31.89/10.31 proper(0) -> ok(0) 31.89/10.31 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 31.89/10.31 proper(x(X1, X2)) -> x(proper(X1), proper(X2)) 31.89/10.31 proper(and(X1, X2)) -> and(proper(X1), proper(X2)) 31.89/10.31 proper(isNat(X)) -> isNat(proper(X)) 31.89/10.31 U11(ok(X1), ok(X2)) -> ok(U11(X1, X2)) 31.89/10.31 U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) 31.89/10.31 s(ok(X)) -> ok(s(X)) 31.89/10.31 plus(ok(X1), ok(X2)) -> ok(plus(X1, X2)) 31.89/10.31 U31(ok(X)) -> ok(U31(X))
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