Runtime Complexity: TRS pair #487110420

details

property	value
status	complete
benchmark	PEANO_nokinds_noand_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n141.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	6.34592 seconds
cpu usage	21.8984
user time	20.5843
system time	1.31408
max virtual memory	1.9342144E7
max residence set size	3683992.0

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/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms]
(2) CpxTRS
    (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
    (4) CpxTRS
    (5) CpxTrsMatchBoundsTAProof [FINISHED, 100 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), 406 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), 131 ms]
            (20) typed CpxTrs
            (21) RewriteLemmaProof [LOWER BOUND(ID), 73 ms]
            (22) typed CpxTrs
            (23) RewriteLemmaProof [LOWER BOUND(ID), 73 ms]
            (24) typed CpxTrs
            (25) RewriteLemmaProof [LOWER BOUND(ID), 117 ms]
            (26) typed CpxTrs
            (27) RewriteLemmaProof [LOWER BOUND(ID), 102 ms]
            (28) typed CpxTrs
            (29) RewriteLemmaProof [LOWER BOUND(ID), 101 ms]
            (30) typed CpxTrs
            (31) RewriteLemmaProof [LOWER BOUND(ID), 143 ms]
            (32) 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(U11(tt, V2)) -> mark(U12(isNat(V2)))
   active(U12(tt)) -> mark(tt)
   active(U21(tt)) -> mark(tt)
   active(U31(tt, N)) -> mark(N)
   active(U41(tt, M, N)) -> mark(U42(isNat(N), M, N))
   active(U42(tt, M, N)) -> mark(s(plus(N, M)))
   active(isNat(0)) -> mark(tt)
   active(isNat(plus(V1, V2))) -> mark(U11(isNat(V1), V2))
   active(isNat(s(V1))) -> mark(U21(isNat(V1)))
   active(plus(N, 0)) -> mark(U31(isNat(N), N))
   active(plus(N, s(M))) -> mark(U41(isNat(M), M, N))
   active(U11(X1, X2)) -> U11(active(X1), X2)
   active(U12(X)) -> U12(active(X))
   active(U21(X)) -> U21(active(X))
   active(U31(X1, X2)) -> U31(active(X1), X2)
   active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3)
   active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3)
   active(s(X)) -> s(active(X))
   active(plus(X1, X2)) -> plus(active(X1), X2)
   active(plus(X1, X2)) -> plus(X1, active(X2))
   U11(mark(X1), X2) -> mark(U11(X1, X2))
   U12(mark(X)) -> mark(U12(X))
   U21(mark(X)) -> mark(U21(X))
   U31(mark(X1), X2) -> mark(U31(X1, X2))
   U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3))
   U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3))
   s(mark(X)) -> mark(s(X))
   plus(mark(X1), X2) -> mark(plus(X1, X2))
   plus(X1, mark(X2)) -> mark(plus(X1, X2))
   proper(U11(X1, X2)) -> U11(proper(X1), proper(X2))
   proper(tt) -> ok(tt)
   proper(U12(X)) -> U12(proper(X))
   proper(isNat(X)) -> isNat(proper(X))
   proper(U21(X)) -> U21(proper(X))
   proper(U31(X1, X2)) -> U31(proper(X1), proper(X2))
   proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3))
   proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3))
   proper(s(X)) -> s(proper(X))
   proper(plus(X1, X2)) -> plus(proper(X1), proper(X2))
   proper(0) -> ok(0)
   U11(ok(X1), ok(X2)) -> ok(U11(X1, X2))
   U12(ok(X)) -> ok(U12(X))
   isNat(ok(X)) -> ok(isNat(X))
   U21(ok(X)) -> ok(U21(X))
   U31(ok(X1), ok(X2)) -> ok(U31(X1, X2))
   U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3))
   U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3))
   s(ok(X)) -> ok(s(X))
   plus(ok(X1), ok(X2)) -> ok(plus(X1, X2))

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