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Deriv Compl Full Rewri 33144 pair #381922156
details
property
value
status
complete
benchmark
24.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n070.star.cs.uiowa.edu
space
Various_04
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_dc
runtime (wallclock)
88.2602660656 seconds
cpu usage
180.430678221
max memory
2.64996864E9
stage attributes
key
value
output-size
4362
starexec-result
WORST_CASE(?,O(n^1))
output
/export/starexec/sandbox/solver/bin/starexec_run_tct_dc /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?,O(n^1)) * Step 1: WeightGap WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: max(L(x)) -> x max(N(L(x),N(y,z))) -> max(N(L(x),L(max(N(y,z))))) max(N(L(0()),L(y))) -> y max(N(L(s(x)),L(s(y)))) -> s(max(N(L(x),L(y)))) - Signature: {max/1} / {0/0,L/1,N/2,s/1} - Obligation: derivational complexity wrt. signature {0,L,N,max,s} + Applied Processor: WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = NoUArgs, wgOn = WgOnAny} + Details: The weightgap principle applies using the following nonconstant growth matrix-interpretation: We apply a matrix interpretation of kind triangular matrix interpretation: Following symbols are considered usable: all TcT has computed the following interpretation: p(0) = [8] p(L) = [1] x1 + [8] p(N) = [1] x1 + [1] x2 + [0] p(max) = [1] x1 + [1] p(s) = [1] x1 + [3] Following rules are strictly oriented: max(L(x)) = [1] x + [9] > [1] x + [0] = x max(N(L(0()),L(y))) = [1] y + [25] > [1] y + [0] = y max(N(L(s(x)),L(s(y)))) = [1] x + [1] y + [23] > [1] x + [1] y + [20] = s(max(N(L(x),L(y)))) Following rules are (at-least) weakly oriented: max(N(L(x),N(y,z))) = [1] x + [1] y + [1] z + [9] >= [1] x + [1] y + [1] z + [18] = max(N(L(x),L(max(N(y,z))))) Further, it can be verified that all rules not oriented are covered by the weightgap condition. * Step 2: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: max(N(L(x),N(y,z))) -> max(N(L(x),L(max(N(y,z))))) - Weak TRS: max(L(x)) -> x max(N(L(0()),L(y))) -> y max(N(L(s(x)),L(s(y)))) -> s(max(N(L(x),L(y)))) - Signature: {max/1} / {0/0,L/1,N/2,s/1} - Obligation: derivational complexity wrt. signature {0,L,N,max,s} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 1. The enriched problem is compatible with follwoing automaton. 0_0() -> 1 0_0() -> 5 0_0() -> 7 L_0(1) -> 1 L_0(1) -> 5 L_0(1) -> 7 L_1(1) -> 3 L_1(5) -> 4 L_1(7) -> 3 N_0(1,1) -> 1 N_0(1,1) -> 5 N_0(1,1) -> 7 N_1(1,1) -> 6 N_1(3,3) -> 8 N_1(3,4) -> 2 max_0(1) -> 1 max_0(1) -> 5 max_0(1) -> 7 max_1(2) -> 1 max_1(2) -> 5 max_1(2) -> 7 max_1(6) -> 1 max_1(6) -> 5 max_1(6) -> 7 max_1(8) -> 7 s_0(1) -> 1 s_0(1) -> 5 s_0(1) -> 7 s_1(7) -> 1 s_1(7) -> 5
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