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Runti Compl Full Rewri 10127 pair #381902488
details
property
value
status
complete
benchmark
Ex4_7_15_Bor03_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n071.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rc
runtime (wallclock)
0.0266799926758 seconds
cpu usage
0.039414692
max memory
5529600.0
stage attributes
key
value
output-size
5840
starexec-result
WORST_CASE(Omega(n^1),O(n^1))
output
/export/starexec/sandbox/solver/bin/starexec_run_tct_rc /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1),O(n^1)) * Step 1: Sum WORST_CASE(Omega(n^1),O(n^1)) + Considered Problem: - Strict TRS: a__f(X) -> f(X) a__f(0()) -> cons(0(),f(s(0()))) a__f(s(0())) -> a__f(a__p(s(0()))) a__p(X) -> p(X) a__p(s(0())) -> 0() mark(0()) -> 0() mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(f(X)) -> a__f(mark(X)) mark(p(X)) -> a__p(mark(X)) mark(s(X)) -> s(mark(X)) - Signature: {a__f/1,a__p/1,mark/1} / {0/0,cons/2,f/1,p/1,s/1} - Obligation: runtime complexity wrt. defined symbols {a__f,a__p,mark} and constructors {0,cons,f,p,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: a__f(X) -> f(X) a__f(0()) -> cons(0(),f(s(0()))) a__f(s(0())) -> a__f(a__p(s(0()))) a__p(X) -> p(X) a__p(s(0())) -> 0() mark(0()) -> 0() mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(f(X)) -> a__f(mark(X)) mark(p(X)) -> a__p(mark(X)) mark(s(X)) -> s(mark(X)) - Signature: {a__f/1,a__p/1,mark/1} / {0/0,cons/2,f/1,p/1,s/1} - Obligation: runtime complexity wrt. defined symbols {a__f,a__p,mark} and constructors {0,cons,f,p,s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: mark(x){x -> cons(x,y)} = mark(cons(x,y)) ->^+ cons(mark(x),y) = C[mark(x) = mark(x){}] ** Step 1.b:1: ToInnermost WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: a__f(X) -> f(X) a__f(0()) -> cons(0(),f(s(0()))) a__f(s(0())) -> a__f(a__p(s(0()))) a__p(X) -> p(X) a__p(s(0())) -> 0() mark(0()) -> 0() mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(f(X)) -> a__f(mark(X)) mark(p(X)) -> a__p(mark(X)) mark(s(X)) -> s(mark(X)) - Signature: {a__f/1,a__p/1,mark/1} / {0/0,cons/2,f/1,p/1,s/1} - Obligation: runtime complexity wrt. defined symbols {a__f,a__p,mark} and constructors {0,cons,f,p,s} + Applied Processor: ToInnermost + Details: switch to innermost, as the system is overlay and right linear and does not contain weak rules ** Step 1.b:2: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: a__f(X) -> f(X) a__f(0()) -> cons(0(),f(s(0()))) a__f(s(0())) -> a__f(a__p(s(0()))) a__p(X) -> p(X) a__p(s(0())) -> 0() mark(0()) -> 0() mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(f(X)) -> a__f(mark(X)) mark(p(X)) -> a__p(mark(X)) mark(s(X)) -> s(mark(X)) - Signature: {a__f/1,a__p/1,mark/1} / {0/0,cons/2,f/1,p/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {a__f,a__p,mark} and constructors {0,cons,f,p,s} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 3. The enriched problem is compatible with follwoing automaton. 0_0() -> 2 0_1() -> 1 0_1() -> 3 0_1() -> 6
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