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Runti Compl Full Rewri 10127 pair #381903028
details
property
value
status
complete
benchmark
2.39.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n072.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rc
runtime (wallclock)
1.99484801292 seconds
cpu usage
7.52158209
max memory
8.0474112E7
stage attributes
key
value
output-size
28077
starexec-result
WORST_CASE(Omega(n^1),O(n^2))
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^2)) * Step 1: Sum WORST_CASE(Omega(n^1),O(n^2)) + Considered Problem: - Strict TRS: ++(.(x,y),z) -> .(x,++(y,z)) ++(nil(),y) -> y car(.(x,y)) -> x cdr(.(x,y)) -> y null(.(x,y)) -> false() null(nil()) -> true() rev(.(x,y)) -> ++(rev(y),.(x,nil())) rev(nil()) -> nil() - Signature: {++/2,car/1,cdr/1,null/1,rev/1} / {./2,false/0,nil/0,true/0} - Obligation: runtime complexity wrt. defined symbols {++,car,cdr,null,rev} and constructors {.,false,nil,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: ++(.(x,y),z) -> .(x,++(y,z)) ++(nil(),y) -> y car(.(x,y)) -> x cdr(.(x,y)) -> y null(.(x,y)) -> false() null(nil()) -> true() rev(.(x,y)) -> ++(rev(y),.(x,nil())) rev(nil()) -> nil() - Signature: {++/2,car/1,cdr/1,null/1,rev/1} / {./2,false/0,nil/0,true/0} - Obligation: runtime complexity wrt. defined symbols {++,car,cdr,null,rev} and constructors {.,false,nil,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: ++(y,z){y -> .(x,y)} = ++(.(x,y),z) ->^+ .(x,++(y,z)) = C[++(y,z) = ++(y,z){}] ** Step 1.b:1: ToInnermost WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: ++(.(x,y),z) -> .(x,++(y,z)) ++(nil(),y) -> y car(.(x,y)) -> x cdr(.(x,y)) -> y null(.(x,y)) -> false() null(nil()) -> true() rev(.(x,y)) -> ++(rev(y),.(x,nil())) rev(nil()) -> nil() - Signature: {++/2,car/1,cdr/1,null/1,rev/1} / {./2,false/0,nil/0,true/0} - Obligation: runtime complexity wrt. defined symbols {++,car,cdr,null,rev} and constructors {.,false,nil,true} + 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: DependencyPairs WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: ++(.(x,y),z) -> .(x,++(y,z)) ++(nil(),y) -> y car(.(x,y)) -> x cdr(.(x,y)) -> y null(.(x,y)) -> false() null(nil()) -> true() rev(.(x,y)) -> ++(rev(y),.(x,nil())) rev(nil()) -> nil() - Signature: {++/2,car/1,cdr/1,null/1,rev/1} / {./2,false/0,nil/0,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {++,car,cdr,null,rev} and constructors {.,false,nil,true} + Applied Processor: DependencyPairs {dpKind_ = DT} + Details: We add the following dependency tuples: Strict DPs ++#(.(x,y),z) -> c_1(++#(y,z)) ++#(nil(),y) -> c_2() car#(.(x,y)) -> c_3() cdr#(.(x,y)) -> c_4() null#(.(x,y)) -> c_5() null#(nil()) -> c_6() rev#(.(x,y)) -> c_7(++#(rev(y),.(x,nil())),rev#(y)) rev#(nil()) -> c_8() Weak DPs
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