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Runti Compl Inner Rewri 22807 pair #381904615
details
property
value
status
complete
benchmark
mul_better.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n041.star.cs.uiowa.edu
space
Frederiksen_Glenstrup
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rci
runtime (wallclock)
6.88148117065 seconds
cpu usage
27.120579382
max memory
1.93982464E8
stage attributes
key
value
output-size
40159
starexec-result
WORST_CASE(Omega(n^1),O(n^3))
output
/export/starexec/sandbox2/solver/bin/starexec_run_tct_rci /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1),O(n^3)) * Step 1: Sum WORST_CASE(Omega(n^1),O(n^3)) + Considered Problem: - Strict TRS: add0(C(x,y),y') -> add0(y,C(S(),y')) add0(Z(),y) -> y goal(xs,ys) -> mul0(xs,ys) isZero(C(x,y)) -> False() isZero(Z()) -> True() mul0(C(x,y),y') -> add0(mul0(y,y'),y') mul0(Z(),y) -> Z() second(C(x,y)) -> y - Signature: {add0/2,goal/2,isZero/1,mul0/2,second/1} / {C/2,False/0,S/0,True/0,Z/0} - Obligation: innermost runtime complexity wrt. defined symbols {add0,goal,isZero,mul0,second} and constructors {C,False,S ,True,Z} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: add0(C(x,y),y') -> add0(y,C(S(),y')) add0(Z(),y) -> y goal(xs,ys) -> mul0(xs,ys) isZero(C(x,y)) -> False() isZero(Z()) -> True() mul0(C(x,y),y') -> add0(mul0(y,y'),y') mul0(Z(),y) -> Z() second(C(x,y)) -> y - Signature: {add0/2,goal/2,isZero/1,mul0/2,second/1} / {C/2,False/0,S/0,True/0,Z/0} - Obligation: innermost runtime complexity wrt. defined symbols {add0,goal,isZero,mul0,second} and constructors {C,False,S ,True,Z} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: add0(y,z){y -> C(x,y)} = add0(C(x,y),z) ->^+ add0(y,C(S(),z)) = C[add0(y,C(S(),z)) = add0(y,z){z -> C(S(),z)}] ** Step 1.b:1: DependencyPairs WORST_CASE(?,O(n^3)) + Considered Problem: - Strict TRS: add0(C(x,y),y') -> add0(y,C(S(),y')) add0(Z(),y) -> y goal(xs,ys) -> mul0(xs,ys) isZero(C(x,y)) -> False() isZero(Z()) -> True() mul0(C(x,y),y') -> add0(mul0(y,y'),y') mul0(Z(),y) -> Z() second(C(x,y)) -> y - Signature: {add0/2,goal/2,isZero/1,mul0/2,second/1} / {C/2,False/0,S/0,True/0,Z/0} - Obligation: innermost runtime complexity wrt. defined symbols {add0,goal,isZero,mul0,second} and constructors {C,False,S ,True,Z} + Applied Processor: DependencyPairs {dpKind_ = DT} + Details: We add the following dependency tuples: Strict DPs add0#(C(x,y),y') -> c_1(add0#(y,C(S(),y'))) add0#(Z(),y) -> c_2() goal#(xs,ys) -> c_3(mul0#(xs,ys)) isZero#(C(x,y)) -> c_4() isZero#(Z()) -> c_5() mul0#(C(x,y),y') -> c_6(add0#(mul0(y,y'),y'),mul0#(y,y')) mul0#(Z(),y) -> c_7() second#(C(x,y)) -> c_8() Weak DPs and mark the set of starting terms. ** Step 1.b:2: UsableRules WORST_CASE(?,O(n^3)) + Considered Problem: - Strict DPs: add0#(C(x,y),y') -> c_1(add0#(y,C(S(),y'))) add0#(Z(),y) -> c_2() goal#(xs,ys) -> c_3(mul0#(xs,ys)) isZero#(C(x,y)) -> c_4() isZero#(Z()) -> c_5() mul0#(C(x,y),y') -> c_6(add0#(mul0(y,y'),y'),mul0#(y,y')) mul0#(Z(),y) -> c_7() second#(C(x,y)) -> c_8() - Weak TRS: add0(C(x,y),y') -> add0(y,C(S(),y')) add0(Z(),y) -> y goal(xs,ys) -> mul0(xs,ys)
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