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Runti Compl Inner Rewri 22807 pair #381904437
details
property
value
status
complete
benchmark
mul.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n053.star.cs.uiowa.edu
space
Frederiksen_Glenstrup
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rci
runtime (wallclock)
5.89303612709 seconds
cpu usage
23.005663881
max memory
1.82042624E8
stage attributes
key
value
output-size
35012
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(Cons(x,xs),y) -> add0(xs,Cons(S(),y)) add0(Nil(),y) -> y goal(xs,ys) -> mul0(xs,ys) mul0(Cons(x,xs),y) -> add0(mul0(xs,y),y) mul0(Nil(),y) -> Nil() - Signature: {add0/2,goal/2,mul0/2} / {Cons/2,Nil/0,S/0} - Obligation: innermost runtime complexity wrt. defined symbols {add0,goal,mul0} and constructors {Cons,Nil,S} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: add0(Cons(x,xs),y) -> add0(xs,Cons(S(),y)) add0(Nil(),y) -> y goal(xs,ys) -> mul0(xs,ys) mul0(Cons(x,xs),y) -> add0(mul0(xs,y),y) mul0(Nil(),y) -> Nil() - Signature: {add0/2,goal/2,mul0/2} / {Cons/2,Nil/0,S/0} - Obligation: innermost runtime complexity wrt. defined symbols {add0,goal,mul0} and constructors {Cons,Nil,S} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: add0(y,z){y -> Cons(x,y)} = add0(Cons(x,y),z) ->^+ add0(y,Cons(S(),z)) = C[add0(y,Cons(S(),z)) = add0(y,z){z -> Cons(S(),z)}] ** Step 1.b:1: DependencyPairs WORST_CASE(?,O(n^3)) + Considered Problem: - Strict TRS: add0(Cons(x,xs),y) -> add0(xs,Cons(S(),y)) add0(Nil(),y) -> y goal(xs,ys) -> mul0(xs,ys) mul0(Cons(x,xs),y) -> add0(mul0(xs,y),y) mul0(Nil(),y) -> Nil() - Signature: {add0/2,goal/2,mul0/2} / {Cons/2,Nil/0,S/0} - Obligation: innermost runtime complexity wrt. defined symbols {add0,goal,mul0} and constructors {Cons,Nil,S} + Applied Processor: DependencyPairs {dpKind_ = DT} + Details: We add the following dependency tuples: Strict DPs add0#(Cons(x,xs),y) -> c_1(add0#(xs,Cons(S(),y))) add0#(Nil(),y) -> c_2() goal#(xs,ys) -> c_3(mul0#(xs,ys)) mul0#(Cons(x,xs),y) -> c_4(add0#(mul0(xs,y),y),mul0#(xs,y)) mul0#(Nil(),y) -> c_5() Weak DPs and mark the set of starting terms. ** Step 1.b:2: UsableRules WORST_CASE(?,O(n^3)) + Considered Problem: - Strict DPs: add0#(Cons(x,xs),y) -> c_1(add0#(xs,Cons(S(),y))) add0#(Nil(),y) -> c_2() goal#(xs,ys) -> c_3(mul0#(xs,ys)) mul0#(Cons(x,xs),y) -> c_4(add0#(mul0(xs,y),y),mul0#(xs,y)) mul0#(Nil(),y) -> c_5() - Weak TRS: add0(Cons(x,xs),y) -> add0(xs,Cons(S(),y)) add0(Nil(),y) -> y goal(xs,ys) -> mul0(xs,ys) mul0(Cons(x,xs),y) -> add0(mul0(xs,y),y) mul0(Nil(),y) -> Nil() - Signature: {add0/2,goal/2,mul0/2,add0#/2,goal#/2,mul0#/2} / {Cons/2,Nil/0,S/0,c_1/1,c_2/0,c_3/1,c_4/2,c_5/0} - Obligation: innermost runtime complexity wrt. defined symbols {add0#,goal#,mul0#} and constructors {Cons,Nil,S} + Applied Processor: UsableRules + Details: We replace rewrite rules by usable rules: add0(Cons(x,xs),y) -> add0(xs,Cons(S(),y)) add0(Nil(),y) -> y mul0(Cons(x,xs),y) -> add0(mul0(xs,y),y) mul0(Nil(),y) -> Nil() add0#(Cons(x,xs),y) -> c_1(add0#(xs,Cons(S(),y))) add0#(Nil(),y) -> c_2() goal#(xs,ys) -> c_3(mul0#(xs,ys)) mul0#(Cons(x,xs),y) -> c_4(add0#(mul0(xs,y),y),mul0#(xs,y))
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