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TRS Innermost pair #487524242
details
property
value
status
complete
benchmark
Ex4_4_Luc96b_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n146.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.154871940613 seconds
cpu usage
0.067055103
max memory
4050944.0
stage attributes
key
value
output-size
5257
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR v_NonEmpty:S X:S X1:S X2:S Y:S) (RULES a__f(g(X:S),Y:S) -> a__f(mark(X:S),f(g(X:S),Y:S)) a__f(X1:S,X2:S) -> f(X1:S,X2:S) mark(f(X1:S,X2:S)) -> a__f(mark(X1:S),X2:S) mark(g(X:S)) -> g(mark(X:S)) ) (STRATEGY INNERMOST) Problem 1: Dependency Pairs Processor: -> Pairs: A__F(g(X:S),Y:S) -> A__F(mark(X:S),f(g(X:S),Y:S)) A__F(g(X:S),Y:S) -> MARK(X:S) MARK(f(X1:S,X2:S)) -> A__F(mark(X1:S),X2:S) MARK(f(X1:S,X2:S)) -> MARK(X1:S) MARK(g(X:S)) -> MARK(X:S) -> Rules: a__f(g(X:S),Y:S) -> a__f(mark(X:S),f(g(X:S),Y:S)) a__f(X1:S,X2:S) -> f(X1:S,X2:S) mark(f(X1:S,X2:S)) -> a__f(mark(X1:S),X2:S) mark(g(X:S)) -> g(mark(X:S)) Problem 1: SCC Processor: -> Pairs: A__F(g(X:S),Y:S) -> A__F(mark(X:S),f(g(X:S),Y:S)) A__F(g(X:S),Y:S) -> MARK(X:S) MARK(f(X1:S,X2:S)) -> A__F(mark(X1:S),X2:S) MARK(f(X1:S,X2:S)) -> MARK(X1:S) MARK(g(X:S)) -> MARK(X:S) -> Rules: a__f(g(X:S),Y:S) -> a__f(mark(X:S),f(g(X:S),Y:S)) a__f(X1:S,X2:S) -> f(X1:S,X2:S) mark(f(X1:S,X2:S)) -> a__f(mark(X1:S),X2:S) mark(g(X:S)) -> g(mark(X:S)) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: A__F(g(X:S),Y:S) -> A__F(mark(X:S),f(g(X:S),Y:S)) A__F(g(X:S),Y:S) -> MARK(X:S) MARK(f(X1:S,X2:S)) -> A__F(mark(X1:S),X2:S) MARK(f(X1:S,X2:S)) -> MARK(X1:S) MARK(g(X:S)) -> MARK(X:S) ->->-> Rules: a__f(g(X:S),Y:S) -> a__f(mark(X:S),f(g(X:S),Y:S)) a__f(X1:S,X2:S) -> f(X1:S,X2:S) mark(f(X1:S,X2:S)) -> a__f(mark(X1:S),X2:S) mark(g(X:S)) -> g(mark(X:S)) Problem 1: Reduction Pairs Processor: -> Pairs: A__F(g(X:S),Y:S) -> A__F(mark(X:S),f(g(X:S),Y:S)) A__F(g(X:S),Y:S) -> MARK(X:S) MARK(f(X1:S,X2:S)) -> A__F(mark(X1:S),X2:S) MARK(f(X1:S,X2:S)) -> MARK(X1:S) MARK(g(X:S)) -> MARK(X:S) -> Rules: a__f(g(X:S),Y:S) -> a__f(mark(X:S),f(g(X:S),Y:S)) a__f(X1:S,X2:S) -> f(X1:S,X2:S) mark(f(X1:S,X2:S)) -> a__f(mark(X1:S),X2:S) mark(g(X:S)) -> g(mark(X:S)) -> Usable rules: a__f(g(X:S),Y:S) -> a__f(mark(X:S),f(g(X:S),Y:S)) a__f(X1:S,X2:S) -> f(X1:S,X2:S) mark(f(X1:S,X2:S)) -> a__f(mark(X1:S),X2:S) mark(g(X:S)) -> g(mark(X:S)) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [a__f](X1,X2) = 2.X1 + 2 [mark](X) = X [f](X1,X2) = 2.X1 + 2 [fSNonEmpty] = 0 [g](X) = X + 1 [A__F](X1,X2) = 2.X1 + 2 [MARK](X) = 2.X + 1 Problem 1:
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