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TRS Stand 20472 pair #381711575
details
property
value
status
complete
benchmark
005.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n034.star.cs.uiowa.edu
space
AotoYamada_05
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
0.0503511428833 seconds
cpu usage
0.042348917
max memory
3588096.0
stage attributes
key
value
output-size
4828
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 f x y) (RULES add -> app(curry,plus) app(app(app(curry,f),x),y) -> app(app(f,x),y) app(app(plus,app(s,x)),y) -> app(s,app(app(plus,x),y)) app(app(plus,0),y) -> y ) Problem 1: Innermost Equivalent Processor: -> Rules: add -> app(curry,plus) app(app(app(curry,f),x),y) -> app(app(f,x),y) app(app(plus,app(s,x)),y) -> app(s,app(app(plus,x),y)) app(app(plus,0),y) -> y -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: APP(app(app(curry,f),x),y) -> APP(app(f,x),y) APP(app(app(curry,f),x),y) -> APP(f,x) APP(app(plus,app(s,x)),y) -> APP(app(plus,x),y) APP(app(plus,app(s,x)),y) -> APP(s,app(app(plus,x),y)) -> Rules: add -> app(curry,plus) app(app(app(curry,f),x),y) -> app(app(f,x),y) app(app(plus,app(s,x)),y) -> app(s,app(app(plus,x),y)) app(app(plus,0),y) -> y Problem 1: SCC Processor: -> Pairs: APP(app(app(curry,f),x),y) -> APP(app(f,x),y) APP(app(app(curry,f),x),y) -> APP(f,x) APP(app(plus,app(s,x)),y) -> APP(app(plus,x),y) APP(app(plus,app(s,x)),y) -> APP(s,app(app(plus,x),y)) -> Rules: add -> app(curry,plus) app(app(app(curry,f),x),y) -> app(app(f,x),y) app(app(plus,app(s,x)),y) -> app(s,app(app(plus,x),y)) app(app(plus,0),y) -> y ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: APP(app(plus,app(s,x)),y) -> APP(app(plus,x),y) ->->-> Rules: add -> app(curry,plus) app(app(app(curry,f),x),y) -> app(app(f,x),y) app(app(plus,app(s,x)),y) -> app(s,app(app(plus,x),y)) app(app(plus,0),y) -> y ->->Cycle: ->->-> Pairs: APP(app(app(curry,f),x),y) -> APP(app(f,x),y) APP(app(app(curry,f),x),y) -> APP(f,x) ->->-> Rules: add -> app(curry,plus) app(app(app(curry,f),x),y) -> app(app(f,x),y) app(app(plus,app(s,x)),y) -> app(s,app(app(plus,x),y)) app(app(plus,0),y) -> y The problem is decomposed in 2 subproblems. Problem 1.1: Reduction Pairs Processor: -> Pairs: APP(app(plus,app(s,x)),y) -> APP(app(plus,x),y) -> Rules: add -> app(curry,plus) app(app(app(curry,f),x),y) -> app(app(f,x),y) app(app(plus,app(s,x)),y) -> app(s,app(app(plus,x),y)) app(app(plus,0),y) -> y -> Usable rules: app(app(app(curry,f),x),y) -> app(app(f,x),y) app(app(plus,app(s,x)),y) -> app(s,app(app(plus,x),y)) app(app(plus,0),y) -> y ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2
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