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TRS Stand 20472 pair #381712155
details
property
value
status
complete
benchmark
Ex1SimplyTyped.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n009.star.cs.uiowa.edu
space
AotoYamada_05
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
0.139517068863 seconds
cpu usage
0.12834499
max memory
6119424.0
stage attributes
key
value
output-size
4754
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR f x xs y) (RULES app(app(add,app(s,x)),y) -> app(s,app(app(add,x),y)) app(app(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs)) app(app(map,f),nil) -> nil app(add,0) -> id app(id,x) -> x ) Problem 1: Innermost Equivalent Processor: -> Rules: app(app(add,app(s,x)),y) -> app(s,app(app(add,x),y)) app(app(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs)) app(app(map,f),nil) -> nil app(add,0) -> id app(id,x) -> x -> 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(add,app(s,x)),y) -> APP(app(add,x),y) APP(app(add,app(s,x)),y) -> APP(add,x) APP(app(add,app(s,x)),y) -> APP(s,app(app(add,x),y)) APP(app(map,f),app(app(cons,x),xs)) -> APP(app(cons,app(f,x)),app(app(map,f),xs)) APP(app(map,f),app(app(cons,x),xs)) -> APP(app(map,f),xs) APP(app(map,f),app(app(cons,x),xs)) -> APP(cons,app(f,x)) APP(app(map,f),app(app(cons,x),xs)) -> APP(f,x) -> Rules: app(app(add,app(s,x)),y) -> app(s,app(app(add,x),y)) app(app(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs)) app(app(map,f),nil) -> nil app(add,0) -> id app(id,x) -> x Problem 1: SCC Processor: -> Pairs: APP(app(add,app(s,x)),y) -> APP(app(add,x),y) APP(app(add,app(s,x)),y) -> APP(add,x) APP(app(add,app(s,x)),y) -> APP(s,app(app(add,x),y)) APP(app(map,f),app(app(cons,x),xs)) -> APP(app(cons,app(f,x)),app(app(map,f),xs)) APP(app(map,f),app(app(cons,x),xs)) -> APP(app(map,f),xs) APP(app(map,f),app(app(cons,x),xs)) -> APP(cons,app(f,x)) APP(app(map,f),app(app(cons,x),xs)) -> APP(f,x) -> Rules: app(app(add,app(s,x)),y) -> app(s,app(app(add,x),y)) app(app(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs)) app(app(map,f),nil) -> nil app(add,0) -> id app(id,x) -> x ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: APP(app(add,app(s,x)),y) -> APP(app(add,x),y) APP(app(map,f),app(app(cons,x),xs)) -> APP(app(map,f),xs) APP(app(map,f),app(app(cons,x),xs)) -> APP(f,x) ->->-> Rules: app(app(add,app(s,x)),y) -> app(s,app(app(add,x),y)) app(app(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs)) app(app(map,f),nil) -> nil app(add,0) -> id app(id,x) -> x Problem 1: Subterm Processor: -> Pairs: APP(app(add,app(s,x)),y) -> APP(app(add,x),y) APP(app(map,f),app(app(cons,x),xs)) -> APP(app(map,f),xs) APP(app(map,f),app(app(cons,x),xs)) -> APP(f,x) -> Rules: app(app(add,app(s,x)),y) -> app(s,app(app(add,x),y)) app(app(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs)) app(app(map,f),nil) -> nil app(add,0) -> id app(id,x) -> x ->Projection: pi(APP) = 2 Problem 1: SCC Processor: -> Pairs: APP(app(add,app(s,x)),y) -> APP(app(add,x),y)
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