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TRS Standard pair #487068209
details
property
value
status
complete
benchmark
2.45.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n179.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0182381 seconds
cpu usage
0.018729
user time
0.005939
system time
0.01279
max virtual memory
113188.0
max residence set size
4400.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S u:S v:S x:S y:S z:S) (RULES admit(x:S,.(u:S,.(v:S,.(w,z:S)))) -> cond(=(sum(x:S,u:S,v:S),w),.(u:S,.(v:S,.(w,admit(carry(x:S,u:S,v:S),z:S))))) admit(x:S,nil) -> nil cond(ttrue,y:S) -> y:S ) Problem 1: Innermost Equivalent Processor: -> Rules: admit(x:S,.(u:S,.(v:S,.(w,z:S)))) -> cond(=(sum(x:S,u:S,v:S),w),.(u:S,.(v:S,.(w,admit(carry(x:S,u:S,v:S),z:S))))) admit(x:S,nil) -> nil cond(ttrue,y:S) -> y:S -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: ADMIT(x:S,.(u:S,.(v:S,.(w,z:S)))) -> ADMIT(carry(x:S,u:S,v:S),z:S) ADMIT(x:S,.(u:S,.(v:S,.(w,z:S)))) -> COND(=(sum(x:S,u:S,v:S),w),.(u:S,.(v:S,.(w,admit(carry(x:S,u:S,v:S),z:S))))) -> Rules: admit(x:S,.(u:S,.(v:S,.(w,z:S)))) -> cond(=(sum(x:S,u:S,v:S),w),.(u:S,.(v:S,.(w,admit(carry(x:S,u:S,v:S),z:S))))) admit(x:S,nil) -> nil cond(ttrue,y:S) -> y:S Problem 1: SCC Processor: -> Pairs: ADMIT(x:S,.(u:S,.(v:S,.(w,z:S)))) -> ADMIT(carry(x:S,u:S,v:S),z:S) ADMIT(x:S,.(u:S,.(v:S,.(w,z:S)))) -> COND(=(sum(x:S,u:S,v:S),w),.(u:S,.(v:S,.(w,admit(carry(x:S,u:S,v:S),z:S))))) -> Rules: admit(x:S,.(u:S,.(v:S,.(w,z:S)))) -> cond(=(sum(x:S,u:S,v:S),w),.(u:S,.(v:S,.(w,admit(carry(x:S,u:S,v:S),z:S))))) admit(x:S,nil) -> nil cond(ttrue,y:S) -> y:S ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ADMIT(x:S,.(u:S,.(v:S,.(w,z:S)))) -> ADMIT(carry(x:S,u:S,v:S),z:S) ->->-> Rules: admit(x:S,.(u:S,.(v:S,.(w,z:S)))) -> cond(=(sum(x:S,u:S,v:S),w),.(u:S,.(v:S,.(w,admit(carry(x:S,u:S,v:S),z:S))))) admit(x:S,nil) -> nil cond(ttrue,y:S) -> y:S Problem 1: Subterm Processor: -> Pairs: ADMIT(x:S,.(u:S,.(v:S,.(w,z:S)))) -> ADMIT(carry(x:S,u:S,v:S),z:S) -> Rules: admit(x:S,.(u:S,.(v:S,.(w,z:S)))) -> cond(=(sum(x:S,u:S,v:S),w),.(u:S,.(v:S,.(w,admit(carry(x:S,u:S,v:S),z:S))))) admit(x:S,nil) -> nil cond(ttrue,y:S) -> y:S ->Projection: pi(ADMIT) = 2 Problem 1: SCC Processor: -> Pairs: Empty -> Rules: admit(x:S,.(u:S,.(v:S,.(w,z:S)))) -> cond(=(sum(x:S,u:S,v:S),w),.(u:S,.(v:S,.(w,admit(carry(x:S,u:S,v:S),z:S))))) admit(x:S,nil) -> nil cond(ttrue,y:S) -> y:S ->Strongly Connected Components: There is no strongly connected component The problem is finite.
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