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TRS Standard pair #516966486
details
property
value
status
complete
benchmark
4.27.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n028.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0658860206604 seconds
cpu usage
0.020903208
max memory
1757184.0
stage attributes
key
value
output-size
3807
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 v_NonEmpty:S x:S y:S) (RULES int(0,0) -> .(0,nil) int(0,s(y:S)) -> .(0,int(s(0),s(y:S))) int(s(x:S),0) -> nil int(s(x:S),s(y:S)) -> int_list(int(x:S,y:S)) int_list(.(x:S,y:S)) -> .(s(x:S),int_list(y:S)) int_list(nil) -> nil ) Problem 1: Innermost Equivalent Processor: -> Rules: int(0,0) -> .(0,nil) int(0,s(y:S)) -> .(0,int(s(0),s(y:S))) int(s(x:S),0) -> nil int(s(x:S),s(y:S)) -> int_list(int(x:S,y:S)) int_list(.(x:S,y:S)) -> .(s(x:S),int_list(y:S)) int_list(nil) -> nil -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: INT(0,s(y:S)) -> INT(s(0),s(y:S)) INT(s(x:S),s(y:S)) -> INT(x:S,y:S) INT(s(x:S),s(y:S)) -> INT_LIST(int(x:S,y:S)) INT_LIST(.(x:S,y:S)) -> INT_LIST(y:S) -> Rules: int(0,0) -> .(0,nil) int(0,s(y:S)) -> .(0,int(s(0),s(y:S))) int(s(x:S),0) -> nil int(s(x:S),s(y:S)) -> int_list(int(x:S,y:S)) int_list(.(x:S,y:S)) -> .(s(x:S),int_list(y:S)) int_list(nil) -> nil Problem 1: SCC Processor: -> Pairs: INT(0,s(y:S)) -> INT(s(0),s(y:S)) INT(s(x:S),s(y:S)) -> INT(x:S,y:S) INT(s(x:S),s(y:S)) -> INT_LIST(int(x:S,y:S)) INT_LIST(.(x:S,y:S)) -> INT_LIST(y:S) -> Rules: int(0,0) -> .(0,nil) int(0,s(y:S)) -> .(0,int(s(0),s(y:S))) int(s(x:S),0) -> nil int(s(x:S),s(y:S)) -> int_list(int(x:S,y:S)) int_list(.(x:S,y:S)) -> .(s(x:S),int_list(y:S)) int_list(nil) -> nil ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: INT_LIST(.(x:S,y:S)) -> INT_LIST(y:S) ->->-> Rules: int(0,0) -> .(0,nil) int(0,s(y:S)) -> .(0,int(s(0),s(y:S))) int(s(x:S),0) -> nil int(s(x:S),s(y:S)) -> int_list(int(x:S,y:S)) int_list(.(x:S,y:S)) -> .(s(x:S),int_list(y:S)) int_list(nil) -> nil ->->Cycle: ->->-> Pairs: INT(0,s(y:S)) -> INT(s(0),s(y:S)) INT(s(x:S),s(y:S)) -> INT(x:S,y:S) ->->-> Rules: int(0,0) -> .(0,nil) int(0,s(y:S)) -> .(0,int(s(0),s(y:S))) int(s(x:S),0) -> nil int(s(x:S),s(y:S)) -> int_list(int(x:S,y:S)) int_list(.(x:S,y:S)) -> .(s(x:S),int_list(y:S)) int_list(nil) -> nil The problem is decomposed in 2 subproblems. Problem 1.1: Subterm Processor: -> Pairs: INT_LIST(.(x:S,y:S)) -> INT_LIST(y:S) -> Rules: int(0,0) -> .(0,nil) int(0,s(y:S)) -> .(0,int(s(0),s(y:S))) int(s(x:S),0) -> nil int(s(x:S),s(y:S)) -> int_list(int(x:S,y:S))
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