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TRS Standard pair #516966491
details
property
value
status
complete
benchmark
2.39.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n174.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0733909606934 seconds
cpu usage
0.020756245
max memory
1765376.0
stage attributes
key
value
output-size
3778
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 z:S) (RULES ++(.(x:S,y:S),z:S) -> .(x:S,++(y:S,z:S)) ++(nil,y:S) -> y:S car(.(x:S,y:S)) -> x:S cdr(.(x:S,y:S)) -> y:S null(.(x:S,y:S)) -> ffalse null(nil) -> ttrue rev(.(x:S,y:S)) -> ++(rev(y:S),.(x:S,nil)) rev(nil) -> nil ) Problem 1: Innermost Equivalent Processor: -> Rules: ++(.(x:S,y:S),z:S) -> .(x:S,++(y:S,z:S)) ++(nil,y:S) -> y:S car(.(x:S,y:S)) -> x:S cdr(.(x:S,y:S)) -> y:S null(.(x:S,y:S)) -> ffalse null(nil) -> ttrue rev(.(x:S,y:S)) -> ++(rev(y:S),.(x:S,nil)) rev(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: ++#(.(x:S,y:S),z:S) -> ++#(y:S,z:S) REV(.(x:S,y:S)) -> ++#(rev(y:S),.(x:S,nil)) REV(.(x:S,y:S)) -> REV(y:S) -> Rules: ++(.(x:S,y:S),z:S) -> .(x:S,++(y:S,z:S)) ++(nil,y:S) -> y:S car(.(x:S,y:S)) -> x:S cdr(.(x:S,y:S)) -> y:S null(.(x:S,y:S)) -> ffalse null(nil) -> ttrue rev(.(x:S,y:S)) -> ++(rev(y:S),.(x:S,nil)) rev(nil) -> nil Problem 1: SCC Processor: -> Pairs: ++#(.(x:S,y:S),z:S) -> ++#(y:S,z:S) REV(.(x:S,y:S)) -> ++#(rev(y:S),.(x:S,nil)) REV(.(x:S,y:S)) -> REV(y:S) -> Rules: ++(.(x:S,y:S),z:S) -> .(x:S,++(y:S,z:S)) ++(nil,y:S) -> y:S car(.(x:S,y:S)) -> x:S cdr(.(x:S,y:S)) -> y:S null(.(x:S,y:S)) -> ffalse null(nil) -> ttrue rev(.(x:S,y:S)) -> ++(rev(y:S),.(x:S,nil)) rev(nil) -> nil ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ++#(.(x:S,y:S),z:S) -> ++#(y:S,z:S) ->->-> Rules: ++(.(x:S,y:S),z:S) -> .(x:S,++(y:S,z:S)) ++(nil,y:S) -> y:S car(.(x:S,y:S)) -> x:S cdr(.(x:S,y:S)) -> y:S null(.(x:S,y:S)) -> ffalse null(nil) -> ttrue rev(.(x:S,y:S)) -> ++(rev(y:S),.(x:S,nil)) rev(nil) -> nil ->->Cycle: ->->-> Pairs: REV(.(x:S,y:S)) -> REV(y:S) ->->-> Rules: ++(.(x:S,y:S),z:S) -> .(x:S,++(y:S,z:S)) ++(nil,y:S) -> y:S car(.(x:S,y:S)) -> x:S cdr(.(x:S,y:S)) -> y:S null(.(x:S,y:S)) -> ffalse null(nil) -> ttrue rev(.(x:S,y:S)) -> ++(rev(y:S),.(x:S,nil)) rev(nil) -> nil The problem is decomposed in 2 subproblems. Problem 1.1:
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