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TRS Conditional pair #516978554
details
property
value
status
complete
benchmark
292.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n086.star.cs.uiowa.edu
space
COPS
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0804090499878 seconds
cpu usage
0.023605892
max memory
2138112.0
stage attributes
key
value
output-size
7299
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 v_NonEmpty:S l:S x:S y:S) (RULES le(0,s(x:S)) -> ttrue le(s(x:S),s(y:S)) -> le(x:S,y:S) le(x:S,0) -> ffalse min(cons(x:S,nil)) -> x:S min(cons(x:S,l:S)) -> min(l:S) | le(x:S,min(l:S)) ->* ffalse min(cons(x:S,l:S)) -> min(l:S) | min(l:S) ->* x:S min(cons(x:S,l:S)) -> x:S | le(x:S,min(l:S)) ->* ttrue ) Problem 1: Valid CTRS Processor: -> Rules: le(0,s(x:S)) -> ttrue le(s(x:S),s(y:S)) -> le(x:S,y:S) le(x:S,0) -> ffalse min(cons(x:S,nil)) -> x:S min(cons(x:S,l:S)) -> min(l:S) | le(x:S,min(l:S)) ->* ffalse min(cons(x:S,l:S)) -> min(l:S) | min(l:S) ->* x:S min(cons(x:S,l:S)) -> x:S | le(x:S,min(l:S)) ->* ttrue -> The system is a deterministic 3-CTRS. Problem 1: Dependency Pairs Processor: Conditional Termination Problem 1: -> Pairs: LE(s(x:S),s(y:S)) -> LE(x:S,y:S) MIN(cons(x:S,l:S)) -> MIN(l:S) | le(x:S,min(l:S)) ->* ffalse MIN(cons(x:S,l:S)) -> MIN(l:S) | min(l:S) ->* x:S -> QPairs: Empty -> Rules: le(0,s(x:S)) -> ttrue le(s(x:S),s(y:S)) -> le(x:S,y:S) le(x:S,0) -> ffalse min(cons(x:S,nil)) -> x:S min(cons(x:S,l:S)) -> min(l:S) | le(x:S,min(l:S)) ->* ffalse min(cons(x:S,l:S)) -> min(l:S) | min(l:S) ->* x:S min(cons(x:S,l:S)) -> x:S | le(x:S,min(l:S)) ->* ttrue Conditional Termination Problem 2: -> Pairs: MIN(cons(x:S,l:S)) -> LE(x:S,min(l:S)) MIN(cons(x:S,l:S)) -> MIN(l:S) -> QPairs: LE(s(x:S),s(y:S)) -> LE(x:S,y:S) MIN(cons(x:S,l:S)) -> MIN(l:S) | le(x:S,min(l:S)) ->* ffalse MIN(cons(x:S,l:S)) -> MIN(l:S) | min(l:S) ->* x:S -> Rules: le(0,s(x:S)) -> ttrue le(s(x:S),s(y:S)) -> le(x:S,y:S) le(x:S,0) -> ffalse min(cons(x:S,nil)) -> x:S min(cons(x:S,l:S)) -> min(l:S) | le(x:S,min(l:S)) ->* ffalse min(cons(x:S,l:S)) -> min(l:S) | min(l:S) ->* x:S min(cons(x:S,l:S)) -> x:S | le(x:S,min(l:S)) ->* ttrue The problem is decomposed in 2 subproblems. Problem 1.1: SCC Processor: -> Pairs: LE(s(x:S),s(y:S)) -> LE(x:S,y:S) MIN(cons(x:S,l:S)) -> MIN(l:S) | le(x:S,min(l:S)) ->* ffalse MIN(cons(x:S,l:S)) -> MIN(l:S) | min(l:S) ->* x:S -> QPairs: Empty -> Rules: le(0,s(x:S)) -> ttrue le(s(x:S),s(y:S)) -> le(x:S,y:S) le(x:S,0) -> ffalse min(cons(x:S,nil)) -> x:S min(cons(x:S,l:S)) -> min(l:S) | le(x:S,min(l:S)) ->* ffalse min(cons(x:S,l:S)) -> min(l:S) | min(l:S) ->* x:S min(cons(x:S,l:S)) -> x:S | le(x:S,min(l:S)) ->* ttrue ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: MIN(cons(x:S,l:S)) -> MIN(l:S) | le(x:S,min(l:S)) ->* ffalse MIN(cons(x:S,l:S)) -> MIN(l:S) | min(l:S) ->* x:S -> QPairs: Empty ->->-> Rules: le(0,s(x:S)) -> ttrue le(s(x:S),s(y:S)) -> le(x:S,y:S)
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