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TRS Conditional pair #487562959
details
property
value
status
complete
benchmark
gcd.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n054.star.cs.uiowa.edu
space
Mixed_CTRS
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0694019794464 seconds
cpu usage
0.068584509
max memory
3850240.0
stage attributes
key
value
output-size
11825
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 gcd(0,s(y:S)) -> s(y:S) gcd(s(x:S),0) -> s(x:S) gcd(s(x:S),s(y:S)) -> gcd(minus(x:S,y:S),s(y:S)) | less(y:S,x:S) ->* ttrue gcd(s(x:S),s(y:S)) -> gcd(s(x:S),minus(y:S,x:S)) | less(x:S,y:S) ->* ttrue gcd(x:S,x:S) -> x:S less(0,s(x:S)) -> ttrue less(s(x:S),s(y:S)) -> less(x:S,y:S) less(x:S,0) -> ffalse minus(0,s(y:S)) -> 0 minus(s(x:S),s(y:S)) -> minus(x:S,y:S) minus(x:S,0) -> x:S ) Problem 1: Valid CTRS Processor: -> Rules: gcd(0,s(y:S)) -> s(y:S) gcd(s(x:S),0) -> s(x:S) gcd(s(x:S),s(y:S)) -> gcd(minus(x:S,y:S),s(y:S)) | less(y:S,x:S) ->* ttrue gcd(s(x:S),s(y:S)) -> gcd(s(x:S),minus(y:S,x:S)) | less(x:S,y:S) ->* ttrue gcd(x:S,x:S) -> x:S less(0,s(x:S)) -> ttrue less(s(x:S),s(y:S)) -> less(x:S,y:S) less(x:S,0) -> ffalse minus(0,s(y:S)) -> 0 minus(s(x:S),s(y:S)) -> minus(x:S,y:S) minus(x:S,0) -> x:S -> The system is a deterministic 3-CTRS. Problem 1: Dependency Pairs Processor: Conditional Termination Problem 1: -> Pairs: GCD(s(x:S),s(y:S)) -> GCD(minus(x:S,y:S),s(y:S)) | less(y:S,x:S) ->* ttrue GCD(s(x:S),s(y:S)) -> GCD(s(x:S),minus(y:S,x:S)) | less(x:S,y:S) ->* ttrue GCD(s(x:S),s(y:S)) -> MINUS(x:S,y:S) | less(y:S,x:S) ->* ttrue GCD(s(x:S),s(y:S)) -> MINUS(y:S,x:S) | less(x:S,y:S) ->* ttrue LESS(s(x:S),s(y:S)) -> LESS(x:S,y:S) MINUS(s(x:S),s(y:S)) -> MINUS(x:S,y:S) -> QPairs: Empty -> Rules: gcd(0,s(y:S)) -> s(y:S) gcd(s(x:S),0) -> s(x:S) gcd(s(x:S),s(y:S)) -> gcd(minus(x:S,y:S),s(y:S)) | less(y:S,x:S) ->* ttrue gcd(s(x:S),s(y:S)) -> gcd(s(x:S),minus(y:S,x:S)) | less(x:S,y:S) ->* ttrue gcd(x:S,x:S) -> x:S less(0,s(x:S)) -> ttrue less(s(x:S),s(y:S)) -> less(x:S,y:S) less(x:S,0) -> ffalse minus(0,s(y:S)) -> 0 minus(s(x:S),s(y:S)) -> minus(x:S,y:S) minus(x:S,0) -> x:S Conditional Termination Problem 2: -> Pairs: GCD(s(x:S),s(y:S)) -> LESS(x:S,y:S) GCD(s(x:S),s(y:S)) -> LESS(y:S,x:S) -> QPairs: LESS(s(x:S),s(y:S)) -> LESS(x:S,y:S) -> Rules: gcd(0,s(y:S)) -> s(y:S) gcd(s(x:S),0) -> s(x:S) gcd(s(x:S),s(y:S)) -> gcd(minus(x:S,y:S),s(y:S)) | less(y:S,x:S) ->* ttrue gcd(s(x:S),s(y:S)) -> gcd(s(x:S),minus(y:S,x:S)) | less(x:S,y:S) ->* ttrue gcd(x:S,x:S) -> x:S less(0,s(x:S)) -> ttrue less(s(x:S),s(y:S)) -> less(x:S,y:S) less(x:S,0) -> ffalse minus(0,s(y:S)) -> 0 minus(s(x:S),s(y:S)) -> minus(x:S,y:S) minus(x:S,0) -> x:S The problem is decomposed in 2 subproblems. Problem 1.1: SCC Processor: -> Pairs: GCD(s(x:S),s(y:S)) -> GCD(minus(x:S,y:S),s(y:S)) | less(y:S,x:S) ->* ttrue GCD(s(x:S),s(y:S)) -> GCD(s(x:S),minus(y:S,x:S)) | less(x:S,y:S) ->* ttrue GCD(s(x:S),s(y:S)) -> MINUS(x:S,y:S) | less(y:S,x:S) ->* ttrue GCD(s(x:S),s(y:S)) -> MINUS(y:S,x:S) | less(x:S,y:S) ->* ttrue LESS(s(x:S),s(y:S)) -> LESS(x:S,y:S) MINUS(s(x:S),s(y:S)) -> MINUS(x:S,y:S)
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