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	n058.star.cs.uiowa.edu
space	Mixed_CTRS

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.116375923157 seconds
cpu usage	0.069495225
max memory	3981312.0

stage attributes

key	value
output-size	11822
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 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) popout

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actions

all output return to TRS Conditional