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TRS Condi 20667 pair #381733012
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
n041.star.cs.uiowa.edu
space
Mixed_CTRS
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
1.0437309742 seconds
cpu usage
1.003164531
max memory
1.20631296E8
stage attributes
key
value
output-size
15029
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 x y) (RULES gcd(0,s(y)) -> s(y) gcd(s(x),0) -> s(x) gcd(s(x),s(y)) -> gcd(minus(x,y),s(y)) | less(y,x) -> true gcd(s(x),s(y)) -> gcd(s(x),minus(y,x)) | less(x,y) -> true gcd(x,x) -> x less(0,s(x)) -> true less(s(x),s(y)) -> less(x,y) less(x,0) -> false minus(0,s(y)) -> 0 minus(s(x),s(y)) -> minus(x,y) minus(x,0) -> x ) Problem 1: Valid CTRS Processor: -> Rules: gcd(0,s(y)) -> s(y) gcd(s(x),0) -> s(x) gcd(s(x),s(y)) -> gcd(minus(x,y),s(y)) | less(y,x) -> true gcd(s(x),s(y)) -> gcd(s(x),minus(y,x)) | less(x,y) -> true gcd(x,x) -> x less(0,s(x)) -> true less(s(x),s(y)) -> less(x,y) less(x,0) -> false minus(0,s(y)) -> 0 minus(s(x),s(y)) -> minus(x,y) minus(x,0) -> x -> The system is a deterministic 3-CTRS. Problem 1: Dependency Pairs Processor: Conditional Termination Problem 1: -> Pairs: GCD(s(x),s(y)) -> GCD(minus(x,y),s(y)) | less(y,x) -> true GCD(s(x),s(y)) -> GCD(s(x),minus(y,x)) | less(x,y) -> true GCD(s(x),s(y)) -> MINUS(x,y) | less(y,x) -> true GCD(s(x),s(y)) -> MINUS(y,x) | less(x,y) -> true LESS(s(x),s(y)) -> LESS(x,y) MINUS(s(x),s(y)) -> MINUS(x,y) -> QPairs: Empty -> Rules: gcd(0,s(y)) -> s(y) gcd(s(x),0) -> s(x) gcd(s(x),s(y)) -> gcd(minus(x,y),s(y)) | less(y,x) -> true gcd(s(x),s(y)) -> gcd(s(x),minus(y,x)) | less(x,y) -> true gcd(x,x) -> x less(0,s(x)) -> true less(s(x),s(y)) -> less(x,y) less(x,0) -> false minus(0,s(y)) -> 0 minus(s(x),s(y)) -> minus(x,y) minus(x,0) -> x Conditional Termination Problem 2: -> Pairs: GCD(s(x),s(y)) -> LESS(x,y) GCD(s(x),s(y)) -> LESS(y,x) -> QPairs: GCD(s(x),s(y)) -> GCD(minus(x,y),s(y)) | less(y,x) -> true GCD(s(x),s(y)) -> GCD(s(x),minus(y,x)) | less(x,y) -> true GCD(s(x),s(y)) -> MINUS(x,y) | less(y,x) -> true GCD(s(x),s(y)) -> MINUS(y,x) | less(x,y) -> true LESS(s(x),s(y)) -> LESS(x,y) MINUS(s(x),s(y)) -> MINUS(x,y) -> Rules: gcd(0,s(y)) -> s(y) gcd(s(x),0) -> s(x) gcd(s(x),s(y)) -> gcd(minus(x,y),s(y)) | less(y,x) -> true gcd(s(x),s(y)) -> gcd(s(x),minus(y,x)) | less(x,y) -> true gcd(x,x) -> x less(0,s(x)) -> true less(s(x),s(y)) -> less(x,y) less(x,0) -> false minus(0,s(y)) -> 0 minus(s(x),s(y)) -> minus(x,y) minus(x,0) -> x The problem is decomposed in 2 subproblems. Problem 1.1: SCC Processor: -> Pairs: GCD(s(x),s(y)) -> GCD(minus(x,y),s(y)) | less(y,x) -> true
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