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TRS Stand 20472 pair #381714320
details
property
value
status
complete
benchmark
wiehe12.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n055.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
ttt2-1.17+nonreach
configuration
ttt2-1.17+nonreach
runtime (wallclock)
5.9316649437 seconds
cpu usage
21.606939631
max memory
8.84207616E8
stage attributes
key
value
output-size
45349
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem: g(s(x),s(y)) -> if(and(f(s(x)),f(s(y))),t(g(k(minus(m(x,y),n(x,y)),s(s(0()))),k(n(s(x),s(y)),s(s(0()))))), g(minus(m(x,y),n(x,y)),n(s(x),s(y)))) n(0(),y) -> 0() n(x,0()) -> 0() n(s(x),s(y)) -> s(n(x,y)) m(0(),y) -> y m(x,0()) -> x m(s(x),s(y)) -> s(m(x,y)) k(0(),s(y)) -> 0() k(s(x),s(y)) -> s(k(minus(x,y),s(y))) t(x) -> p(x,x) p(s(x),s(y)) -> s(s(p(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y))))) p(s(x),x) -> p(if(gt(x,x),id(x),id(x)),s(x)) p(0(),y) -> y p(id(x),s(y)) -> s(p(x,if(gt(s(y),y),y,s(y)))) minus(x,0()) -> x minus(s(x),s(y)) -> minus(x,y) id(x) -> x if(true(),x,y) -> x if(false(),x,y) -> y not(x) -> if(x,false(),true()) and(x,false()) -> false() and(true(),true()) -> true() f(0()) -> true() f(s(x)) -> h(x) h(0()) -> false() h(s(x)) -> f(x) gt(s(x),0()) -> true() gt(0(),y) -> false() gt(s(x),s(y)) -> gt(x,y) Proof: DP Processor: DPs: g#(s(x),s(y)) -> g#(minus(m(x,y),n(x,y)),n(s(x),s(y))) g#(s(x),s(y)) -> n#(s(x),s(y)) g#(s(x),s(y)) -> k#(n(s(x),s(y)),s(s(0()))) g#(s(x),s(y)) -> n#(x,y) g#(s(x),s(y)) -> m#(x,y) g#(s(x),s(y)) -> minus#(m(x,y),n(x,y)) g#(s(x),s(y)) -> k#(minus(m(x,y),n(x,y)),s(s(0()))) g#(s(x),s(y)) -> g#(k(minus(m(x,y),n(x,y)),s(s(0()))),k(n(s(x),s(y)),s(s(0())))) g#(s(x),s(y)) -> t#(g(k(minus(m(x,y),n(x,y)),s(s(0()))),k(n(s(x),s(y)),s(s(0()))))) g#(s(x),s(y)) -> f#(s(y)) g#(s(x),s(y)) -> f#(s(x)) g#(s(x),s(y)) -> and#(f(s(x)),f(s(y))) g#(s(x),s(y)) -> if#(and(f(s(x)),f(s(y))),t(g(k(minus(m(x,y),n(x,y)),s(s(0()))),k(n(s(x),s(y)),s(s(0()))))), g(minus(m(x,y),n(x,y)),n(s(x),s(y)))) n#(s(x),s(y)) -> n#(x,y) m#(s(x),s(y)) -> m#(x,y) k#(s(x),s(y)) -> minus#(x,y) k#(s(x),s(y)) -> k#(minus(x,y),s(y)) t#(x) -> p#(x,x) p#(s(x),s(y)) -> id#(y) p#(s(x),s(y)) -> id#(x) p#(s(x),s(y)) -> not#(gt(x,y)) p#(s(x),s(y)) -> if#(not(gt(x,y)),id(x),id(y)) p#(s(x),s(y)) -> gt#(x,y) p#(s(x),s(y)) -> if#(gt(x,y),x,y) p#(s(x),s(y)) -> p#(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y))) p#(s(x),x) -> id#(x) p#(s(x),x) -> gt#(x,x) p#(s(x),x) -> if#(gt(x,x),id(x),id(x)) p#(s(x),x) -> p#(if(gt(x,x),id(x),id(x)),s(x)) p#(id(x),s(y)) -> gt#(s(y),y) p#(id(x),s(y)) -> if#(gt(s(y),y),y,s(y)) p#(id(x),s(y)) -> p#(x,if(gt(s(y),y),y,s(y))) minus#(s(x),s(y)) -> minus#(x,y) not#(x) -> if#(x,false(),true()) f#(s(x)) -> h#(x) h#(s(x)) -> f#(x) gt#(s(x),s(y)) -> gt#(x,y) TRS: g(s(x),s(y)) -> if(and(f(s(x)),f(s(y))),t(g(k(minus(m(x,y),n(x,y)),s(s(0()))),k(n(s(x),s(y)),s(s(0()))))), g(minus(m(x,y),n(x,y)),n(s(x),s(y)))) n(0(),y) -> 0() n(x,0()) -> 0() n(s(x),s(y)) -> s(n(x,y)) m(0(),y) -> y m(x,0()) -> x m(s(x),s(y)) -> s(m(x,y)) k(0(),s(y)) -> 0() k(s(x),s(y)) -> s(k(minus(x,y),s(y))) t(x) -> p(x,x) p(s(x),s(y)) -> s(s(p(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y))))) p(s(x),x) -> p(if(gt(x,x),id(x),id(x)),s(x)) p(0(),y) -> y p(id(x),s(y)) -> s(p(x,if(gt(s(y),y),y,s(y))))
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