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TRS Stand 20472 pair #381710453
details
property
value
status
complete
benchmark
selsort.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n091.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
0.0986170768738 seconds
cpu usage
0.099878515
max memory
5812224.0
stage attributes
key
value
output-size
26384
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 K L M N X Y) (RULES eq(0,0) -> true eq(0,s(Y)) -> false eq(s(X),0) -> false eq(s(X),s(Y)) -> eq(X,Y) ifmin(false,cons(N,cons(M,L))) -> min(cons(M,L)) ifmin(true,cons(N,cons(M,L))) -> min(cons(N,L)) ifrepl(false,N,M,cons(K,L)) -> cons(K,replace(N,M,L)) ifrepl(true,N,M,cons(K,L)) -> cons(M,L) ifselsort(false,cons(N,L)) -> cons(min(cons(N,L)),selsort(replace(min(cons(N,L)),N,L))) ifselsort(true,cons(N,L)) -> cons(N,selsort(L)) le(0,Y) -> true le(s(X),0) -> false le(s(X),s(Y)) -> le(X,Y) min(cons(0,nil)) -> 0 min(cons(s(N),nil)) -> s(N) min(cons(N,cons(M,L))) -> ifmin(le(N,M),cons(N,cons(M,L))) replace(N,M,cons(K,L)) -> ifrepl(eq(N,K),N,M,cons(K,L)) replace(N,M,nil) -> nil selsort(cons(N,L)) -> ifselsort(eq(N,min(cons(N,L))),cons(N,L)) selsort(nil) -> nil ) Problem 1: Innermost Equivalent Processor: -> Rules: eq(0,0) -> true eq(0,s(Y)) -> false eq(s(X),0) -> false eq(s(X),s(Y)) -> eq(X,Y) ifmin(false,cons(N,cons(M,L))) -> min(cons(M,L)) ifmin(true,cons(N,cons(M,L))) -> min(cons(N,L)) ifrepl(false,N,M,cons(K,L)) -> cons(K,replace(N,M,L)) ifrepl(true,N,M,cons(K,L)) -> cons(M,L) ifselsort(false,cons(N,L)) -> cons(min(cons(N,L)),selsort(replace(min(cons(N,L)),N,L))) ifselsort(true,cons(N,L)) -> cons(N,selsort(L)) le(0,Y) -> true le(s(X),0) -> false le(s(X),s(Y)) -> le(X,Y) min(cons(0,nil)) -> 0 min(cons(s(N),nil)) -> s(N) min(cons(N,cons(M,L))) -> ifmin(le(N,M),cons(N,cons(M,L))) replace(N,M,cons(K,L)) -> ifrepl(eq(N,K),N,M,cons(K,L)) replace(N,M,nil) -> nil selsort(cons(N,L)) -> ifselsort(eq(N,min(cons(N,L))),cons(N,L)) selsort(nil) -> nil -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: EQ(s(X),s(Y)) -> EQ(X,Y) IFMIN(false,cons(N,cons(M,L))) -> MIN(cons(M,L)) IFMIN(true,cons(N,cons(M,L))) -> MIN(cons(N,L)) IFREPL(false,N,M,cons(K,L)) -> REPLACE(N,M,L) IFSELSORT(false,cons(N,L)) -> MIN(cons(N,L)) IFSELSORT(false,cons(N,L)) -> REPLACE(min(cons(N,L)),N,L) IFSELSORT(false,cons(N,L)) -> SELSORT(replace(min(cons(N,L)),N,L)) IFSELSORT(true,cons(N,L)) -> SELSORT(L) LE(s(X),s(Y)) -> LE(X,Y) MIN(cons(N,cons(M,L))) -> IFMIN(le(N,M),cons(N,cons(M,L))) MIN(cons(N,cons(M,L))) -> LE(N,M) REPLACE(N,M,cons(K,L)) -> EQ(N,K) REPLACE(N,M,cons(K,L)) -> IFREPL(eq(N,K),N,M,cons(K,L)) SELSORT(cons(N,L)) -> EQ(N,min(cons(N,L))) SELSORT(cons(N,L)) -> IFSELSORT(eq(N,min(cons(N,L))),cons(N,L)) SELSORT(cons(N,L)) -> MIN(cons(N,L)) -> Rules: eq(0,0) -> true eq(0,s(Y)) -> false eq(s(X),0) -> false eq(s(X),s(Y)) -> eq(X,Y) ifmin(false,cons(N,cons(M,L))) -> min(cons(M,L)) ifmin(true,cons(N,cons(M,L))) -> min(cons(N,L)) ifrepl(false,N,M,cons(K,L)) -> cons(K,replace(N,M,L)) ifrepl(true,N,M,cons(K,L)) -> cons(M,L) ifselsort(false,cons(N,L)) -> cons(min(cons(N,L)),selsort(replace(min(cons(N,L)),N,L))) ifselsort(true,cons(N,L)) -> cons(N,selsort(L)) le(0,Y) -> true le(s(X),0) -> false le(s(X),s(Y)) -> le(X,Y) min(cons(0,nil)) -> 0 min(cons(s(N),nil)) -> s(N) min(cons(N,cons(M,L))) -> ifmin(le(N,M),cons(N,cons(M,L))) replace(N,M,cons(K,L)) -> ifrepl(eq(N,K),N,M,cons(K,L)) replace(N,M,nil) -> nil
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