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TRS Standard pair #516964646
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
n090.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.222259044647 seconds
cpu usage
0.141232424
max memory
5988352.0
stage attributes
key
value
output-size
32248
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 K:S L:S M:S N:S X:S Y:S) (RULES eq(0,0) -> ttrue eq(0,s(Y:S)) -> ffalse eq(s(X:S),0) -> ffalse eq(s(X:S),s(Y:S)) -> eq(X:S,Y:S) ifmin(ffalse,cons(N:S,cons(M:S,L:S))) -> min(cons(M:S,L:S)) ifmin(ttrue,cons(N:S,cons(M:S,L:S))) -> min(cons(N:S,L:S)) ifrepl(ffalse,N:S,M:S,cons(K:S,L:S)) -> cons(K:S,replace(N:S,M:S,L:S)) ifrepl(ttrue,N:S,M:S,cons(K:S,L:S)) -> cons(M:S,L:S) ifselsort(ffalse,cons(N:S,L:S)) -> cons(min(cons(N:S,L:S)),selsort(replace(min(cons(N:S,L:S)),N:S,L:S))) ifselsort(ttrue,cons(N:S,L:S)) -> cons(N:S,selsort(L:S)) le(0,Y:S) -> ttrue le(s(X:S),0) -> ffalse le(s(X:S),s(Y:S)) -> le(X:S,Y:S) min(cons(0,nil)) -> 0 min(cons(s(N:S),nil)) -> s(N:S) min(cons(N:S,cons(M:S,L:S))) -> ifmin(le(N:S,M:S),cons(N:S,cons(M:S,L:S))) replace(N:S,M:S,cons(K:S,L:S)) -> ifrepl(eq(N:S,K:S),N:S,M:S,cons(K:S,L:S)) replace(N:S,M:S,nil) -> nil selsort(cons(N:S,L:S)) -> ifselsort(eq(N:S,min(cons(N:S,L:S))),cons(N:S,L:S)) selsort(nil) -> nil ) Problem 1: Innermost Equivalent Processor: -> Rules: eq(0,0) -> ttrue eq(0,s(Y:S)) -> ffalse eq(s(X:S),0) -> ffalse eq(s(X:S),s(Y:S)) -> eq(X:S,Y:S) ifmin(ffalse,cons(N:S,cons(M:S,L:S))) -> min(cons(M:S,L:S)) ifmin(ttrue,cons(N:S,cons(M:S,L:S))) -> min(cons(N:S,L:S)) ifrepl(ffalse,N:S,M:S,cons(K:S,L:S)) -> cons(K:S,replace(N:S,M:S,L:S)) ifrepl(ttrue,N:S,M:S,cons(K:S,L:S)) -> cons(M:S,L:S) ifselsort(ffalse,cons(N:S,L:S)) -> cons(min(cons(N:S,L:S)),selsort(replace(min(cons(N:S,L:S)),N:S,L:S))) ifselsort(ttrue,cons(N:S,L:S)) -> cons(N:S,selsort(L:S)) le(0,Y:S) -> ttrue le(s(X:S),0) -> ffalse le(s(X:S),s(Y:S)) -> le(X:S,Y:S) min(cons(0,nil)) -> 0 min(cons(s(N:S),nil)) -> s(N:S) min(cons(N:S,cons(M:S,L:S))) -> ifmin(le(N:S,M:S),cons(N:S,cons(M:S,L:S))) replace(N:S,M:S,cons(K:S,L:S)) -> ifrepl(eq(N:S,K:S),N:S,M:S,cons(K:S,L:S)) replace(N:S,M:S,nil) -> nil selsort(cons(N:S,L:S)) -> ifselsort(eq(N:S,min(cons(N:S,L:S))),cons(N:S,L:S)) 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),s(Y:S)) -> EQ(X:S,Y:S) IFMIN(ffalse,cons(N:S,cons(M:S,L:S))) -> MIN(cons(M:S,L:S)) IFMIN(ttrue,cons(N:S,cons(M:S,L:S))) -> MIN(cons(N:S,L:S)) IFREPL(ffalse,N:S,M:S,cons(K:S,L:S)) -> REPLACE(N:S,M:S,L:S) IFSELSORT(ffalse,cons(N:S,L:S)) -> MIN(cons(N:S,L:S)) IFSELSORT(ffalse,cons(N:S,L:S)) -> REPLACE(min(cons(N:S,L:S)),N:S,L:S) IFSELSORT(ffalse,cons(N:S,L:S)) -> SELSORT(replace(min(cons(N:S,L:S)),N:S,L:S)) IFSELSORT(ttrue,cons(N:S,L:S)) -> SELSORT(L:S) LE(s(X:S),s(Y:S)) -> LE(X:S,Y:S) MIN(cons(N:S,cons(M:S,L:S))) -> IFMIN(le(N:S,M:S),cons(N:S,cons(M:S,L:S))) MIN(cons(N:S,cons(M:S,L:S))) -> LE(N:S,M:S) REPLACE(N:S,M:S,cons(K:S,L:S)) -> EQ(N:S,K:S) REPLACE(N:S,M:S,cons(K:S,L:S)) -> IFREPL(eq(N:S,K:S),N:S,M:S,cons(K:S,L:S)) SELSORT(cons(N:S,L:S)) -> EQ(N:S,min(cons(N:S,L:S))) SELSORT(cons(N:S,L:S)) -> IFSELSORT(eq(N:S,min(cons(N:S,L:S))),cons(N:S,L:S)) SELSORT(cons(N:S,L:S)) -> MIN(cons(N:S,L:S)) -> Rules: eq(0,0) -> ttrue eq(0,s(Y:S)) -> ffalse eq(s(X:S),0) -> ffalse eq(s(X:S),s(Y:S)) -> eq(X:S,Y:S) ifmin(ffalse,cons(N:S,cons(M:S,L:S))) -> min(cons(M:S,L:S)) ifmin(ttrue,cons(N:S,cons(M:S,L:S))) -> min(cons(N:S,L:S)) ifrepl(ffalse,N:S,M:S,cons(K:S,L:S)) -> cons(K:S,replace(N:S,M:S,L:S)) ifrepl(ttrue,N:S,M:S,cons(K:S,L:S)) -> cons(M:S,L:S) ifselsort(ffalse,cons(N:S,L:S)) -> cons(min(cons(N:S,L:S)),selsort(replace(min(cons(N:S,L:S)),N:S,L:S))) ifselsort(ttrue,cons(N:S,L:S)) -> cons(N:S,selsort(L:S)) le(0,Y:S) -> ttrue le(s(X:S),0) -> ffalse le(s(X:S),s(Y:S)) -> le(X:S,Y:S) min(cons(0,nil)) -> 0 min(cons(s(N:S),nil)) -> s(N:S) min(cons(N:S,cons(M:S,L:S))) -> ifmin(le(N:S,M:S),cons(N:S,cons(M:S,L:S))) replace(N:S,M:S,cons(K:S,L:S)) -> ifrepl(eq(N:S,K:S),N:S,M:S,cons(K:S,L:S)) replace(N:S,M:S,nil) -> nil
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