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HRS union beta 16688 pair #381734825
details
property
value
status
complete
benchmark
Applicative_AG01_innermost__#4.36.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
Uncurried_Applicative_11
run statistics
property
value
solver
sol 37957
configuration
default
runtime (wallclock)
0.145992040634 seconds
cpu usage
0.15664694
max memory
1.2906496E7
stage attributes
key
value
output-size
29724
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 We split firstr-order part and higher-order part, and do modular checking by a general modularity. ******** FO SN check ******** Check SN using NaTT (Nagoya Termination Tool) Input TRS: 1: eq(0(),0()) -> true() 2: eq(0(),s(X)) -> false() 3: eq(s(Y),0()) -> false() 4: eq(s(V),s(U)) -> eq(V,U) 5: le(0(),W) -> true() 6: le(s(P),0()) -> false() 7: le(s(Y1),s(X1)) -> le(Y1,X1) 8: min(cons(0(),nil())) -> 0() 9: min(cons(s(U1),nil())) -> s(U1) 10: min(cons(W1,cons(V1,P1))) -> ifxb6220min(le(W1,V1),cons(W1,cons(V1,P1))) 11: ifxb6220min(true(),cons(Y2,cons(X2,U2))) -> min(cons(Y2,U2)) 12: ifxb6220min(false(),cons(W2,cons(V2,P2))) -> min(cons(V2,P2)) 13: replace(Y3,X3,nil()) -> nil() 14: replace(W3,V3,cons(U3,P3)) -> ifxb6220replace(eq(W3,U3),W3,V3,cons(U3,P3)) 15: ifxb6220replace(true(),U4,Y4,cons(X4,V4)) -> cons(Y4,V4) 16: ifxb6220replace(false(),X5,P4,cons(W4,Y5)) -> cons(W4,replace(X5,P4,Y5)) 17: sort(nil()) -> nil() 18: sort(cons(U5,V5)) -> cons(min(cons(U5,V5)),sort(replace(min(cons(U5,V5)),U5,V5))) 19: _(X1,X2) -> X1 20: _(X1,X2) -> X2 Number of strict rules: 20 Direct POLO(bPol) ... failed. Uncurrying min 1: eq(0(),0()) -> true() 2: eq(0(),s(X)) -> false() 3: eq(s(Y),0()) -> false() 4: eq(s(V),s(U)) -> eq(V,U) 5: le(0(),W) -> true() 6: le(s(P),0()) -> false() 7: le(s(Y1),s(X1)) -> le(Y1,X1) 8: min^1_cons(0(),nil()) -> 0() 9: min^1_cons(s(U1),nil()) -> s(U1) 10: min^1_cons(W1,cons(V1,P1)) -> ifxb6220min(le(W1,V1),cons(W1,cons(V1,P1))) 11: ifxb6220min(true(),cons(Y2,cons(X2,U2))) -> min^1_cons(Y2,U2) 12: ifxb6220min(false(),cons(W2,cons(V2,P2))) -> min^1_cons(V2,P2) 13: replace(Y3,X3,nil()) -> nil() 14: replace(W3,V3,cons(U3,P3)) -> ifxb6220replace(eq(W3,U3),W3,V3,cons(U3,P3)) 15: ifxb6220replace(true(),U4,Y4,cons(X4,V4)) -> cons(Y4,V4) 16: ifxb6220replace(false(),X5,P4,cons(W4,Y5)) -> cons(W4,replace(X5,P4,Y5)) 17: sort(nil()) -> nil() 18: sort(cons(U5,V5)) -> cons(min^1_cons(U5,V5),sort(replace(min^1_cons(U5,V5),U5,V5))) 19: _(X1,X2) -> X1 20: _(X1,X2) -> X2 21: min(cons(_1,_2)) ->= min^1_cons(_1,_2) Number of strict rules: 20 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #ifxb6220min(true(),cons(Y2,cons(X2,U2))) -> #min^1_cons(Y2,U2) #2: #ifxb6220min(false(),cons(W2,cons(V2,P2))) -> #min^1_cons(V2,P2) #3: #replace(W3,V3,cons(U3,P3)) -> #ifxb6220replace(eq(W3,U3),W3,V3,cons(U3,P3)) #4: #replace(W3,V3,cons(U3,P3)) -> #eq(W3,U3) #5: #le(s(Y1),s(X1)) -> #le(Y1,X1) #6: #min^1_cons(W1,cons(V1,P1)) -> #ifxb6220min(le(W1,V1),cons(W1,cons(V1,P1))) #7: #min^1_cons(W1,cons(V1,P1)) -> #le(W1,V1) #8: #min(cons(_1,_2)) ->? #min^1_cons(_1,_2) #9: #ifxb6220replace(false(),X5,P4,cons(W4,Y5)) -> #replace(X5,P4,Y5) #10: #eq(s(V),s(U)) -> #eq(V,U) #11: #sort(cons(U5,V5)) -> #min^1_cons(U5,V5) #12: #sort(cons(U5,V5)) -> #sort(replace(min^1_cons(U5,V5),U5,V5)) #13: #sort(cons(U5,V5)) -> #replace(min^1_cons(U5,V5),U5,V5) #14: #sort(cons(U5,V5)) -> #min^1_cons(U5,V5) Number of SCCs: 5, DPs: 8 SCC { #10 } POLO(Sum)... succeeded. le w: 0 s w: x1 + 1 #le w: 0 ifxb6220replace w: 0 #ifxb6220min w: 0 min^1_cons w: 0 eq w: 0 false w: 0 #ifxb6220replace w: 0 #min w: 0 _ w: 0 true w: 0 #eq w: x1 + x2 #sort w: 0 ifxb6220min w: 0 0 w: 0 nil w: 0 sort w: 0 #replace w: 0 #_ w: 0 min w: 0 #min^1_cons w: 0 cons w: 0
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